New Evidence on State-Dependent Dynamics of … copy available at : http ://ssrn.com /abstract = 2527213 New Evidence on State-Dependent Dynamics of Risk, In ation, and Asset Valuation…

Electronic copy available at: http://ssrn.com/abstract=2527213

New Evidence on State-Dependent Dynamics of

Risk, Inflation, and Asset Valuation1

Robert Connolly

Finance Area

Kenan-Flagler School of Business

University of North Carolina

Chapel Hill, NC

David Dubofsky

Department of Finance

College of Business

University of Louisville

Louisville, KY

Chris Stivers

Department of Finance

College of Business

University of Louisville

Louisville, KY

This version: March 23, 2015

1We thank Ric Colacito, Cami Kuhnen, Ahn Le, Cipriana Prepeliuc, and seminar participants at

UNC-Chapel Hill and the University of Louisville for helpful comments. Please address comments to

Robert Connolly (email: Robert [email protected]; phone: (919) 962-0053); David Dubofsky (email:

[email protected]; phone: (502) 852-3016); or Chris Stivers (e-mail: [email protected];

phone: (502) 852-4829).

Electronic copy available at: http://ssrn.com/abstract=2527213

New Evidence on State-Dependent Dynamics of

Risk, Inflation, and Asset Valuation

Abstract

Over 1997 to 2013, we find striking economic-state differences in how bond and stock values

are linked to innovations in risk and inflation. We identify two prolonged periods (October 2001

- April 2004 and January 2009 - December 2013) that we characterize as ‘recessionary/post-

recessionary’ (RPR) states, where: (1) increases in perceived equity (bond) risk are strongly and

very reliably linked to higher (lower) T-bond returns and a decreased (increased) term-structure

slope, with regression R2 values up to 50% at the monthly horizon; and (2) inflation is positively

linked to stock returns. These RPR periods are also distinguished by an elevated stock-market

variance risk premium, lower economic growth, lower inflation, a close proximity to sizable stock

market declines, a relatively larger term yield spread as compared to very low T-bill yields,

and presumably higher risk aversion. Over the non-RPR growth periods in our sample, the

comparable risk-to-return connection in longer-term Treasuries is much weaker or non-existent

and the link between inflation and stock returns is negative or statistically insignificant. Our

findings fit with key implications from recent theory that emphasize time-varying risk aversion

and the signaling role of inflation.

JEL Classification: G12

Keywords: Treasury-bond and Stock futures returns, Forward interest rates, Equity and Bond

risk, Inflation news, Economic states

1. Introduction

Asset-class risk perceptions and inflation are of fundamental importance in asset pricing, port-

folio construction, and risk management. This paper uncovers striking economic-state differences

over 1997 to 2013 in how bond and stock values are linked to innovations in asset-class risk and

inflation. By ‘asset-class risk’, we refer to risk perceptions for T-bonds and equities, as measured

by the implied volatilities from 10-year T-Note futures options and S&P 500 options, respectively.

Our economic states are also distinguished by notable differences in the stock market’s variance

risk premium, economic growth, inflation, proximity to sizable stock market declines, the bond

market’s term yield spread relative to T-bill yields, and presumably risk aversion.

Specifically, we identify two prolonged periods (October 2001 - April 2004 and January 2009

- December 2013) that we characterize as ‘recessionary/post-recessionary’ (RPR) states, where:

(1) increases in perceived equity (bond) risk are strongly and reliably linked to higher (lower)

T-bond returns and a decreased (increased) term-structure slope; and (2) inflation is positively

related to stock market returns. Conversely, over the remaining non-RPR periods, the comparable

risk-return connection in longer-term Treasuries is much weaker or non-existent and the relation

between stock returns and inflation news is either negative or statistically insignificant over the

expansionary economic months. These stylized differences across economic states fit with key

implications from recent theory that emphasize time-varying risk aversion and the signaling role

of inflation; see especially Bekaert, Engstrom, and Xing (2009), Bekaert and Engstrom (2013),

and David and Veronesi (2013).

Our study commences in October 1997 due to data limitations, combined with evidence sug-

gesting a regime-shift around 1997 in stock-bond return dynamics and Treasury bond risk premia.

Baele, Bekaert, and Inghelbrecht (2010) show that the stock-bond return correlation shifted from

almost exclusively positive over the 1970’s through mid-1997 to predominantly negative around

October 1997.1 Analysis in Campbell, Sunderam, and Viceira (2013) and Campbell, Pflueger,

and Viceira (2014) also suggest a prominent regime shift about this time; since then Treasury

bonds appear to serve as more of a hedge instrument against the risk of a stock market decline

1Aslandis and Christiansen (2012) find a similar correlation shift using high-frequency intraday stock and T-

bond futures returns.

1

and/or a weak macroeconomy. In contrast, over the 1970s and 1980s, Treasury bonds added to

an investor’s macroeconomic risk exposure.

While perhaps no theoretical model is rich enough to encompass all these economic state dif-

ferences in a tractable fashion, our empirical investigation draws much from models in Bekaert,

Engstrom, and Xing (2009) (BEX), Bekaert and Engstrom (2013) (BE), and David and Veronesi

(2013) (DV). In the BEX framework, both economic uncertainty and risk aversion vary counter-

cyclically over time, where economic uncertainty refers to the volatility of economic fundamentals

such as the dividend growth rate. Risk aversion increases as consumption moves toward a sub-

sistence or habit level. ‘Flight-to-quality’ (FTQ) episodes arise endogenously in their model, as

increases in fundamental volatility lead to higher bond prices and may lead to lower equity prices

in some economic states. This occurs when heightened economic uncertainty acts to depress

interest rates due to a precautionary savings motive, and to depress stock values due to a risk-

premium feedback. Their model calibration indicates a very high correlation between expected

equity volatility and economic uncertainty, which suggests equity implied-volatility changes may

be a good proxy for changes in economic uncertainty. Periods with higher risk aversion also have

a stronger precautionary savings motive. This suggests a stronger positive link between changes

in economic uncertainty and bond values in weaker economic times. Thus, the risk-to-return

connections in Treasuries may vary with the economic state and risk aversion.

BE (2013) introduce non-Gaussian fundamentals where consumption dynamics are different

for good and bad economic times. During bad times with higher risk aversion, their framework

suggests: (1) a stronger precautionary saving effect, because a sizable negative shock to con-

sumption is more likely, and (2) an elevated equity variance risk premium. This perspective also

suggests important economic-state differences in risk-return dynamics.

In DV (2013), economic states vary along the two dimensions of economic growth and infla-

tion, but they assume constant relative risk aversion. In a low-growth/low-inflation state, news of

higher inflation is bad news for nominal bonds but good news for stocks because higher inflation

may signal that the economy is not slipping into a deflationary state with very low growth or

contraction. Thus, the reaction of stock prices to inflation news varies with the economic state,

and inflation news can generate a negative stock-bond return correlation.2

2Guidolin and Timmermann (2006) analyze monthly stock and bond returns over 1954 to 1999, and their results

2

Our empirical investigation identifies two prolonged RPR periods that are distinguished by

a noteworthy set of economically-important commonalities. In addition to the dramatically

stronger risk-return connection in longer-term Treasuries, both RPR periods: (1) exhibit a strong

and reliably positive link between inflation news and stock returns; (2) exhibit a higher variance-

risk premium in the stock market and a greater difference between the stock-market’s implied

volatility and subsequent realized volatility; (3) commence in the later part of a formal NBER

economic recession, after the Federal Reserve has largely or totally concluded its monetary easing

in the targeted Fed Funds rate; (4) have a relatively much larger term yield spread, as compared

to the very low T-bill yields; (5) can be characterized as a lower-growth and lower-inflation

economic state, especially relative to the preceding expansion; and (6) commence following a

sizable downturn in the stock market, with a decline exceeding 35% from the preceding stock

market peak.3 Figure 1 depicts this variation in the term-yield spreads (relative to the T-bill

yield) and the equity variance risk premium. Collectively, the higher variance risk premium, the

weak economic state, and the preceding stock-market decline suggest that our two RPR periods

have relatively higher aggregate risk aversion.4

To illustrate the economic-state differences, consider a regression of monthly T-Bond-futures

returns as the dependent variable against the concurrent and lagged monthly changes in the

asset-class risk as explanatory terms. For our two RPR periods (encompassing 91 months),

this regression has an average R2 value of 41.7%. For the other non-RPR periods in sample

(encompassing 104 months), the comparable average R2 value is 2.3%. For weekly returns, the

indicate that economic states are important for understanding the joint stock-bond return distribution.3To identify these two RPR periods, we primarily utilize the ‘structural break’ statistical methods of Bai and

Perron (1998) and (2003), but we also consider variations in the other market variables and characteristics described

here. Our Section 2.5 and Appendix A presents details for the structural-break analysis and the other economic

differences summarized in this paragraph.4See Bollerslev, Tauchen, and Zhou (2009), Bollerslev, Gibson, and Zhou (2011), and Bekaert, Hoerova, and Lo

Duca (2013) for discussion that links the variance risk premium to movements in aggregate risk aversion. Fama and

French (1993), Campbell and Cochrane (1999), and BEX (2009) present evidence that aggregate risk aversion is

countercyclical. Guiso, Sapienza, and Zingales (2014) present both survey and experimental evidence that suggests

higher risk aversion is likely following dramatic stock market declines. In controlled experiments with financial

professionals, Cohn, Engelmann, Fehr, and Marechal (2014) find convincing evidence in favor of the countercyclical

risk aversion hypothesis.

3

comparable average R2 value is 29.1% for our RPR periods versus 4.2% for the non-RPR periods.

Our ‘risk-to-Treasury-values’ findings fit with key empirical implications in BEX (2009) and

BE (2013). Consistent with BEX, we show empirically that bond values tend to increase with

heightened economic uncertainty, and there is a much stronger risk-return relation in longer-term

Treasuries over weak economic times with presumably higher risk aversion. Consistent with BE,

our findings suggest that bad economic times are likely to have both a stronger precautionary

savings motive and an elevated equity variance risk premium.

Consistent with Campbell, Sunderam, and Viceira (2013) (CSV), our findings suggest that

longer-term Treasuries became more of a hedge instrument against economic uncertainty and/or

equity risk since around 2000. Stronger FTQ linkages in the longer-term Treasury market over

our RPR periods (especially 2009-2013) seem intuitive because of the relatively low inflation risk,

the relatively high term yield spread, and the near-zero money market yields.

Our findings regarding economic-state differences in the stock-inflation connection fit with the

key empirical implication in DV (2013) that inflation news provides a signal about the underlying

economic state. Over our two RPR periods (which have low-growth and low inflation), we

find that the relation between inflation news and stock returns is appreciably and statistically-

reliably positive, coincident with a more negative stock-bond return correlation.5 Over the

non-RPR growth periods in our sample, the relation between inflation news and stock returns

is either reliably negative or statistically insignificant and the stock-bond return correlation is

either positive or appreciably less negative.

When evaluated jointly, we find that both equity-risk innovations and inflation news are

important in understanding the stock-bond return correlation over our sample. Thus, our evi-

dence suggests that both the economic-uncertainty perspective in BEX (2009) and the inflation

perspective in DV (2013) are valuable in understanding asset return dynamics.

To combat the severe economic downturn of 2008-09, the Federal Reserve undertook unprece-

dented large-scale purchases in the longer-term fixed income markets, commencing in early 2009.

There is evidence (e.g., Krishnamurthy and Vissing-Jorgensen (2011) and Jarrow and Li (2013))

that the intensity of Fed purchases affected Treasury yields; which suggests a possible link to our

5Inflation news is measured primarily by deduction from movements in TIPS and nominal Treasury yields, per

Gurkaynak, Sack, and Wright (2010). Inflation news based on CPI and PPI releases yield consistent results.

4

principal findings regarding the strong ‘risk-to-Treasury value’ connection over 2009-2013. We

present evidence in Section 6 that is inconsistent with a ‘Federal Reserve intensity’ explanation

of the strong risk-return connection over our 2009-2013 RPR period.

In sum, we document striking economic-state differences in both risk-return and inflation-

return connections. Our work is related to the existing literature that studies risk and return

in the Treasury markets, but unlike much of the term-structure literature we jointly explore the

impact of both bond and equity risk on Treasury values.6 Further, our work also looks across

markets by showing that the economic-state divisions that bear on understanding the risk-to-

Treasury-return connection are also the same economic-state divisions that bear on understanding

the inflation-to-stock-return connection.

The remainder of our study is organized as follows. Section 2 describes the data. Section 3

establishes our main empirical findings regarding the connection between asset-class risk percep-

tions and returns/yields. Section 4 expands our empirical investigation to also consider changes

in inflation expectations. Section 5 describes other properties of our two RPR periods. Finally,

Section 6 provides additional analysis concerning an alternative “Fed Intensity” hypothesis, and

Section 7 concludes.

2. Data Description and Sample Selection

2.1. Asset-class Risk from the Implied Volatility of Options

We use equity and T-Note implied volatility as observable, high-quality, and dynamic measures

of risk expectations (or risk perceptions) for each asset class. For equity risk, we use the Chicago

Board Options Exchange (CBOE) VIX measure, derived from options on the S&P 500. For the

risk of longer-term Treasuries, we use the implied volatility from 10-year T-Note futures options

from Bloomberg. Both implied volatilities are standardized to provide an annualized volatility

6For affine-quadratic models, see Ahn, Dittmar, Gao, and Gallant (2003), Leippold and Wu (2002), and Ahn,

Dittmar, and Gallant (2002). For regime-switching models, see Bansal and Zhou (2002), Bansal, Tauchen, and

Zhou (2004), Ang and Bekaert (2002), and Dai, Singleton, and Yang (2007). For nonlinear models, see Ahn and

Gao (1999) and Feldhutter, Heyerdahl-Larsen, and Illeditsch (2013). See Ghysels, Le, Park, and Zhu (2014) for

a discrete-time no-arbitrage term structure model that combines the tractability of affine term structure models

with the ability of GARCH models to deliver an accurate measure of yield volatility.

5

estimate over the subsequent one month.7 The VIX is available from 1990 and the T-Note-futures

implied volatility (TIV) from mid-1993, which limits our sample choices.

We also note that both the VIX and TIV are sizably positively correlated, with a correlation of

0.66 between their levels, 0.344 for the one-month changes, and 0.227 for the one-week changes.

Figure 2 depicts this time-series behavior for both the VIX and TIV values and their weekly

changes. This positive correlation makes economic sense; because, to some extent, stocks and

bonds may share exposure to the same economic risk factors (see, e.g., Fama and French (1993)).

This positive correlation also indicates the importance of including both stock and bond risk

when trying to isolate a partial risk-return relation linked to a specific asset-class risk.

Our empirical analysis relies upon the assumption that VIX and TIV are good proxies for the

forward-looking risk, or expected return volatility, of each respective asset-class return series. In

Appendix B, we report evidence that supports the use of VIX and TIV as comparable forward-

looking asset-class risk measures for equities and T-bonds.

Table 1 reports univariate summary statistics for the VIX and TIV percentage changes over

rolling one-week periods. Our empirical work focuses on these variables to measure implied-

volatility dynamics; denoted ∆log(IVt/IVt−j) as a ‘continuous percentage change’ variable with

IV indicating the implied volatility, either V IX or TIV in annualized percentage units, and

where j equals 5 (22) trading days for the rolling weekly (monthly) analysis. With this method,

the volatility of the VIX-changes and TIV-changes are more comparable and their volatility is

less variable across subperiods; see subperiod statistics in Table 1. Later, in robustness checks,

we find similar results when using the simple IV changes in place of the log changes.

If the VIX changes have much more volatility in our RPR periods, then this might help

explain why the regression R2 values are much greater when relating equity risk to longer-term

Treasuries over our RPR periods (see Forbes and Rigobon (2002)). Accordingly, we compare

the VIX variability during our RPR periods to the VIX variability during our non-RPR periods.

Table 1 reports the standard deviation of our primary ∆log(V IXt,t−5) weekly-change variable

7See Whaley (2000) and Blair, Poon, and Taylor (2001) for more background information on VIX, including

additional supportive evidence about the forward-looking volatility information in VIX. For the TIV series, we

smoothed out a few extreme data points that were inexplicably much different than the prior and subsequent day’s

value (about 0.5% of the observations), by replacing the inconsistent daily values with the prior day’s value.

6

for our RPR and non-RPR subperiods. The standard deviations are remarkably similar across

subperiods, all in the 0.10 to 0.13 range. The similarity in the VIX variability across our RPR

and non-RPR subperiods can also be seen in Figure 2, Panel B. Further, the average absolute

∆log(V IXt,t−5) is not statistically reliably different across our RPR and non-RPR periods. We

conclude there is not a pervasive or pronounced difference in the VIX variability across our RPR

and non-RPR periods.

2.2. Futures Contract Returns

To capture the dynamic behavior of stock and Treasury bond prices, we use the returns implied

by the prices of 30-year T-Bond, 10-year T-Note, and S&P 500 futures contracts. These fu-

tures contracts are all very widely traded, so stale prices and other liquidity concerns should be

minimized; see, e.g., Ahn, Boudoukh, Richardson, and Whitelaw (2002).

To calculate the implied returns, we use the continuous futures price series from Datastream

for the three contracts, where the futures prices are from the daily settlement prices, with rolling

contracts to provide a continuous series. These series from DataStream International (with codes

CUSCS04, CTY CS04, and ISPCS04) are constructed so that the returns derived from the price

series may be interpreted as excess returns. Table 1 reports univariate summary statistics for

these futures returns at the weekly horizon over our subperiods of interest.

2.3. Treasury Yields and Forward Interest Rates

For our Treasury yield data, we primarily rely on the data set as described in Gurkaynak, Sack,

and Wright (2007). Our study uses their zero-coupon bond yields and forward interest rates. For

our calculation of the term-structure’s principal components, we use their 10 zero-coupon bond

yields at years one to 10. We also use their instantaneous continuously-compounded forward-

rate (FR) yields to evaluate the dynamics of marginal interest rates at specific points in the term

structure; see Figure 3 for the time-series of the FR yields over our sample. Table 1 reports

univariate summary statistics for weekly changes in these forward rates over our subperiods of

interest. Our investigation also uses ‘inflation compensation’ data, based on yield differences

between 10-year TIPS and 10-year nominal Treasuries, using the method from Gurkaynak, Sack,

7

and Wright (2010). Finally, we use the 10-year and 6-month Treasury Constant Maturity (TCM)

yields from the Federal Reserve as an estimate of the term yield spread.

2.4. Realized Stock Market Volatility

To estimate the equity ‘variance risk premium’, we construct a rolling 22-trading-day realized

volatility measure from 5-minute returns on the widely traded SPY S&P 500 ETF. Our equity

‘variance risk premium’ equals the difference between VIX at the close of day t and the realized

volatility from 5-minute returns over trading days t−21 through day t. Bollerslev, Tauchen, and

Zhou (2009) and Bollerslev, Gibson, and Zhou (BGZ) (2011) refer to this implied-minus-realized

volatility difference as the ‘variance risk premium’ and BGZ note that it “is sometimes used by

market participants as a measure for the market-implied risk aversion” (page 239). Appendix C

provides details on the data and how we calculated this realized volatility.

2.5. Selection of our Two ‘Recessionary/Post-Recessionary’ (RPR) Periods

In Appendix A, we provide details for our rationale and procedures for selecting the RPR periods

that are featured in our paper. The first-order criteria is a ‘structural break’ analysis for the

risk-return relation in longer-term Treasuries, using the statistical methods of Bai and Perron

(1998, 2003). Additionally, we also consider several other economic properties that reinforce the

selection of our two RPR periods. Details are relegated to Appendix A for brevity in our main

text, with Appendix A.8 elaborating on related evidence in CSV (2013).

As we noted in our introduction, our RPR periods commence later in a recession after the

Federal Reserve has totally or largely completed their easing in the targeted Fed Funds rate

(FFR). Further, our first RPR period ended a few months before the Fed finally began increasing

the targeted FFR; and our second RPR period was ongoing at the end of our sample period with

the Fed maintaining a near-zero targeted FFR. In Appendix A.4, we discuss our RPR periods in

the context of these Fed actions.

