Global Asset Pricing and Financial Intermediary Leverage - Leandro de Miranda Gomespdf

*E-mail: [email protected]

Global Asset Pricing and Financial Intermediary Leverage

Leandro de Miranda Gomes*

PUC-RIO

March 2015

Abstract

We propose a 2-factor global asset pricing model based on prices of risk of financial

intermediary firms leverage and US market returns. We show that our model present

considerably better statistical and economic properties, as small intercept and

economically meaningful prices of risk, than benchmarks like US Fama-French 3-

factor, Global US Fama-French and single factor leverage model. There are also

considerably improvements when simultaneously pricing US and International

portfolios in comparison to US-only portfolios, indicating a global presence of US

financial intermediary system on asset pricing through different markets. We use

conventional 25 size-book to market sorted US and International portfolios, but our

results are robust to the inclusion of momentum portfolios and maturity sorted bonds

portfolios.

1. Introduction

At the Federal Reserve Bank of Bostons 56th

Economic Conference on October

2011, the President & Chief Executive Officer of the institution, Eric S. Rosegreen,

addressed the long term effects of the Great Recession, highlighting the role of large

global financial intermediaries as they suffered severe distress on the events of the crisis

and had a decisive role transmitting the shocks to the wider global financial system

through their interconnectedness with other financial institutions.

Given its relevant size on the financial system, the intermediary sector is not

only an important global financial link, but also plays a relevant role on the US

Financial Markets. Within the intermediary sector, security dealers and brokers and

institutions from the shadow banking system appear to be the most prominent ones,

presenting strong explanatory power for many financial asset returns, as suggested by

Adrian, Moench and Shin (2010), including a relevant role on the explanation of the

cross sectional US portfolios returns through a single US Security Dealers and Brokers

Leverage Factor model proposed by Adrian, Etula and Muir (2010, 2015).

Based on the global nature of US Security Dealers and Brokers, we argue that

the US Security Dealers and Brokers Leverage Factor is also useful in explaining the

cross section of Global Portfolios, following an intermediary financial Stochastic

Discount Factor framework as in Adrian, Etula and Muir (2010,2015). Using different

combinations of US and International Stocks Portfolios sorted by Size, Book to Market

and Momentum, as well as different maturities for Bonds Portfolios, we show that a US

2-factor model with the US Security Dealers and Brokers Leverage and the US Excess

Market Return as factors, is the most stable and robust among all models tested, like

Adrian, Etula and Muir(2010,2015) single leverage model, International 2-Factors

Model1 and both International and US Fama French 3 Factors Model.

Although no model can consistently price the cross-section of US or

International excess returns, we find that adding International portfolios to the analysis

1 International 2-Factors are US Security Dealers and Brokers Leverage Factor and International Excess

Market Return. In the absence of Global Leverage data, USs may be seen as a proxy.

does improve our cross-sectional results as pricing errors become gerenally smaller and

prices of risk become consistent with theory. The US 2-Factor Models present the most

significant improvements, even when challenging Momentum Portfolios are added.

While the addition of Global portfolios lead to the most noteworthy improvements, the

model is also robust to the inclusion of European-only or even UK-only portfolios.

While our goal is to show that the leverage factor is priced in the cross-section of

Global portfolios, a minor contribution to the literature is to address the robustness of

Adrian, Etula and Muir(2010,2015) single leverage factor model to changes in

definition of leverage and to sample period. On the June 5, 2014 publication of the

Flow of Funds, there was an important change on one of the variables that were used to

construct the leverage factor in Adrian, Etula and Muir(2010,2015). Before, the

Security Repurchase Agreements appeared only as a net variable on the liabilities

section, while on the updated version it appears both on the assets and liabilities. Table

1 shows the implications of this change on the construction of the Leverage in both

scenarios for the fourth quarter of 2013.

The change, in absolute terms, is non-negligible. Unfortunately, because of data

availability constraints, theres no way to fully replicate the old methodology to look for

possible implications on the dynamics of the transformation. However, in order to

investigate imaginable problems arising, the old data is artificially reconstructed

subtracting the security REPO from both the total financial assets and total liabilities,

recreating the net variable on the liabilities side. Intuitively, theres no economic

explanation for the use of the old variable, nonetheless the following analyses will

report both versions. Results report a considerable sensibility towards this methodology

change. In addition, results show that when we consider the 1981-2014 or 1991-2014

windows, where the latter is the same as the used on global portfolios, the single

leverage factor models performance is considerably worse, indicating a lack of

robustness to shorter time periods. Because data is quarterly, this can be attributed to the

lack of betas variability, which may prevent a precise estimate of leverage price of risk.

2. Related Literature

Leverage started to gain attention primarily after the Great Recession, even

though leverage cycle theory existed prior to the crisis, as seen in Geanokoplos

(1997,2003) and Fostel and Geanokoplos (2008). Contrarily to standard economic

theory, the Leverage Cycle Theory suggests that asset prices and consequently the real

economic activity, are driven not by interest rate, but by endogenous leverage and

volatility, through the role of collateral. Additionally, as presented in Fostel and

Geanokoplos (2013), the cycle component of this theory focus on how low volatility

and safe economic perspective can lead the real economic to a boom and a highly

leveraged economy, as well as a confluence of factors, primarily a bad news leading to

increased volatility and uncertainty can lead to credit tightening and a severe

deleverage, and thus, a market crash.

Empirically, Adrian, Moench and Shin (2010) documented the high pro-

cyclicality of the leverage cycle, where low asset prices are associated to an also low

Leverage, and proposed that this cyclical characteristic may be due to regulatory or

other constraints, such as Value at Risk limits. Another approach to rationalize the

stylized fact emphasizes how personal experience of agents can shape risk preferences,

as theoretically proposed by Krishnamuty (2009) and empirically suggested by

Malmendier and Nagel (2011) that look to the role of the Great Depression on

individuals willingness to invest in equities, and Koudijs and Both (2014) that

investigate the collateralized Amsterdam loan market in the 18th

century.

Given the relevance of financial intermediary firms, Adrian, Etula and Muir

(2010, 2015) suggest a shift on the traditional asset pricing theory emphasis on

household Stochastic Discount Factor (SDE) to an intermediary SDE. They argue that

the assumptions of a household SDE are easily violated, like full market participation of

all households, absence of transaction costs, and the need of continuous optimized

expectations, while the financial intermediary firms fit the hypothesis more naturally.

Furthermore, they construct a single factor model based on a non-seasonal log

innovations of US Security Dealers and Brokers Leverage that outperforms US Fama

French 3-factor and CAPM models on the 1968-2009 time window. Adrian, Moench

and Shin (2014) also extends these results to a dynamic framework using the Dynamic

Asset Pricing Model (Adrian, Crump and Moench, 2014) that allows for time-varying

price of risk and time-varying betas.

Nonetheless, US security dealers and brokers are genuine global companies,

incorporating shocks from all parts of the world through its subsidiaries, or foreign

holders. Since there is no availability of data for security dealers and brokers from

others countries, it is impossible to calculate a true global leverage factor.

The US Leverage Factor has been used inthe literature as a proxy for the

unavailable global variable. Stressing the global nature of the financial system and the

leverage cycles, Bruno and Shin (2014a) propose a global banking model, where

regional banks borrow in US dollars from global banks and then lend to local corporate

owners, emphasizing that the global intermediary financial system is responsible for the

aggregate credit risk, and consequently, global liquidity. Testing theory predictions,

they also construct a panel including 46 countries using global factors, as the US

Security Dealers and Brokers leverage as a proxy, to support their predictions.

