Persistence, Predictability and Portfolio Planning M.J. Brennan - PowerPoint PPT Presentation

Persistence, Predictability and Portfolio Planning M.J. Brennan – UCLA Yihong Xia – University of Pennsylvania

Stocks are sometimes cheap and sometimes dear. Important for long run investors? Price/10 year Average Earnings 1880-2003 50 45 2000 40 1929 35 Price-Earnings Ratio 30 1901 1966 25 20 15 10 5 0 1860 1880 1900 1920 1940 1960 1980 2000 2020 Year

Background � Academic studies have found: • stock returns predictable by such variables as Dividend yield, B/M, interest rates etc • But virtually no out of sample return predictability � Does this mean that investors should ignore time variation in returns and behave as though expected returns constant? � NO!

We show that: � Return predictability that is of first order importance to long run investors will be: • associated with large price variation. • hard to detect using standard regression framework even when a perfect signal is available • hard to estimate for portfolio planning purposes � A promising alternative to popular academic predictors is forward looking forecasts of long run returns from DDM • Convert long run forecasts to short run

A Simple Model of Return Predictability dP = μ + σ dt dz P P P μ = κ μ − μ + σ ( ) d dt dz μ μ Mean reverting expected return �

Parameters for simulations chosen so that: � Unconditional distribution of μ is fixed at μ = ν = N ( 9 %, 4 %) • � varies a lot: 1 sigma interval (5% to 14%) � Consistent with a 14% annual stock return volatility � Risk free rate is constant at 3%, implying 6% equity premium. � Nine scenarios from the combination of ( ) κ = ρ = = − − 0 . 02 , 0 . 10 , 0 . 5 , and corr dz P dz , 0 . 0 , 0 . 5 , 0 . 9 u

Strategy Use this (simulation) model to show this amount of expected return variability • Implies big variability in prices • Little short run return predictability an dis hard to detect • Possibly strong long run return predictability Later we will show: • The data consistent with this amount of predictability • How to exploit it

P/D Ratios implied by the scenarios dD = + σ � Dividend Process: gdt dz D D D � Expected Rate of Return: + ⎡ ⎤ E Ddt dV ⎥ = μ μ = κ μ − μ + σ dt ⎢ d ( ) dt dz ⎣ ⎦ V μ μ � Differential equation allows us to solve for price as a function of dividend growth rate: P (D, μ ) = Pv( μ )

Dividend yields can vary a lot as μ changes even though dividend growth assumed constant (g = 1.85%) 10% 9% mubar-sig 8% mubar mubar+sig 7% 6% 5% c 4% 3% 2% 1% 0% 1 2 3 4 5 6 7 8 9

� Under our scenarios • Prices vary a lot • Expected returns vary a lot (5%-13%) � Are we likely to detect this predictability by regressing returns on � (or proxies for � )? + τ = + μ + ε R t t ( , ) a b + τ t t t ,

Distribution of corrected t -ratios on the predictor using 70 years of simulated monthly returns 3 25% Median 2.5 75% 2 1.5 1 0.5 0 1 2 3 4 5 6 7 8 9 Scenario

R 2 (%) in an Annual Return Predictive Regression (70-years simulated returns) 14 25% 12 Median 75% 10 8 6 4 2 0 1 2 3 4 5 6 7 8 9

R 2 as a function of horizon for different values of κ and ρ 0.8 k=0.02,rh0=-0.9 k=0.10,rh0=-0.9 0.7 k=0.50,rh0=-0.9 k=0.02,rh0=-0.5 k=0.10,rh0=-0.5 k=0.50,rh0=-0.5 0.6 k=0.02,rh0=0.0 k=0.10,rh0=0.0 k=0.50,rh0=0.0 0.5 0.4 0.3 0.2 0.1 0.0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Years

� Short run predictability is hard to detect and measure. � Would it be valuable if we could detect it? e.g observe �

Economic Value of Market Timing � Investor is assumed to maximize expected CRRA utility ( RRA = 5) over terminal wealth. � Measure economic value using certainty equivalent wealth ratio between different strategies (CEWR) • Optimal dynamic strategy • Myopic strategy • Unconditional strategy

Value of (optimal) dynamic strategy relative to unconditional strategy: CEW(O)/CEW(U) (T=20, σ P =0.14, σ μ =0.04, μ = 9%=mubar) Scenario (vi) ρ =-0.9, κ =0.1 1.6 1.5 1.4 R W 1.3 E C 1.2 1.1 1 0.5 -0.9 kappa 0.1 -0.5 rho 0 0.02

Value of (optimal) dynamic strategy relative to myopic strategy: CEW(O)/CEW(M) (T=20, σ P =0.14, σ μ =0.04, μ = 9%=mubar) Scenario (vi) ρ =-0.9, κ =0.1 1.60 1.50 1.40 Ratio 1.30 CEW 1.20 1.10 1.00 -0.9 0.5 -0.5 rho 0.1 kappa 0 0.02

Value of Market Timing (CEWR ou ) for Investors with 20-year horizon 1 year R 2 tells us nothing about value of timing 1.6 κ =0.1 ρ =-0.9 κ =0.5 1.5 ρ =-0.9 R 2 =4.8% 1.4 u o R W E κ =0.5 C κ =0.02 1.3 ρ =-0.5 ρ =-0.9 R 2 =7.4% 1.2 κ =0.5 1.1 ρ =0.0 1.0 0.04 0.045 0.05 0.055 0.06 0.065 0.07 0.075 0.08 One-Year R 2