In Appendix A.4, we discuss why the early parts of the recessions are not included in our

RPR periods. We present evidence there that suggests that Federal Reserve actions are likely to

have obscured the risk-return Treasury connections around the onset of recessions, as both risk

8

perceptions and Treasury values may have been responding to Fed actions rather than typical

free-market forces. The Fed lowered the targeted Fed Funds rate 11 times in 2001 and 7 times in

2008. Given these observations, our empirical investigation contrasts our RPR periods to both:

(1) the full non-RPR periods (1997:10 - 2001:09 and 2004:05 - 2008:12) that contain economic-

growth periods and the onset of the recession; and (2) subsets of the non-RPR periods that

include months with economic growth only, or non-RPR-growth periods (1997:10 - 2001:02 and

2004:05 - 2007:11). With this approach, we investigate whether the results for the non-RPR

periods are appreciably different when omitting the onset of the recessions.

3. The Risk-to-Return Connection and Economic States

In this section, we present our primary empirical results analyzing the connection between changes

in asset-class risk perceptions and three aspects of the Treasury market: (1) T-Bond and 10-year

T-Note futures returns; (2) changes in Treasury forward rates at the 1-, 5-, and 10-year points

in the term structure; and (3) changes in the term-structure’s slope. We also present evidence

regarding the relation between stock returns and changes in asset-class risk perceptions.

We investigate the Treasury forward rates as a complement to analysis of the longer-term

Treasury-futures return because the instantaneous forward rates indicate the marginal interest

rate at specific points on the yield curve. Thus, changes in forward rates should better capture

pricing influences at different specific points in the yield curve. We investigate the instantaneous

forward interest rates from Gurkaynak, Sack, Wright (GSW, 2007) that are 1-year, 5-years, and

10-years out to capture short-, mid-, and longer-horizon points in the term structure.8

We report on two measures of the change in the Treasury term-structure’s slope. The first is

the change in the term-structure’s second principal component, where the principal components

are estimated from the 10 zero-coupon bond yields with maturities from 1-year to 10-years using

8Additionally, the GSW forward-rate data is constructed from spot quotes on Treasury bonds, so our analysis is

extended beyond the futures market. GSW’s intent is to estimate a yield curve that is suitable for “understanding

its fundamental determinants such as ... perceived risk, and investors’ risk preferences” (page 2295). Their

parametric yield curve allows for very rich shapes of the forward curve while largely ruling out variation resulting

from anomalous prices of a small number of securities.

9

the GSW data.9 The second is the change in the term yield spread, where the term yield spread

is defined as the difference between the 10-year and 6-month Treasury Constant Maturity Yield

from the Federal Reserve.

We choose to investigate the sizable change horizons of one week and one month for two

reasons. First, the longer horizons should eliminate some of the noise that would be evident in a

daily or intra-day analysis, such as non-synchronous market closings that introduce measurement

errors in daily data. Second, our view is that relations at these longer horizons are more likely

to reflect fundamental underlying economic forces. Shorter-horizon changes (such as daily or

intra-day changes) are more likely to be distorted by market microstructure influences.

In this section, we motivate and interpret our empirical investigation primarily from the

theoretical framework of BEX (2009). Accordingly, we begin by providing further background

on their model.

3.1. Implications from BEX’s (2009) Theoretical Framework

The BEX (2009) theoretical framework features time-variation in both economic uncertainty and

risk aversion. Economic uncertainty refers to the conditional variance of fundamentals, such as

dividend growth. Risk aversion is countercyclical and varies with the difference between current

consumption and an ‘external habit level,’ following from the preference structure in Campbell

and Cochrane (1999).10 BEX evaluate the relative importance of uncertainty and risk aversion

in understanding equity risk premia, equity volatility, and the term structure of interest rates.

They calibrate their model to actual U.S. economic data over 1927 to 2004.

There are several prominent dimensions of BEX that are central to our empirical investiga-

tion. First, because their measure of economic uncertainty is highly correlated with conditional

stock market variance (ρ = 0.88), we posit that time-variation in the stock-market’s conditional

variance is a reasonable proxy for movements in their concept of economic uncertainty (at least as

9Previous research has shown that the term-structure’s first three principal components are closely related to

its level, slope, and curvature, respectively. See, e.g., Diebold, Piazzesi, and Rudebusch (2005), who find that the

first two principal components account for almost all (99 percent) of the variation in the yields.10Bekaert, Engstrom, and Grenadier (2010) also use this preference structure and note that it suggests “moody

investors”, since risk aversion can increase dramatically as consumption falls back to near the habit level.

10

a first-order interpretation).11 Thus, when interpreting our empirical investigation from BEX’s

perspective, we assume that VIX movements are a reasonable proxy for short-horizon movements

in economic uncertainty and that TIV movements are more related to bond-specific risk.12

Second, in BEX, a higher economic uncertainty is associated with a higher precautionary

savings motive. This feature can induce a FTQ effect on bonds, where increased economic

uncertainty can drive up bond prices.

Third, because our RPR periods commence later in recessions and are ongoing through the

beginning of an uncertain economic recovery, consumption in our RPR periods should be rela-

tively closer to the habit/subsistence consumption level. If so, under BEX, risk aversion would

be both higher during our RPR periods and more sensitive to small consumption changes. In

Section 3.6, we argue that this risk-aversion property suggests that FTQ influences, where in-

creased economic uncertainty acts to drive down interest rates, is likely to be stronger over our

RPR periods. The intuition is that weak economic times have higher risk aversion and risk aver-

sion is more sensitive to consumption changes, so when uncertainty increases there is a relatively

stronger precautionary savings effect in these states.

Fourth, the effect of time-varying economic uncertainty on stock prices is ambiguous and

can vary with the economic state, because of opposing economic forces that affect stock prices.

To begin with, greater economic uncertainty lowers interest rates; which, ceteris paribus, would

promote lower discount rates for stock valuation and higher stock prices. On the other hand, the

11In BEX (2009), the stock-market’s conditional variance is also modestly correlated with the inverse of the

surplus ratio (ρ=0.38), a key driver in risk aversion movements. This implies that movements in the stock-

market’s conditional variance are likely to be associated with movements in risk aversion to a lesser degree. BEX

argue that risk aversion is less variable than economic uncertainty, so presumably our weekly and monthly VIX

changes should largely reflect variation in uncertainty.12An alternative to using VIX-changes directly would be to decompose the VIX into an economic-uncertainty

component and a risk-aversion component along the lines of Bekaert, Hoerova, and Lo Duca (2013) (BHL), and then

evaluate changes in the uncertainty component (rather than VIX). With that approach, the uncertainty component

is the projected conditional variance from a regression of the realized variance against the lagged VIX and lagged

realized variance. The risk-aversion component is the difference between VIX and the projected variance. We

evaluated this approach using equation (1) in BHL (page 774). Over our sample, the realized variance loaded more

heavily on the VIX. Thus, changes in VIX (as used as an explanatory variable in equation (1)) and comparable

changes in the projected conditional variance had extremely high positive correlations (ρ > 0.98).

11

increased economic uncertainty also increases stock risk with a higher conditional stock variance,

which would promote higher equity risk premia and lower stock prices. With the two opposing

effects, the net effect may vary with the economic state. From BEX, “there may be instances

where our model will generate a classic ‘flight to quality’ effect with uncertainty lowering interest

rates, driving up bond prices, and depressing equity prices” (page 72).13

Finally, the results from the BEX calibration over 1927 to 2004 suggests that increases in

uncertainty should be associated with a steeper real term structure. However, there are opposing

effects with complex interactions between uncertainty and risk aversion, so this prediction may

not hold in all economic states.

The flexibility and complexity of the BEX framework suggest it is an interesting empirical

question to evaluate how the risk-return connections vary with the economic state. In this section,

we investigate four empirical questions. First, is there a positive relation between economic-

uncertainty changes (as proxied by VIX movements) and Treasury values; and, if so, is this

positive risk-return connection reliably stronger over our RPR periods with presumably higher

risk aversion? Second, under a premise of higher risk aversion, is the relation between bond

returns and own-bond risk stronger over our RPR periods? Third, does the relation between the

term-structure’s slope and economic uncertainty vary with the economic states? Finally, under

a premise of higher risk aversion, is the relation between stock returns and economic-uncertainty

changes stronger over our RPR periods?

3.2. Estimation with State-dependent Risk-to-Treasuries Relations

To investigate the first two questions, we begin by estimating variations of the regression:

TrFtRtt−j,t = α0 + (λ1 + λ2D0104t + λ3D

0913t )∆log(V IXt−j,t)+ (1)

(γ1 + γ2D0104t + γ3D

0913t )∆log(TIVt−j,t) + ϵt−j,t

13The BEX (2009) model is complex, with five state variables, 19 parameters, and 34 moment conditions in

their estimation. “Our model involves more state variables and parameters than much of the existing literature,

making it difficult to trace pricing effects back to any single parameter’s value,” (BEX, 2009, page 62). As such,

there are complex interactions such that movement in state variables can sometimes have different influences on

asset-pricing issues for different economic conditions.

12

where TrFtRt indicates the percentage change in the Treasury futures contract’s price or the

‘futures return’ over the period from t−j to t; V IX and TIV are the equity and T-bond implied

volatilities; the ∆log and subscripts t − j, t indicate the difference in the log of each variable

between trading days t− j and t; D0104t is a dummy variable that equals one over our first RPR

period over 2001:10 - 2004:04; D0913t is a dummy variable that equals one over our second RPR

period over 2009:01 - 2013:12; ϵt−j,t is the residual; and the α, λ’s and γ’s are coefficients to

be estimated. The dependent variable is either the 30-year T-Bond futures return (TB) or the

10-year T-Note futures return (TN), and j is either 5 or 22, indicating rolling 5-trading-day

and 22-trading-day returns and change horizons. We also report on comparable estimations, but

where the dependent variables are changes-in-forward rates for 10-year, 5-year, and 1-year out

forward rates (FR10, FR05 and FR01). We later report on a similar specification that includes

time-varying volatility of ϵt−j,t.

Table 2, Panel A, reports the results for Treasury futures returns. The regressions in rows 1,

3, 5, and 7 report the results on the unconditional relation (without the dummy variables). These

unconditional relations indicate that the VIX-changes (TIV-changes) are positively (negatively)

related to the futures returns in all four cases (T-Bond-futures and T-Note-futures, for both

weekly and monthly returns). Thus, estimates for our full sample indicate a classic FTQ dynamic,

as suggested in BEX (2009), where longer-term Treasury values increase reliably with increased

equity risk perceptions. The relation to the TIV-changes suggests a risk-premium-feedback effect,

where increases in own-asset-class risk are associated with declining prices.

Estimates from the full model are reported in Table 2, Panel A, rows 2, 4, 6, and 8. In all

four cases, we find that the risk-return connection is much stronger for our two RPR periods. For

example, in row 2, the estimated relation between the monthly VIX-changes and the monthly

T-bond-futures return is 7.26 for our first RPR period (λ1 + λ2) and 8.85 for our second RPR

period (λ1 + λ3), versus 0.35 for the remainder of our sample (λ1 only). In row 4, the estimated

relation between the monthly TIV-changes and the monthly T-note-futures return is -5.19 for

our first RPR period (γ1+γ2) and -4.53 for our second RPR period (γ1+γ3), versus 1.13 for the

remainder of our sample (γ1 only). The estimated λ2, λ3, γ2, and γ3 coefficients are all highly

statistically significant. For the monthly horizon, there is no reliable relation between the risk

13

changes and the Treasury-futures return for the non-RPR periods (λ1 and γ1).

Table 2, Panel B, reports the results for the change in the forward rates (FR). The results for

the 5-year and 10-year FRs depict the same qualitative relation as those in Panel A: (1) overall,

unconditionally, VIX-increases (TIV-increases) are associated with declining (increasing) FRs;

and (2) the conditional relations are much stronger over our RPR periods. For the monthly

horizon for the 5-year and 10-year FRs, note that the ∆V IX-∆FR relation has a different

algebraic sign for the RPR versus non-RPR periods.

The results for the 1-year FR, FR01, are somewhat different with the ∆V IX-∆FR relation

being stronger for our first RPR period but weaker for our second RPR period. By December

2008, the Federal Reserve had essentially locked T-bill yields to near zero for the remainder of

our sample. This suggests little variability in short rates over this period, so we would expect

smaller variability in the 1-year FR over our later RPR period. Figure 3 displays the time-

series of FR levels over our sample, and shows that the 1-year FR fell below 1% in early 2009

where it remained for the majority of our second RPR period. By mid 2011, the one-year FR

became especially low, with little variability. Given these observations, it is not surprising that

the connection between the 1-year FR and the risk changes is weaker over our second RPR

period, with the weakening for the ‘1-year FR’-risk connection corresponding with a substantial

strengthening for the ‘10-year FR’-risk connection.

3.3. Separate Risk-to-Treasuries Estimations for RPR & Non-RPR Subperiods

Next, we expand our analysis along two dimensions. First, we estimate the risk-to-Treasuries

connection separately for key subperiods so we can compare each RPR period with our non-RPR

periods. Second, we also add the lagged risk-change terms as additional explanatory terms to

evaluate the intertemporal risk relation. If there is any reliable relation between the dependent

variables and the lagged risk changes, then the evidence may prove useful in interpreting the

concurrent relation. For example, if the T-bond return’s relation to the concurrent ∆V IX term

and the lagged ∆V IX term have different algebraic signs, then this would indicate a reversal of

the concurrent relation. A reversal would suggest that the concurrent relation is partially due

to a premium earned by liquidity providers to absorb any concurrent demand and supply shocks

14

that are associated with the risk changes.

We report on variations of the following model:

TrV art−j,t = α0 + λ1∆log(V IXt−j,t) + λ2∆log(V IXt−2j,t−j)+ (2)

γ1∆log(TIVt−j,t) + γ2∆log(TIVt−2j,t−j) + ϵt−j,t

where TrV art−j,t indicates one of five different Treasury-related dependent variables over t − j

to t as in Section 3.2 and Table 2; the subscripts t−2j,t−j on a variable indicate the first-order

lags of the respective term; and the other terms are as defined for equation (1). We report on

rolling monthly and weekly horizons, where j equals 22 or 5 trading days.

Table 3, Panel A, reports on these estimations over the RPR subperiods. For the longer-term

Treasury-futures returns and the 5- and 10-year FR changes, we note that the R2 values are all

quite sizable. For example, for the T-Bond and T-Note futures returns at the monthly horizon,

the average R2 value is over 45% across Panels A.1 to A.4. The estimated λ1 coefficients (γ1

coefficients) on the concurrent ∆V IX (∆TIV ) term are sizable and highly statistically significant

for all eight cases (rows 1 to 4 and 6 to 9); indicating that VIX increases (TIV increases) are

associated with increasing (decreasing) bond prices and decreasing (increasing) distant forward

rates. The strong risk-return connections over the 2011:07 - 2013:12 subperiod (Panel A.4)

indicate that the strong connection over 2009-2013 is not simply due to extreme market dynamics

over the 2008-09 recession and financial crisis, since this subperiod begins over two years after

this recession formally ended in June 2009.14

Regarding the intertemporal relation between the Treasury variables and the lagged risk-

change terms for the RPR periods, we find that the coefficients on the lagged risk-change terms

have the same algebraic sign as the comparable coefficients on the concurrent risk-change terms

for all but three of the 64 estimated coefficients for the TB, TN, FR05, and FR10 variables (Panels

A.1 to A.4). A majority of the estimated λ2 and γ2 coefficients are statistically significant. This

continuation in the risk-return relations for our RPR periods casts doubt on a ‘return to liquidity

provider’ explanation for the concurrent relations and suggests a striking risk-return linkage that

14We evaluate one-half subperiods for our second RPR period because the second-half of this RPR period is

substantially removed from the economic crisis of 2008-09 and a 30-month one-half RPR subperiod evaluation

seemed of adequate length. The first RPR is only 31 months so we did not evaluate one-half subperiods for it.

15

extends beyond the concurrent relation.

The FR01 results are similar. However, as compared to the risk-FR relations for FR05 and

FR10, the relations between FR01 changes and the risk changes tend to be stronger over our first

RPR period (2001:10 - 2004:04), but weaker over our second RPR period (2009:01 - 2013:12), in

terms of the size of the estimated coefficients and the R2 values. Our discussion in Section 3.2

discusses likely influences behind these differences.

Table 3, Panel B, reports coefficient estimates for our non-RPR subperiods, with separate

estimations for both the full non-RPR period and the portion of the non-RPR periods that is

classified as being in an economic expansion by the NBER (or ‘non-RPR-Growth’ subperiods, see

Section 2.5 and Appendix A). We evaluate the growth portion of the non-RPR period separately

to ensure our results are not being driven by the early recession months. For the longer-term

Treasury-futures returns and the 5- and 10-year FR changes, we note that the risk-return connec-

tions are much weaker, as compared to Panel A. The estimated λ1 coefficients on the concurrent

VIX-change term are not statistically significant for the 10-year FR, at either time horizon for

either non-RPR period. The estimated γ1 coefficients on the concurrent TIV-change terms are

mixed. For FR05 and FR10, only one of the estimated coefficients on the lagged risk-change

terms is statistically significant at a 5% p-value.

The contrast between the Panel A and Panel B results is striking. The average R2 of rows 1-4

and 6-9 for the four RPR subperiods (Panel A) is 36.7% with a range of 16.9% to 61.5% versus a

comparable average R2 for the four non-RPR periods (Panel B) of 3.6% with a range of 0.5% to

11.1%. The estimated coefficients (λ1 and γ1) also tend to have a much larger magnitude for our

RPR periods. For example, for the 5-year FR, the average estimated λ1’s on the ∆V IX term is

-1.09 (-0.68) for the monthly (weekly) horizon for the four RPR periods in Panel A versus -0.08

(-0.11) for the monthly (weekly) horizon for the four non-RPR periods in Panel B.

The results are somewhat different for the 1-year FR in Panel B. In all four subpanels in Panel

B, the connection between ∆V IX and the 1-year FR is negative and statistically significant for

the weekly change horizon. The R2 values are somewhat higher than for FR05 and FR10, ranging

from 4 to 26%. This finding is suggestive that FTQ pricing influences over the non-RPR periods

(while seemingly less important as compared to our RPR periods) were likely more tied to linkages

16

with the money market. Recall that the T-bill yields were appreciably higher over these periods,

and the term-yield-spread appreciably lower, which suggests that the money market might have

been the more favored safe-haven lower-risk asset.

To evaluate further the efficacy of our RPR vs. non-RPR economic-state divisions, we es-

timate the same risk-return Treasury connections for the weekly horizon over rolling one-year

estimation periods of 251 trading days each. We then retain the R2 values for each of the rolling

regressions for the Treasury-futures returns and plot the time-series of R2 values in Figure 4. The

results indicate much higher R2 values since about January 2009, corresponding to our second

RPR period. The figure also indicate a second region where the R2 values tend to be consistently

elevated, roughly corresponding to our first RPR period over October 2001 to April 2004. The

consistency of these elevated R2 values across these two RPR periods reinforces the notion of

prolonged periods with different risk-return dynamics, rather than limited results linked to a few

isolated extreme cases.

3.4. The Risk-to-‘Term Structure Slope’ Connection in Treasuries

Next, we evaluate the connection between the term-structure’s slope and changes in asset-class

risk perceptions, which addresses our third empirical question. We estimate the following model:

∆TSSt−j,t = α0 + (λ1 + λ2D0104t + λ3D

0913t )∆log(V IXt−j,t)+ (3)

(γ1 + γ2D0104t + γ3D

0913t )∆log(TIVt−j,t) + ϵt−j,t

where ∆TSS indicates the change in the Treasury term-structure’s slope over the period from

t−j to t; and the other terms are as defined for equation (1). We use two measures of the change

in the term-structure’s slope: (1) the change in the term-structure’s second principal component

(∆PC2), and (2) the change in the term yield spread(∆TY S). The principal components are

estimated from the 10 zero-coupon bond yield with maturities from 1-year to 10-years, and the

term yield spread is defined as the difference between the 10-year and 6-month Treasury Constant

Maturity Yield. As before, we report on the monthly and weekly change horizons.