Credit conditions are also determined by global factors in Bruno and Shin

(2014b), that also synchronizes the corporate risk-taking of different regions and

sectors. Empirically, they show that US Security Dealers and Brokers as a proxy for

Global Liquidity is indeed a relevant global risk-taking factor. Bruno and Shin (2014c)

also present the monetary policy risk-taking channel of capital flows, where US

monetary policy is relevant to both international banks leverage and cross-borders

capital flows.

Finally, the Global Asset Pricing literature so far has struggled to propose a

global-factors only model, and Lewis (2011), explore possible explanations that make

this a hard task to be accomplished, highlighting the domestic nature of monetary and

fiscal policies and the home equity bias, as well as the exchange risk included on global

portfolios. However, Lewis points out that a world CAPM still is the most common

benchmark when looking to Global Portfolios.

3.Data

The US Security Dealers and Brokers Leverage is defined as:

Both Total Financial Assets and Total Liabilities are from the L.128 Table from

Flow of Funds Report, now Z1 Release, as December 11, 2014. Data is quarterly. To

approximate the old methodology, the approach is to recreate the NET Repo Agreement

variable on the liabilities side. Precisely, Old Leverage is defined as:

To construct the Leverage Factor, we first take the Leverage Log Innovation,

i.e., log(Leverage), and make it seasonally adjusted using expanding windows starting

in 19652. Following Adrian, Etula and Shin(2010,2015), as the data before mid-60s

doesnt seem reliable because of negative or too low leverage, the time series of the

factor will start at 1968.

The Portfolios used for the US analysis are the 25 Size-Book to Market and 10

Momentum from Frenchs library. US Treasury Bonds Portfolios are sorted by

maturities, 0-6 months, 12-18months, 24-30 months, 36-42 months, 48-54 months and

5-10 years. The data is from CRSP.

International Portfolios, both 25-Size Book to Market and 25-Size Momentum,

are constructed using data from 22 Developed Countries excluding the US, and are

available only starting at 1991. European 25-Size Book to Market and 25-Size

Momentum are from 16 countries and available at the same source. Finally, UK 25

2 Following the same methodology, the season adjustment is proceeded using expanding windows, i.e.,

using all the data up to date, starting three years before the initial starting date (1968). Therefore, through

the regressions below, the leverage factor is adjusted using data starting in 1965.

Size-Book to Market are from Xfi Centre For Finance and Investment by University of

Exeter and are available since 1981.

When we refer to Global portfolios, both International and US-only portfolios

are being simultaneously used, unless further noticed. In only one situation another set

of Global portfolios is used, which are constructed very similarly of International

portfolios, but also includes US portfolios. This data is also available at Frenchs

library.

For the excess return calculations, all Portfolios above use the 3-Month T-Bill as

the risk-free rate, with the exception to the UKs, that use the Risk-Free rate from

Exeter database. As the leverage is only available at a quarterly frequency, all excess

returns are time-aggregated into quarterly excess returns, and then multiplied by four to

transform them in annual excess returns.

Three different sets of factors are used. US, Global3 and European Fama-French

Factors are from Frenchs library, while UKs Factors are from Exeter Univeristy

library.

For USs Portfolios, four different dates combinations will be used to allow us

compare the modes performance through time: 1968-2009, the time window used by

Adrian, Etula, Shin (2010,2015), 1968-2014, 1981-2014 and 1991-2014. For UKs

Portfolios, only 1981-2014 and 1991-2014, while for the others, 1991-2014.

US 25, International 25, Europe 25 and UK 25 portfolios are sorted by size-book

to market only, while US 31 and 35 include, respectively, 6 Bonds and 10 Momentum

portfolios. US 41 includes both of them and International, Europe and UK 50 Portfolios

both 25 size-book to market and 25 size-momentum portfolios.

4. Methodology

For all different portfolios, i=1,,N, each factors beta is estimated through

conventional time-series regressions, i.e.,

Ri,te = ai + i,f ft + ei,t , t=1,...,T.

3 The Global Factors, differently from International Portfolios, take the United States into account.

Then, as usual, the factors price of risk, f, is calculated through the cross

section of Portfolios Expected Returns, where, vi + c is the pricing error.

E[Ri,te] = c + i,f f + vi , i=1,...,N

Good model properties are a small intercept, as well as stable and economically

significant prices of risk. Although the conventional t-statistic is presented (in italic), it

is prudent to take into consideration that the betas are estimated and thus already have

own estimation errors, hence we also report the t-statistic correction as proposed by

Shanken (1992). We also hope for a small Mean Absolute Pricing Error (MAPE), i.e.,

, and non-rejection of the null hypothesis that all pricing errors are

jointly equals to zero, using the Gibbons-Ross-Shanken (1989), GRS statistic.

5. Results

Since Adrian, Etula and Muir (2010,2015) proposed the Leverage Factor, the

definition of the variables used in its construction has changed. As one of ours main

goals is to compare models performance in the pricing of International portfolios, first

we look at the US-only case, taking a closer attention to the robustness over the

methodology change and to changes in the sample period as International data is

considerably shorter. Tables 2-4 provide the comparison between old and new Leverage

Factor in four different time windows, 1968-2009, 1968-2014, 1981-2014 and 1991-

2014. We also compared their performance to an alternative US 2-factor that also

includes the market return as a factor, and to the US Fama French 3-factor models, . We

test these model using US 25, US 31 and US 41 Portfolios.

Next, we take a Global perspective, pricing simultaneously US and International

Portfolios4. In addition to using International portfolios, we also test the effect of adding

European-only and UK-only portfolios for robustness.. Tables 5-9 present the

comparison between a range of models (Leverage Single Factor, US 2-Factors, US

Fama French 3-factor, Global 2-factor and Global 3-factor) using different portfolio

combinations: US 25 + International 25, International 25, US 31 + Interntional 25, US

4 Data for 25 Size-Book to Market and 25 Size-Momentum sorted portfolios are also available at Frenchs

library. However, due to a small time frame, we prefer to include International portfolios to estimate

leverage price of risk more precisely.

35 + International 50 and US 41 + International 50.CAPM performs considerable

worse, so results are not reported.

We also show, a horse race between the 2-US Factor and 4-US Factor, which is

a combination of the leverage factor and the three factors on Fama French model, on

table 10, and the use of a different global portfolios set on table 11 to assess robustness.

5.1 US-only Portfolios

First, we address the possible problems concerning the methodology change of

the leverage calculation, as well as the model performance over shorter time periods.

The results shown in tables 2-4 imply that the old leverage calculation methodology

performs considerably better than the new-definition leverage. Nonetheless, there are

some shortcomings on the older methodology, as Both GRS statistic and pricing errors

increase considerably on shorter time-windows. For example, when all 41 US

portfolios are analyzed, the intercept goes from 0.36 on the 1968-2009 time frame to

7.97 on 1991-2014. This pattern can be seen in all other models, but the increase is not

nearly as steep as for the old Leverage 1-factor model. Also, both new and old leverage

price of risk remains stable through different portfolios sets, time-frames and

methodologies approach. When we add the 6 bonds or 10 momentum portfolios,

however, US 2-factor outperform both old and new leverage 1-factor, presenting

smaller and non-significant intercepts, at the 1.5-3.25 range, while maintaining the price

of risk stability for both leverage and market.

Finally, while GRS tests reject all the tested models, the relevant leverage price

of risk in all the models, as well as higher than 60% Adjusted R2 estimates, provide

some evidence on the role of the US Security Dealers and Brokers on the cross section

of asset markets.

