Dynamic Consumption and Portfolio Choice with Stochastic Volatility in Incomplete Markets

This paper analyzes optimal portfolio choice and consumption with stochastic volatility in incomplete markets. Using the Duffie-Epstein (1992) formulation of recursive utility in continuous time, it shows that the optimal portfolio demand for stocks under stochastic volatility varies strongly with the investor's coefficient of relative risk aversion, but only slightly with her elasticity of intertemporal substitution;by contrast, optimal consumption relative to wealth depends on both preference parameters. This paper also shows that stochastic variation in volatility produces an optimal intertemporal heding demand for stocks which is negative when changes in volatility are instantaneously negatively correlated with excess stock returns and investors have coefficients of relative risk aversion larger than one. The absolute size of this demand increase with the size of this correlation, and also with the persistence of shocks to volatility. An application to the US stock market shows that empirically this correlation is negative and large, which implies a negative hedging demand for stocks. This application also shows that only low frequency shocks to volatility exhibit enough persistence to generate sizable hedging demands by long-term, risk averse investors. A comparative statics exercise shows that the size of hedging deamnds is considerably more sensitive to changes in correlation.Intertemporal portfolio choice, continuous-time, stochastic volatility, long-term investors, recursive utility, characteristic function, spectral GMM.

Dynamic Consumption and Portfolio Choice with Stochastic Volatility in Incomplete Markets

This paper analyzes optimal portfolio choice and consumption with stochastic volatility in incomplete markets. Using the Duffie-Epstein (1992) formulation of recursive utility in continuous time, it shows that the optimal portfolio demand for stocks under stochastic volatility varies strongly with the investor's coefficient of relative risk aversion, but only slightly with her elasticity of intertemporal substitution; by contrast, optimal consumption relative to wealth depends on both preference parameters. This paper also shows that stochastic variation in volatility produces an optimal intertemporal hedging demand for stocks which is negative when changes in volatility are instantaneously negatively correlated with excess stock returns and investors have coefficients of relative risk aversion larger than one. The absolute size of this demand increases with the size of this correlation, and also with the persistence of shocks to volatility. An application to the US stock market shows that empirically this correlation is negative and large, which implies a negative hedging demand for stocks. This application also shows that only low frequency shocks to volatility exhibit enough persistence to generate sizable hedging demands by long-term, risk averse investors. A comparative statics exercise shows that the size of hedging demands is considerably more sensitive to changes in persistence than to changes in correlation.

The Term Structure of the Risk-Return Tradeoff

Recent research in empirical finance has documented that expected excess returns on bonds and stocks, real interest rates, and risk shift over time in predictable ways. Furthermore, these shifts tend to persist over long periods of time. In this paper we propose an empirical model that is able to capture these complex dynamics, yet is simple to apply in practice, and we explore its implications for asset allocation. Changes in investment opportunities can alter the risk-return tradeoff of bonds, stocks, and cash across investment horizons, thus creating a ``term structure of the risk-return tradeoff.'' We show how to extract this term structure from our parsimonious model of return dynamics, and illustrate our approach using data from the U.S. stock and bond markets. We find that asset return predictability has important effects on the variance and correlation structure of returns on stocks, bonds and T-bills across investment horizons.

The Excess Burden of Government Indecision

Governments are known for procrastinating when it comes to resolving painful policy problems. Whatever the political motives for waiting to decide, procrastination distorts economic decisions relative to what would arise with early policy resolution. In so doing, they engender excess burden. This paper posits, calibrates, and simulates a life cycle model with earnings, lifespan, investment return, and future policy uncertainty. It then measures the excess burden from delayed resolution of policy uncertainty. The first uncertain policy we consider concerns the level of future Social Security benefits. Specifically, we examine how an age-25 agent would respond to learning at an early age whether she will experience a major Social Security benefit cut starting at age 65. We show that having to wait to learn materially affects consumption, saving, and portfolio decisions. It also reduces welfare. Indeed, we show that the excess burden of government indecision can, in this instance, range as large as 0.6 percent of the agent’s economic resources. This is a significant distortion in of itself. It’s also significant when compared to other distortions measured in the literature.

Return Predictability in the Treasury Market: Real Rates, Inflation, and Liquidity

Estimating the liquidity differential between inflation-indexed and nominal bond yields, we separately test for time-varying real rate risk premia, inflation risk premia, and liquidity premia in U.S. and U.K. bond markets. We find strong, model independent evidence that real rate risk premia and inflation risk premia contribute to nominal bond excess return predictability to quantitatively similar degrees. The estimated liquidity premium between U.S. inflation-indexed and nominal yields is systematic, ranges from 30 bps in 2005 to over 150 bps during 2008-2009, and contributes to return predictability in inflation-indexed bonds. We find no evidence that bond supply shocks generate return predictability.