� Market timing valuable if we could observe � . � But in practice we can only rely on proxies for � (dividend yields) and badly estimated regression coefficients. � A better approach is to rely on direct estimates of � that do not rely on regression estimates

A Forward-Looking Method: DDM Model [ ] E D ∞ � DCF approach = ∑ + τ t t P ( ) τ + t 1 k τ = 1 t • Forecasts of future dividends provided by analysts yield current estimates of long run expected returns on stocks, k t • Problem: How to map k into short run expected rate of return μ μ = κ μ − μ + σ d ( ) dt dz μ μ

DDM approach to estimating � If we know the parameters of the Vasicek interest rate model � we can infer the short rate, r, from the long rate, l. In same way, if we know the parameters of � μ = κ μ − μ + σ μ d ( ) dt dz μ we can infer � from k t Iterative procedure for inferring � and updating parameters � Also estimate model in which dividend growth rate follows O- � U process:

Four DDM k series • Arnott & Bernstein (A&B) (2002), and Ilmanen (IL) (2003) • 1950.1 - 2002.2 quarterly • real, ex-post (back-casted) • based on smoothed GDP growth rate • Barclays Global Investors (BGI) and Wilshire Associates (WA) • 1973.1 to 2002.2 monthly – converted to quarterly • nominal, ex-ante (real time) • using I/B/E/S consensus estimates

Estimates of μ from the WA DDM k series (1973.Q1 to 2002.Q2) 30% 25% k4 μ4,1 20% μ4,2 15% 10% 5% 0% 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 200303 -5%

Estimated μ process parameters � Similar across 4 models and Close to scenario (vi) Real Nominal Scenario (A&B) (IL) (BGI) (WA) (vi) 0.085 0.122 0.091 0.122 κ μ 0.1 (0.083) (0.115) (0.085) (0.095) 0.017 0.0196 0.024 0.034 σ μ 0.018 (0.017) (0.022) (0.021) (0.027) 0.042 0.040 0.056 0.068 ν μ 0.04 (0.042) (0.047) (0.052) (0.061) -0.98 -0.88 -0.81 -0.68 ρ μ P -0.9 (-0.98) (-0.89) (-0.66) (-0.71)

Statistical Significance: In-Sample Quarterly Predictive Regressions � Regression: ⎡ − κ ⎤ − 0 . 25 1 . 0 e + = + μ + ε , 2 i ⎢ ⎥ R ( t , t 0 . 25 ) a a κ 0 1 t t ⎣ ⎦ = i 1 (A & B) , 2 (IL) , 3 (BGI) , 4 (WA) � Theoretical value: a 1 =1.0

In-Sample Quarterly Predictive Regressions Results a_1 R 2 Predictor N (%) H0: a_1=1 0.874 209 μ 1,2 1.43 [1.60] (1950.Q2 – 2002. Q2) 0.701 209 μ 2,2 1.12 [1.27] (1950.Q2 - 2002. Q2) 1.026 117 μ 3,2 2.89 [1.69] (1973.Q2 to 2002.Q2) 0.924 117 μ 4,2 2.74 [1.66] (1973.Q2 to 2002.Q2)

Economic Importance: Simulation of Market Timing and Unconditional Strategies � RRA = 5 μ − * = r � Unconditional Strategy: x γσ 2 P � Optimal Market Timing: μ − * = r x t plus hedging terms γσ 2 P � Risky asset: S&P500 � Riskless asset: 30 day T-Bill

Proportion of Wealth Invested in Stocks 1.2 Unconditional (based on full sample mean) Unconditional (based on gradually updated sample mean) Optimal 1.0 0.8 0.6 0.4 0.2 0.0 Mar-73 Mar-75 Mar-77 Mar-79 Mar-81 Mar-83 Mar-85 Mar-87 Mar-89 Mar-91 Mar-93 Mar-95 Mar-97 Mar-99 Mar-01

Wealth under optimal and unconditional Strategies for a 20-year horizon constrained investor using μ 4,2 (RRA = 5, 1973.Q2 -1993.Q1) 12 10 uncondtional optimal 8 6 4 2 0 Sep-73 Sep-75 Sep-77 Sep-79 Sep-81 Sep-83 Sep-85 Sep-87 Sep-89 Sep-91

Wealth under optimal and unconditional Strategies for a 9-year horizon constrained investor using μ 4,2 (RRA = 5, 1993.Q2 - 2002.Q2) 2.5 Unconditional 2.0 Optimal 1.5 1.0 0.5 0.0 Jun-93 Jun-95 Jun-97 Jun-99 Jun-01

Wealth under optimal and unconditional Strategies for a 29-year horizon constrained investor using μ 4,2 (RRA = 5, 1973.Q2 – 2002.Q2) 25 20 uncondtional optimal 15 10 5 0 Jun-73 Jun-76 Jun-79 Jun-82 Jun-85 Jun-88 Jun-91 Jun-94 Jun-97 Jun-00

Conclusion � Time-varying expected returns economically important, even though • Hard to detect, measure � Substantial benefit from the optimal strategy � DDM discount rates are a useful input for long run investor. � Long run investors (pension, insurance) should hedge against changes in investment opportunities.