Table 4 reports the results. We note two primary findings. First, the estimated relation

between ∆TSS and ∆V IX is positive, but statistically insignificant, over the non-RPR periods

(λ1 in the row-2,-4,-6, and -8 models). Second, the ∆TSS-∆V IX relation is negative and much

17

lower for our two RPR periods (λ2 and λ3 in the row-2,-4,-6, and -8 models). The findings reflect

the relatively stronger relation between equity-risk innovations and longer-term Treasuries over

our RPR periods (relative to short-term Treasuries), which suggest that longer-term Treasuries

became relatively more of a favored safe-haven asset over our RPR periods (in a FTQ sense).

We also note that the estimated relation between ∆TSS and ∆TIV tends to become more

positive over our RPR periods, but only reliably so for our second RPR period (2009:01 - 2013:12).

This suggests that an increased TIV induces relatively higher term risk premia over our RPR

periods, presumably through an own-asset risk feedback mechanism. If so, this seems consistent

with the notion of higher risk aversion over our RPR periods. Collectively, the Table 4 evidence

again indicates state-dependent dynamics between risk and term-structure behavior.

3.5. Robustness with Alternative Specifications

In Appendix D, we investigate robustness of results in Tables 2 through 4 with a variety of

alternative empirical approaches, including: (1) jointly estimating the conditional mean and

conditional volatility in a specification that also models time-variation in volatility; (2) a specifi-

cation that includes additional term-structure state variables and the lagged dependent variable

as additional explanatory terms; (3) specifications that consider alternative functional forms for

the VIX and TIV changes. To summarize, our primary results depicted in Tables 2 through 4

remain reliably evident.

3.6. Risk and Return in Treasuries and BEX (2009) and BE (2013)

Our findings bear on empirical implications from BEX (2009) and BE (2013). First, the BEX

model generates a FTQ effect where higher economic uncertainty is associated with lower interest

rates due to a precautionary savings effect. This dynamic is evident in our estimates. The

unconditional relations depicted in Table 2 (models in rows 1, 3, 5, 7, 9 and 11) support this

implication.15

Second, we find that the risk-return connections are dramatically stronger for the longer-term

Treasuries in our RPR state, as compared to the much weaker or even non-existent connections

15Bansal, Connolly, and Stivers (2014) find similar unconditional results in comparable regressions on monthly

returns that also include the concurrent stock return as an additional explanatory variable.

18

for our non-RPR state. Qualitatively, we argue that these state-dependent differences are also

suggested by the economic forces inherent in the BEX framework. Such an interpretation requires

a more detailed review of their model, which we provide next.16

In BEX (2009), risk aversion increases as current consumption declines toward a habit or

subsistence consumption level. Specifically, the coefficient of relative risk aversion is equal to

γCt

Ct−Ht; where γ is a risk-aversion parameter, Ct is current consumption, and Ht is a subsistence

or habit level of consumption. They define Qt =Ct

Ct−Htas a preference shock. In BEX, “increased

volatility (referring to higher economic uncertainty) unambiguously drives up bond prices” (page

63), due to a precautionary saving motive. The response of interest rates to movements in

economic uncertainty is shown in their equation (28) (BEX page 70). There, the relation between

interest rates and economic uncertainty movements is more negative when either the positive risk

aversion parameter γ is larger or when the negative σqc parameter is more negative, where σqc is

a correlation parameter between consumption growth and qt (qt = ln(Qt)).17

We expect that σqc would become relatively more negative in our RPR state. Recall that

our RPR periods commence later in recessions (after most or all of the Fed easing in the Fed

Funds rate has occurred) and continue through the early, uncertain stages of recovery. Thus,

over our RPR periods, current consumption should be relatively closer to the habit/subsistence

consumption level. If so, qt is relatively high, driving up risk aversion, and changes in qt will

also be more sensitive to small consumption changes. Thus, one would expect a relatively more

negative σqc in our RPR state. In addition, higher risk aversion in our RPR periods could also be

linked to a relatively larger γ parameter, presumably reflecting investor psychology in the RPR

state with a weak economy that followed a dramatic stock market decline.

For these reasons, we argue that the much stronger relation between ∆V IX and the Treasury

values fits a ‘conditional version’ of the BEX framework, in an intuitive ‘comparative statics’ sense

16Our discussion in this subsection appeals to intuition and qualitative deduction from the BEX and BE frame-

works, rather than exact quantitative results based on their formal calibrations or model. The BEX calibrations

focus on unconditional parameters, while our focus is on economic-state-based differences.17We note that the BEX equation (28) applies strictly to real interest rates, but their results relating uncertainty

to nominal rates are similar. Additionally, with generally modest and stable inflation over our sample period,

movement in nominal rates should be largely aligned with movements in real rates over our sample, especially for

modest one-week and one-month horizons.

19

where our RPR state seems likely to have a more negative σqc and/or larger γ. The opposing

‘comparative static’ state is a more typical growth state where one would expect lower risk

aversion with a less negative σqc. The economic intuition is that bad economic times have higher

risk aversion that is also more sensitive to consumption changes. Thus, positive uncertainty

shocks generate relatively stronger precautionary savings responses in our RPR state.

Third, BEX’s calibration predicts a complex but positive relation between changes in eco-

nomic uncertainty and the term-structure’s slope. Based on their calibration estimates, the

influence of the Expectations Hypothesis of term structure is the dominant effect, and it predicts

a positive relation between economic uncertainty and the term premium. Our point estimates of

λ1 are positive in Table 4, rows 2, 4, 6, and 8, which supports this implication but only over our

non-RPR periods (however, our coefficient estimates there are statistically insignificant).

The slope relations for our RPR state are notably different: there is a strong negative relation

between movements in economic uncertainty and the term-structure’s slope. Thus, our findings

support the notion that the uncertainty-slope relation is a complex time-varying one, and indicate

that the sign and magnitude of the relation can change with the economic state. Our findings

further suggest that the impact of the ‘precautionary savings effect/FTQ effect’ shifted out along

the yield curve to longer maturities for our RPR periods. The notion that longer-term Treasuries

have become more of a hedge instrument in recent times also fits with arguments in CSV (2013).

Our state-dependent results for the risk-return Treasury connections also fit qualitatively

with implications in Bekaert and Engstrom (BE) (2013). The BE framework has the same habit-

based preference structure as BEX, but they factor in the asymmetric nature of consumption

growth in good and bad times. Specifically, during bad times such as around recessions, there

is a greater chance of a negative shock to consumption. They find that precautionary saving

demands are exacerbated during such bad times with greater negative skewness in consumption

growth. Given this observation, it seems plausible that bond values would be more responsive to

uncertainty shocks during weak economic times with higher risk aversion, such as our RPR state.

Further, the BE framework with non-Gaussian fundamentals naturally generates a meaningful

variance risk premium, in contrast to comparable Gaussian models; which is consistent with the

time-variation in the equity variance risk premium that we find.

20

3.7. Equity-Risk Innovations, Stock Returns, and the Economic State

Our fourth empirical question asks whether there is a stronger relation between stock returns

and economic-uncertainty changes (as proxied for by VIX changes) in our RPR state. The row-3

model in Table 5 reports regression results for a model in which the stock-futures return (as the

dependent variable) is regressed against the risk-change terms (as explanatory variables). We

find that the ‘∆V IX-stock return’ relation is highly significantly negative for all our subperiods

of interest, which suggests the dominant effect over our sample period is a risk-premium feedback

effect between equity risk and equity prices.

The strong negative relation between VIX changes and stock returns is well known and the

unconditional relation is not the focus of this subsection. Rather, our primary interest is whether

the ‘∆V IX-stock return’ relation is appreciably different for our RPR and non-RPR periods. We

evaluate this issue using a variety of different specifications and empirical approaches (tabular

results available upon request) and conclude that the ‘∆V IX-stock return’ relation is similarly

strong for both RPR and non-RPR periods.

At first glance, the lack of difference in the ‘risk-stock return’ relation may seem puzzling. We

have argued that risk aversion is likely higher for our RPR state, and we have documented that

there is a much stronger positive relation between ∆V IX and T-bond returns for our RPR state

as compared to the non-RPR state. Given this, we might expect to see a stronger risk-return

feedback effect in stock returns, with a resulting prediction of a more negative relation between

stock returns and ∆V IX over our RPR periods.

However, opposing forces in BEX’s (2009) model can help us understand this lack of economic-

state contrast in the ‘∆V IX-stock return’ relation. First, under the premise of higher risk

aversion in our RPR state, it would seem that the risk-premium-feedback effect would be stronger

in our RPR state, suggesting a more negative ‘∆V IX-stock return’ relation. However, increases

in economic uncertainty are also associated with declining interest rates that should drive down

the discount rate that investors use to value the future cash flows from equity securities, which

would promote higher equity prices (ceteris paribus). We have documented that the negative

‘economic-uncertainty/interest-rate’ relation is much stronger in our RPR state, especially for

longer-term interest rates that are typically used for determining the discount rates for equities

21

(see, e.g., Brotherson et al (2013)). Thus, it seems plausible that these opposing influences, the

risk-premium-feedback effect and the interest-rate effect, are both stronger in our RPR state

such that the changes might offset each other. If so, this would be consistent with our finding

that the the ‘∆V IX-stock return’ relation is not notably stronger in our RPR state.

4. Stock and Bond Returns, Inflation, and Asset-Class Risk

4.1. Theoretical Motivation and Empirical Questions

At a basic level, the analysis in Section 3 shows that economic states play a substantial role in

explaining changes in the response of asset prices to changes in risk perceptions. There, we relied

heavily on the BEX (2009) model to organize and interpret our findings, with time-varying risk

aversion playing an essential role. Our evidence is consistent with prior studies, such as BEX and

Campbell and Cochrane (1999), that indicate risk aversion is countercyclical and a fundamental

dimension of risk-return dynamics in asset pricing.

While our findings in Section 3 provide considerable support to key implications in BEX

(2009), we have not yet considered the role of inflation in stock/bond return dynamics. BEX

include inflation in their model, but it has no pivotal role in determining equity prices or real

bond prices. In this section, we extend our empirical investigation to consider the theoretical

framework in David and Veronesi (2013) (DV), where inflation news has an important role because

it provides a signal to investors about the underlying economic state.

DV define two-dimensional economic states in terms of economic growth and inflation. In

their framework, investors are uncertain about the underlying economic state, and inflation news

provides a signal to investors about the underlying state. News of higher inflation has dia-

metrically opposite implications for stock values and stock-bond return comovement, depending

upon how investors view the current economic state. For example, in low growth/low inflation

states, news of higher inflation sends nominal bond prices down but raises stock prices because

the inflation shock signals that the economy may not be slipping into a very low growth (or

contractionary) economic state.

Our investigation in this section focuses on the following empirical issues. First, does inflation

news have an important role in understanding equity prices (as suggested in DV), and does the

22

inflation-stock relation depend on the economic state? Second, what are the implications for

understanding the stock-bond return correlation in a framework that jointly controls for changes

in equity risk, T-bond risk, and inflation? Third, do the key risk-to-Treasury relations from

Section 3 remain reliably evident when controlling for inflation?

Our empirical investigation here is linked to our prior work in Section 3 because we evaluate

the same economic states. Our underlying premise is that our RPR periods are ‘low inflation/low

growth’ economic states from a DV perspective. We will present evidence of a strong dichotomy

in the inflation-stock relation across our economic states, consistent with DV’s model.

To implement these empirical tests, we desire a market-driven measure of inflation expecta-

tions that is observed daily to match the remainder of our data. We use the ‘inflation compensa-

tion’ (IC) measure from Gurkaynak, Sack, and Wright (GSW, 2010), based on the yield difference

between 10-year nominal Treasury bonds and 10-year TIPS. While this measure can also move

with the time variation in the liquidity preferences of nominal bonds over TIPS and with time

variation in inflation risk compensation, it should also clearly move with inflation expectations.

By jointly controlling for VIX and TIV changes, we hope to improve the partial link between

GSW’s IC measure and simple inflation expectations.18 We also evaluate the robustness of our

findings by using news shocks in CPI and PPI news releases as, perhaps, a more direct measure

of inflation news, in place of the GSW (2010) measure.

4.2. Empirical Findings with Inflation News

We begin by estimating variations of the following regression:

FtRtt−5,t = α0 + λ1∆log(V IXt−5,t) + γ1∆log(TIVt−5,t) + ψ1∆ICt−5,t + ϵt−5,t (4)

where FtRtt−5,t is the percentage change in the futures contract price over trading days t−5 to t,

estimated for both the 10-year T-Note and the S&P 500 futures as the dependent variable, ∆IC

is the change in ‘inflation compensation’ based on the yield difference between 10-year nominal

18In particular, we feel it is important to control for ∆V IX because periods with sharp increases in VIX are

also likely to be times with an increasing liquidity preference. Including the ∆V IX term should hopefully capture

such a ‘liquidity preference shift’, to some extent, which should leave the partial ∆IC relation to largely reflect

inflation expectations.

23

Treasury Bonds and TIPS per GSW (2010), over trading days t − 5 to t; the α, λ, γ, and ψ

are coefficients to be estimated, and the other terms are as defined for Tables 2 and 3. Table

5 reports on separate coefficient estimates for each of our two RPR periods and the non-RPR-

growth periods over 1999:01 - 2001:02 and 2004:05 - 2007:11. Here, we focus on the expansionary

portion of our non-RPR periods because they are a better fit to contrast with our RPR periods

in the DV framework. The IC data is not available until 1999, so the first non-RPR estimation

period here starts in January 1999. We refer to ∆IC as ‘inflation news’.

Table 5 reports the estimates in panels organized by the economic state. We begin with the

∆IC findings. IC increases are reliably associated with higher stock returns for our two RPR

periods (Panel A), but not for the non-RPR growth periods (Panel B); compare the estimated

ψ1 coefficients in lines 5 and 7 of each panel. For the non-RPR-growth periods, the ψ1 estimate

is negative and statistically significant over 1999:01 to 2001:02, and positive, but small and

statistically insignificant, over 2004:05 to 2007:11. Thus, concerning our first empirical question

above, we find that the relation between stock returns and IC changes is: (1) sizable and reliably

positive in our RPR state; but, (2) negative or statistically insignificant over our the non-RPR

growth state. This finding directly supports the empirical prediction in DV (2013).

In Appendix E, we report qualitatively consistent evidence when using the CPI/PPI news as

our ‘inflation news’ variable. We also discuss earlier CPI/PPI inflation-stock studies there.

Second, we find that ∆IC promotes a negative stock-bond return correlation over our RPR

periods, but not over the non-RPR growth periods. In Table 5, Panel A for the RPR periods, the

ψ1 estimates for the T-Note-futures returns (line-4) and for the S&P 500-futures returns (line-5)

are both reliably estimated, but they have opposite signs. Thus, in our RPR state, the inflation

news looks to drive stock and bond returns in opposite directions. Note that the correlation

between raw T-Note and stock-futures returns is sizably negative at -0.43 and -0.39 for our first

and second RPR periods (line 1 in Table 5). After regressing out the relation with ∆IC, the

correlation in the residuals for the T-Note and stock futures returns falls to -0.33 and -0.19 for

our first and second RPR periods. Thus, while the inflation news promotes a negative stock-bond

return correlation in RPR periods, the residual correlation is still substantially negative.

By comparison, the regressions in lines 2 and 3 in Table 5 report the results from regressing

24

the futures returns against the asset-class risk-change terms. For our RPR periods, the ∆V IX

term is sizably and reliably related to both the stock and bond futures returns, but in the

opposite direction. After regressing out the risk-change relations, the residual correlations are

only -0.26 and -0.15 for our first and second RPR periods, smaller than the comparable residual

correlation for the ∆IC regressions in lines 4 and 5.19 For our non-RPR growth periods, the

relation between ∆V IX and the Treasury futures return is much smaller, so the contribution of

equity risk changes to a negative stock-bond correlation is accordingly smaller.

Finally, the regressions in lines 6 and 7 in Table 5 include both the ∆IV and ∆IC terms. For

our RPR periods, we find that both the VIX changes and the IC changes are reliably related to

both T-Note futures and stock futures, but in the opposite direction; this suggests fluctuations in

both economic uncertainty and inflation perceptions contribute to the negative stock-bond return

correlation. Here, the residual correlation falls to essentially zero for our second RPR period (and

to -0.24 for our first RPR period). Thus, regarding our second empirical question above, both

inflation news (∆IC) and economic-uncertainty changes (∆V IX) appear to contribute to the

sizably negative stock-bond return correlation in our RPR state.

These state-dependent differences in the stock-inflation relation and the bond-VIX relation

fit with the state-dependent differences in the stock-bond return correlation. For our non-RPR

growth periods, the stock-bond correlation in weekly returns is 0.15 and -0.22 for the first and

second non-RPR-growth periods, versus -0.43 and -0.39 for our two RPR periods.

Regarding our last empirical question stated in Section 4.1, we note that the strong link

between asset-class risk perceptions and the T-Note futures returns remains reliably evident for

our RPR periods, even when controlling for ∆IC. Appendix D.4 reports qualitatively consistent

results in an alternative framework that allows for time-variation in the conditional volatility.

Next, we extend our investigation by estimating variations of the following equation:

SP5t−j,t = α0 + (λ1 + λ2D0101t + λ3D

0104t + λ4D

0708t + λ5D

0913t )∆log(V IXt−j,t)+ (5)

(γ1 + γ2D0101t + γ3D

0104t + γ4D

0708t + γ5D

0913t )∆log(TIVt−j,t)+

(θ1 + θ2D0101t + θ3D

0104t + θ4D

0708t + θ5D

0913t )∆ICt−j,t + ϵt−j,t

19Similarly, Bansal, Connolly, and Stivers (2014) find that the partial stock-bond return relation weakens ap-

preciably when controlling for equity and bond implied volatility changes.

25

where SP5t−j,t indicates the S&P 500 futures return over t − j to t; the Dit variables are four

dummy variables that equal one over the following periods and zero otherwise; D0101 over 2001:03

- 2001:09 (a non-RPR recessionary period), D0104 over 2001:10 - 2004:04 (our first RPR period),

D0708 over 2007:12 to 2008:12 (a non-RPR recessionary period), and D0913 over 2009:01 - 2013:12

(our second RPR period); the α, λ’s, γ’s, and θ’s are coefficients to be estimated; j is 5 or 22 for

weekly or monthly change horizons; and the other terms are as defined for equations (1) and (4).

Thus, the base periods that are not covered by dummy terms are the non-RPR-growth periods.

This estimation extends our prior investigation in Table 5 by: (1) reporting on a single

estimation over the full period, which allows us to evaluate whether the change in the stock-

inflation relation is statistically significantly different between our RPR periods and non-RPR-

growth periods; and (2) evaluating the monthly change horizon.

Table 6 reports the results for the θ coefficients (full results available upon request). For both

the weekly and monthly changes, we find that the estimated stock-inflation relation is negative for

the non-RPR-growth periods, with statistically significant relations for all but one case. Next, we

find evidence that the stock-inflation relation is reliably greater for the RPR periods as compared

to the non-RPR growth periods. The θ5 coefficient for the 2009-2013 RPR period is positive and

statistically significant in both model variations and for both the weekly and monthly changes.

The θ3 for the 2001-2004 RPR period is positive and statistically significant for three of the four

cases. Thus, Table 6 provides further evidence supporting the David-Veronesi premise that the

stock-inflation relation can vary substantially with the economic state.

4.3. Summary of Stock-Inflation Findings and Implications in DV (2013)

Our findings support the key empirical implication in DV (2013) that the relation between stock

returns and inflation news can vary appreciably across economic states, with ‘low growth/low

inflation’ economic states having a reliably positive stock-inflation relation. However, our findings

also indicate that this DV inflation perspective is only one dimension of the negative stock-

bond return correlation over our RPR periods. Rather, VIX shocks (or shocks to economic

uncertainty in the BEX framework) also remain reliably important and of comparable importance

for understanding the stock-bond return correlation.