Optimal Value and Growth Tilts in Long-Horizon Portfolios

We develop an analytical solution to the dynamic portfolio choice problem of an investor with power utility defined over wealth at a finite horizon who faces an investment opportunity set with time-varying risk premia, real interest rates and inflation. The variation in investment opportunities is captured by a flexible vector autoregressive parameterization, which readily accommodates a large number of assets and state variables. We find that the optimal dynamic portfolio strategy is an affine function of the vector of state variables describing investment opportunities, with coefficients that are a function of the investment horizon. We apply our method to the optimal portfolio choice problem of an investor who can choose between value and growth stock portfolios, and among these equity portfolios plus bills and bonds. For equity-only investors, the optimal mean allocation of short-horizon investors is heavily tilted away from growth stocks regardless of their risk aversion. However, the mean allocation to growth stocks increases dramatically with the investment horizon, implying that growth is less risky than value at long horizons for equity-only investors. By contrast, long-horizon conservative investors who have access to bills and bonds do not hold equities in their portfolio. These investors are concerned with interest rate risk, and empirically growth stocks are not particularly good hedges for bond returns. We also explore the welfare implications of adopting the optimal dynamic rebalancing strategy vis a vis other intuitive, but suboptimal, portfolio choice schemes and find significant welfare gains for all long-horizon investors.

Consumption and Portfolio Decisions When Expected Returns are Time Varying

This paper presents an approximate analytical solution to the optimal consumption and portfolio choice problem of an infinitely lived investor with Epstein-Zin-Weil utility who faces a constant riskless interest rate and a time-varying equity premium. When the model is calibrated to U. S. stock market data, it implies that intertemporal hedging motives greatly increase, and may even double, the average demand for stocks by investors whose risk-aversion coefficients exceed one. The optimal portfolio policy also involves timing the stock market. Failure to time or to hedge can cause large welfare losses relative to the optimal policy.Economic

Understanding Inflation-Indexed Bond Markets

This paper explores the history of inflation-indexed bond markets in the US and the UK. It documents a massive decline in long-term real interest rates from the 1990's until 2008, followed by a sudden spike in these rates during the financial crisis of 2008. Breakeven inflation rates, calculated from inflation-indexed and nominal government bond yields, stabilized until the fall of 2008, when they showed dramatic declines. The paper asks to what extent short-term real interest rates, bond risks, and liquidity explain the trends before 2008 and the unusual developments in the fall of 2008. Low inflation-indexed yields and high short-term volatility of inflation-indexed bond returns do not invalidate the basic case for these bonds, that they provide a safe asset for long-term investors. Governments should expect inflation-indexed bonds to be a relatively cheap form of debt financing going forward, even though they have offered high returns over the past decade.Expectations hypothesis, Liquidity, Term premia, TIPS

A Multivariate Model of Strategic Asset Allocation

Much recent work has documented evidence for predictability of asset returns. We show how such predictability can affect the portfolio choices of long-lived investors who value wealth not for its own sake but for the consumption their wealth can support. We develop an approximate solution method for the optimal consumption and portfolio choice problem of an infinitely-lived investor with Epstein-Zin utility who faces a set of asset returns described by a vector autoregression in returns and state variables. Empirical estimates in long-run annual and postwar quarterly US data suggest that the predictability of stock returns greatly increases the optimal demand for stocks. The role of nominal bonds in long-term portfolios depends on the importance of real interest rate risk relative to other sources of risk. We extend the analysis to consider long-term inflation-indexed bonds and find that these bonds greatly increase the utility of conservative investors, who should hold large positions when they are available.

Who Should Buy Long-Term Bonds?

According to conventional wisdom, long-term bonds are appropriate for conservative long-term investors. This paper develops a model of optimal consumption and portfolio choice for infinite-lived investors with recursive utility who face stochastic interest rates, solves the model using an approximate analytical method, and evaluates conventional wisdom. As risk aversion increases, the myopic component of risky asset demand disappears but the intertemporal hedging component does not. Conservative investors hold assets to hedge the risk that real interest rates will decline. Long-term inflation-indexed bonds are most suitable for this purpose, but nominal bonds may also be used if inflation risk is low.Economic