5. 2 International and Global Portfolios Pricing

In this section, we test our main hypothesis that the US leverage factor can price

the cross-section of global portfolios, i.e., international and US portfolios. We test the

conjecture that the addition of international portfolios can improve the overall

performance of the model due to a more precise estimate of the price of leverage risk,

relying on the hypothesis that the US leverage factor is a good proxy for an

unobservable global leverage factor. Overall, tables 5-9 show that the inclusion of

international portfolios turn all models better, but mainly US 2-factor and US FF.

The inclusion of only 25 International portfolios on US original 25 portfolios is

already enough to improve the results, as seen in table 5. Our US 2-factor model, for

example, presents a smaller intercept of 2.61, against a 9.11 with US-only 25 portfolios,

while maintaining relevant and positive leverage and market prices of risk. However

US Fama-French model intercept also declines from 10.18, when US-only portfolios are

used, to 0.24, when international and US portfolios are priced simultaneously. Although

all models present better economic and statistical properties, the steepest improvements

happen with the US 2-factors and US FFs models. We also show on table 6 that models

also improve from International-only portfolios when US portfolios are included.

However, the US Fama-French model is not as robust as the US 2-factor model

to the inclusion of different types of portfolios. Although adding bonds portfolios seems

make all models better, US 2-factor presents considerable improvements when

compared to US Fama-French model. US 2-factor is the only model to present non-

significant intercepts, and present stable coefficients when comparing the US-only 25 to

US 25 + International 25 portfolios, which is a highly desirable economic feature. We

also show on table 8, when momentum portfolios are included, and on table 9, when

both momentum and bond portfolios are added, that the US-factor clearly presents the

best results. While US Fama-French model presents a high intercept of 7.88 and a

negative price of risk on the first case, US 2-factor model presents a sign of market

price of risk that is consistent with economic theory, whereas maintaining a stable

leverage price of risk and low intercept.

GRS tests interpretation does not permit us to statistically reject the null

hypothesis of jointly zero jointly prices errors, however, US 2-factor model intercepts

are all between 2.49 and 4.67 and are all insignificant., which is an unique feature

among all models. Also, from the economic theory stand point, the fact that leverage

price of risk always lies between 67-73 and market price of risk between 3.17-5.36,

suggest an interesting stability over different cross-sectional results. Both statistical and

economic properties across portfolios can be visualized in the figures 1-5.

When we add Europe and UK-only portfolios, as seen in tables 5-9, results

suggests the US 2-factor as the most consistent model, albeit not performing well in

some cases, as we can see on the significant intercept on UK 25 + US 41 and Europe 50

+ US 35 besides a negative market price of risk on Europe 50 + US 35. Also, Tables 5

and 6 also provide evidence on the improvements when US 25 Portfolios are added to

Europe or UK 25 portfolios. US 2-Factors present significant 16.22 and 8.96 intercepts

on Europe-only and UK-only 25, correspondingly, while when including US 25, turn to

respectively a not significant 5.35 and 6.88.

On a horse race between US 2-factor, US 4-factor and Global 4-factor models,

table 10 shows that the results to US models are similar, and considerably superior to

the Global model. Indeed, US 4-factor model also present a similar low intercept, but

also shows a higher adjusted R2. However, this model lack robustness when we include

of momentum portfolios. Thus, as US 2-factor is a more parsimoniously model,

presenting generally better results, we do not find added to value to the extra factors

considered on the 4-factor model.

Finally, we assess the performance of US-2 factor model when US portfolios are

already used on the construction of Global portfolios. The main shortcoming to this

approach is the potential lack of variability that can hurt the estimated betas precision.

Nonetheless, table 11 suggest that although US 2-factor model maintains the relative

best economic and statistical properties, the performance with Global 25 portfolios and

Global 50 portfolios are much worse than the benchmark case.

6. Conclusion

We show that US 2-factor model can consistently price cross-sectional returns of

global portfolios, presenting small pricing errors and prices of risk compatible to

economic theory. The results are also considerable stable across different sets of

portfolios, including momentum and bonds. Also, this is the only model that present

non-significant intercepts on all different global portfolios combinations.

Other robustness tests include the addition of other non-US portfolios, as

European and UKs, a horse race with 4-factor model, and a different construction of

global portfolios. In all these scenarios, US 2-factor perform substantially better than

single factor leverage, or global and US Fama-French models.

One question that emerges when looking to these results why a Global 2-Factor

model doesnt seem to be the most consistent, if indeed this economic story of a

relevant intermediary financial system is true. One speculative answer is that financial

intermediary firms base their decision on a US framework, since most of them are from

there, or because its the most important benchmark/market available. Another

speculative answer is that this only happened due to the absence of a true Global

Leverage Factor and if we could use this variable along with the Global Market Excess

Return, the results could be improved. One last explanation draws the attention to the

Risk-Free rate, which even for Global and European Portfolios, is a common 3 month

T-Bill. Perhaps a better proxy for a global risk-free rate could lead to significantly

different results.

7. Appendix: tables and figures

Figure 1 Actual vs predicted results from US 2-factor for US 25

Figures 2-3 : Actual vs predicted results from US 2-factor for US 25 + International 25

and US 31 + International 25

Figures 4- 5: Actual vs predicted results from US 2-factor for US 35 + International 50

and US 41 + International 50

Table 1: US security dealers and brokers leverage using September 18 and March 6

versions of Flow of Funds for the fourth quarter of 2013

4Q 2013 L.128 as of September 18 (new)

total financial assets 3,408,371 total liabilities 3,324,558

checkable deposits and currency 111,720 security repurchase agreements 1,768,587

security repurchase agreements 1,320,966 credit market instruments 112,398

credit market instruments 476,894 corporate and foreign bonds 112,398

commercial paper 28,654 depository institution loans n.e.c. -

Treasury securities 136,043 trade payables 14,540

agency- and GSE-backed securities 114,164 security credit 897,052

municipal securities and loans; 18,637 Households and nonprofit organizations; security

credit; asset 815,484

corporate and foreign bonds 128,949 U.S.-chartered depository institutions; security credit;

asset 52,885

syndicated loans to nonfinancial corporate

business 50,447

Foreign banking offices in the U.S.; security credit;

asset 28,683

corporate equities 172,386 taxes payable 3,723

security credit 339,184 foreign direct investment in U.S. 119,540

U.S. direct investment abroad 225,786 total miscellaneous liabilities 408,718

total miscellaneous assets 761,435 equity investment by parent companies 1,671,859

unidentified miscellaneous liabilities -1,263,141

Leverage = 40.7

4Q 2013 L.128 as of March 6 (old)

total financial assets 2,087,400 total liabilities 1,992,300

checkable deposits and currency 111,700 security repurchase agreements (net) 135,300

security repurchase agreements - credit market instruments 112,400

credit market instruments 476,900 corporate and foreign bonds 122,025

open market paper 28,700 depository institution loans n.e.c. 112,400

Treasury securities 136,000 trade payables 14,500

agency- and GSE-backed securities 114,200 security credit 1,209,300

municipal securities and loans; 18,600 Customer credit balances 833,800

corporate and foreign bonds 133,100 U.S.-chartered depository institutions; security credit;

asset 187,100

others loans and advances 46,300 Foreign banking offices in the U.S.; security credit;

asset 188,400

corporate equities 172,400 taxes payable 3,700

security credit 339,200 foreign direct investment in U.S. 108,300

total miscellaneous liabilities 517,000

total miscellaneous assets 987,200 equity investment by parent companies 1,659,100

unidentified miscellaneous liabilities -1,250,400

Leverage = 22

Table 2. US 25: On this table we present the cross-sectional results for US single leverage based on old and new methodologies (Lev and Lev_old, respectively), US 2-factor, US Fama-French models,, where Lev and Lev_old

are respective, new and old leverage factors, for 25 US Size-bookt to market sorted portfolios.We present intercept,

leverage factor (LevFac) and the standard 3-factors from Fama French models coefficients, along with the respectives

t-statistics, below coefficients. T-shanken statistics are reported beneath standard t-statistics. We also report adjusted

R2, adjR2, Mean Asset Pricing Error (MAPE) and Gibbons, Ross, Shanken statistic, along with its respective p-value.

