Estimating Time-Varying Equity Risk Premium The Japanese Stock Market 1980-2012 Ibbotson Associates Japan President Katsunari Yamaguchi, PhD/CFA/CMA Northfield Asia Research Seminar Hong Kong, November 19, 2013
Estimating Time-Varying Equity Risk Premium
The Japanese Stock Market 1980-2012
Ibbotson Associates Japan President
Katsunari Yamaguchi, PhD/CFA/CMA
Northfield Asia Research Seminar Hong Kong, November 19, 2013
The Universe is made of ……
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The Dark Energy of Stock Market Universe “The risk premium is a concept that is so central to our field of endeavor that it might properly be called the financial equivalent of a cosmological concept.” Martin Leibowitz (2002)
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A Result of This Study
Questions on ERP (Equity Risk Premium) Q1: How much ERP drives Market Volatility? Stock prices are driven not only by fundamentals but also by ERP reflecting investors’ risk aversion. Q2: How ERP moved over time? How have ERP varied over time in the history of Japanese stock market since 1980? Bubbles & Lost Decades. Q3: Why ERP changed over time? How have domestic / foreign factors contributed to ERP variation over time? Why?
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Equity Risk Premium (ERP) • Definition
– Excess return over risk-free rate required by investors who take extra risk for investing in equity.
• Consensus? – ERP is varying over time. – Supply-side estimates are more reliable.
• Debates over ERP 1. Ex-post (historical) vs. Ex-ante (forward looking) “ERP
Puzzle” 2. Demand-side (investors) vs. Supply-side (firms) 3. Econometrics (inductive) vs. Finance Theory (deductive) 4. Forecasting (future) vs. Predicting (contemporaneous) 5. Rational (equilibrium) vs. Behavioral (over/under-reaction)
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Methodology: Basic Ideas
• How to detect time-varying ERP?
• Valuation Model • Regression – monthly changes
• Time-varying ERP (λ) causes εt
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( ) **1*
grdP
f −+=
λ
ttfttt rgDP εβββα +∆⋅+∆⋅+∆⋅+=∆ ,3*
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ε t = X・λ-1
Basic Valuation Model • Constant Growth Model
– Appropriate for aggregate market for long-run – Two variables (*) are hard to estimate! – Price change is driven by;
• changes in four “internal” variables • any other “external” variables?
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( ) **1*
grdP
f −+=
λ
Stock price goes up if Sign
D : dividend next year increase +
g*: expected growth become higher +
rf : risk-free interest rate goes down -
λ: risk premium goes down -
Earnings Spread as Proxy for Expected Growth • Definition
• Meaning – ROE: economic return generated by firms by using equity
capital (BV). Source of return supplied to investors. – E/P: economic return that investors pay for current income.
Partly cost of capital for firms.
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EPB
PE
BE
eldEarningsYiROEg
⋅
−=
−=
−=
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*
ROE, E/P and Earnings Spread July 1980 – December 2012
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Graph 1
B/P and Earnings Spread July 1980 – December 2012
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Figure 1
Residual Income Model
• Ohlson Model
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( )
GBr
BrEBPi
iE
iEi
+=+
⋅−+= ∑
∞
=
−
0
1*
1*
0*
)1(
Equity Capital (Book Value)
NOW
Present Value of Economic Income Stream
FUTURE
Present Value of Growth Opportunity
Two Models are Consistent
• Earnings Spread ⇒
