Estimating Time-Varying Equity Risk Premium The Japanese Stock Market

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1 Norhfield Asia Research Seminar Hong Kong, November 19, 2013 Esimaing Time-Varying Equiy Risk Premium The Japanese Sock Marke Ibboson Associaes Japan Presiden Kasunari Yamaguchi, PhD/CFA/CMA

2 The Universe is made of 2

3 The Dark Energy of Sock Marke Universe The risk premium is a concep ha is so cenral o our field of endeavor ha i migh properly be called he financial equivalen of a cosmological concep. Marin Leibowiz (2002) A Resul of This Sudy 3

4 Quesions on ERP (Equiy Risk Premium) Q1: How much ERP drives Marke Volailiy? Sock prices are driven no only by fundamenals bu also by ERP reflecing invesors risk aversion. Q2: How ERP moved over ime? How have ERP varied over ime in he hisory of Japanese sock marke since 1980? Bubbles & Los Decades. Q3: Why ERP changed over ime? How have domesic / foreign facors conribued o ERP variaion over ime? Why? 4

5 Equiy Risk Premium (ERP) Definiion Excess reurn over risk-free rae required by invesors who ake exra risk for invesing in equiy. Consensus? ERP is varying over ime. Supply-side esimaes are more reliable. Debaes over ERP 1. Ex-pos (hisorical) vs. Ex-ane (forward looking) ERP Puzzle 2. Demand-side (invesors) vs. Supply-side (firms) 3. Economerics (inducive) vs. Finance Theory (deducive) 4. Forecasing (fuure) vs. Predicing (conemporaneous) 5. Raional (equilibrium) vs. Behavioral (over/under-reacion) 5

6 Mehodology: Basic Ideas How o deec ime-varying ERP? Valuaion Model Regression monhly changes Time-varying ERP (λ) causes ε 6 ( ) 1 g r d P f + = λ f r g D P ε β β β α =, ε = X λ -1

7 Basic Valuaion Model Consan Growh Model Appropriae for aggregae marke for long-run Two variables () are hard o esimae! Price change is driven by; P changes in four inernal variables any oher exernal variables? Sock price goes up if Sign D : dividend nex year increase + g: expeced growh become higher + r f : risk-free ineres rae goes down - λ: risk premium goes down - = d 1 ( ) r + λ g f 7

8 Earnings Spread as Proxy for Expeced Growh Definiion g = ROE EarningsYield E E = B P 1 1 = E B P Meaning ROE: economic reurn generaed by firms by using equiy capial (BV). Source of reurn supplied o invesors. E/P: economic reurn ha invesors pay for curren income. Parly cos of capial for firms. 8

9 ROE, E/P and Earnings Spread July 1980 December 2012 Graph 1 9

10 B/P and Earnings Spread July 1980 December 2012 Figure 1 10

11 Residual Income Model Ohlson Model P = B + 0 i= = B + G 0 1 ( E r B ) E i (1 + r E ) i 1 i Equiy Capial (Book Value) NOW Presen Value of Economic Income Sream FUTURE Presen Value of Growh Opporuniy 11

12 Two Models are Consisen Earnings Spread g = E P ( P ) 1 B Solve for P/B P B = 1+ P g E Ohlson Model P = B0 + G Divide by B P = 1+ B0 G B 0 From above P E g = G B g 1 = ROE G P

13 Variables influencing sock prices Sock Prices Domesic Facors Foreign Facors ERP λ Dividend D Risk-free Rae rf Currency FX Foreign Equiy FE High correlaion Growh Rae g Yield Spread YS Inernal (Valuaion) Facors Exernal (Foreign) Facors 13

14 Regression Models Model I : all variables Model II : inernal (valuaion) variables Model III : exernal (foreign) variables 14 f FX FE YS r g D P ε β β β β β β α = 6 5 4, YS g D P ε β β β α = FX FE P ε β β α = 6 5

15 Basic Saisics Table 1 A: Descripive Saisics P D g r f FE FX YS N of Obs Median Mean Sd Dev Max Min Auocorrelaion B: Correlaion D g r f FE FX YS D g r f FE FX YS

16 Independen Variables Inernal Valuaion Facors Appendix 1 Exernal Marke Facors 16

17 Regression Summary Table 2 Period All Period 1980s 1990s 2000s from Aug-80 Aug-80 Jan-90 Jan-00 o Dec-12 Dec-89 Dec-99 Dec-12 Number of Observaions Coeff -sa Coeff -sa Coeff -sa Coeff -sa Model I Adj-R Inercep Domesic D g r f YS Foreign FE FX Model II Adj-R Inercep Domesic D g YS Model III Adj-R Foreign Inercep FE FX