Periods analysed are 1968-2009, 1968-2014, 1981-2014 and 1991-2014.

Lev Lev_old US 2-

Factor US FF Lev Lev_old

US 2-

Factor US FF

1968-2009 1968-2014

Intercept 3.12 0.71 5.18 13.09 4.67 2.15 6.68 13.74

4.31 0.71 2.6 2.45 6.83 2.13 3.28 2.46

0.72 0.13 1 3.02 1.19 0.45 1.36 3.2

LevFac 47.39 61.67 45.88

42.47 55.22 41.2

7.26 7.5 6.91

6.66 6.84 6.36

2.59 2.39 2.5

2.6 2.41 2.51

Market-

RF 0.49 -7.81

0.11 -7.28

0.3 -1.48

0.06 -1.32

0.08 -1.52

0.02 -1.45

SMB

1.98

1.73

3.22

2.79

1.1

1.04

HML

5.5

4.94

7.16

6.41

2.77 2.73

Adj R2 0.68 0.7 0.69 0.71 0.64 0.66 0.65 0.66

MAPE 3.12 1.20 5.18 13.09 4.67 2.18 6.68 13.74

GRS 44.18 20.79 43.82 54.35 27.26 23.02 53.11 64.42

1% 65% 0% 0% 29% 52% 0% 0%

1981-2014 1991-2014

Intercept 8.71 5.85 11.292 22.62 10.35 9.78 9.11 18.79

19.17 6.62 3.51 3.86 20.98 15.83 2.9 4.44

2.07 1.1 1.9 4.72 2.26 2.05 1.42 4.02

LevFac 43.82 56.58 38.84

38.17 38.82 40.63

5.16 4.97 3.69

3.98 3.58 3.52

2.08 1.85 1.89

1.42 1.33 1.61

Market-

RF -2.58 -14.68

0.89 -10.18

-0.91 -2.56

0.32 -2.46

-0.38 -2.64

0.12 -1.76

SMB

0.78

2.42

1.04

3.42

0.46

1.16

HML

4.85

3.67

5.17

4.15

2.25 1.37

Adj R2 0.52 0.5 0.51 0.59 0.38 0.33 0.36 0.6

MAPE 8.71 5.85 11.29 22.62 10.35 9.78 9.11 18.79

GRS 49.06 41.74 67.62 68.76 56.75 56.13 52.69 54.95

0% 1% 0% 0% 0% 0% 0% 0%

Table 3. US 31: On this table we present the cross-sectional results for US single leverage based on old and new methodologies (Lev and Lev_old, respectively), US 2-factor, US Fama-French models, where Lev and Lev_old

are respective, new and old leverage factors, for 25 US Size-bookt to market sorted portfolios and 6 bond portfolios

sorted by maturity. We present intercept, leverage factor (LevFac) and the standard 3-factors from Fama French

models coefficients, along with the respective t-statistics, located below coefficients. T-shanken statistics are

reported beneath standard t-statistics. We also report adjusted R2, adjR2, Mean Asset Pricing Error (MAPE) and

Gibbons, Ross, Shanken statistic, along with its respective p-value. Periods analyzed are 1968-2009, 1968-2014,

1981-2014 and 1991-2014.

Lev Lev_old US 2-


US 2-

Factor US FF

1968-2009 1968-2014

Intercept 2.04 0.59 1.50 1.49 2.84 1.06 1.65 1.58

4.10 1.11 2.42 2.28 5.05 1.94 2.57 2.44

0.92 0.34 1.40 2.18 1.30 0.67 1.73 2.55

LevFac 55.92 62.62 51.85

57.24 63.40 48.37

11.20 12.89 9.10

9.80 13.07 8.05

2.36 2.18 2.87

2.48 2.30 2.91

Market-

RF 3.49 3.59

4.25 4.64

5.79 4.26

6.74 5.54

1.07 1.25

1.40 1.73

SMB

2.04

1.84

3.37

3.02

1.13

1.11

HML

5.74

5.18

7.64

6.84

2.89 2.86

Adj R2 0.81 0.85 0.81 0.82 0.76 0.66 0.81 0.83

MAPE 2.19 1.06 1.70 1.64 2.92 1.34 1.81 1.69

GRS 49.91 25.67 52.10 77.37 2.92 25.84 62.43 89.79

1% 69% 1% 0% 0% 68% 0% 0%

1981-2014 1991-2014

Intercept 7.27 3.65 2.94 2.93 8.38 7.38 3.00 3.06

11.59 4.79 3.43 3.41 10.83 8.76 3.62 3.82

2.05 1.11 3.07 4.64 2.17 1.89 3.80 5.70

LevFac 54.35 80.35 55.62

55.70 66.20 53.67

4.17 7.40 6.24

3.32 4.03 3.62

2.48 2.31 2.49

1.90 1.94 1.85

Market-

RF 4.69 4.49

6.17 5.07

5.42 3.96

7.31 4.71

1.37 1.48

1.58 1.44

SMB

1.23

2.71

1.46

3.19

0.73

1.31

HML

5.46

4.87

5.21

4.89

2.53 1.80

Adj R2 0.35 0.64 0.70 0.71 0.25 0.34 0.75 0.78

MAPE 7.27 3.73 3.04 2.99 8.38 7.38 3.08 3.09

GRS 113.98 54.49 106.90 172.34 109.72 94.49 106.98 158.99

0% 0% 0% 0% 0% 0% 0% 0%

Table 4. US 35: On this table we present the cross-sectional results for US single leverage based on old and new methodologies (Lev and Lev_old, respectively), US 2-factor, US Fama-French models, for 25 US Size-book to

market sorted portfolios and 6 bond portfolios sorted by maturity and 10 momentum sorted portfolios. We present

intercept, leverage factor (LevFac) and the standard 3-factors from Fama French models coefficients, along with the

respective t-statistics, located below coefficients. T-shanken statistics are reported beneath standard t-statistics. We

also report adjusted R2, adjR2, Mean Asset Pricing Error (MAPE) and Gibbons, Ross, Shanken statistic, along with its

respective p-value. Periods analyzed are 1968-2009, 1968-2014, 1981-2014 and 1991-2014.