• Ohlson Model ⇒ From above… ⇒
( )1* −= BP
PEg
*1 gEP
BP ⋅+=
Solve for P/B
*0
* GBP +=0
*
0
*1 B
GB
P +=Divide by B
BGgE
P ** =⋅P
GROE
g **
1 =≥
Variables influencing stock prices
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Growth Rateg*
DividendDt
Yield SpreadYS
Risk-free Raterf
DomesticFactors
CurrencyFX
Foreign EquityFE
ForeignFactors
ERPλ
Stock Prices
Internal (Valuation) Factors
External (Foreign) Factors
High correlation
Regression Models
Model I : all variables Model II : internal (valuation) variables Model III : external (foreign) variables
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tttt
tfttt
FXFEYS
rgDP
εβββ
βββα
+∆⋅+∆⋅+∆⋅+
∆⋅+∆⋅+∆⋅+=∆
654
,3*
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ttttt YSgDP εβββα +∆⋅+∆⋅+∆⋅+=∆ 4*
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tttt FXFEP εββα +∆⋅+∆⋅+=∆ 65
Basic Statistics
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Table 1
A: Descriptive Statistics⊿P ⊿D ⊿g ⊿r f ⊿FE ⊿FX ⊿YS
N of Obs 389 389 389 389 389 389 389
Median 0.004 0.003 0.000 -0.030 0.011 0.001 -0.032Mean 0.003 0.003 -0.014 -0.020 0.007 -0.002 -0.017Std Dev 0.054 0.047 0.200 0.254 0.044 0.033 0.487
Max 0.182 0.263 0.727 1.120 0.114 0.101 5.311Min -0.204 -0.173 -1.214 -1.270 -0.220 -0.150 -3.430
Autocorrelation 0.109 -0.278 -0.026 0.104 0.095 0.029 0.090
B: Correlation⊿D ⊿g ⊿r f ⊿FE ⊿FX ⊿YS
⊿D 1.000⊿g 0.229 1.000⊿r f -0.071 -0.065 1.000⊿FE 0.214 0.328 -0.017 1.000⊿FX 0.064 0.005 0.150 -0.042 1.000⊿YS 0.027 0.140 0.508 0.098 0.110 1.000
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Independent Variables Internal Valuation Factors External Market Factors
Appendix 1
Regression Summary
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Table 2 Period All Period 1980s 1990s 2000s
from Aug-80 Aug-80 Jan-90 Jan-00to Dec-12 Dec-89 Dec-99 Dec-12
Number of Observations 389 113 120 156
Coeff t-stat Coeff t-stat Coeff t-stat Coeff t-stat
Model I Adj-R2 0.503 0.520 0.712 0.565
Intercept 0.08 0.39 0.94 3.20 * 0.05 0.13 -0.38 -1.37
Domestic ⊿D 34.99 8.09 * 49.18 5.67 * 26.73 3.74 * 14.87 2.65 *⊿g 9.65 9.11 * 4.81 2.60 * 14.35 8.79 * 7.48 4.80 *⊿r f -1.50 -1.65 -11.60 -4.50 * -10.98 -5.95 * 8.24 3.47 *⊿YS 1.41 2.97 * 10.00 4.19 * 10.91 7.90 * 0.12 0.25
Foreign ⊿FE 0.37 7.87 * 0.18 2.43 * 0.30 3.13 * 0.45 7.47 *⊿FX 0.07 1.09 0.03 0.36 0.04 0.46 0.33 3.25 *
Model II Adj-R2 0.422 0.390 0.588 0.348
Intercept 0.37 1.74 1.41 4.42 * 0.63 1.61 -0.45 -1.33
Domestic ⊿D 40.89 8.92 * 63.37 6.90 * 45.82 5.78 * 25.46 3.81 *⊿g 12.19 11.20 * 7.58 3.92 * 14.70 7.76 * 12.83 7.36 *⊿YS 1.23 2.83 * 0.37 0.40 4.13 4.31 * 0.35 0.62
Model III Adj-R2 0.247 0.182 0.192 0.433
Foreign Intercept -0.10 -0.41 1.24 3.30 * -1.13 -2.03 * -0.35 -1.12
⊿FE 0.61 11.31 * 0.43 5.03 * 0.79 5.47 * 0.61 9.67 *⊿FX 0.12 1.62 -0.07 -0.70 -0.05 -0.34 0.53 4.89 *
Risk Decomposition: TOPIX
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Table 3 A: Percent variance explained by factors
All Period 1980s 1990s 2000s
Domestic - Valuation Factors 42.2% 39.0% 58.8% 34.8%Foreign - Market Factors 24.7% 18.2% 19.2% 43.3%Covariance effect -16.7% -5.3% -6.8% -21.7%% explained by Factors 50.3% 52.0% 71.2% 56.5%
Time-Varying ERP 49.7% 48.0% 28.8% 43.5%
TOPIX Monthly Price Variation 100.0% 100.0% 100.0% 100.0%
B: Aannualized standard deviation attributed to factors (%, annual)All Period 1980s 1990s 2000s
Domestic - Valuation Factors 12.3 9.3 17.2 10.5Foreign - Market Factors 9.4 6.4 9.8 11.8Covariance effect -7.7 -3.4 -5.9 -8.3S.D. attributable to Factors 13.4 10.7 18.9 13.4
S.D. attributable to Time-Varying ERP 13.3 10.3 12.1 11.8
TOPIX annual standard deviation 18.9 14.9 22.4 17.9
How to estimate ERP?