26

5. Other Economic Traits for our RPR Periods

In our introduction and in Appendix A, we highlighted other important economic differences

between our RPR and non-RPR periods. In this section, we provide details on the following

important differences for our RPR periods that we feel merit further quantification: (1) an

elevated equity variance-risk premium (VRP) and stronger bias between the option market’s

implied equity volatility and subsequent realized equity volatility; and (2) a much higher term

yield spread (TYS), relative to very low T-bill yields.

5.1. VIX and the Realized Stock Volatility

We follow Bollerslev, Tauchen, and Zhou (2009) and estimate the stock-market’s variance risk

premium (VRP) as the difference between the CBOE’s VIX and the recent realized variance of

the S&P 500 index (see Section 2.4 and Appendix C). Figure 1, Panel B, depicts the time-series

behavior of this VRP and shows that it is notably higher over our RPR periods. In Table 7,

Panel A, we show that the average VRP across our two RPR periods is over twice the average

VRP for the remainder of our sample.

Results in Appendix A, Table A1, show that the bias in VIX as a forecast for the subsequent

realized volatility is much larger over our two RPR periods. We regress the realized volatility

over day t to t + 21 against the closing VIX from day t − 1. For our two RPR periods, VIX

has a positive bias of about 15%, and the difference relative to the remainder of our sample is

statistically significant at a 1% p-value. This state-based difference in the VRP and VIX bias is

consistent with the notion of higher risk aversion over our two RPR periods (Bollerslev, Tauchen,

and Zhou (2009), Bollerslev, Gibson, and Zhou (2011), Bekaert, Hoerova, and Lo Duca (2013)).

5.2. The Term Yield Spread (TYS) and T-bill Yields

The TYS is considerably higher over our two RPR periods, reflecting in large part the very low

T-bill yields, see Figure 1, Panel A. Table 7 analyzes the difference between the TYS and the

6-month T-bill yield. We refer to this yield difference as the ‘relative TYS’, since it indicates the

size of the TYS relative to the money-market yield. We find that the average of this ‘relative

TYS’ is over 500 basis points higher over our two RPR periods, as compared to both the full

27

non-RPR periods (Panel A) and the expansionary portion of the non-RPR periods (Panel B).

This behavior indicates that: (1) our RPR periods occur after the Federal Reserve has already

taken dramatic action to lower the T-bill yields to very low levels, and (2) the opportunity for

investors to earn additional yield in longer-term Treasuries is greater over our RPR periods.

5.3. Summary Comments Concerning our RPR Periods

These collective economic traits lead us to believe that it is plausible and intuitive that risk

movements would be associated with stronger FTQ linkages to longer-term Treasuries (relative

to short term T-Bills) over our RPR periods. First, the RPR periods commence following both

economic contraction and a large stock market decline, and the RPR periods exhibit a substan-

tially elevated VRP. Thus, risk aversion is presumably higher (see discussion in footnote 5 and

Section 3.6), which would likely intensify the precautionary saving effect when uncertainty in-

creases. Second, it seems likely that longer-term Treasury bonds would have become relatively

more important as a safe-haven asset (in a FTQ sense) due to the relatively low inflation risk,

and a relatively high term yield spread with near-zero money market yields. Further, over our

second RPR period, longer-term Treasuries received unprecedented support through large-scale

purchases by the Federal Reserve, which may also have served to lower their perceived risk. Fi-

nally, the notion that longer-term Treasuries have become more of a hedge instrument against

economic uncertainty in recent times fits with related arguments in CSV (2013).

6. Federal Reserve Large-Scale Asset Purchases over 2009-2013

Our 2009:01 - 2013:12 RPR period has one unique feature, as contrasted with the remainder of

our sample and all earlier U.S. economic history. First announced in late November 2008 but

not seriously commencing until early 2009, the Federal Reserve conducted several quantitative

easing (QE) operations featuring large-scale purchases of longer-maturity debt. This unprece-

dented action reached a pinnacle with approximately $85 billion worth of purchases per month,

announced in September 2012, that was ongoing through the end of our sample period.

A natural question is whether these large-scale asset purchases are connected to the unusually

strong risk-Treasuries connection over our second RPR period. For example, if the intensity of the

28

Fed QE purchases rose during times of increasing uncertainty (coincident with a corresponding

VIX increase), then it might be possible that the QE purchases amplified any pricing influences

linked to the uncertainty changes. We refer to such a possibility as a ‘Fed Intensity’ hypothesis.20

We provide some evidence on this issue in Appendix F- Table F1. Over 2009 to 2013, we

find that there is essentially no unconditional correlation between the weekly VIX changes and

the weekly changes in the longer-term debt holdings on the Federal Reserve’s Balance Sheet.

Next, focusing only on weeks with the largest VIX changes, we find that the Fed’s longer-term

debt holdings do not increase (decrease) during the weeks with the largest VIX increases (VIX

decreases). Also, Figure F1, which depicts the time-series of the debt holdings on the Federal

Reserve’s balance sheet, does not suggest any noticeable relation between the VIX change and

the change in the Federal Reserve’s debt holdings. Collectively then, we believe that the evidence

in Appendix F provides no support for a ‘Fed intensity’ hypothesis.

7. Conclusions

We present new evidence on state-dependent dynamics of risk, inflation, and asset valuation. Our

empirical analysis relies on changes in the implied volatility from equity-index options and 10-

year T-Note futures options as observable high-quality measures of changes in risk perceptions,

and changes in yield differences between nominal 10-year Treasuries and TIPS as a measure of

inflation news.

We find a striking set of stylized differences between what we characterize as a ‘recession-

ary/post recessionary’ (RPR) economic state (91 total months over 2001:10 - 2004:04 and 2009:01

- 2013:12) and the remainder of our sample (104 total months over 1997:10 - 2001:09 and 2004:05

- 2008:12). In our RPR state, we find: (1) increases in perceived equity (bond) risk are strongly

and reliably linked to higher (lower) T-bond returns and a decreased (increased) term structure

slope at both the weekly and monthly horizons; (2) inflation news is strongly positively related to

stock market returns, and (3) the equity variance risk premium is substantially elevated. Further,

20See Krishnamurthy and Vissing-Jorgensen (2011) and Jarrow and Li (2013) for evidence that the QE programs

likely served to reduce interest rates. However, such a conclusion does not necessarily suggest that weekly (monthly)

variations in the QE intensity was linked to weekly (monthly) uncertainty variations.

29

in our RPR state, both equity-risk innovations and inflation news are strongly associated with

movements in stock and bond prices in the opposite direction, coincident with the relatively large

negative stock-bond correlation in this state. Over the remaining non-RPR periods, the com-

parable risk-return connection in longer-term Treasuries is much weaker or non-existent and the

relation between stock returns and inflation news is either negative or statistically insignificant

over the expansionary economic months. Our RPR state is also distinguished by relatively lower

economic growth, lower inflation, a larger term yield spread relative to very low T-bill yields, a

close proximity to sizable stock market declines, and presumably higher risk aversion.

We argue that recent theory in BEX (2009), BE (2013), and DV (2013) is useful in under-

standing our empirical findings. The economic traits of our RPR periods suggest that they can

be considered both: (1) a BEX- and BE-style higher risk aversion state, with consumption closer

to its habit/persistence level; and (2) a DV-style low-growth/low-inflation economic state. Un-

der this interpretation of our RPR periods and when interpreting short-horizon VIX changes as

primarily reflecting changes in BEX-style economic uncertainty, the evidence in Sections 3 and 4

supports key implications from the theory in these three papers. First, our evidence affirms BEX

implications that economic-uncertainty changes and bond values will have a much stronger link

in weak economic states where risk aversion and the precautionary savings motive are presum-

ably both elevated. Second, our findings support BE implications regarding bad economic times

having both a stronger precautionary savings motive and an elevated equity variance risk pre-

mium. Third, our evidence supports the implication in DV (2013) that inflation news can serve

as a signal about the unobservable underlying economic state; while inflation news is strongly

positively related to stock returns over our RPR low-growth/low-inflation economic states, it is

negatively or not related to stock returns over the non-RPR growth periods in our sample.

Consistent with evidence and arguments in Campbell, Sunderam, and Viceira (2013), our

findings also suggest that longer-term Treasuries became relatively more important as a safe-

haven (or hedge) asset over our RPR periods as compared to the other periods in our sample.

It seems likely that the response of the Federal Reserve to weak economic times has a role in

understanding the economic-state divisions in our study. Our RPR periods commence later in a

recession after the Federal Reserve had largely or totally completed their easing in the targeted

30

Fed Funds rate (FFR). All of our RPR months are associated with very low targeted FFR, with

none of our RPR months coinciding with an increase in the targeted FFR. In Appendix A.4, we

discuss this in depth and suggest that it is likely that the Fed response to the onset of recessions

may have obscured the typical ‘bad economy’ risk-return Treasury connections. If so, this would

help understand why earlier recession months are not categorized as part of our RPR periods by

the Bai and Perron (1998, 2003) structural break analysis.

From the DV (2013) perspective, it is important to note that our entire 1997-2013 sample

can generally be regarded as having modest inflation expectations, but with substantial time-

variation in economic growth.21 Earlier recessions with higher inflation risk, such as around

recessions in the 1970’s and early 1980’s, are not likely to have our above-noted RPR risk-return

connections in longer-term Treasuries and inflation-return connection in stock prices. DV suggest

a negative inflation-stock relation in high-inflation/weak economic times, and CSV (2013) suggest

that longer-term Treasuries added to the macroeconomic risk faced by investors in times such as

the 1970’s and 1980’s.

Our findings may bear on other areas of the term-structure and asset-pricing literature. For

example, Greenwood and Vayanos (2010) state that the preferred habitat view of the term-

structure implies that there is price pressure in the bond market. Their findings suggest that

“term-structure movements cannot always be understood in terms of changes in expected short-

term interest rates, inflation, or other macroeconomic variables, but that shifts in clientele de-

mand and bond supply are also an important driver” (page 585). If the strong risk-return linkages

over our RPR periods can be somewhat attributed to price pressure with changing clientele de-

mand, then our principal results might provide some support for this view.

Additionally, Andersen and Benzoni (2010)) present evidence that widely used affine term-

structure models cannot accommodate the observed yield volatility, which suggests that term-

structure/bond-pricing models need to look beyond traditional bond-market variables. When

interpreted from the BEX (2009) framework, our evidence suggests that measures of economic

uncertainty, outside the bond market, are good candidates to improve bond pricing models.

21Over the 1999-2013 period with available ‘inflation expectations’ data (based on differences in Treasury 10-year

nominal and TIPS yield in accordance with GSW (2010)), the ‘inflation expectation’ values range between 1.5%

and 3% for over 95% of the days, and between 1.75% and 2.75% for over 90% of the days.

31

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34

Table 1: Summary Statistics

This table reports the mean (µ) and standard deviation (σ) of the variables denoted in the column

heading over the period denoted at the beginning of the row. This table reports on the weekly change

horizon. ∆V IX5 and ∆TIV5 indicate ∆log(V IXt−5,t) and ∆log(TIVt−5,t), respectively, as the difference

between the log of the respective implied volatility at the close of day t and day t− 5; with the implied

volatilities in annualized percentage units. TB-Rt5, TN-Rt5, and SP5-Rt5 indicate weekly returns for

the 30-year T-Bond, 10-year T-Note, and S&P 500 futures contract from the close of trading days t− 5

to t, where the return is the percentage change in the futures contract’s price. ∆FR105, ∆FR055, and

∆FR015 indicates the weekly change in the Treasury instantaneous forward-rate at the 10-, 5- and 1-year

point in the yield curve over trading days t and t − 5. Period 1 reports on the full sample. Periods 2

to 5 and 6 to 9 below report subperiod statistics for our RPR and non-RPR subperiods, respectively,

corresponding to the regression subperiods in Table 3. Period 2 is the first full RPR subperiod, period 3

is the second full RPR subperiod, period 4 is the first-half of the second RPR subperiod, and period 5 is

the second-half of the second RPR subperiod. Period 6 is the first full non-RPR subperiod, period 7 is

the expansionary portion of the first non-RPR period, period 8 is the second full non-RPR period, and

period 9 is the expansionary portion of the second non-RPR period.

Period: ∆V IX5 ∆TIV5 TB-Rt5 TN-Rt5 SP5-Rt5 ∆FR105 ∆FR055 ∆FR015

Full Sample:

1. 1997:10 µ: -0.001 0.000 0.096 0.085 0.093 -0.002 -0.003 -0.007

-2013:12 σ: 0.120 0.118 1.376 0.866 2.672 0.152 0.165 0.139

Recessionary/Post-Recessionary (RPR) Subperiods:

2. 2001:10 µ: -0.005 0.001 0.109 0.100 0.084 0.001 -0.001 -0.002

-2004:04 σ: 0.099 0.114 1.571 1.033 2.763 0.144 0.178 0.185

3. 2009:01 µ: -0.005 -0.003 0.067 0.073 0.345 0.000 0.001 -0.001

-2013:12 σ: 0.129 0.136 1.464 0.822 2.583 0.171 0.185 0.081

4. 2009:01 µ: -0.006 -0.003 0.040 0.084 0.348 0.006 0.001 -0.002

-2011:06 σ: 0.124 0.125 1.488 0.920 2.841 0.165 0.194 0.107

5. 2011:07 µ: -0.002 -0.003 0.101 0.069 0.314 -0.007 0.000 -0.001

-2013:12 σ: 0.133 0.146 1.438 0.705 2.288 0.178 0.175 0.040

Non-RPR Subperiods:

6. 1997:10 µ: 0.002 0.002 0.071 0.070 -0.022 0.000 -0.003 -0.015

-2001:09 σ: 0.120 0.097 1.168 0.791 2.864 0.131 0.141 0.144

7. 1997:10 µ: 0.001 0.002 0.069 0.052 0.096 -0.003 -0.004 -0.009

-2001:02 σ: 0.117 0.101 1.151 0.776 2.759 0.126 0.143 0.133

8. 2004:05 µ: 0.004 0.001 0.160 0.110 -0.108 -0.009 -0.010 -0.009

-2008:12 σ: 0.121 0.115 1.280 0.861 2.499 0.146 0.149 0.154

9. 2004:05 µ: 0.002 -0.001 0.085 0.047 0.115 -0.007 -0.006 0.002

-2007:11 σ: 0.115 0.119 0.985 0.627 1.506 0.108 0.104 0.122

35

Table 2: Treasury Returns, Forward-Rate Changes, and Asset-class Risk Changes (I)

This table reports how longer-term Treasury futures returns and forward rates move contempora-

neously with changes in the risk of the equity market and Treasury bond market. Panel A reports on

variations of the following model:

TrFtRtt−j,t = α0 + (λ1 + λ2D0104t + λ3D

0913t )∆log(V IXt−j,t)+

(γ1 + γ2D0104t + γ3D

0913t )∆log(TIVt−j,t) + ϵt−j,t

where TrFtRt indicates the percentage change in the Treasury Futures contract’s price or the ‘futures

return’ over the close of trading days t − j to t; V IX and TIV are the equity and T-bond implied

volatilities; the ∆log and subscripts t − j, t indicate the difference in the log of each variable between

trading days t − j and t; D0104t is a dummy variable that equals one over 2001:10 - 2004:04; D0913

t

is a dummy variable that equals one over 2009:01 - 2013:12; ϵt−j,t is the residual; and the α, λ’s and

γ’s are coefficients to be estimated. Panel A reports on the estimation for the 30-year T-Bond futures

return (TBj) and 10-year T-Note futures return (TNj). Panel B reports on comparable estimations, but

where the dependent variables are changes in forward rates for 10-year, 5-year, and 1-year out forward

rates (FR10j , FR05j and FR01j). We report on returns and changes at the 1-month (j=22) and 1-

week (j=5) horizons. The sample period is 1997:10 - 2013:12. T-statistics, in parentheses, indicate

whether the estimated coefficients are statistically different than zero, calculated with heteroskedastic

and autocorrelation consistent standard errors.

Panel A: Treasury Futures Returns

∆log(V IX) terms ∆log(TIV ) terms

λ1 λ2 λ3 γ1 γ2 γ3 R2

Dp. Vr. 0104 0913 0104 0913 (%)

1.TB22 4.45 (4.85) -4.59 (-4.94) 11.0

2.TB22 0.35 (0.33) 6.91 (3.72) 8.50 (5.44) 0.74 (0.68) -9.36 (-3.52) -8.63 (-6.09) 20.4

3.TN22 2.75 (4.91) -2.45 (-3.90) 9.6

4.TN22 0.47 (0.62) 5.37 (4.48) 3.94 (4.08) 1.13 (1.37) -6.32 (-3.77) -5.66 (-5.76) 18.4

5.TB5 3.70 (11.76) -2.69 (-7.91) 12.3

6.TB5 1.64 (4.26) 3.39 (3.51) 4.43 (7.31) -0.90 (-2.10) -3.36 (-3.14) -3.02 (-4.46) 16.3

7.TN5 2.33 (12.64) -1.63 (-7.72) 12.0

8.TN5 1.38 (5.42) 2.37 (4.08) 1.68 (4.70) -0.40 (-1.41) -2.48 (-3.55) -1.95 (-4.71) 15.0

36

Table 2: (continued)

Panel B: Forward-Rate Changes

∆log(V IX) terms ∆log(TIV ) terms

λ1 λ2 λ3 γ1 γ2 γ3 R2

Dp. Vr. 0104 0913 0104 0913 (%)

1.FR1022 -0.33 (-2.82) 0.54 (6.31) 9.1

2.FR1022 0.14 (1.01) -0.60 (-3.01) -1.13 (-6.07) 0.16 (1.50) 0.65 (2.56) 0.63 (4.24) 19.4

3.FR0522 -0.46 (-3.57) 0.63 (5.36) 10.8

4.FR0522 0.05 (0.34) -1.00 (-4.37) -1.04 (-4.82) 0.01 (0.10) 0.86 (2.65) 1.06 (5.52) 20.4

5.FR0122 -0.49 (-6.57) 0.09 (0.92) 11.0

6.FR0122 -0.37 (-3.87) -0.83 (-3.67) 0.12 (1.13) -0.41 (-2.84) 1.17 (4.75) 0.66 (4.30) 20.5

7.FR105 -0.30 (-7.33) 0.27 (7.41) 7.8

8.FR105 -0.04 (-0.77) -0.29 (-2.72) -0.64 (-8.02) 0.15 (3.07) 0.21 (1.96) 0.23 (3.11) 13.0

9.FR055 -0.40 (-10.45) 0.36 (8.37) 11.8

10.FR055 -0.15 (-3.20) -0.44 (-4.14) -0.54 (-7.23) 0.15 (2.77) 0.33 (2.62) 0.40 (4.38) 16.0

11.FR015 -0.36 (-10.53) 0.12 (4.21) 9.1

12.FR015 -0.37 (-7.03) -0.37 (-3.26) 0.19 (3.28) -0.01 (-0.17) 0.43 (3.93) 0.12 (2.35) 12.6

37

Table 3: Treasury Returns, Forward-Rate Changes, and Asset-class Risk Changes (II)

This table reports how longer-term Treasury futures prices and forward rates move with changes in

the risk of the equity market and Treasury bond market for key subperiods. We report on variations of

the following model:

TrV art−j,t = α0+λ1∆log(V IXt−j,t)+λ2∆log(V IXt−2j,t−j)+γ1∆log(TIVt−j,t)+γ2∆log(TIVt−2j,t−j)+ϵt−j,t

where TrV art−j,t indicates a Treasury-related dependent variable over trading days t − j to t; the

subscripts t−j,t−2j on a variable indicate the first-order lags of the respective term; and the other terms

are as defined for Table 2. We report on cases where the dependent variable is the 30-year T-Bond futures

return (TBj), the 10-year T-Note futures return (TNj), or the changes in forward rates for 10-year, 5-year,

and 1-year out forward rates (FR10j , FR05j and FR01j). Panels A and B report on RPR subperiods

and ‘non-RPR’ subperiods, respectively. The subperiod dates are provided with each panel heading.

We report on returns and changes at the 1-month (j=22) and 1-week (j=5) horizons. The full sample

period is 1997:10 - 2013:12. T-statistics, in parentheses, indicate whether the estimated coefficients are

statistically different than zero, calculated with heteroskedastic and autocorrelation consistent standard

errors.

