estimating time -varying equity risk premiumestimating time -varying equity risk premium the...
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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
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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
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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
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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 -
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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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*
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ROE, E/P and Earnings Spread July 1980 – December 2012
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Graph 1
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B/P and Earnings Spread July 1980 – December 2012
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Figure 1
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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
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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 =≥
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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
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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
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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
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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 *
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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
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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∆+=∏
=
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Time-Varying ERP Index
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Figure 2
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ERP Index in Three Sub-periods
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Estimation by Model I (all variables)
Figure 3
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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
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TOPIX Daily Volatility
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Figure 4
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ERP and Volatility
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Figure 5
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Foreign Investor’s Trading Share
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Figure 6
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Relative Return: Cumulative Index
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Figure 7A
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Relative Risk : TOPIX / MSCI xJ
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Figure 7B Rolling 60 months Standard Deviation Ratio
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Correlation: TOPIX vs. MSCI xJ
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Figure 7C
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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
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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.
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【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
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【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
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【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)