John H. Cochrane. April University of Chicago Booth School of Business

Transcription

1 Comments on "Volatility, the Macroeconomy and Asset Prices, by Ravi Bansal, Dana Kiku, Ivan Shaliastovich, and Amir Yaron, and An Intertemporal CAPM with Stochastic Volatility John Y. Campbell, Stefano Giglio, Christopher Polk, and Robert Turley John H. Cochrane University of Chicago Booth School of Business April

2 A skeptic s questions Do long run risks/recursive utility matter? (E t+1 E t ) ln m t+1 = γ c t+1 + (1 γ) j=1 β j c t+j E (Rt+1 e ) = cov(re t+1, c t+1)γ + cov(rt+1 e, β j c t+j ) (γ 1) j=1 Are people really afraid of j=1 βj c t+1+j holding constant c t? Is j=1 βj c t+1+j the second factor? Is there really much variation in E t j=1 βj c t+1+j not reflected in current state variables ( c t+1?)? Long run risks does not necessarily mean recursive utility, sensitivity to news

3 More skeptic s questions (E t+1 E t ) ln m t+1 = γ c t+1 + (1 γ) j=1 β j c t+j E (Rt+1 e ) = cov(re t+1, c t+1)γ + cov(rt+1 e, β j c t+j ) (γ 1) j=1 Does time-varying consumption volatility σ 2 t ( c t+1 ) generate time-varying expected returns σ t ln m t+1? (Vs. time-varying risk aversion; habits or leverage, etc.) Is there really enough variation in σ t ( c t+1 )? (factor of 2) Is there really much variation in j=1 βj σ 2 ( ) t ct+1+j?

4 Paper 1 answers: persistent volatility? Is there really much variation in E t j=1 βj c t+1+j?, σ t ( c t+1 )? j=1 βj σ 2 ( ) t ct+1+j? 1. RV t = j=0 ip2 t j /12 = realized industrial production volatility. 2. Forecast RV t+1 from VAR using annual data from 1930 c t y t r t pd t RV t R 2 RV t (0.001) (0.001) (0.001) (0.001) (0.004) 3. Assume σ 2 t ( c t+1 ) = E t RV t+1! ( permanent income? GE? ) 4. Even so, little persistence, little long-run volatility j=1 βj σ 2 ( ) t ct+1+j?

5 10 Realized ip volatility Consumption growth

6 Table 8: VAR Estimation Results c t y t r t pd t RV t R 2 c t (0.028) (0.036) (0.001) (0.001) (0.193) y t (0.056) (0.078) (0.001) (0.001) (0.452) r t (4.335) (5.448) (0.110) (0.075) (30.751) pd t (4.060) (5.026) (0.104) (0.085) (33.888) RV t (0.001) (0.001) (0.001) (0.001) (0.004)

7 Is volatility an important Merton state variable? Does volatility matter to long-run investors? Is volatility the missing second factor for which hml is proxy? w t = 1 Σt 1 E t (Rt+1 e γ ) + β η t R,z = market-time + hedge t γ t γ t = WV WW (W, z) ; η V W (W, z) t = V Wz (W, z) V W (W, z) E t (R e t+1 ) = cov t (R e t+1, Rem t+1 )γm t cov t (R e t+1, z t+1)η m t Is η large for z t = σ 2 t? (Theory) Is cov t (hml t, σ 2 t ) large? (CGPR is about the hedging component /unconditional means only)

8 Bond price Is η = V Wz /V W large for z t = σ 2 t? Example Campbell/Wachter: Long-run bond is the riskless asset for a long-run investor Time 2. The long run bond investor does not care about volatility. V (W, yield) not V (W, σ 2 (yield)) 3. (Long run: Thinking about long-run bond investing as one period mean/variance, + state variable hedging, is nuts. )