Panel A: RPR Subperiods

∆log(V IX) terms ∆log(TIV ) terms

(t-j,t) (t-2j,t-j) (t-j,t) (t-2j,t-j) R2

Dp. Vr. λ1 λ2 γ1 γ2 (%)

Panel A.1: 2001:10 - 2004:04 (First RPR Period)

1.TB22 7.65 (6.05) 0.15 (0.05) -9.88 (-3.66) -3.28 (-1.51) 32.6

2.TN22 6.19 (7.38) 0.78 (0.45) -5.91 (-3.63) -1.68 (-1.34) 38.6

3.FR1022 -0.46 (-4.04) 0.11 (0.45) 0.90 (3.49) 0.28 (1.37) 28.6

4.FR0522 -0.99 (-6.61) -0.07 (-0.20) 1.05 (3.37) 0.47 (1.88) 33.1

5.FR0122 -1.23 (-6.56) -0.20 (-0.82) 0.75 (3.56) -0.06 (-0.34) 43.1

6.TB5 5.44 (6.37) 2.43 (3.11) -5.21 (-4.98) -2.59 (-3.67) 24.9

7.TN5 4.07 (8.12) 1.84 (3.48) -3.46 (-5.24) -1.54 (-3.57) 28.5

8.FR105 -0.36 (-4.04) -0.18 (-2.42) 0.43 (4.08) 0.20 (2.78) 16.9

9.FR055 -0.65 (-7.03) -0.32 (-3.70) 0.57 (4.78) 0.24 (3.28) 25.1

10.FR015 -0.78 (-7.74) -0.28 (-2.85) 0.59 (5.04) 0.29 (3.26) 26.9

38

Table 3: (continued)

Panel A: RPR Subperiods (continued)

∆log(V IX) terms ∆log(TIV ) terms

(t-j,t) (t-2j,t-j) (t-j,t) (t-2j,t-j) R2

Dp. Vr. λ1 λ2 γ1 γ2 (%)

Panel A.2: 2009:01 - 2013:12 (Second RPR Period)

1.TB22 9.75 (9.29) 3.39 (4.77) -8.35 (-8.29) -2.25 (-2.14) 50.8

2.TN22 4.83 (7.89) 1.43 (2.95) -4.84 (-7.27) -1.25 (-1.81) 44.3

3.FR1022 -1.09 (-9.02) -0.42 (-3.91) 0.80 (7.80) 0.19 (1.62) 47.1

4.FR0522 -1.11 (-7.47) -0.38 (-3.81) 1.19 (7.28) 0.40 (2.25) 46.5

5.FR0122 -0.25 (-4.17) -0.05 (-0.93) 0.24 (4.33) 0.01 (0.05) 16.1

6.TB5 6.18 (12.12) 0.58 (1.22) -4.33 (-7.76) -1.19 (-2.87) 33.3

7.TN5 3.10 (11.43) 0.24 (0.94) -2.59 (-8.16) -0.68 (-2.76) 30.2

8.FR105 -0.69 (-10.89) -0.07 (-1.17) 0.41 (6.78) 0.12 (2.29) 28.0

9.FR055 -0.69 (-10.78) -0.05 (-0.73) 0.60 (7.70) 0.16 (2.73) 30.6

10.FR015 -0.18 (-6.43) -0.03 (-1.17) 0.13 (5.37) 0.05 (2.03) 9.4

Panel A.3: 2009:01 - 2011:06 (1st Half of Second RPR Period)

1.TB22 9.85 (9.65) 2.88 (2.55) -8.23 (-4.49) -1.51 (-1.05) 42.1

2.TN22 6.12 (8.21) 1.76 (2.37) -5.74 (-5.08) -1.58 (-1.46) 44.2

3.FR1022 -0.87 (-8.51) -0.21 (-1.57) 0.67 (3.59) -0.07 (-0.49) 33.1

4.FR0522 -1.22 (-6.69) -0.41 (-2.51) 1.25 (4.37) 0.39 (1.67) 42.0

5.FR0122 -0.48 (-6.23) -0.13 (-1.63) 0.41 (3.96) 0.02 (0.19) 25.5

6.TB5 6.26 (9.19) 0.92 (1.41) -4.46 (-4.10) -1.26 (-1.75) 27.2

7.TN5 3.70 (9.22) 0.67 (1.79) -3.15 (-5.16) -0.95 (-2.05) 27.8

8.FR105 -0.57 (-7.40) -0.03 (-0.34) 0.38 (3.17) 0.09 (1.14) 18.2

9.FR055 -0.71 (-7.76) -0.09 (-1.02) 0.64 (4.34) 0.19 (1.72) 24.9

10.FR015 -0.35 (-7.69) -0.08 (-1.97) 0.25 (4.82) 0.07 (1.70) 16.4

Panel A.4: 2011:07 - 2013:12 (2nd Half of Second RPR Period)

1.TB22 9.76 (5.72) 3.73 (4.52) -8.69 (-7.29) -2.93 (-2.06) 60.4

2.TN22 3.94 (4.06) 1.13 (2.34) -4.30 (-6.29) -0.99 (-1.22) 50.7

3.FR1022 -1.27 (-7.95) -0.58 (-5.42) 0.92 (7.38) 0.40 (2.80) 61.5

4.FR0522 -1.05 (-4.44) -0.36 (-3.17) 1.17 (6.08) 0.42 (1.66) 52.9

5.FR0122 -0.08 (-1.22) 0.02 (0.42) 0.12 (3.38) -0.03 (-0.77) 16.5

6.TB5 6.08 (7.92) 0.29 (0.42) -4.25 (-7.39) -1.18 (-2.29) 39.4

7.TN5 2.59 (6.63) -0.08 (-0.22) -2.24(-6.90) -0.45 (-1.70) 36.0

8.FR105 -0.79 (-8.77) -0.10 (-1.25) 0.43 (6.98) 0.15 (2.29) 37.6

9.FR055 -0.66 (-7.17) -0.01 (-0.08) 0.57 (6.78) 0.14 (2.13) 37.0

10.FR015 -0.05 (-1.62) 0.01 (0.49) 0.06 (3.76) 0.01 (0.46) 6.1

39

Table 3: (continued)

Panel B: Non-RPR Subperiods

∆log(V IX) terms ∆log(TIV ) terms

(t-j,t) (t-2j,t-j) (t-j,t) (t-2j,t-j) R2

Dp. Vr. λ1 λ2 γ1 γ2 (%)

Panel B.1: 1997:10 to 2001:09 (First Non-RPR Period)

1.TB22 2.09 (2.33) -0.53 (-0.41) 0.39 (0.25) 1.49 (1.01) 4.0

2.TN22 1.80 (2.76) 0.06 (0.07) 0.87 (0.70) 1.02 (0.85) 6.7

3.FR1022 -0.12 (-1.08) 0.10 (0.76) 0.20 (1.28) -0.10 (-0.67) 3.0

4.FR0522 -0.28 (-2.41) -0.02 (-0.09) 0.04 (0.21) -0.09 (-0.48) 3.5

5.FR0122 -0.30 (-2.42) 0.01 (0.07) -0.38 (-1.59) -0.22 (-1.00) 10.4

6.TB5 1.52 (2.75) 0.49 (0.97) -2.00 (-2.57) 0.03 (0.04) 3.3

7.TN5 1.45 (3.66) 0.34 (0.92) -1.06 (-1.94) 0.36 (0.71) 4.6

8.FR105 -0.02 (-0.28) -0.03 (-0.38) 0.29 (3.37) 0.06 (0.72) 4.1

9.FR055 -0.17 (-2.56) -0.02 (-0.34) 0.27 (2.57) 0.03 (0.30) 3.4

10.FR015 -0.36 (-4.00) -0.05 (-0.64) 0.06 (0.82) -0.11 (-1.54) 8.3

Panel B.2: 1997:10 to 2001:02 (First Non-RPR-Growth Period)

1.TB22 1.73 (1.69) -0.01 (-0.00) 0.73 (0.47) 1.56 (1.01) 3.3

2.TN22 1.18 (1.60) 0.22 (0.21) 1.14 (0.92) 1.09 (0.88) 4.7

3.FR1022 -0.16 (-1.35) 0.02 (0.12) 0.20 (1.19) -0.10 (-0.63) 2.7

4.FR0522 -0.22 (-1.67) -0.06 (-0.34) 0.01 (0.04) -0.10 (-0.46) 2.3

5.FR0122 -0.14 (-1.09) 0.05 (0.27) -0.45 (-1.85) -0.26 (-1.17) 8.7

6.TB5 1.44 (2.43) 0.38 (0.72) -1.82 (-2.28) -0.18 (-0.24) 2.9

7.TN5 0.94 (2.34) -0.07 (-0.18) -0.91 (-1.63) 0.36 (0.69) 2.5

8.FR105 -0.09 (-1.54) -0.07 (-1.39) 0.29 (3.23) 0.10 (1.29) 4.6

9.FR055 -0.13 (-1.75) 0.02 (0.24) 0.25 (2.31) 0.04 (0.42) 2.9

10.FR015 -0.22 (-3.39) 0.05 (0.72) 0.03 (0.37) -0.15 (-1.94) 4.5

40

Table 3: (continued)

Panel B: Non-RPR Subperiods (continued)

∆log(V IX) terms ∆log(TIV ) terms

(t-j,t) (t-2j,t-j) (t-j,t) (t-2j,t-j) R2

Dp. Vr. λ1 λ2 γ1 γ2 (%)

Panel B.3: 2004:05 to 2008:12 (Second Non-RPR Period)

1.TB22 -0.74 (-0.40) -0.28 (-0.18) 1.47 (0.83) -0.19 (-0.15) 0.5

2.TN22 -0.43 (-0.35) 0.22 (0.20) 1.92 (1.64) 0.65 (0.65) 1.8

3.FR1022 0.32 (1.62) 0.26 (1.83) 0.11 (0.65) 0.24 (1.86) 11.1

4.FR0522 0.29 (1.25) 0.18 (0.97) -0.06 (-0.32) 0.06 (0.38) 4.1

5.FR0122 -0.40 (-3.82) -0.20 (-1.32) -0.60 (-3.17) -0.41 (-2.07) 26.0

6.TB5 1.71 (2.90) -1.25 (-1.92) -0.41 (-0.75) -0.43 (-0.98) 5.0

7.TN5 1.34 (3.44) -0.73 (-1.64) -0.07 (-0.19) -0.27 (-0.92) 5.7

8.FR105 -0.03 (-0.39) 0.19 (2.36) 0.10 (1.72) 0.09 (1.76) 3.6

9.FR055 -0.11 (-1.46) 0.15 (1.67) 0.11 (1.68) 0.07 (1.49) 3.3

10.FR015 -0.40 (-5.85) 0.01 (0.17) -0.07 (-1.12) -0.02 (-0.38) 11.1

Panel B.4: 2004:05 to 2007:11 (Second Non-RPR-Growth Period)

1.TB22 1.36 (1.34) -0.43 (-0.41) 0.11 (0.07) -0.46 (-0.40) 2.2

2.TN22 1.30 (1.74) 0.10 (0.13) 0.70 (0.69) -0.05 (-0.06) 4.5

3.FR1022 -0.02 (-0.22) 0.08 (0.93) 0.15 (1.24) 0.12 (1.31) 2.1

4.FR0522 -0.11 (-1.00) 0.03 (0.27) 0.02 (0.13) 0.05 (0.37) 1.2

5.FR0122 -0.34 (-2.19) -0.04 (-0.27) -0.34 (-1.81) -0.16 (-0.99) 12.4

6.TB5 1.41 (2.95) -0.16 (-0.40) -0.09 (-0.16) 0.16 (0.39) 2.9

7.TN5 1.12 (3.68) -0.03 (-0.12) 0.17 (0.50) 0.11 (0.41) 4.5

8.FR105 -0.09 (-1.61) 0.03 (0.68) 0.06 (1.24) 0.02 (0.50) 1.5

9.FR055 -0.11 (-2.07) 0.02 (0.50) 0.03 (0.53) -0.01 (-0.23) 1.7

10.FR015 -0.29 (-4.63) -0.02 (-0.39) -0.11 (-1.73) -0.06 (-1.20) 8.8

41

Table 4: The Term-Structure’s Slope, Asset-class Risk Changes, and the Economic State

This table reports how the Treasury term-structure’s slope moves contemporaneously with changes in

the risk of the equity market and Treasury bond market. We report on variations of the following model:

∆TSSt−j,t = α0 + (λ1 + λ2D0104t + λ3D

0913t )∆log(V IXt−j,t)+

(γ1 + γ2D0104t + γ3D

0913t )∆log(TIVt−j,t) + ϵt−j,t

where ∆TSS indicates the change in the Treasury term-structure’s slope (TSS) over the period from trading

days t − j to t; and the other terms are as defined in Table 2. We report on the following two measures of

the change in the term-structure’s slope: (1) the change in the term-structure’s second principal component

(∆PC2j), where the principal components are estimated from the 10 zero-coupon bond yield with maturities

from 1-year to 10-years using the GSW (2007) data, and (2) the change in the term yield spread(∆TY Sj),

where the term yield spread is defined as the difference between the 10-year and 6-month Treasury Constant

Maturity Yield from the Federal Reserve. We report on changes at the 1-month (j=22) and 1-week (j=5)

horizons. The sample period is 1997:10 - 2013:12. T-statistics, in parentheses, indicate whether the estimated

coefficients are statistically different than zero, calculated with heteroskedastic and autocorrelation consistent

standard errors.

∆log(V IX) terms ∆log(TIV ) terms

λ1 λ2 λ3 γ1 γ2 γ3 R2

Dp. Vr. 0104 0913 0104 0913 (%)

1.∆PC222 -0.197 (-2.30) 0.427 (7.02) 12.1

2.∆PC222 0.120 (1.20) -0.516 (-3.51) -0.742 (-5.49) 0.181 (2.47) 0.271 (1.44) 0.453 (4.31) 22.8

3.∆TY S22 -0.316 (-3.11) 0.580 (7.15) 12.0

4.∆TY S22 0.068 (0.57) -0.905 (-4.52) -0.820 (-5.24) 0.381 (3.00) 0.259 (1.04) 0.305 (1.98) 19.9

5.∆PC25 -0.177 (-6.86) 0.216 (8.64) 9.7

6.∆PC25 0.005 (0.13) -0.233 (-3.61) -0.434 (-9.18) 0.114 (3.77) 0.107 (1.58) 0.209 (3.98) 16.3

7.∆TY S5 -0.222 (-5.98) 0.278 (8.09) 7.6

8.∆TY S5 0.019 (0.37) -0.442 (-4.83) -0.532 (-8.10) 0.189 (3.44) 0.105 (1.13) 0.168 (2.34) 12.5

42

Table 5: Stock Returns, Inflation Compensation, and the Stock-Bond Return Correlation

This table reports on the following regression, estimated separately for stock-futures and 10-year T-Note

futures returns:

FtRtt−5,t = α0 + λ1∆log(V IXt−5,t) + γ1∆log(TIVt−5,t) + ψ1∆ICt−5,t + ϵt−5,t

where FtRtt−5,t is the percentage change in the futures contract price over trading days t−5 to t, estimated

for both the 10-year T-Note (TN5) and the S&P 500 (SP55) as the dependent variable, ∆IC is the change

in ‘inflation compensation’ (or inflation news) from the close of trading days t − 5 to t, based on the

yield difference between 10-year nominal Treasury Bonds and TIPS per GSW (2010); the α, λ, γ, and ψ

are coefficients to be estimated, and the other terms are as defined for Tables 2 and 3. We estimate three

variations of the model, as denoted below. Panels A and B report on our RPR periods and the expansionary

portion of the non-RPR periods, respectively, with sample dates provided with each panel heading. Column

8 reports the correlation between either: (a) the simple stock and bond futures returns (row 1), or (b) the

residuals from the respective regressions on the stock and bond futures returns (rows 2&3, 4&5, and 6&7).

T-statistics, in parentheses, indicate whether the estimated coefficients are statistically different than zero,

calculated with heteroskedastic and autocorrelation consistent standard errors.

Panel A: RPR Periods

1. Dep. 2. 3. λ1 4. γ1 5. ψ1 6. R2 7. Corr. 8. Corr.

Var. Description ∆VIX ∆TIV ∆IC (%) Betw. Value

Panel A.1: 2001:10 - 2004:04 (First RPR Period)

1. n/a Simple Corr. n/a n/a n/a n/a Returns -0.434

2.TN5 Imp. Vol. 3.77 (7.30) -2.89 (-4.55) n/a 23.0 Residuals

3.SP55 only -20.65 (-13.38) 1.18 (1.49) n/a 54.5 Rows 2&3 -0.259

4.TN5 Infl.Comp. n/a n/a -8.93 (-14.51) 52.1 Residuals

5.SP55 only n/a n/a 10.05 (4.99) 9.2 Rows 4&5 -0.325

6.TN5 Imp. Vol.& 1.83 (4.22) -1.63 (-3.80) -7.81 (-13.00) 57.5 Residuals

7.SP55 Infl.Comp. -19.91 (-12.85) 0.71 (0.93) 2.96 (2.12) 55.2 Rows 6&7 -0.240

Panel A.2: 2009:01-2013:12 (Second RPR Period)

1. n/a Simple Corr. n/a n/a n/a n/a Returns -0.386

2.TN5 Imp. Vol. 3.06 (12.15) -2.36 (-7.76) n/a 29.1 Residuals

3.SP55 only -15.04 (-21.31) 0.72 (1.12) n/a 55.0 Rows 2&3 -0.153

4.TN5 Infl.Comp. n/a n/a -4.07 (-8.39) 23.2 Residuals

5.SP55 only n/a n/a 13.44 (7.51) 25.6 Rows 4&5 -0.187

6.TN5 Imp. Vol.& 2.11 (7.22) -2.11 (-6.82) -2.89 (-6.45) 38.8 Residuals

7.SP55 Infl.Comp. -12.91 (-14.63) 0.16 (0.23) 6.53 (4.18) 60.0 Rows 6&7 -0.035

43

Table 5: (continued)

Panel B: Expansionary Portions of Non-RPR Periods

1. Dep. 2. 3. λ1 4. γ1 5. ψ1 6. R2 7. Corr. 8. Corr.

Var. Description ∆VIX ∆TIV ∆IC (%) Betw. Value

Panel B.1: 1999:01 - 2001:02 (First Non-RPR-Growth Period)

1. n/a Simple Corr. n/a n/a n/a 0 Returns 0.153

2.TN5 Imp. Vol. 0.02 (0.05) -1.62 (-2.79) n/a 3.6 Residuals

3.SP55 only -19.23 (-20.49) -1.34 (-1.14) n/a 56.6 Rows 2&3 0.153

4.TN5 Infl.Comp. n/a n/a -6.40 (-27.89) 78.8 Residuals

5.SP55 only n/a n/a -5.64 (-3.26) 5.0 Rows 4&5 -0.100

6.TN5 Imp. Vol.& 0.57 (2.84) 0.21 (0.77) -6.54 (-28.56) 79.5 Residuals

7.SP55 Infl.Comp. -19.01 (-19.79) -0.64 (-0.57) -2.51 (-1.94) 57.5 Rows 6&7 0.053

Panel B.2: 2004:05 - 2007:11 (Second Non-RPR-Growth Period)

1. n/a Simple Corr. n/a n/a n/a 0 Returns -0.219

2.TN5 Imp. Vol. 1.12 (3.98) 0.15 (0.46) n/a 4.4 Residuals

3.SP55 only -10.73 (-24.07) -0.39 (-1.11) n/a 67.6 Rows 2&3 -0.085

4.TN5 Infl.Comp. n/a n/a -5.81 (-10.54) 22.1 Residuals

5.SP55 only n/a n/a 1.88 (1.13) 0.4 Rows 4&5 -0.215

6.TN5 Imp. Vol.& 1.05 (4.11) 0.16 (0.62) -5.74 (-10.43) 26.0 Residuals

7.SP55 Infl.Comp. -10.71 (-24.03) -0.40 (-1.11) 1.24 (1.45) 67.8 Rows 6&7 -0.057

44

Table 6: Stock Returns, Inflation Compensation, and Asset-class Risk Changes

This table reports how S&P 500 futures returns move contemporaneously with inflation compensation,

changes in equity-risk perceptions, and changes in T-bond risk perceptions. We report on four variations

of the following model for both the weekly and monthly change horizons. Each estimation is over the full

sample with available data (1999:01 - 2013:12):

SP5t−j,t = α0 + (λ1 + λ2D0101t + λ3D

0104t + λ4D

0708t + λ5D

0913t )∆log(V IXt−j,t)+

(γ1 + γ2D0101t + γ3D

0104t + γ4D

0708t + γ5D

0913t )∆log(TIVt−j,t)+

(θ1 + θ2D0101t + θ3D

0104t + θ4D

0708t + θ5D

0913t )∆ICt−j,t + ϵt−j,t

where SP5t−j,t indicates the percentage change in the S&P 500 futures contract’s price or the ‘futures

return’ over the close of trading days t − j to t; ∆ICt−j,t is the change in the inflation-compensation

(IC) value from t − j to t as in Table 5; the Dit variables are four dummy variables that equal one over

the following periods and zero otherwise, D0101 over 2001:03 - 2001:09 (a non-RPR recessionary period),

D0104 over 2001:10 - 2004:04 (our first RPR period), D0708 over 2007:12 - 2008:12 (a non-RPR recessionary

period), and D0913 over 2009:01 - 2013:12 (our second RPR period), the α, λ’s, γ’s, and θ’s are coefficients

to be estimated, and the other terms are as defined for Table 2. We report on returns and changes at

the 1-month (j=22) and 1-week (j=5) horizons. The row-1 model includes only the ∆IC term with no

dummy-terms (θ1 only). The row-2 model includes only the ∆IC term, but includes the IC dummy-

variable terms (θ1 to θ5). The row-3 model includes all three explanatory variables, but no dummy terms

(λ1, γ1, and θ1 only). The row-4 model reports on the full equation above. The λ and γ coefficients

are not reported below for brevity, but are available upon request. T-statistics, in parentheses, indicate

whether the estimated coefficients are statistically different than zero, calculated with heteroskedastic and

autocorrelation consistent standard errors.