Lev Lev_old US 2-


US 2-

Factor US FF

1968-2009 1968-2014

Intercept 2.19 0.36 1.9 2.47 3.2 0.99 2.07 2.46

3.41 0.5 2.05 1.96 5 1.42 2.27 2.07

0.83 0.16 1.55 3.38 1.23 0.48 1.9 3.73

LevFac 53.83 63.64 52.46

53.99 63.69 49.1

7.68 9.19 6.81

7.47 9.74 6.44

2.63 2.56 3.18

2.8 2.67 3.26

Market-

RF 2.97 2.62

3.75 3.72

3.38 1.77

4.33 2.67

0.9 0.91

1.23 1.39

SMB

1.6

1.45

1.52

1.44

0.88

0.87

HML

4.6

4.26

3.34

3.21

2.3 2.34

Adj R2 0.59 0.68 0.58 0.34 0.58 0.7 0.6 0.4

MAPE 2.61 1.36 2.37 2.79 3.49 1.62 2.47 2.74

GRS 85.82 43.81 86.37 144.87 90.20 40.60 95.47 153.11

0% 31% 0% 0% 0% 44% 0% 0%

1981-2014 1991-2014

Intercept 7.55 4.38 3.07 3.65 8.81 7.97 3.25 4.04

15.33 7.06 3.51 3.17 14.91 12.35 3.78 3.93

2.1 1.14 2.79 5.19 2.3 1.98 3.38 5.92

LevFac 49.43 69.75 56.97

43.54 52.07 53.48

4.68 7.66 7.13

3.35 4.03 6.18

2.69 3.3 2.97

2.3 2.16 2.21

Market-

RF 4.54 3.84

5.84 4.12

5.27 2.81

6.93 3.38

1.31 1.26

1.49 1.16

SMB

0.82

2.49

0.82

2.57

0.48

1.2

HML

4.43

4.04

3.37

3.31

2.04 1.49

Adj R2 0.34 0.59 0.63 0.4 0.2 0.28 0.66 0.53

MAPE 7.55 4.49 3.29 3.79 8.81 7.97 3.47 4.20

GRS 152.70 80.15 129.57 221.95 176.40 157.11 146.85 222.71

0% 0% 0% 0% 0% 0% 0% 0%

Table 5. US 25 + 25: On this table we present the cross-sectional results for US single leverage based on new methodology (Lev), US 2-factor, US Fama-French, Global 2-factor and Global Fama-French models, for 25 US

Size-book sorted portfolios along International, Europe or UK 25 Size-book to market portfolios. We present




respective p-value. Periods is 1991-2014.

Lev US 2-

Factor

Global

2-

Factor

US FF Global

FF Lev

US 2-

Factor

Global

2-

Factor

US FF Global

FF

US 25 US 25 + International 25

Intercept 10.35 9.11 8.99 18.79 17.40 8.00 2.61 8.20 0.24 11.08

20.98 2.90 2.81 4.44 3.73 20.49 1.43 2.49 0.10 2.04

2.26 1.42 1.45 4.02 3.91 1.53 0.28 1.12 0.03 3.64

LevFac 38.17 40.63 40.48

69.98 73.76 69.64

3.98 3.52 3.63

7.03 7.94 6.06

1.42 1.61 1.61

1.94 1.89 1.87

Market-

RF 0.89 0.72 -10.18 -8.14

5.24 -1.19 5.36 -3.01

0.32 0.24 -2.46 -1.69

2.79 -0.39 1.97 -0.56

0.12 0.09 -1.76 -1.42

0.60 -0.15 0.68 -0.64

SMB

2.42 3.63

4.23 -0.37

3.42 3.71

4.74 -0.36

1.16 1.68

1.88 -0.23

HML

3.67 3.41

6.86 3.58

4.15 4.02

6.56 2.78

1.37 1.39 2.32 1.59

Adj R2 0.38 0.36 0.36 0.60 0.55 0.52 0.57 0.49 0.58 0.14

MAPE 10.35 9.11 8.99 18.79 17.40 8.00 2.95 8.20 1.85 11.08

GRS 56.75 52.69 53.21 54.95 55.58 105.06 98.11 105.36 181.31 203.12

0% 0% 0% 0% 0% 0% 0% 0% 0% 0%

US 25 + Europe 25 US 25 + UK 25

Intercept 8.83 5.35 12.15 8.09 19.46 9.33 6.88 6.95 5.34 4.74

25.43 2.51 4.23 2.42 5.53 26.00 1.21 3.22 2.22 1.68

1.82 0.54 2.15 1.51 2.67 2.03 1.21 1.46 1.32 1.42

LevFac 54.07 58.52 48.89

46.12 48.42 48.00

6.40 6.70 5.13

5.60 5.78 5.73

1.95 1.84 1.93

1.75 1.87 1.88

Market-

RF 3.14 -3.82 -1.78 -11.14

2.17 1.70 1.66 4.28

1.51 -1.46 -0.54 -3.29

1.14 0.80 0.66 1.42

0.34 -0.57 -0.34 -1.44

0.36 0.27 0.34 0.85

SMB

3.93 2.17

3.15 0.62

5.65 2.53

3.58 0.71

1.54 1.24

1.47 0.32

HML

5.12 3.26

4.69 3.36

5.58 4.00

5.25 4.41

1.84 1.37 1.58 1.41

Adj R2 0.45 0.47 0.45 0.55 0.35 0.38 0.39 0.39 0.43 0.28

MAPE 8.83 5.35 12.15 8.09 191.04 9.33 6.88 6.95 5.34 4.75

GRS 139.62 130.18 149.32 201.41 19.46 123.32 114.56 116.38 155.45 164.72

Table 6. US/International/Europe/UK-only 25: On this table we present the cross-sectional results for US single leverage based on new methodology (Lev), US 2-factor, US Fama-French, Global 2-factor and Global

Fama-French models, for 25 US/International/Europe/UK-only portfolios sorted by size-book to market. We present




respective p-value. Periods is 1991-2014.