9 Do long-run investors care about volatility? 1. Ex. 2: Max EU(W T ) investor correctly ignores short term changes in volatility because it does not much affect σ 2 (R 0 T ) = σ 2 ( r t+j ) 2. Is there variation in long-run volatility? Paper: Do it right with theory: η, V Wz. Recursive utility machinery to derive

10 Do long-run investors care about volatility? Doing it right with Theory 1. Recursive utility machinery to derive η, V Wz. 2. Yes, this investor cares (ω), about long-run volatility E t r i,t+1 r ft = γ cov t (r i,t+1, N CF,t+1 ) + cov t (r i,t+1, N DR,t+1 ) 1 2 ω(γ,..) cov t [r i,t+1, N V,t+1 ] (18) N V,t+1 = (E t+1 E t ) ρ j 1 σ 2 t+j (r t+j ) j=0 3. Is there variation in long-run volatility? (Again)

11 Paper 2: Is there variation in long run volatility? Step 1: Create EVAR forecast of realized volatility. r t RVAR t PE t TY t DEF t VS t R 2 RVAR t % (0.021) (0.061) (0.007) (0.002) (0.006) (0.008) EVAR t = E t (RVAR t+1 ), keeping all the coeffi cients.

12 This graph is a dramatic failure.

13 Step 2: VAR for EVAR r t EVAR t PE t TY t DEF t VS t r t (se) (0.082) (0.93) (0.039) (0.009) (0.028) (0.047) EVAR t (se) (0.005) (0.085) (0.007) (0.001) (0.004) (0.008) PE t (se) (0.079) (0.88) (0.037) (0.008) (0.027) (0.044) TY t (se) (0.37) (4.01) (0.160) (0.039) (0.13) (0.20) DEF t (se) (0.20) (1.82) (0.080) (0.020) (0.064) (0.10) VS t (se) (0.073) (0.74) (0.033) (0.008) (0.025) (0.041) Step 3: Calculate N V = (E t E t 1 ) ρ j 1 EVAR t+j Using these point estimates Danger: spurious forecasts from slow moving variables dominate long-run

14 C umulative return % The big recent data point Vix Hml Rm Issue 1: Why do you hold the market as σ rises from = to = 0.64? w t = 1 E t (Rt+1 e ) γ t σ 2 t (R t+1 e ) + β R,z η t γ t

15 C umulative return % The big recent data point Vix Hml Rm Issue 2: is hml really a great volatility hedge? Is volatility really the explanation for hml?

16 Is volatility the extra state variable that explains the value effect? We should just be pricing hml, not the 25! FF : E (R ei ) = b i E (rmrf ) + h i E (hml) + s i E (smb) R ei = b i rmrf + h i hml + s i smb; R 2 = 0.95

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19 Why does beta spread disappear in the earlier period? Why to the volatility betas change sign in the earlier period? Where do the betas come from? (Cash flow, discount rate, volatility)

20 Betas Why does beta spread disappear in the earlier period? Why to the volatility betas change sign in the earlier period? Where do the betas come from? (Cash flow, discount rate, volatility) What about the FF factor structure? How much R 2 is absorbed by variance in the time-series regression R ei t = α i + b i rmrf t + h i hml t + s i smb t + ε i t; R 2 = 0.95 R ei t = a i + d i N DRt + c i N CFt + v i N Vt ε i t; R 2 =? Again, Fama and French tell us that you price the 25 if you price hml. Does this price hml? What s the correlation of hml and N V?

21 Bottom line: 1. Hooray for the long run! p t d t = j=1 ρ j 1 r t+j ρ j 1 d t+j j=1 ρ j 1 r t+j = ρ j 1 d t+j (p t d t ) j=1 j=1 1.1 Prices, long-run returns not one-period returns 1.2 Long run betas are all cashflow betas 1.3 State variables disappear from long run portfolio / equilibrium problems. 2. Not convinced yet on recursive utility, long run news shocks, that volatility is the crucial state variable (not, say nontraded income) explaining value, or very persistent volatility.