∆IC coefficients

θ1 θ2 θ3 θ4 θ5 V IX Di R2

Dp. Vr. 0101 0104 0708 0913 &TIV terms (%)

1.SP522 7.43 (3.43) No No 8.3

2.SP522 -3.46 (-2.00) 21.74 (6.97) 8.20 (1.98) 17.07 (3.07) 16.08 (4.21) No Yes 16.7

3.SP522 3.24 (2.12) Yes No 56.7

4.SP522 -2.17 (-1.38) 12.32 (2.19) -1.54 (-0.63) 9.17 (3.89) 9.15 (2.76) Yes Yes 62.3

5.SP55 7.87 (7.46) No No 7.9

6.SP55 -3.39 (-2.49) 6.21 (1.32) 13.40 (5.52) 14.92 (4.98) 16.97 (7.37) No Yes 14.1

7.SP55 3.59 (4.65) Yes No 56.6

8.SP55 -1.93 (-1.93) 1.94 (0.72) 4.81 (2.79) 7.60 (5.21) 8.59 (4.53) Yes Yes 61.1

45

Table 7: Differences in the VRP and the Relative TYS across Key Subperiods

This table reports how the stock market’s average variance risk premium (VRP) and the bond market’s

average relative Term Yield Spread (TYS) varies across key subperiods of interest. We report on a VRP

that equals the difference between the option-implied VIX at the end of day t and the Realized Volatility

from 5-minute returns of the SPY ETF over trading days t− 21 to t (or a rolling 22 trading-day period).

We report on a relative TYS that equals the difference between the Treasury Term Yield Spread (TYS)

and the Treasury short rate, where the TYS is the difference between the Treasury Constant Maturity

10-year and 6-month yields, and the short rate is the Treasury 6-month Constant Maturity yield. Panel

A contrasts our RPR periods with the full non-RPR periods, and Panel B contrasts our RPR periods

with only the non-RPR months in economic expansions (or non-RPR-growth periods). Specifically, Panel

A reports on the differences in the average VRP and relative TYS for the following subperiods: 1997:10 -

2001:09 & 2004:05 - 2008:12 (together) vs. both 2001:10 - 2004:04 and 2009:01 - 2013:12 separately. Panel

B reports on differences in the average VRP and the relative TYS for the following subperiods: 1997:10 -

2001:02 & 2004:05 - 2007:10 (together) vs. both 2001:10 - 2004:04 and 2009:01 - 2013:12 separately. The

columns labeled ‘Difference’ report on the difference in the averages across the denoted subperiods, with

a T-statistics in parenthesis that indicates whether the difference is statistically significant, calculated

with heteroskedastic and autocorrelation consistent standard errors.

Panel A: Average V RP and Relative TYS: Non-RPR Periods vs. RPR Periods

1. Variable 2. 1997:10-2001:09 3. 2001:10- 4. Difference 5. 2009:01- 6. Difference

& 2004:05-2008:12 2004:04 Col.(3)-(2) 2013:12 Col.(5)-(2)

1. V RP 1.79 4.03 2.24 (3.11) 4.54 2.75 (5.30)

2. ‘TY S-T6m’ -3.51 1.51 5.02 (9.22) 2.36 5.87 (10.65)

Panel B: Average V RP and Relative TYS: Non-RPR-Growth Periods vs. RPR Periods

1. Variable 2. 1997:10-2001:02 3. 2001:10- 4. Difference 5. 2009:01- 6. Difference

& 2004:05-2007:11 2004:05 Col.(3)-(2) 2013:12 Col.(5)-(2)

1. V RP 2.04 4.02 1.98 (2.78) 4.53 2.49 (4.86)

2. ‘TY S-T6m’ -4.17 1.52 5.69 (11.27) 2.37 6.54 (12.62)

46

Figure 1: The Term Yield Spread, Treasury 6-month Yield, and Equity Variance Risk Premium

Panel A below displays the time series of: (1) the Treasury term yield spread (TYS), defined as the

difference between the yield of the 10-year and 6-month Treasury Constant Maturity series; and (2) the

6-month Treasury Constant Maturity yield. The TYS is the thinner darker line, and the 6-month yield

is the thicker lighter line. Panel B below displays the time series of the equity variance risk premium

(VRP), defined as the difference between VIX at the end of day t and the annualized realized volatility

from 5-minute SPY returns over trading days t − 21 to t, in percentage units. The continuous variable is

the 6-month rolling average of the VRP, where the axis date is the midpoint. The step-wise line depicts the

average VRP for three key subperiods: (a) 1997:10-2001:09 and 2004:05-2008:12 together (our non-RPR

periods), (b) 2001:10-2004:04 (our first RPR period), and (c) 2009:01-2013:12 (our second RPR period).

-1

0

1

2

3

4

5

6

7

Oct-

97

Oct-

98

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99

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00

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Panel A: Term Yield Spread and 6-month Treasury Yield

-4

-2

0

2

4

6

8

Oct

-97

Oct

-98

Oct

-99

Oct

-00

Oct

-01

Oct

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Oct

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Oct

-08

Oct

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Oct

-10

Oct

-11

Oct

-12

Oct

-13

Panel B: Equity Variance Risk Premium

47

Figure 2: Time-Series of the VIX and TIV Implied-Volatility Series

This figure displays the time-series of the VIX and TIV implied volatilities over our sample period, where

VIX is a standardized implied volatility from S&P 500 options and TIV is a standardized implied volatility

from 10-year T-Note futures options, both over a one-month horizon. Panel A reports their levels in

‘annualized percentage standard deviation’ units that reflect the volatility over the next month. In Panel

A, VIX is the upper series and TIV is the lower series. Panels B and C display the weekly log changes

of VIX and TIV, respectively, for a week ending on Wednesday. The sample period is October 1997 to

December 2013.

0

10

20

30

40

50

60

70

80

Oct

-97

Oct

-98

Oct

-99

Oct

-00

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-03

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Oct

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Oct

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Oct

-07

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Oct

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Oct

-10

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-11

Oct

-12

Oct

-13

Panel A: Raw VIX and TIV Values

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

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-97

Jul-

98

Ap

r-9

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r-0

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r-0

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r-1

1

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-12

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13

Panel B: Weekly Changes in log(VIX)

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

Oct

-97

Jul-

98

Ap

r-9

9

Jan

-00

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01

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r-0

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r-1

1

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-12

Oct

-12

Jul-

13

Panel C: Weekly Changes in log(TIV)

48

Figure 3: Time-series of Treasury Forward Rates

Panels A, B, and C below display the time-series of Treasury forward rates at 10-years, 5-years, and 1-year

out, respectively. The forward rates are instantaneous forward rates from the Gurkaynak, Sack, and Wright

(2007) data. The sample period is 1997:10 - 2013:12.

0

1

2

3

4

5

6

7

8

Oct

-97

Jul-

98

Ap

r-9

9

Jan

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01

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r-0

2

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r-1

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Panel A: 10-year Treasury Forward Rate

0

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r-9

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r-1

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Panel B: 5-year Treasury Forward Rate

0

1

2

3

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8

Oct

-97

Jul-

98

Ap

r-9

9

Jan

-00

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-03

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r-0

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r-0

8

Jan

-09

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-09

Jul-

10

Ap

r-1

1

Jan

-12

Oct

-12

Jul-

13

Panel C: 1-year Treasury Forward Rate

49

Figure 4: Rolling R2’s from Regressing Treasury Futures Returns against ∆V IX and ∆TIV

Panel A below displays the time-series of R2 values at time t for a regression of the weekly 30-year T-

Bond futures return (over the close of trading days t − 5 to t) against ∆V IX and ∆TIV per equation

(1) (without the dummy variables), with approximately one-year rolling estimation periods over trading

days t to t+ 250. Panel B reports on the same rolling regressions, except that the 10-year T-Note futures

returns is the dependent variable. The sample period is 1997:10 - 2013:12.

0

0.1

0.2

0.3

0.4

0.5

0.6

Oct

-97

Jul-

98

Ap

r-9

9

Jan

-00

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-00

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01

Ap

r-0

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8

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10

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r-1

1

Jan

-12

Oct

-12

Panel A: Rolling R2 for Weekly T-Bond Futures Returns

0

0.1

0.2

0.3

0.4

0.5

0.6

Oct

-97

Jul-

98

Ap

r-9

9

Jan

-00

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01

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r-0

2

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r-0

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07

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r-0

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10

Ap

r-1

1

Jan

-12

Oct

-12

Panel B: Rolling R2 for Weekly 10-yr T-Note Futures Returns

50

Appendix A:

Selection of our Recessionary/Post-Recessionary (RPR) Periods

In this appendix, we provide our rationale and procedures for selecting the RPR periods that are

featured throughout our paper, 2001:10 - 2004:04 and 2009:01 - 2013:12. In Section A.1 below, we discuss

our primary risk-to-return and risk-to-yield-change analysis using the Bai-Perron statistical methods. In

addition, in our paper’s introduction, we list six other items that factored into the selection of our two

RPR periods. In Sections A.2 through A.7 below, we follow with a sequential discussion of these additional

six items that reinforces the notion of important economic differences that distinguish our RPR periods.

Finally, Section A.8 below discusses our RPR period classification from the perspective of related evidence

in Campbell, Sunderam, and Viceira (2013).

A.1. Bai-Perron Analysis of the Risk-to-Return Connection in Longer-term Treasuries.

We initially investigate the 30-year T-bond futures contract and the 10-year forward rate because of our

interest in the more distant portion of the Treasury term structure, with the short-end of the yield curve

presumably more tied to Federal Reserve policy. The underlying bond for the T-bond futures contract

must not mature for at least 15 years.

To begin with, over October 1997 to December 2013, we estimate the following equations on the weekly

T-Bond-futures returns and weekly changes in the 10-year forward rate, when allowing for structural breaks

using the method of Bai and Perron (1998, 2003).

TrFtRtt−5,t = λ0 + λ1∆log(V IXt−5,t) + λ2∆log(TIVt−5,t) + ϵt−5,t (6)

∆FR10t−5,t = λ0 + λ1∆log(V IXt−5,t) + λ2∆log(TIVt−5,t) + ϵt−5,t (7)

where the terms are as defined for Table 2, except that here we use non-overlapping Friday-to-Friday weekly

returns. When allowing for three structural breaks with a minimum subperiod length of 10% of the sample,

the estimation identifies three breaks with the following four subperiods for both the weekly T-Bond-

futures returns and the weekly changes in the 10-year forward rates: 10/3/1997-10/26/2001, 11/02/2001-

4/23/2004, 4/30/2004-1/9/2009, and 1/16/2009-12/27/2013. The 2001:10 - 2004:04 and 2009:01 - 2013:12

subperiods here have strong ‘risk-return’ and ‘risk-FR’ connections. For the 30-year T-Bond-futures

(change in 10-year forward rates), the λ1’s average 5.68 (-0.53) for these two high-connection subperiods

vs. an average λ1 of 1.65 (-0.02) over the remaining 1997-2001 and 2004-2008 subperiods. When allowing

for a maximum of five structural breakpoints, the indicated strong-connection subperiods are similar.

We favor the approach with three structural breaks, because of the links to formal recessions and other

economic-state distinctions (see A.2 through A.7 in this appendix). Thus, we select the periods over

2001:10-2004:04 and 2009:01-2013:12 as our ‘recessionary/post-recessionary’ (RPR) periods that have

relatively strong risk-return connections in longer-term Treasuries. The remaining two subperiods in our

sample, 1997:10 - 2001:09 and 2004:05 - 2008:12, are referred to as non-RPR periods.

We also analyze weekly 10-year T-Note futures returns using the same structural-break methods. For

the weekly 10-year T-Note futures return when allowing for three structural breakpoints, we estimate that

the high risk-return subperiods are 12/15/2000 to 4/23/04 and 12/28/07 to 12/27/13. These subperiods

51

are similar to our RPR periods above, but the beginning dates here are somewhat earlier in December

2000 and December 2007. These December 2000 and December 2007 dates are around the beginning of

the nearby recession (March 2001 and December 2007 are the recession-start months).

Thus, the results for the 10-year T-Note futures returns suggest that we also evaluate the 1997:10 -

2001:02 and 2004:05 - 2007:11 as alternative non-RPR periods that only contain NBER expansion months,

which we refer to as non-RPR-growth periods. Accordingly, in Tables 3, 5, 6, and 7, we evaluate the non-

RPR-growth periods as a comparison to the full non-RPR periods proposed above. If our findings are

similar for each non-RPR period and the corresponding inclusive expansionary non-RPR period, then this

would imply that our results for the full non-RPR periods are not being dominated by high volatility

times associated with the onset of the corresponding regression. Contrasting the expansionary non-

RPR periods with our RPR periods also fits with theoretical implications in David and Veronesi (2013),

regarding economic-state differences in the relation between stock returns and inflation news. Also, see

our supporting discussion in Section A.3, regarding Federal Reserve action around the onset of recessions.

A.2. Economic-State Differences in the Relation between Stock Returns and Inflation

News. This is the focus of Section 4 in our main text, so we refer readers to that section.

A.3. Bai-Perron Analysis of the Variance-Risk Premium and the Bias in VIX for Fore-

casting the Subsequent Realized Volatility. The stock-market’s variance risk premium (VRP) in-

dicates when option values are high relative to the recent realized stock volatility, measured in our case

by the difference between the implied stock-market volatility (VIX) at the close of day t and the realized

volatility of the SPY ETF using 5-minute stock returns over trading days t− 21 to t. Movements in the

VRP are likely due to variations in the premium linked to high uncertainty about the underlying volatility

and, perhaps, a higher aggregate risk aversion in the market (see Bollerslev, Tauchen, and Zhou (2009);

Bollerslev, Gibson, and Zhou (2011); and Bekaert, Hoerova, and Lo Duca (2013)). When we estimate

a Bai-Perron structural break model on the average VRP over October 1997 - December 2013, we find

high-VRP subperiods over 2001:10 - 2004:11 and 2009:01 - 2013:12. These high-VRP subperiods overlap

closely with the RPR periods proposed in A.1 above. We describe this VRP behavior in Table 7 and

Figure 1 in the main text. Similarly, Appendix Table A1 shows that the bias in VIX is reliably higher for

our RPR periods.

A.4. Relation to Economic Recessions and Federal Reserve Action. The onset of our RPR

periods occurs after NBER recessions have been ongoing for some time, with the timing appearing to have

ties to Federal Reserve actions. Consider Federal Reserve actions over the 2008-2009 economic crisis. Over

2008, the Federal Reserve lowered the targeted Fed Funds rate (FFR) seven times from a beginning-of-the

year value of 4.25% down to an end-of-the year value of ‘0 to 0.25%’ with the final change on 12/16/2008.

The targeted FFR remained at essentially zero through our sample end-date of December 2013. This final

reduction in the FFR was just two weeks prior to the onset of our second RPR period in January 2009.

Additionally, the Federal Reserve announced their Quantitative Easing I on November 25, 2008, when

it announced the intention of purchasing $800 billion in bank debt, MBS, and Treasury Notes. Sizable

purchases began in early 2009. Thus, by January 2009, the Federal Reserve had essentially completed its

available easing in the short-end of the yield curve and announced a major initiative in the longer-end of

52

the yield curve. This suggests, by January 2009, that the Federal Reserve had limited additional options

to influence prices with traditional monetary policy tools. Thus, by then, weekly and monthly changes in

market-based risk perceptions might have become relatively more important for understanding Treasury

values, rather than direct Federal Reserve actions or announcements. We also note that January 2009, the

first month of this RPR period, is also in the later stages of a recession. The NBER dated the so-called

Great Recession as occurring over December 2007 to June 2009, with the the official announcement of the

beginning month in December 2008.22

Next, recall that our first RPR period commenced in October 2001. October 2001 followed a major

civil crisis, the 9/11 terrorist attack, and was in the later stages of the recession that occurred over March

to November 2001. This recession’s beginning was retroactively announced in November 2001, within one

month of the beginning of our first RPR period; this recession’s end was retroactively declared on July

17, 2003. Over 2001, the Federal Reserve lowered the targeted FFR 11 times from 6.5% at the beginning-

of-the year to 1.75% at the end-of-the year, with the last decrease on 12/11/2001. After 2001, the Federal

Reserve lowered the targeted FFR only twice more (to 1.25% on 11/6/2002, and to 1.0% on 6/25/2003)

before reversing and raising the targeted FFR to 1.25% on June 30, 2004. Note that this increase in June

2004 was within a couple months of the ending month for our first RPR period (April 2004).

We have argued that our RPR periods were likely to have had greater aggregate risk aversion, especially

relative to the higher growth expansionary periods in our sample. However, there is a sizable proportion

of the early stages of each corresponding recession that is not included in our RPR periods.

We were initially puzzled by the fact that earlier recession months are not in our RPR periods. We

offer the Fed’s strong fast responses to the recession as a potential explanation. To probe this issue, we

analyze the calendar year 2008 and examine whether the relation between VIX changes and bond returns

is different around days on which the Federal Reserve announced a lowering of the targeted FFR. Since

the announcements come late in the day (2:15 PM Eastern time), we analyze two-day returns and two-day

VIX changes to cover the announcement day and subsequent day. Over 2008, for the non-announcement

periods, we find that the typical positive relation between VIX changes and T-Note returns is reliably

evident. However, for the announcement periods, we find that the relation between VIX changes and the

T-Note return is negative and reliably lower.

These findings are largely tied to the episodes over October 8-9 and December 16-17, 2008. On October

8, the targeted FFR was lowered from 2% to 1.5%; and over October 8-9, the VIX increased 10.2%, the

S&P 500 futures return was -9.1%, and the 10-year T-Note futures return was -3.1%. This large negative

T-Note futures return with such a large VIX increase is unusual. For this FFR announcement, the

market appeared to be either disappointed that the FFR reduction was not larger, or interpreted the

FFR reduction as confirming a collapsing economy which spurred a flight to the safest T-Bills.23 Next, on

December 16, 2008, the targeted FFR was lowered from 1% to ‘0 to 0.25%’; and over December 16-17, the

22On September 20, 2010, the NBER announced an end date of June 2009 for the 2008-09 recession.23Kontonikas, MacDonald, and Saggu (2013) argue that over the 2008 financial crisis that the stock market

appeared to interpret some FFR reductions as signals of worsening future economic conditions, with a corresponding

stock decline.