Lev US 2-

Factor

Global

2-Factor US FF

Global

FF Lev

US 2-

Factor

Global

2-Factor US FF

Global

FF

US 25 International 25

Intercept 10.35 9.11 8.99 18.79 17.40 6.73 11.79 13.29 6.96 6.04

20.98 2.90 2.81 4.44 3.73 17.07 4.31 3.65 2.16 1.46

2.26 1.42 1.45 4.02 3.91 1.00 1.73 1.59 1.52 1.20

LevFac 38.17 40.63 40.48

97.80 72.81 80.70

3.98 3.52 3.63

5.20 3.26 3.98

1.42 1.61 1.61

1.46 1.60 1.59

Market-

RF 0.89 0.72 -10.18 -8.14

-6.72 -7.62 -3.48 -2.07

0.32 0.24 -2.46 -1.69

-1.88 -2.21 -1.03 -0.56

0.12 0.09 -1.76 -1.42

-0.93 -0.94 -0.61 -0.36

SMB

2.42 3.63

0.42 0.88

3.42 3.71

0.18 1.13

1.16 1.68

0.08 0.52

HML

3.67 3.41

9.05 5.73

4.15 4.02

5.35 6.04

1.37 1.39 2.33 2.42

Adj R2 0.38 0.36 0.36 0.60 0.55 0.52 0.57 0.56 0.63 0.63

MAPE 10.35 9.11 8.99 18.79 17.40 6.73 11.79 13.29 6.96 6.04

GRS 56.75 52.69 53.21 54.95 55.58 19.98 28.03 25.04 48.86 51.71

0.00 0.00 0.00 0.00 0.00 0.70 0.26 0.40 0.00 0.00

Europe 25 UK 25

Intercept 7.72 16.22 18.26 9.76 9.38 8.49 8.96 6.32 5.10 3.92

19.57 4.41 4.18 4.39 3.40 16.74 2.95 2.06 1.66 1.43

1.44 2.57 2.30 2.08 1.91 1.79 1.57 1.16 1.15 0.93

LevFac 54.16 34.73 49.80

39.43 39.08 38.44

3.72 2.21 3.73

2.65 2.54 2.54

1.46 1.10 1.38

1.08 1.09 1.05

Market-

RF -9.48 -10.39 -4.92 -3.06

-0.73 1.65 0.58 2.40

-2.40 -2.61 -2.26 -1.24

-0.23 0.53 0.19 0.79

-1.36 -1.31 -0.86 -0.54

-0.10 0.24 0.10 0.41

SMB

-5.29 -0.91

3.93 2.50

-3.74 -1.68

1.44 1.86

-0.95 -0.46

0.87 1.07

HML

9.20 5.54

4.13 2.48

11.52 10.65

2.73 2.73

2.15 2.22 0.93 0.86

Adj R2 0.35 0.45 0.46 0.86 0.82 0.20 0.17 0.18 0.30 0.39

MAPE 7.72 16.22 18.26 9.76 9.38 8.49 8.96 6.32 5.17 4.05

GRS 25.01 30.50 25.12 21.54 32.86 22.71 21.10 22.10 29.53 31.88

41% 17% 40% 0% 11% 54% 63% 51% 20% 0%


Size-book sorted portfolios along 6 bonds portfolios sorted by maturity and International, Europe or UK 25 Size-book

to market portfolios. We present intercept, leverage factor (LevFac) and the standard 3-factors from Fama French

models coefficients, along with the respective t-statistics, located below coefficients. T-shanken statistics are

reported beneath standard t-statistics. We also report adjusted R2, adjR2, Mean Asset Pricing Error (MAPE) and

Gibbons, Ross, Shanken statistic, along with its respective p-value. Periods is 1991-2014.

Lev US 2-

Factor

Global

2-

Factor

US FF Global

FF Lev

US 2-

Factor

Global

2-

Factor

US FF Global

FF

US 31 International 25 Size + US 31

Intercept 8.38 3.00 3.03 3.06 3.11 7.34 2.49 2.95 2.30 2.99

10.83 3.62 3.69 3.82 3.88 16.85 3.05 3.00 2.67 2.33

2.17 3.80 4.01 5.70 5.70 1.56 1.18 2.76 2.03 5.65

LevFac 55.70 53.67 51.60

72.32 73.75 78.59

3.32 3.62 5.36

6.16 8.34 7.88

1.90 1.85 1.80

1.99 1.99 2.06

Market-

RF 6.17 6.14 5.07 6.58

5.36 3.69 3.16 4.90

7.31 6.78 4.71 6.41

6.02 3.71 2.85 3.30

1.58 1.44 1.44 1.75

1.34 0.94 0.88 1.36

SMB

2.71 1.90

4.24 -0.51

3.19 2.05

4.91 -0.52

1.31 0.96

1.85 -0.31

HML

4.87 4.45

6.71 4.33

4.89 5.02

6.71 3.72

1.80 1.85 2.38 1.91

Adj R2 0.25 0.75 0.75 0.78 0.78 0.40 0.66 0.58 0.66 0.31

MAPE 8.38 3.08 3.11 3.09 3.13 7.35 2.82 3.35 2.72 3.77

GRS 109.72 106.98 111.65 158.99 158.74 155.74 148.06 139.61 282.59 296.12

0% 0% 0% 0% 0% 0% 0% 0% 0% 0%

Europe 25 + US 31 UK 25 + US 31

Intercept 8.07 2.93 3.36 2.94 3.84 8.51 3.36 3.27 2.98 2.88

18.73 3.63 3.67 3.69 3.49 18.86 3.98 3.81 3.58 3.12

1.83 1.76 3.73 5.32 5.50 2.05 2.78 3.40 4.65 5.11

LevFac 58.12 61.76 63.00

49.87 52.06 51.20

5.24 7.60 7.04

4.55 6.37 6.27

2.06 2.11 2.15

1.86 1.90 1.88

Market-

RF 5.47 4.13 3.23 3.71

5.55 5.24 4.05 6.23

6.52 4.57 3.53 3.07

6.31 5.81 3.86 5.43

1.40 1.07 0.85 1.03

1.40 1.24 1.10 1.65

SMB

4.04 1.40

3.23 0.46

5.90 1.44

3.80 0.56

1.62 0.85

1.53 0.24

HML

5.64 3.70

4.84 3.41

6.61 3.97

5.64 4.68

2.00 1.60 1.62 1.43

Adj R2 0.33 0.64 0.56 0.68 0.39 0.26 0.59 0.59 0.63 0.55

MAPE 8.07 3.04 3.52 3.11 4.10 8.51 3.53 3.42 3.19 3.24

GRS 224.28 206.01 203.44 340.76 356.38 318.36 299.39 302.32 443.45 442.39

0% 0% 0% 0% 0% 0% 0% 0% 0% 0%


Size-book sorted portfolios along 10 US portfolios sorted by maturity, International, Europe or UK 25 Size-book to

market portfolios and International, Europe Size-momentum portfolios. We present intercept, leverage factor

(LevFac) and the standard 3-factors from Fama French models coefficients, along with the respective t-statistics,

located below coefficients. T-shanken statistics are reported beneath standard t-statistics. We also report adjusted R2,

adjR2, Mean Asset Pricing Error (MAPE) and Gibbons, Ross, Shanken statistic, along with its respective p-value.

Periods is 1991-2014.

Lev US 2-

Factor

Global

2-

Factor

US FF Global

FF Lev

US 2-

Factor

Global

2-

Factor

US FF Global

FF

US 35 International 50 + US 35

Intercept 10.08 8.47 8.64 18.54 20.41 7.93 4.67 11.10 7.88 17.98

24.53 3.45 3.60 7.38 6.64 22.01 2.77 4.32 3.69 6.31

2.29 1.58 1.73 3.51 3.61 1.64 0.62 2.13 1.40 4.70

LevFac 36.33 40.29 39.79

61.45 67.36 53.01

4.35 3.91 3.92

6.02 6.44 4.34

1.57 1.66 1.64

2.02 1.83 1.65

Market-

RF 1.25 0.83 -9.81 -11.34

3.17 -3.88 -2.28 -9.86

0.57 0.38 -3.97 -3.49

1.78 -1.61 -0.96 -3.44

0.19 0.13 -1.53 -1.68

0.44 -0.61 -0.40 -1.88

SMB

2.62 4.02

3.74 -0.44

3.74 3.89

3.27 -0.55

1.26 1.68

1.74 -0.25

HML

2.73 2.26

3.80 0.64

3.01 2.58

2.71 0.57

0.99 0.92 1.28 0.27

Adj R2 0.34 0.33 0.33 0.50 0.39 0.30 0.32 0.30 0.16 0.13

MAPE 10.08 8.47 8.64 18.54 20.41 8.03 5.01 11.10 7.97 17.98

GRS 90.89 84.44 84.54 92.39 88.03 1038.44 934.47 1153.65 1709.91 1704.43

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Europe 50 + US 35 UK 25 + US 35

Intercept 8.87 9.64 15.58 21.61 24.02 9.38 7.07 7.25 9.15 8.78

23.77 4.18 5.84 8.46 9.36 28.84 4.11 4.00 4.37 3.68

1.89 1.26 3.07 3.95 4.74 2.13 1.66 1.88 2.88 2.90

LevFac 48.20 46.36 31.77

41.24 45.17 44.55

4.93 4.13 2.77

5.52 5.68 5.61

2.15 1.64 1.42

1.81 1.99 1.99

Market-

RF -1.04 -6.77 -13.90 -15.03

2.03 1.49 -1.62 0.24

-0.45 -2.82 -5.44 -5.97

1.22 0.85 -0.76 0.10

-0.14 -1.07 -2.29 -2.50

0.38 0.26 -0.36 0.05

SMB

3.28 2.26

2.48 0.56

3.50 2.51

2.90 0.68

1.33 1.35

1.18 0.29

HML

0.81 1.06

3.73 2.77

0.69 1.19

4.00 3.59

0.26 0.43 1.26 1.17

Adj R2 0.22 0.21 0.27 0.30 0.28 0.33 0.34 0.34 0.27 0.15

MAPE 8.99 9.72 15.58 21.61 24.02 9.38 7.07 7.25 9.15 8.78

GRS 1323.52 1353.77 1581.04 1520.13 1572.83 204.80 188.72 191.97 254.64 270.19

0% 0% 0% 0% 0% 0% 0% 0% 0% 0%


Size-book sorted portfolios along 10 US portfolios sorted by maturity, 6 bond maturity sorted portfolios,

International, Europe or UK 25 Size-book to market portfolios and International, Europe Size-momentum portfolios.

