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)