Long-Run Stockholder Consumption Risk and Asset Returns Malloy, Moskowitz and Vissing-Jørgensen
Outline Introduction Equity premium puzzle Recent contribution Contribution of this paper Long-Run Risk Model Recursive utility function & Non iid consumption growth SDF and Euler equation Data Household-level consumption data Aggregation of the data Estimation Result Stockholder, Top stockholder, Nonstockholder Results with factor-mimicking portfolio Conclusion 1
INTRODUCTION 2
Motivation C-CAPM with CRRA utility function and iid (or short memory) consumption growth are unable to generate a high equity premium or low risk-free rate We need tremendously high risk aversion coefficient in order to explain the actual U.S. equity premium. Equity Premium Puzzle (Mehra and Prescott(1985)) 3
Motivation A number of solutions have been proposed, but still a puzzle. habit preference, rare disaster, transaction cost, liquidity GOAL Explain the cross-sectional variation of risk premium by consumption-based asset pricing model with plausible risk aversion coefficient. 4
Recent Contribution Long-Run Risk Model (Bansal and Yaron (2004) etc.) Recursive utility function with non iid consumption growth Asset returns are affected by the long-term future consumption risk. Limited Stock Market Participation Model (Vissing- Jørgensen (2002) etc.) Not all of the consumers take part in the capital markets. Stockholders bear a disproportionate amount of aggregate consumption risk relative to nonstockholders. 5
Contribution of this paper Malloy, Moskowitz and Vissing-Jørgensen (2009, henceforth MMV) intersects the recent literature on the long-run risk model and the limited stock market participation. MMV show that the long-run consumption risk of households who hold financial assets is particularly relevant for asset pricing. Their structural estimate of the risk aversion coefficient implied by the premium for stockholders is around 15, and for the wealthiest third of the stockholders is around 10. On the other hand, the implied risk aversion coefficient for nonstockholders is ranging from about 50 to 100 6
Long-Run Risk Model 7
Long-Run Risk Model Recursive Utility Function Non iid Consumption Growth Process Long-run component in consumption growth process 8
Why Recursive Utility Function? Problem of CRRA Utility Function Risk aversion EIS RRA= EIS= We need high RRA in order to explain actual equity premium EIS becomes low Risk-free rate becomes very high Risk-free rate puzzle by Weil (1989) 9
Recursive Utility Function Let Certainty equivalence of future utility Recursive utility function is CES utility function with C t and CE t RRA= EIS= MMV mainly focus on the case where the EIS=1 The empirical results when EIS 1 are similar to EIS=1 10
Non iid Consumption Growth Process The growth of consumption follows MA( ), NOT iid Empirical support for the long-run component of consumption growth, for example, Colacito and Croce (2008), Hansen, Heaton and Li (2008) Literatures on the Long-run risk model often use stochastic volatility in consumption process, but MMV don t. 11
SDF and Euler Equation Stochastic Discount Factor Euler Equation Unexpected innovation about the discounted value of future consumption growth Unconditional Covariances Covariances of Conditional Expectations 12
SDF and Euler Equation Problem: Estimating conditional expectations is difficult task with the household-level consumption data since it spans only 23 years If Expected excess returns are constant over time The covariance between is identical across the set of test assets and We can ignore the second term of the right hand side or regard it as constant MMV mainly use unconditional covariances only and use conditional covariances for robustness check 13
DATA 14
Data Consumption Data Household-level consumption data from Consumer Expenditure Survey (CEX) for the period March1982 - November 2004. MMV make three groups from CEX, 1. stockholders, 2. wealthiest third of stockholders (top stockholders), 3. nonstockholders Aggregate per capita nondurable and service consumption growth rates from NIPA from June 1959 to November 2004. Asset Returns Data The returns of the 25 size and book-to-market equity sorted portfolios of Fama and French from July 1926 to November 2004. The returns on eight Treasury bond portfolios with average maturities of 3 months, 1, 2, 5, 7, 10, 20 and 30 years, obtained from CRSP for the period March1982 - November 2004. 15
Aggregation of Household Consumption The average growth rate from t to t+1 for a group g (e.g., stockholders) The number of households in group g in quarter t The quarterly log consumption of household h in group g for quarter t The Euler equation becomes following cross-sectional regression Estimate and via GMM (assume =0.95 1/4 ) with S=1,2,4,8,12,16,20, 24. 16
ESTIMATION RESULTS 17
Regression Result stockholder 18
Regression Result top stockholder 19
Regression Result nonstockholder 20
Graphical interpretation 21
Factor-Mimicking Portfolios Measuring long-run risks with CEX data is challenging since the sample size of CEX is small. Construct factor-mimicking portfolios that allow a longer time series of data. The consumption growth factor portfolio, CGF, is created by estimating the following regression. Estimate the cross sectional regression with CGF, instead of 22
Regression Result with CGF 23
Robustness check with other assets MMV use three other assets instead of 25 Fama-French portfolios for robustness check. 1. CRSP value-weighted index 2. Bond portfolios 3. Individual stocks 24
Regression result for other assets 25
Graphical Interpretation-bond portfolio 26
Conclusion Long-run stockholder consumption risk captures the return premia associated with size and value portfolios, the aggregate stock market, bond portfolios, and the entire cross-section of stocks with a moderate risk aversion coefficient of about 10 for the wealthiest stockholders. There are still open questions How do these long-run patterns emerge as an equilibrium outcome? Why stockholders take on more of the aggregate consumption risk? These research will improve our knowledge of what is driving these long-run relationship. 27