We present intercept, leverage factor (LevFac) and the standard 3-factors from Fama French models coefficients,

along with the respective t-statistics, located below coefficients. T-shanken statistics are reported beneath standard t-

statistics. We also report adjusted R2, adjR2, Mean Asset Pricing Error (MAPE) and Gibbons, Ross, Shanken statistic,

along with its respective p-value. Periods is 1991-2014.

Lev US 2-

Factor

Global

2-Factor US FF

Global

FF Lev

US 2-

Factor

Global 2-

Factor US FF

Global

FF

US 41 International 50 + US 41

Intercept 8.81 3.25 3.34 4.04 3.96 7.54 3.24 4.13 4.18 5.53

14.91 3.78 3.88 3.93 3.61 20.27 3.31 3.54 3.59 3.96

2.30 3.38 3.58 5.92 6.13 1.68 1.16 2.96 2.42 6.35

LevFac 43.54 53.48 52.88

60.96 69.67 70.97

3.35 6.18 6.07

5.60 6.97 6.50

2.30 2.21 2.19

2.00 2.13 2.26

Market-

RF 5.84 5.63 4.12 5.83

4.63 2.59 1.66 2.38

6.93 6.37 3.38 4.43

4.33 2.27 1.17 1.55

1.49 1.35 1.16 1.58

1.14 0.65 0.46 0.65

SMB

2.49 0.62

3.75 -0.94

2.57 0.56

3.29 -1.09

1.20 0.32

1.75 -0.55

HML

4.04 3.33

4.20 1.83

3.31 2.94

3.04 1.51

1.49 1.40 1.46 0.79

Adj R2 0.20 0.66 0.65 0.53 0.47 0.25 0.39 0.39 0.22 0.02

MAPE 8.81 3.47 3.54 4.20 4.13 7.67 3.85 4.58 4.58 5.93

GRS 176.40 146.85 150.40 222.71 227.40 1770.23 1539.75 1519.80 3129.49 3278.19

0% 0% 0% 0% 0% 0% 0% 0% 0% 0%

Europe 50 + US 41 UK 25 + US 41

Intercept 8.42 4.26 4.91 6.30 6.73 8.70 3.60 3.58 3.83 3.65

21.37 3.68 3.96 4.65 4.70 21.74 4.29 4.22 4.13 3.68

1.92 1.93 3.75 6.07 6.91 2.17 3.14 3.49 5.56 5.72

LevFac 49.07 59.14 57.76

43.22 51.16 50.37

4.60 5.74 5.43

4.48 6.74 6.63

2.20 2.56 2.61

1.90 2.17 2.15

Market-

RF 4.22 2.73 1.03 1.59

5.31 4.97 3.63 5.64

3.55 2.34 0.69 1.05

6.26 5.73 3.33 4.78

1.04 0.67 0.27 0.44

1.35 1.18 1.02 1.51

SMB

3.17 0.21

2.63 -0.07

2.81 0.20

3.00 -0.09

1.33 0.13

1.25 -0.04

HML

2.25 1.11

4.17 2.97

1.62 0.99

4.39 3.85

0.76 0.46 1.41 1.26

Adj R2 0.18 0.29 0.25 0.10 0.00 0.23 0.53 0.53 0.46 0.40

MAPE 8.57 4.81 5.36 6.59 6.97 8.70 3.81 3.77 4.02 3.98

GRS 5493.39 4706.07 4823.46 8014.77 8276.72 589.02 515.19 519.13 767.20 762.56

0% 0% 0% 0% 0% 0% 0% 0% 0% 0%

Table 10. 4-factor and 2-factor horse race: On this table we present the cross-sectional results for, US 2-factor, US 4-factors and Global 4-factors models, for 25 US Size-book sorted portfolios along 10 US

portfolios sorted by maturity, International, Europe or UK 25 Size-book to market portfolios and International,

Europe Size-momentum portfolios. We present intercept, leverage factor (LevFac) and the standard 3-factors from

Fama French models coefficients, along with the respective t-statistics, located below coefficients. T-shanken

statistics are reported beneath standard t-statistics. We also report adjusted R2, adjR2, Mean Asset Pricing Error

(MAPE) and Gibbons, Ross, Shanken statistic, along with its respective p-value. Periods is 1991-2014.

US 2-

Factor

US 4-

Factors

Global 4-

Factors

US 2-

Factor

US 4-

Factors

Global 4-

Factors

US 25 + International 25 US 31 + International 25

Intercept 2.61 2.20 12.27 2.49 2.50 2.96

1.43 0.78 2.98 3.05 2.93 2.94

0.28 0.29 2.51 1.18 2.52 3.56

LevFac 73.76 41.07 88.00 73.75 42.01 87.21

7.94 1.46 6.15 8.34 2.15 6.03

1.89 1.21 1.28 1.99 0.74 1.28

Market-

RF 5.24 4.13 -4.93 5.36 3.84 4.18

2.79 3.76 -1.21 6.02 3.32 3.56

0.60 0.53 -0.83 1.34 1.08 1.14

SMB

3.65 -0.12

3.61 -0.29

6.19 -0.16

3.92 -0.37

1.69 -0.07

1.70 -0.15

HML

7.94 4.55

7.96 5.38

1.79 4.59

6.54 5.77

2.24 1.90 2.07 2.22

Adj R2 0.57 0.59 0.51 0.66 0.68 0.57

MAPE 2.95 2.65 12.27 2.82 2.83 3.30

GRS 98.11 148.43 77.78 148.06 225.02 120.51

0% 0.00 0.01 0.00 0.00 0.00

US 35 + International 50 US 41 + International 50

Intercept 4.67 7.14 12.73 3.24 3.87 4.27

2.77 3.86 5.04 3.31 3.83 3.80

0.62 0.78 1.83 1.16 1.34 2.57

LevFac 67.36 85.32 80.64 69.67 87.63 96.56

6.44 5.64 6.06 6.97 5.82 7.31

1.83 1.37 1.50 2.13 1.46 1.79

Market-

RF 3.17 0.80 -5.17 4.63 4.32 3.07

1.78 0.38 -2.06 4.33 3.27 2.50

0.44 0.09 -0.63 1.14 1.09 0.74

SMB

2.87 0.26

2.85 0.08

2.87 0.39

2.86 0.12

1.24 0.15

1.22 0.05

HML

7.06 2.45

7.48 3.51

5.22 2.48

5.59 3.53

1.58 0.95 1.86 1.41

Adj R2 0.32 0.37 0.37 0.39 0.42 0.38

MAPE 5.01 7.21 12.73 3.85 4.27 4.62

GRS 934.47 704.72 749.21 1539.75 1162.28 1027.14

0.00 0.00 0.00 0 0.00 0.00

Table 11. Other Global Portfolios: On this table we present the cross-sectional results for US single leverage based on new methodology (Lev), US 2-factor, US Fama-French, Global 2-factor and Global Fama-French

models, for Global constructed portfolios, which already use US assets. Portfolios are, Global 25 is constructed using

25 size-book to market global portfolios, Global 50, adding 25 size-momentum portfolios to Global 25, Global 25 + 6

bonds, which includes 6 bond portfolios on Global 25 and Global 50 + 6, which include 6 bond portfolios to Global

50. We present intercept, leverage factor (LevFac) and the standard 3-factors from Fama French models coefficients,

along with the respective t-statistics, located below coefficients. T-shanken statistics are reported beneath standard t-

statistics. We also report adjusted R2, adjR2, Mean Asset Pricing Error (MAPE) and Gibbons, Ross, Shanken statistic,

along with its respective p-value. Periods is 1991-2014.