53

VIX decreased by 6.9%, the S&P 500 futures return was +3.6%, and the 10-year T-Note futures return

was +1.7%. This positive T-Note futures return with such a large VIX decrease is also unusual. So, for

this case, the market seemed to be reassured by the FFR announcement and both stock and longer-term

Treasury investors benefitted. In both of these instances, stocks and bonds moved together (with the same

algebraic signs), with the relation between the T-Note-futures returns and VIX changes being opposite

to its more typical ‘weak economy’ relation. By comparison, over all of 2008, the two-day returns of the

S&P 500 futures and 10-year T-Note futures return had opposite signs over 71% of the time.

In 2001, the targeted FFR was lowered 11 times. While there is not a statistically reliably difference

in the relation between the VIX changes and the Treasury-futures return for the FFR announcement

periods over 2001, we note that there was both a VIX decrease and positive returns for both the stock

and Treasury futures for three of the two-day announcement periods.

The above observations are consistent with the premise that the relation between VIX changes and

T-bond values early in these recessions is likely obscured by strong Federal Reserve responses, at least to

some degree. This is one of the reasons that we evaluate the expansionary non-RPR periods separately

(1997:10 - 2001:02 and 2004:05 - 2007:11), as discussed in Section A.1 above.

A.5. Differences in the Term Yield Spread and T-bill Yields. The Treasury term-yield-spread

(TYS, defined as the difference between the Treasury’s 10-year and 6-month Constant Maturity yields)

and the Treasury short-rate (defined as the 6-month Treasury Constant Maturity yield) also display

considerable state-based variation, with a much higher TYS and lower T-bill yields during our RPR

periods. See Section 5.2, Table 7, and Figure 1 for discussion and evidence.

A.6. Relation to Economic Growth and Inflation. We examine the quarterly growth in real U.S.

GDP. Over 1960 through the third quarter 1997 (preceding our sample period), the average annualized

quarterly GDP growth was 3.45%. Over October 1997 to December 2000 (our first expansionary non-RPR

period), the average GDP growth rate was a relatively high 4.09%. For our subsequent RPR period over

October 2001 to March 2004, the average GDP growth rate was 2.85% over the full subperiod and 1.81%

for the first half of the subperiod.24 Next, over April 2004 to September 2007 (our second expansionary

non-RPR period), the average GDP growth was 2.68%. For our subsequent RPR period over January

2009 to December 2013, the average GDP growth rate was 1.80% over the full subperiod and 1.19% for

the first half of the subperiod. Thus, relative to the preceding period back to 1960 and relative to the

preceding economic expansion, both our RPR subperiods had low GDP growth.

We also evaluate inflation over our RPR periods, using the the monthly percentage change in the CPI

index (CPI for All Urban Consumers: All Items). Over 1960 through the third quarter 1997 (preceding our

sample period), the average annualized monthly inflation rate was 4.52%, with an average of 6.07% over

the 1970’s and 80’s. Over October 1997 to February 2001 (our first expansionary non-RPR subperiod),

the average inflation rate was 2.58%. For our subsequent RPR period over October 2001 to March 2004,

the average inflation rate was 1.98%. Next, over April 2004 to November 2007 (our second expansionary

non-RPR period), the average inflation rate was 3.30%. For our subsequent RPR period over January

24Since the GDP numbers are reported quarterly, we select the quarters to best match our subperiods, which

are delineated by calendar months.

54

2009 to December 2013, the average inflation rate was 2.09%. Thus, relative to the preceding period back

to 1960 (and especially relative to the 1970’s and 80’s) and relative to the preceding economic expansion,

both of our RPR subperiods had lower inflation. Overall, the GDP and CPI statistics here support the

premise that our RPR state can be considered as having relatively low economic growth and low inflation.

A.7. Proximity to Stock Market Declines. Both of our RPR periods follow substantial stock

market declines. For our RPR period commencing in October 2001, the stock market had declined by

-35.4% on October 1, 2001 from its peak on March 24, 2000 (based on the CRSP value-weighted stock

index). For our RPR period commencing in January 2009, the stock market had declined by -39.8% on

January 2, 2009 from its peak on October 9, 2007. Evidence in Guiso, Sapienza and Zingales (2013)

suggests that aggregate risk aversion is likely to be higher following such sizable stock market declines.

A.8. Relation to Economic-State Information in Campbell, Sunderam, and Viceira (CSV)

(2013). After completing our analysis in A.1 through A.7 above and the initial draft of our study, we

noted a strong relation between the onset of our RPR periods and movements in a key CSV state variable,

ψ1. In CSV, ψ1 is an important state variable that governs time variation in the volatility of the real

interest rate and its covariation with their stochastic discount factor. CSV note that their ψ1 variable is

identified primarily through the covariance of stock and bond returns and the volatility of bond returns.

We direct readers to Figure 8 in CSV, which depicts the time-series of their ψ1 state variable. First, in

regard to our full October 1997 to December 2013 period, we note that the ψ1 falls precipitously around

1997 until it turns negative in the early 2000’s, and it has remained negative since then (CSV’s graph

stops in late 2009). Recall that the stock-bond return correlation shifted to predominantly negative in the

fall of 1997. Analysis in Campbell, Pflueger, and Viceira (2014) also suggest a regime shift in 1997. These

observations support the notion of a key regime shift around the fall of 1997, which we believe supports

our rationale for starting our analysis then.

We also note that their ψ1 state variable moved to local minimums following the recession of 2001

and in the fall of 2008 (see CSV’s Section 4.3), roughly corresponding to the onset of our RPR periods.

In terms of our RPR classification, we find this observation to be reassuring: CSV’s analysis supports the

notion of economic-state transitions at about the same times as does our empirical-based analysis.

Additionally, CSV’s analysis suggests that longer-term Treasury bonds have become more of a hedge

asset in recent times. Their Figure 10 suggests that the expected excess return of 10-year nominal T-

bonds was negative over much of our two RPR periods, especially around 2009. This is consistent with our

evidence that suggests longer-term Treasuries became more of a favored safe-haven asset over our RPR

periods, especially over our later RPR period from 2009-2013.

While these links to the CSV study are reassuring, we primarily explain our findings in our main text

in relation to BEX (2009), BE (2013), and DV(2013). A key difference between CSV versus BEX and

BE is that time-varying risk aversion is important in BEX and BE, while CSV assume a constant price

of risk. CSV note that they have estimated an extension of their model with time-varying risk aversion,

but their primary paper assumes a constant variance for the stochastic discount factor. Accordingly, the

BEX model seems a better fit for our purposes, especially in view of our evidence that strongly suggests

time-varying risk aversion.

55

Appendix A - Table A1:

VIX and the Future Realized Stock Volatility: Bias Variation Linked to our RPR Periods

This table reports how the option-derived implied stock volatility, VIX, is related to the subsequent

realized stock return volatility. We estimate variations of the following model:

σStt,t+21 = (γ1 + γ2Dum

0104t + γ3Dum

0913t )V IXt−1 + εt,t+21

where, σSTt,t+21 is the annualized standard deviation that is estimated from the volatility of the 5-minute SPY

returns over trading days t to t+21 (see Appendix C); V IXt−1 is the closing V IX from trading day t− 1,

Dum0104t is a dummy variable that equals one if the lagged VIX is in our first RPR period over 2001:10 to

2004:04, Dum0913t is a dummy variable that equals one if the lagged VIX is in our second RPR period over

2009:01 to 2013:12), and the γ’s are coefficients to be estimated. For model variation b. through e., we

report on the model estimated over the denoted subperiod, so the dummy variables are not applicable. The

overall sample period is 1997:10 - 2013:12. T-statistics are in parentheses, calculated with heteroskedastic

and autocorrelation consistent standard errors.

Period Model γ1 γ2 γ3 R2

Full Sample a. 0.946 (23.92) -0.142 (-2.91) -0.168 (-4.15) 66.5%

1997:10-2013:12

Non-RPR I b. 0.958 (31.84) n/a n/a 24.3%

1997:10-2001.09

RPR I c. 0.802 (23.10) n/a n/a 62.7%

2001:10 - 2004:04

Non-RPR II d. 0.954 (14.49) n/a n/a 71.8%

2004:05-2008.12

RPR II e. 0.778 (39.97) n/a n/a 71.5%

2009:01 - 2013:12

56

Appendix B - Table B1:

Implied Volatility and the Future Realized Volatility of Stock and Bond Returns

This table reports how our option-derived implied volatilities, VIX and TIV, are related to the subse-

quent realized stock and T-bond return volatility, respectively. We estimate the following two models for

both the subsequent stock return volatility and the T-bond return volatility.

(a) σzt,t+21 = γ0 + γ1IVt−1 + εt,t+21

(b) log(σzt,t+21) = γ0 + γ1log(IVt−1) + εt,t+21

where, for equation (a), σzt,t+21 is the annualized standard deviation for the returns of asset-class z over

trading-days t to t + 21, calculated as the square-root of the sum of 22 squared daily returns over the

rolling 22-trading-day period; IVt−1 is either the lagged V IX or TIV for the stock-volatility model and

Treasury-volatility model, respectively, where V IX and TIV are the equity and T-note implied volatilities

as explained in Section 2.1, and the γs are coefficients to be estimated. For equation (b), the model is the

same except that we take the log of the realized standard deviation and of the implied volatilities in order

to transform the variables to be closer to normally distributed. Panel A reports on stock-market volatility,

where z indicates stock market returns, using the daily S&P 500 futures returns. Panel B reports on T-bond

volatility, where z indicates 10-year T-Notes, using daily 10-year T-Note futures returns. The sample period

is 1997:10 to 2013:12. T-statistics are in parentheses, calculated with heteroskedastic and autocorrelation

consistent standard errors. The superscript 1 indicates a 1% p-value.

Panel A: Realized Stock Return Volatility over t to t+ 21

as the dependent variable, V IXt−1 as the explanatory variable

Period Model γ1 R2

1997:10-2013:12 a. 0.911 (10.07)1 55.2%

b. 1.050 (21.31)1 60.1%

Panel B: Realized 10-yr T-Note Return Volatility over t to t+ 21

as the dependent variable, TIVt−1 as the explanatory variable

Period Model γ1 R2

1997:10-2013:12 a. 0.872 (16.09)1 52.5%

b. 0.963 (20.31)1 55.5%

57

Appendix C:

Calculation of the Stock Market’s Realized Volatility from High-Frequency Returns

Trading records for the SPY S&P 500 ETF were downloaded from the TAQ dataset on WRDS. We

deleted any trading records with a negative price or trading volume, or where the correction indicator

showed a trade had been corrected or cancelled. We also eliminated any trading record where the sale

condition met any of these criteria: cond =“O”, “Z”, “B”, “T”, “L”, “G”, “W”, “J”, or “K”. These

screens mimic typical filter rules applied in empirical microstructure studies. We also dropped any record

with a timestamp before 9:30 a.m. or after 4:00 p.m.

Using data cleaned in this way, we identify the first trade of the day, and then our algorithm identifies

the first trade after 300 seconds have elapsed, and then the first trade after the next 300-second interval,

and so forth through the end of the trading day. In the early years of the sample, the volume of trading

was sufficiently low on some days such that the interval between trades was larger than 300 seconds, but

this was relatively rare. In later years of the sample when there are multiple trades per second, we use

the first trade after the 300-second interval since trades within the second are arranged in the order of

execution. See Holden and Jacobsen (2014) for details on this timing issue.

We compute five-minute squared returns (r2) from this sequence of 5-minute prices, and with that

sequence, we compute the following estimate of the realized volatility (RV, in standard deviation units):

RVt =√12 ×

√√√√ 21∑i=0

r2t−i (8)

where the summation and i subscript indicates all the five-minute return shocks, calculated in this way,

over trading days t back through t− 21. Thus, the RV denoted on day t captures a rolling 22-trading-day

period to generate a daily estimate of a rolling one-month RV in S&P500 returns. Our RV data is also

computed over 1997:10 - 2013:12.

58

Appendix D:

Robustness of the Risk-Return Connection in Longer-term Treasuries

In this appendix, we probe robustness of our risk-return findings for longer-term Treasuries by report-

ing on different variations of the models that we estimate in Sections 3.2 and 3.4.

D.1. Allowing for Time-variation in Volatility. Time-variation in risk is a fundamental premise

behind our empirical investigation, so it would seem natural to estimate a specification that also allows for

time-varying volatility in our models’ residuals. Accordingly, to probe robustness for our results in Tables

2 through 4, we estimate a system where equation (1) or equation (3) is the conditional mean equation

and the following equation is the conditional variance equation:

vt−j,t = α0 + α1TIVt−j (9)

where vt−j,t is the conditional variance of the residual, ϵt−j,t, either from equation (1) or equation (3);

TIVt−j is the implied volatility from the 10-year T-Note futures options at the close of day t− j; the α’s

are additional coefficients to be estimated, with j=5 for weekly change horizons and j=22 for monthly

change horizons. Results in Appendix B indicate that the TIV provides substantial information about the

subsequent volatility of longer-term Treasury prices, so we use TIV to parsimoniously capture the bond-

market’s volatility environment in this specification.25 We use maximum likelihood estimation that jointly

estimates the conditional mean and conditional variance equations, assuming a conditional normal density.

For the conditional mean equation, we find results that are quite similar to those depicted in Tables 2 and

4. For the conditional variance equation, the estimated α1 coefficient is positive and highly statistically

significant in all cases, which supports the efficacy of using the TIV as a risk measure. With our extensive

evaluation and comparison of subperiods, we elect to present OLS results (with heteroskedastic-consistent

standard errors) in our main tables, due to the simplicity of the OLS model and its intuitive R2 measure.26

D.2. The Risk-Return Connection with Lagged Term-Structure State Variables. Next, to

further probe the relation between T-bond returns and changes in risk perceptions, we extend our prior

models to also control for well-known term-structure state variables and for the lagged dependent variable.

Cochrane and Piazzesi (2005) and others have shown that the term-structure of current yields, or forward

rates, can serve as state variables and provide information about the subsequent Treasury bond returns.

We add the lagged dependent variable to control for and evaluate autoregressive behavior.

25We also evaluated specifications for the conditional variance that include the lagged squared residual, in a

traditional ARCH sense. We find that the lagged residuals do not add additional reliable volatility information

beyond the lagged TIV term.26Tabular results for the specification with time-varying volatility are available from the authors upon request.

59

Accordingly, we next report on variations of the following model:

TrFtRtt−j,t = α0 + (λ1 + λ2DRPRt )∆log(V IXt−j,t) + (λ3 + λ4D

RPRt )∆log(V IXt−2j,t−j)+ (10)

(γ1 + γ2DRPRt )∆log(TIVt−j,t) + (γ3 + γ4D

RPRt )∆log(TIVt−2j,t−j) + κ1TrFtRtt−2j,t−j+

ϕ1PC1t−j + ϕ2PC2t−j + ϕ3PC3t−j + ϵt−j,t

where the subscripts t−2j,t−j on a variable indicate the first-order lags of the respective term; DRPRt

is a dummy variable that equals one over our RPR periods from 2001:10 to 2004:04 and 2009:01 to

2013:12; PC1t−j , PC2t−j , and PC3t−j are the lagged values of the term-structure’s first three principal

components at time t− j; the α, λ’s, γ’s, κ, and ϕ’s are coefficients to be estimated, and the other terms

are as defined for Tables 2 and 3. We report on estimations where the dependent variable is the 30-year

T-Bond-futures returns (TB), the 10-year T-Note-future return (TN), the change in the 10-year FR, and

the change in the 5-year FR. We report on both a one-month change horizon, with j=22 trading days,

and a one-week change horizon, with j= 5 trading days.

Table D1 reports the results from estimating equation (10). The primary coefficients of interest are

the λ2 and γ2 on the dummy variables that allow the concurrent relation between the risk changes and

the dependent variable to be different for our RPR periods. For all four dependent variables and both

time horizons, we find that these dummy variables are sizable and highly statistically significant (p-values

of 1%, or better, in all cases). Thus, the addition of the additional control variables do not change our

fundamental findings, in that VIX increases (TIV increases) are associated with more positive (negative)

Treasury futures returns and larger declines (increases) in the 5- and 10-year FR’s over our RPR periods.

Additionally, we find that the intertemporal relation between the lagged risk changes and the four

dependent variables tends to be stronger over our RPR periods. The estimated relations between the

lagged risk-changes and the four dependent variables have the same algebraic sign as the comparable

concurrent relations and many of the estimated λ4’s and γ4 coefficients are statistically significant, which

indicates that the intertemporal risk-return relations are reliably different for our RPR periods. We also

note that the F-statistic reported in column 11 indicates that the lagged risk-change terms are collectively

important for all eight cases. These results cast doubt on the notion that a ‘return to liquidity providers’

is of first-order importance for understanding the concurrent relations, because a ‘return to liquidity

provider’ explanation implies that the lagged relation will be the opposite to the concurrent relation.

While the lagged principal components as state variables do not change the risk-return connections in

a partial sense, they do tend to provide incremental explanatory information. The F-statistic in column

12 indicates that the three lagged principal components are collectively statistically significant for six

60

of the eight cases. Finally, we find that the lagged dependent variable is unimportant as an additional

explanatory term.

D.3. The Risk-Return Connection in Long-term Treasuries with Simple VIX and TIV

Changes. We also estimate an alternative version of our model in Table 2 that uses the simple VIX-change

(∆V IXt,t−j) and TIV-change (∆V IXt,t−j) as the explanatory variable (rather than the log change). We

find qualitatively similar results, which indicates our results are not unique to the use of a log change for

the implied-volatility variables; see Table D.2 for tabular results.

D.4. Controlling for Inflation Compensation. Finally, in Table 5, we show that: (1) the risk-

to-return connections in longer-term Treasuries, as depicted in Tables 2 and 3, remain reliably evident

when also controlling for the concurrent change in inflation compensation, and (2) inflation compensation

is positively related to stock returns in our RPR periods, but either negatively related or unrelated in our

non-RPR-growth periods. This specification uses the GSW (2010) inflation-compensation data based on

the yield difference between 10-year nominal Treasuries and TIPS. To probe robustness of these results, we

also estimate a system where equation (4) is the conditional mean equation and the following equations are

the conditional variance equation for the T-Note futures-return and S&P 500 futures return, respectively:

vt−5,t = α0 + α1TIVt−5 (11)

vt−5,t = α0 + α1V IXt−5 (12)

where vt−5,t is the conditional variance of ϵt−5,t from equation (4); TIVt−5 is the implied volatility from

the 10-year T-Note futures options at the close of day t−5; V IXt−5 is the implied volatility from the S&P

500 index options at the close of day t−5; and the α’s are additional coefficients to be estimated. Appendix

B shows that the TIV and VIX contain substantial and reliable information about the subsequent T-bond

and stock volatility, respectively. Our estimations indicate that the empirical findings in Table 5 are robust

and quite similar in these specifications that allow for time-varying volatility. The TIV and VIX contain

substantial and reliable volatility information in this setting also. Results are available upon request.

61

Appendix

D-Table

D1:RobustnesswithAlternativeSpecificationsI

Treasury

FuturesReturns,

Forw

ard-R

ate

Changes,andAsset-class

RiskChanges

This

table

extendstheearlierspecification

sbyad

dinglagg

edvalues

oftheconcu

rrentterm

sasadditionalexplanatory

term

san

dbycontrollingfor

theterm

-structure’s

firstthreeprincipal

components

asstatevariab

les.