18 Risk Decomposiion: TOPIX Table 3 A: Percen variance explained by facors All Period 1980s 1990s 2000s Domesic - Valuaion Facors 42.2% 39.0% 58.8% 34.8% Foreign - Marke Facors 24.7% 18.2% 19.2% 43.3% Covariance effec -16.7% -5.3% -6.8% -21.7% % explained by Facors 50.3% 52.0% 71.2% 56.5% Time-Varying ERP 49.7% 48.0% 28.8% 43.5% TOPIX Monhly Price Variaion 100.0% 100.0% 100.0% 100.0% B: Aannualized sandard deviaion aribued o facors (%, annual) All Period 1980s 1990s 2000s Domesic - Valuaion Facors Foreign - Marke Facors Covariance effec S.D. aribuable o Facors S.D. aribuable o Time-Varying ERP TOPIX annual sandard deviaion

19 How o esimae ERP? 1. ERP is a par of discoun rae in valuaion model. 2. The residual erm of sock price reurns mus change inversely by ERP changes. 3. Proporionaely muliplied by X? 4. ERP Index ERP 1 ε = X λ 1 = (1 + ) ε = 0 19

20 Time-Varying ERP Index Figure 2 20

21 ERP Index in Three Sub-periods Figure 3 Esimaion by Model I (all variables) 21

22 Discussions 1. Wha moves ERP; Volailiy or Psychology? 2. Foreign Invesor s influence and globalizaion of Japanese sock marke? 3. Macro-WACC? ERP and Ineres Raes. 22

23 Wha moves ERP? Expeced Reurn Risk Aversion (Psychology)? ERP Rf Volailiy? RISK (Sandard Deviaion) 23

24 TOPIX Daily Volailiy Figure 4 24

25 ERP and Volailiy Figure 5 25

26 Foreign Invesor s Trading Share Figure 6 26

27 Relaive Reurn: Cumulaive Index Figure 7A 27

28 Relaive Risk : TOPIX / MSCI xj Rolling 60 monhs Sandard Deviaion Raio Figure 7B 28

29 Correlaion: TOPIX vs. MSCI xj Figure 7C 29

30 Conclusions Q1: ERP and Marke Volailiy Abou half of sock marke volailiy is NOT explained by fundamenal valuaion facors. The residual mus be explained by ime-varying ERP. ERP variaion drives volailiy, no he laer driving he former. Q2: ERP s movemen over ime ERP varies slowly over ime. Trends persis over some years o one decade. In he long-run, ERP may be mean-revering. For invesmen horizon over a few years, i shows rend. Q3: Why ERP changed over ime Domesic valuaion facors have primary influence on ERP. Japan-specific facors influenced srongly in 1990 s. 30

31 Furher Research We need heory on ERP variaion Basic Ideas for Theory Capial markes clear supply of, and demand for reurns from financial asses (socks and bonds). Supply-curve vs. Demand-curve Economy experiences ho and cold saes cyclically. In shor-run, Supply-curve is sable. I changes only in long-run. Demand-curve changes as invesors risk olerance changes. Invesors risk olerance moves he shape of demand curve. Level - quaniy of risk wih ho and cold economy. 31

32 A Equiy vs. Bond Long-run Mean r Expeced Reurn (Discoun Rae) r E r B P B P E ERP S E D S B Sysemaic Risk Ho Sae of Economy Cold Full employmen Job Unemploymen Inflaion Prices Deflaion High Growh Low Scenario Probabiliy (Objecive)

33 B Equiy vs. Bond Opimisic r D B Expeced Reurn (Discoun Rae) r E r B P B ERP P E D D E S E S B Sysemaic Risk Ho Sae of Economy Cold Full employmen Job Unemploymen Inflaion Prices Deflaion High Growh Low Scenario Probabiliy (Subjecive)

34 C Equiy vs. Bond Pessimisic r D E Expeced Reurn (Discoun Rae) r E P E ERP D B D S E r B P B S B Sysemaic Risk Ho Sae of Economy Cold Full employmen Job Unemploymen Inflaion Prices Deflaion High Growh Low Scenario Probabiliy (Subjecive)

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