LevFac US 2-

Factor

Global

2-Factor US FF

Global

FF LevFac

US 2-

Factor

Global

2-Factor US FF

Global

FF

Global 25 Global 50

Intercept 7.65 14.70 14.16 13.58 6.04 7.97 15.82 15.35 20.14 18.53

0.34 4.56 3.94 3.67 1.46 18.68 4.51 4.40 7.71 5.78

1.57 2.95 2.42 3.38 1.20 1.73 3.42 2.87 4.01 3.80

LevFac 61.10 38.80 47.34

55.16 16.31 26.53

11.72 2.62 3.51

3.20 0.68 1.24

1.57 1.39 1.53

1.55 0.45 0.74

Market-

RF -7.85 -7.03 -8.25 -2.07

-8.76 -7.69 -14.89 -12.30

-2.30 -2.08 -2.17 -0.56

-2.34 -2.37 -5.36 -3.93

-1.21 -1.00 -1.52 -0.36

-1.32 -1.18 -2.38 -2.15

SMB

0.87 0.88

1.87 1.12

0.73 1.13

1.40 1.20

0.30 0.52

0.64 0.73

HML

5.17 5.73

0.13 0.44

4.66 6.04

0.08 0.30

1.78 2.42 0.03 0.16

Adj R2 0.52 0.59 0.57 0.66 0.63 0.16 0.22 0.22 0.38 0.21

MAPE 7.65 14.70 14.16 13.58 6.04 8.15 15.82 15.35 20.14 18.52

GRS 48.82 62.96 56.66 73.79 51.71 188.59 277.18 259.62 244.87 210.65

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Global 25 + 6 Bonds Portfolios Global 50 + 6 Bonds Portfolios

Intercept 6.51 2.83 2.74 2.76 2.41 7.30 3.63 3.59 4.73 4.39

12.94 4.05 3.99 4.57 4.23 15.92 3.24 3.20 4.02 3.45

1.84 3.61 3.60 5.15 4.34 1.90 3.87 3.74 6.37 5.90

LevFac 50.28 74.29 69.81

47.30 73.56 69.30

2.58 5.43 5.31

2.42 3.82 3.69

1.31 1.73 1.71

1.30 1.88 1.87

Market-

RF 4.66 3.68 2.79 1.16

4.19 3.18 1.04 1.08

5.66 5.08 3.27 1.51

3.31 2.86 0.69 0.72

1.05 0.98 0.75 0.33

0.91 0.82 0.28 0.31

SMB

2.71 1.21

3.98 1.46

2.38 1.86

2.37 1.36

0.99 0.74

1.48 0.97

HML

6.81 6.00

2.26 1.13

6.15 6.81

1.17 0.68

2.26 2.47 0.68 0.44

Adj R2 0.16 0.62 0.64 0.72 0.70 0.08 0.24 0.24 0.13

MAPE 6.51 2.95 2.87 2.87 2.53 7.50 4.25 4.22 5.07 4.96

GRS 103.06 71.01 75.52 137.03 78.27 436.63 296.41 314.17 606.65 437.87

0% 0% 0% 0% 0% 0% 0% 0% 0% 0%

8. Bibliography

Adrian, T. Etula, E. Muir, T. 2010. Financial Intermediaries and the Cross-Section of

Asset Returns. . Federal Reserve Bank of New York Staff Reports, No. 464. Revised

September 2013.

Adrian, T. Moench, E., Shin, H.S. 2010. Financial Intermediation, Asset Prices, and

Macroeconomics Dynamics. Federal Reserve Bank of New York Staff Reports, No.

422.

Adrian, T., Shin, H.S. 2010. Liquidity and Leverage . Journal of Financial

Intermediation 19, 418-437.

Adrian, T. Crump, R.K. Moench, E. 2011. Regression-Based Estimation of Dynamic

Asset Pricing Models. . Federal Reserve Bank of New York Staff Reports, No. 464.

Revised December 2014.

Adrian, T. Moench, E., Shin, H.S. 2013. Dynamic Leverage Asset Pricing.. Federal

Reserve Bank of New York Staff Reports, No. 625. Revised December 2014.

Adrian, T. Etula, E. Muir, T. 2015. Financial Intermediaries and the Cross-Section of

Asset Returns. . Forth coming at Journal Of Finance 2015.

Bruno, V., Shin, H.S. 2014a. Cross-Border Banking and Global Liquidity.

Forthcoming in the Review of Economic Studies.

Bruno, V., Shin, H.S. 2014b. Globalization of Corporate Risk Taking. Journal of

International Business Studies.

Bruno, V., Shin, H.S. 2014c. Capital Flows and the risk-taking Channel of monetary

Policy. Forthcoming to Journal of Monetary Economics.

Fostel A, Geanakoplos J. 2008. Lever Cycles and Anxious Economy. American

Economic Review 2008, 98:4, 1211-1244.

Fostel A, Geanakoplos J. 2013. Reviewing the Leverage Cycle. Cowles Foundation

Discussion Paper, No. 1918.

Geanakoplos J. 1997. Promises, Promises. In the Economy as an Evolving Complex

System II, ed. W.Brian Arthur, Steven Durlauf, and David Lane, 285-320. Reading,

MA: Addison-Wesley.

Geanakoplos J. 2003. Liquidity, Default, and Crashes: Endogenous Contracts in

General Equilibrium. In Advances in Economic and Econometrics: Theory and

Application, Eight World Conference, Vol. 2, 170-205. Econometric Society

Monographs.

Gibbons, M. Stephen, A. R. Shanken, J. 1989. A Test of the Efficiency of a Given

Portfolio. Econometrica.

Koudijs, P. Voth, H-S. 2014. Leverage and Beliefs: Personal Experience and Risk

Taking in Margin Lending. . National Bureau of Economic Research, Working Paper

no 19957.

Krishnamurthy, A. 2009. Amplifications Mechanism in Liquidity Crisis. National

Bureau of Economic Research.

Lewis, K.K. 2011. Global Asset Pricing. National Bureau of Economic Research,

Working Paper no 17261.

Malmendier,U. Nagel, S. 2011. Depression Babies: Do Macroeconomic Experiences

Affect Risk Taking? The Quarterly Journal of Economics.

Shanken, J. 1992. On the Estimation of Beta Pricing Models. Review of Financial

Studies.

Global Asset Pricing and Financial Intermediary Leverage - Leandro de Miranda Gomespdf

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