Wereporton

variationsofthefollow

ing:

TrFtRt t−j,t=α0+

(λ1+λ2D

RPR

t)∆log(VIX

t−j,t)+

(λ3+λ4D

RPR

t)∆log(VIX

t−2j,t−

j)+

(γ1+γ2D

RPR

t)∆log(TIVt−

j,t)+

(γ3+γ4D

RPR

t)∆log(TIVt−

2j,t−

j)+κ1TrFtRt t−2j,t−

j+ϕ1PC1 t

−j+ϕ2PC2 t

−j+ϕ3PC3 t

−j+ϵ t

−j,t

wherethesubscripts

t−2j,t−

jonavariab

leindicate

thefirst-order

lags

oftherespectiveterm

;D

RPR

tis

adummyvariable

thatequals

oneover

ourRPR

periodsfrom

2001

:10-200

4:04

and20

09:01-201

3:12

;PC1t−

j,PC2 t

−j,an

dPC3 t

−jarethelaggedvalues

oftheterm

-structure’s

firstthreeprincipal

compon

ents

attimet−j;

theα,λ’s,γ’s,κ,an

dϕ’s

arecoeffi

cients

tobeestimated

,an

dtheother

term

sare

asdefi

ned

forTab

le2.

Thefullsample

periodis19

97:10-201

3:12

.Panel

Areports

onthecaseswheretheTrFtRtterm

sarefrom

the30-yearT-B

ond(TB)an

d10

-yearT-N

ote(TN)futures

contracts.

Pan

elB

reports

onasimilarmodel

buttheTrFtRtterm

sarereplacedbythechan

gein

the10-yearforw

ard

rate

(∆FR10

t−j,t)an

d5-year

forw

ardrate

(∆FR05

t−j,t).

Wereportonbothaone-mon

th(j=22

)an

daon

e-week(j=5)

chan

gehorizon

.Column11

reportsan

F-statistic

that

teststhe

nullhypothesis

thatλ3,λ4,γ3,an

dγ4are

allzero

onthelagg

edrisk-chan

geterm

s;an

dColumn12

reports

anF-statistic

thatteststhenullhypothesis

that

theϕcoeffi

cients

onthethreeprincipal

components

areallzero,with

1(2)indicatingap-valueof1%

(5%)forthenull.T-statistics,in

parentheses,

indicatewhether

theestimatedcoeffi

cients

arestatisticallydifferentthan

zero,calculatedwithheterosked

asticandautocorrelationconsistentstan

dard

errors.

Pan

elA:ResultsforLon

ger-term

Treasury

FuturesReturns

2.λ1

3.λ2

4.λ3

5.λ4

6.γ1

7.γ2

8.γ3

9.γ4

10.κ1

11.F-stat.

12.F-stat.

13.R

2

1.Dep

.∆VIX

DRPR∆VIX

∆VIX

DRPR∆VIX

∆TIV

DRPR∆TIV

∆TIV

DRPR∆TIV

DpVr

(λ3,λ

4,

(ϕ1,ϕ

2,

Var.

(t-j,t)

(t-j,t)

(t-2j,t-j)

(t-2j,t-j)

(t-j,t)

(t-j,t)

(t-2j,t-j)

(t-2j,t-j)

(t-2j,t-j)

γ3,γ

4=

0)ϕ3=

0)

1.TB

22

0.50

8.38

0.17

2.81

0.57

-9.21

-0.56

-2.43

-0.06

3.471

4.85

127.1%

(0.51)

(6.11)

(0.17)

(2.10)

(0.52)

(-5.81

)(-0.47

)(-1.62

)(-0.99)

2.TN

22

0.62

4.40

0.41

1.04

1.11

-6.25

0.14

-1.77

-0.03

2.552

5.28

124.0%

(0.82)

(4.86)

(0.62)

(1.18)

(1.32)

(-5.65

)(0.16)

(-1.63

)(-0.53)

62

Table

D1:(continued)

Pan

elA

(con

tinued

):ResultsforLon

ger-term

Treasury

FuturesReturns

2.λ1

3.λ2

4.λ3

5.λ4

6.γ1

7.γ2

8.γ3

9.γ4

10.κ1

11.

F-stat.

12.F-stat.

13.R

2

1.Dep

.∆VIX

DRPR∆VIX

∆VIX

DRPR∆VIX

∆TIV

DRPR∆TIV

∆TIV

DRPR∆TIV

DpVr

(λ3,λ

4,

(ϕ1,ϕ

2,

Var.

(t-j,t)

(t-j,t)

(t-2j,t-j)

(t-2j,t-j)

(t-j,t)

(t-j,t)

(t-2j,t-j)

(t-2j,t-j)

(t-2j,t-j)

γ3,γ

4=

0)ϕ3=

0)

3.TB

51.56

4.45

-0.34

1.68

-1.00

-3.59

-0.45

-1.39

-0.04

6.521

4.39

118.8%

(3.76)

(7.40)

(-0.78)

(2.82)

(-2.18

)(-5.13

)(-1.11

)(-2.56

)(-1.15)

4.TN

51.33

2.03

-0.13

0.99

-0.41

-2.47

-0.13

-1.00

-0.05

6.29

14.91

117.3%

(4.73)

(5.51)

(-0.44)

(2.57)

(-1.35

)(-5.67

)(-0.49

)(-2.86

)(-1.53)

Pan

elB:ResultsforForward-R

ateChanges

2.λ1

3.λ2

4.λ3

5.λ4

6.γ1

7.γ2

8.γ3

9.γ4

10.κ1

11.F-stat.

12.F-stat.

13.R

2

1.Dep

.∆VIX

DRPR∆VIX

∆VIX

DRPR∆VIX

∆TIV

DRPR∆TIV

∆TIV

DRPR∆TIV

DpVr

(λ3,λ

4,

(ϕ1,ϕ

2,

Var.

(t-j,t)

(t-j,t)

(t-2j,t-j)

(t-2j,t-j)

(t-j,t)

(t-j,t)

(t-2j,t-j)

(t-2j,t-j)

(t-2j,t-j)

γ3,γ

4=

0)ϕ3=

0)

1.FR10 2

20.16

-1.05

0.15

-0.50

0.19

0.63

0.24

0.05

-0.11

4.20

12.58

26.3%

(1.26)

(-6.03)

(1.26)

(-3.17)

(1.77)

(4.04)

(1.97)

(0.34)

(-1.77)

2.FR05

22

0.06

-1.10

0.05

-0.42

0.04

1.10

0.15

0.34

-0.07

4.311

3.24

226.1%

(0.37)

(-5.51)

(0.35)

(-2.34)

(0.26)

(5.13)

(0.89)

(1.61)

(-1.20)

3.FR10

5-0.02

-0.59

0.08

-0.21

0.17

0.23

0.10

0.06

-0.05

5.951

2.16

14.8%

(-0.38

)(-7.38)

(1.45)

(-2.89

)(3.38)

(3.11)

(2.24)

(1.03)

(-1.61

)

4.FR05 5

-0.13

-0.55

0.06

-0.20

0.17

0.42

0.08

0.14

-0.03

5.95

12.77

218.0%

(-2.54

)(-7.35)

(1.03)

(-2.61

)(2.90)

(4.83)

(1.54)

(2.06)

(-1.00

)

63

Appendix D -Table D2: Robustness with Alternative Specifications II

Treasury Futures Returns, Forward-Rate Changes, and Asset-class Risk Changes

This table reports on the same specification as Table 2, but the VIX-change and TIV-change are now

the simple difference rather than the log difference. We report on variations of the following model:

TrFtRtt−j,t = α0 + (λ1 + λ2D0104t + λ3D

0913t )∆(V IXt−j,t)+

(γ1 + γ2D0104t + γ3D

0913t )∆(TIVt−j,t) + ϵt−j,t

where ∆V IX (∆TIV ) is now the simple difference between the equity implied volatility at day t− j and

day t, and the other terms are as defined for Table 2. We report on the cases where the dependent variable

is the 30-year T-Bond futures return (TB), the 10-year T-Note futures return (TN), the change in the 10-

year, 5-year, and 1-year forward rates (∆FR10, ∆FR05 and ∆FR01). We report on returns and changes

at the 1-month and 1-week horizons, respectively, with j =22 or 5 trading days. The sample period is

1997:10 - 2013:12. T-statistics, in parentheses, indicate whether the estimated coefficients are statistically

different than zero, calculated with heteroskedastic and autocorrelation consistent standard errors.

∆(V IX)λ terms ∆(TIV ) γ terms

λ1 λ2 λ3 γ1 γ2 γ3 R2

Dp. Vr. 0104 0913 0104 0913 (%)

TB22 -3.27 (-0.52) 28.1 (3.26) 39.4 (5.05) 23.5 (0.99) -137.9 (-3.79) -127.4 (-4.68) 19.9

TN22 -1.36 (-0.33) 21.7 (4.01) 19.4 (4.08) 23.4 (1.52) -92.6 (-4.09) -83.9 (-4.81) 17.7

∆FR1022 1.06 (1.54) -2.60 (-2.87) -5.10 (-6.00) 1.27 (0.51) 9.56 (2.66) 9.30 (3.30) 20.9

∆FR0522 0.79 (1.02) -4.09 (-4.02) -4.84 (4.96) -0.67 (-0.26) 12.5 (2.94) 15.0 (4.64) 20.6

∆FR0122 -1.22 (-3.46) -2.93 (-3.43) 0.23 (0.54) -7.03 (-3.06) 16.8 (5.06) 10.3 (4.25) 20.6

TB5 5.95 (2.76) 12.3 (2.91) 19.1 (7.08) -13.9 (-1.61) -37.2 (-3.19) -41.6 (-2.96) 16.6

TN5 4.80 (3.38) 8.91 (3.53) 7.90 (4.76) -6.63 (-1.18) -30.7 (-3.30) -24.4 (-3.34) 15.1

∆FR105 -0.15 (-0.47) -1.00 (-1.96) -2.63 (-6.72) 2.40 (2.38) 2.25 (1.53) 2.51 (1.91) 13.4

∆FR055 -0.54 (-2.01) -1.62 (-3.29) -2.31 (-6.92) 2.62 (2.45) 3.56 (2.14) 4.45 (2.88) 16.3

∆FR015 -1.31 (-4.98) -1.45 (-3.28) 0.57 (2.00) -0.14 (-0.16) 5.41 (3.49) 1.74 (1.92) 12.5

64

Appendix E:

Stock Returns and Inflation News with CPI/PPI News Releases

In Section 4, we showed that the relation between stock returns and inflation compensation varied with

the economic state in a manner consistent with empirical implications in DV (2013), when using inflation

compensation data from GSW (2010) to infer ‘inflation news’. Here, we augment our investigation in

Section 4 by examining an alternative inflation-news variable that is equal to the difference between the

monthly CPI and PPI news-release value and the respective median forecasted value.

Earlier studies investigate links between CPI/PPI inflation news and stock returns, and tend to find

either no reliable relation or a modest negative relation. See, e.g., McQueen and Roley (MR) (1993) and

Flannery and Protopapadakis (FP) (2002). MR investigate the 1977 - 1988 period and find a negative

and statistically significant relation only for PPI news, which is stronger in states with higher economic

growth. FP examine the 1980 - 1996 period and find a negative relation between inflation news and stock

returns. From the perspective of DV (2013), the periods studied in this earlier research were ones in which

an increase in inflation news/compensation would have likely signalled that the economy was more likely

to enter a state of excessive inflation. Hence, a negative stock-inflation relation during these time periods

is consistent with the DV framework.

Our sample postdates these earlier studies and includes periods when inflation would likely be good

news for stocks from the perspective of DV (2013). For the CPI/PPI news-release days, we regress the

daily S&P 500 futures return and 10-year T-Note futures return against the inflation-news variable. We

note three principal findings in Table E1. First, similar to earlier studies that try to link such news releases

to stock returns, there is very little relation between the stock-futures returns and the inflation news (in

other words, the R2 values are very small; see the line-1 model that presents the unconditional relation).

Second, consistent with our results in Table 5 and the empirical implications in DV (2013), the estimated

coefficient that relates the inflation news to the stock-futures return is negative for our non-RPR-growth

periods but positive for our RPR periods. This economic-state-based difference is marginally statistically

significant at a 10% p-value (see Table E1, the estimated α2 in the line 2 model). Third, reassuringly,

the inflation-news variable from the CPI/PPI release is positively related to the daily change in the GSW

inflation-compensation value with a 1% p-value (see Table E1, the line-5 model).

65

Appendix E - Table E1:

Daily Financial Asset Returns and CPI/PPI Inflation News

This table reports how the unexpected components of the CPI and PPI news releases are related to the

day’s financial futures returns and the day’s inflation-compensation change from the GSW TIPS data. The

regressions in rows 1 to 4 below report on variations of the following specification:

FtRtt = α0 + (α1 + α2DumRPRt + α3Dum

Non−RPR−Rect )∆Inflt + εt

where FtRtt is either the S&P500 (SP5t) or the 10-year T-Note futures return (TNt) on the day of the CPI

and PPI news releases; ∆Inflt is the ‘inflation news’ indicated by the difference between the actual CPI

or PPI news release and the median forecasted value; DumRPRt is a dummy variable that equals one if the

month is in one of our RPR periods (over 2001:10 - 2004:04 and 2009:01 - 2013:12), and DumNon−RPR−Rect

is a dummy variable that equal one if the month is in a non-RPR period that is also a formal NBER

recession month (2001:03 - 2001:09 and 2007:12 - 2008:12); and the α’s are coefficients to be estimated.

Row-5 below reports on an alternative estimation, estimated only over 1999 to 2013 due to TIPS data

availability, where the ‘change in the day’s inflation compensation’ (per GSW 2010) replaces the futures

returns as the dependent variable. To ensure outliers are not overly influential, we use a 98% winsorization

on the futures returns by replacing the values exceeding the 99th percentile (below the 1st percentile) with

the 99th percentile value (with the 1st percentile value); results with raw variables are qualitatively similar

but slightly weaker. To standardize the variables and evaluate both the CPI and PPI simultaneously, all

variables are converted to ‘standardized variables’ by subtracting the sample mean and then dividing by

the sample standard deviation, before performing the regression. The full sample period for models (a) -

(d) is 1997:10 - 2013:12. T-statistics are in parentheses, calculated with heteroskedastic and autocorrelation

consistent standard errors.

Dependent Variable Model α1 α2 α3 R2

1. SP5t a. -0.0312 (-0.52) 0.10%

2. SP5t b. -0.128 (-1.33) 0.214 (1.75) 0.027 (0.13) 1.1%

3. TNt c. -0.100 (-1.86) n/a n/a 1.0%

4. TNt d. 0.050 (0.66) -0.148 (-1.42) -0.455 (-2.83) 3.6%

5. ∆InflCompt e. 0.187 (3.00) n/a n/a 3.7%

66

Appendix F - Table F1: Weekly Changes in Federal Reserve Holdings and VIX Changes

This table reports how the weekly changes in the Federal Reserve holdings of debt securities vary

with the weekly VIX change over 2009 to 2013. The weekly positions of Treasury, government agency,

and mortgage backed securities (MBS) on the Federal Reserve’s Balance Sheet are obtained from Federal

Reserve release H4.1 with a week ending on Wednesday. We focus on the weekly change of the following six

variables: (a) the simple VIX (∆V IX), (b) the log(VIX) (∆log(V IX)), (c) the holdings of debt securities

with a maturity of 5 years or greater (combination of Treasuries, government agency debt, and MBS)

(∆DSGT5y) ; (d) the holdings of Treasury securities with a maturity of 5 years or greater (∆TSY GT5y);

(e) the holdings of MBS with a maturity of 5 years or greater (∆MBSGT5y);(f) the holdings of debt

securities of all maturities (combination of Treasuries, government agency debt, and MBS) (∆DSall).

Panel A, row 1, reports on the simple correlation between the weekly change in the debt securities and

∆V IX. Panel A, row 2, reports on the simple correlation between the weekly change in the debt securities

and ∆log(V IX). We report on both the entire 2009-2013 period and inclusive one-half subperiods. Panel

B reports on the summary statistics for these variables when the ∆log(V IX) is extreme, defined as above

the 95th percentile or below the 5th percentile. For comparison, Panel B also reports statistics on the

weekly 10-yr T-Note futures return, T-bond futures return, and S&P500 futures return for the different

groupings. For Panel B, the first three columns report on the simple weekly change variable and the

last three columns report on a standardized version of the variable, constructed by demeaning the raw

variable and dividing by the standard deviation with the mean and standard deviation from the entire

2009-2013 period.

Panel A: Weekly Debt Purchases - Correlations to ∆V IX and ∆log(V IX)

Sample ∆DSGT5y ∆TSY GT5y ∆MBSGT5y ∆DSall

Period

2009:01 to 1. ρ∆V IX -0.15 -0.11 -0.13 -0.14

2013:12 2. ρ∆log(V IX) -0.18 -0.13 -0.14 -0.15

2009:01 to 1. ρ∆V IX -0.19 -0.11 -0.16 -0.21

2011:06 2. ρ∆log(V IX) -0.20 -0.14 -0.17 -0.20

2011:07 to 1. ρ∆V IX -0.10 -0.08 -0.07 -0.07

2013:12 2. ρ∆log(V IX) -0.15 -0.14 -0.11 -0.10

67

Appendix F - Table F1: (continued)

Panel B: Summary Statistics for Weeks with

Extreme VIX Changes: 2009:01 - 2013:12

Raw Variables Standardized Variables

mean median stdev mean median stdev

Panel B.1: All Weekly Observations

∆V IX -0.106 -0.185 3.05 0.000 -0.026 1.00

∆DSGT5y 10.590 5.720 21.92 0.000 -0.222 1.00

∆TSY GT5y 4.841 4.500 6.93 0.000 -0.049 1.00

∆MBSGT5y 5.757 0.014 21.26 0.000 -0.270 1.00

∆DSall 12.567 6.861 23.24 0.000 -0.245 1.00

Tr.Note F tRt 0.067 0.107 0.82 0.000 0.048 1.00

Tr.Bond FtRt 0.052 0.086 1.44 0.000 0.023 1.00

SP500 FtRt 0.337 0.547 2.46 0.000 0.086 1.00

Panel B.2: Observations for Largest 5% of ∆log(V IX) Values

∆V IX 6.461 4.760 4.53 2.155 1.597 1.49

∆DSGT5y 9.061 3.304 17.41 -0.070 -0.332 0.79

∆TSY GT5y 4.453 3.303 6.24 -0.056 -0.222 0.90

∆MBSGT5y 4.631 0.000 16.87 -0.053 -0.271 0.79

∆DSall 9.816 5.899 19.63 -0.118 -0.287 0.85

Tr.Note F tRt 0.807 0.978 0.89 0.901 1.109 1.08

Tr.Bond FtRt 1.470 1.576 1.66 0.988 1.062 1.16

SP500 FtRt -3.688 -3.474 2.44 -1.639 -1.551 -4.39

Panel B.3: Observations for Smallest 5% of ∆log(V IX) Values

∆V IX -6.270 -6.180 2.56 -2.023 -1.993 0.84

∆DSGT5y 10.560 11.948 16.3 -0.001 0.062 0.74

∆TSY GT5y 6.350 5.839 7.47 0.218 0.144 1.08

∆MBSGT5y 4.387 0.105 14.62 -0.064 -0.266 0.69

∆DSall 9.403 3.209 15.78 -0.136 -0.403 0.69

Tr.Note F tRt -0.544 -0.371 0.63 -0.745 -0.535 0.77

Tr.Bond FtRt -1.169 -0.951 1.23 -0.851 -0.699 0.86

SP500 FtRt 3.865 3.186 1.7 1.436 1.160 0.69

68

Appendix F - Figure F1: Holdings of Debt Securities on the Federal Reserve’s Balance Sheet

Panel A displays the quantity of debt securities on the Federal Reserve’s Balance sheet over December 18,

2002 through December 25, 2013. The securities include Treasuries, Federal Agency debt, and Mortgage

Backed Securities (MBS), as reported in Federal Reserve weekly release H.4.1. The upper line shows the

debt securities at all maturities, the middle line shows the debt securities at maturities greater than 5

years, and the bottom line shows the U.S. Treasury securities only at maturities greater than 5 years (the

lower and middle lines overlap before 2009, since there were essentially no holdings of MBS or agency debt

prior to then). The units are in hundreds of billions of dollars. Panel B shows the VIX time series.

0

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Panel!A:!!Debt!Securities!on!the!Federal!Reserve!Balance!Sheet

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Panel!B:!!VIX

69