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1. ERP is a part of discount rate in valuation model.
2. The residual term of stock price returns must change inversely by ERP changes.
3. Proportionately multiplied by X ?
4. ERP Index
Xt ×∆=∆λ
ε 1
)11(0 t
t
ttERP
ε∆+=∏
=
Time-Varying ERP Index
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Figure 2
ERP Index in Three Sub-periods
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Estimation by Model I (all variables)
Figure 3
Discussions
1. What moves ERP; Volatility or Psychology?
2. Foreign Investor’s influence and globalization of Japanese stock market?
3. Macro-WACC? ERP and Interest Rates.
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What moves ERP?
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Volatility?
Risk Aversion (Psychology)?
ERP
RISK (Standard Deviation)
Expected Return
Rf
TOPIX Daily Volatility
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Figure 4
ERP and Volatility
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Figure 5
Foreign Investor’s Trading Share
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Figure 6
Relative Return: Cumulative Index
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Figure 7A
Relative Risk : TOPIX / MSCI xJ
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Figure 7B Rolling 60 months Standard Deviation Ratio
Correlation: TOPIX vs. MSCI xJ
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Figure 7C
Conclusions
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Q1: ERP and Market Volatility About half of stock market volatility is NOT explained by fundamental valuation factors. The residual must be explained by time-varying ERP. ERP variation drives volatility, not the latter driving the former. Q2: ERP’s movement over time ERP varies slowly over time. Trends persist over some years to one decade. In the long-run, ERP may be mean-reverting. For investment horizon over a few years, it shows trend. Q3: Why ERP changed over time Domestic valuation factors have primary influence on ERP. Japan-specific factors influenced strongly in 1990’s. Global factors (i e Lehman Euro etc ) caused jumps in
Further Research – We need theory on ERP variation
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Basic Ideas for Theory • Capital markets clear supply of, and demand for
returns from financial assets (stocks and bonds). • Supply-curve vs. Demand-curve
• Economy experiences hot and cold states
cyclically.
• In short-run, • Supply-curve is stable. It changes only in long-run. • Demand-curve changes as investors’ risk tolerance
changes.
• Investors’ risk tolerance moves the shape of demand curve. • Level - quantity of risk with hot and cold economy.
【A】 Equity vs. Bond Long-run Mean
Hot State of Economy Cold Full employment Job Unemployment
Inflation Prices Deflation
High Growth Low
Scenario Probability (Objective)
D
SE
SB
ERP
Systematic Risk
Expected R
eturn (D
iscount Rate)
r
rE
rB
PE
PB
【B】 Equity vs. Bond Optimistic
Scenario Probability (Subjective)
SE
SB
ERP
Systematic Risk
r
rE rB
DB
DE
D
PE
PB
Expected R
eturn (D
iscount Rate)
Hot State of Economy Cold Full employment Job Unemployment
Inflation Prices Deflation
High Growth Low
【C】 Equity vs. Bond Pessimistic
Scenario Probability (Subjective)
SE
SB
ERP
Systematic Risk
r
rE
rB DB
DE
D PE
PB
Hot State of Economy Cold Full employment Job Unemployment
Inflation Prices Deflation
High Growth Low
Expected R
eturn (D
iscount Rate)