This paper examines the effects of uncertainty about the predictability of stock returns on optimal dynamic portfolio choice in a continuous time setting with a long horizon. Uncertainty about the predictive relation affects the optimal portfolio choice through dynamic learning, and leads to a rich set of relations between the optimal portfolio choice and the investment horizon. There are also substantial market timing elements in the optimal hedge demands, which are caused by stochastic covariance and variance terms arising from dynamic learning. The opportunity cost of ignoring predictability or learning is found to be quite substantial.

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## Scholarly Works (10 results)

The determination of stock prices and equilibrium expected rates of return in a general equilibrium setting is still imperfectly understood. In particular, as Grossman and Shiller (1981) and others have argued, stock returns appear to be too volatile given the smooth process for dividends and consumption growth. Mehra and Prescott (1985) claim that this smoothness in consumption and dividend growth gives rise to an “equity premium paradox” since it makes it impossible to explain the equity risk premium with a risk aversion parameter of less than an implausible 35. This paper reconciles the apparent smoothness of aggregate dividends and the volatility of observed stock prices by developing a model of stock prices in a dynamic general equilibrium setting in which learning is important. Dividends, which are one component of the aggregate consumption endowment, are assumed to follow a stochastic process with a mean-reverting drift that is not directly observable by the representative agent but must be estimated from the realized growth rates of dividends and aggregate consumption. The stock price-dividend ratio is shown to depend on the current estimate of the dividend growth rate as well as on the level of uncertainty about the true growth rate. This non-observability of the growth rate of dividends introduces an element of learning into the stock valuation process which is shown to increase the volatility of the stock price and therefore reduce the level of risk aversion required to explain the equity premium. The model is calibrated to the observed joint dividend and consumption process for the US, and is shown to yield an interest rate and stock price process that conform closely to the stylized facts for US capital markets.

The apparent inconsistency between the Tobin Separation Theorem and the advice of popular investment advisors pointed out by Canner et al (1997) is shown to be explicable in terms of the hedging demands of optimising long-term investors in an environment in which the investment opportunity set is subject to stochastic shocks.

We analyze the risk characteristics and the valuation of assets in an economy in which the investment opportunity set is described by the real interest rate and the maximum Sharpe ratio. It is shown that, holding constant the beta of the underlying cash flow, the beta of a security is a function of the maturity of the cash flow. For parameter values estimated from U.S. data, the security beta is always increasing with the maturity of the underlying cash flow, while discount rates for risky cash flows can be increasing, decreasing or nonmonotone functions of the maturity of the cash flow. The variation in discount rates and present value factors that is due to variation in the real interest rate and the Sharpe ratio is shown to be large for long maturity cash flows, and the component of the volatility that is due to variation in the Sharpe ratio is more important than that due to variation in the real interest rate.

The relation between the volatilities of pricing kernels associated with di�erent currencies and the volatility of the exchange rate between the currencies is derived under the assumption of integrated capital markets, and the volatilities of the pricing kernels are related to the foreign exchange risk premium. Time series of pricing kernel volatilities are estimated from panel data on bond yields for five major currencies using a parsimonious term structure model that allows for time varying pricing kernel volatilities. The resulting estimates are used to test hypotheses about the relation between the volatilities of the pricing kernels in di�erent currencies and the volatility of the exchange rate. As predicted, time variation in foreign exchange risk premia is found to be related to time variation in both the volatility of the pricing kernels and the volatility of exchange rates: the estimated pricing kernel volatilities can account for the forward premium puzzle in an ‘average’ sense across exchange rates.

The optimal portfolio strategy is developed for an investor who has detected an asset pricing anomaly but is not certain that the anomaly is genuine rather than merely apparent. He analysis takes account of the fact that the parameters of both the underlying asset pricing model and the anomalous returns are estimated rather than known. The value that an investor would place on the ability to invest to exploit the apparent anomaly is also derived an illustrative calculations are presented for the Fama and French SMB and HML portfolios, whose returns are anomalous relative to the CAPM.

We develop a simple framework for analyzing a finitehorizon investor’s asset allocation problem under inflation when only nominal assets are available. The investor’s optimal investment strategy and indirect utility are given in simple closed form. Hedge demands depend on the investor’s horizon and risk aversion and on the maturities of the bonds included in the portfolio. When short positions are precluded, the optimal strategy consists of investments in cash, equity, and a single nominal bond with optimally chosen maturity. Both the optimal stockbond mix and the optimal bond maturity depend on the investor’s horizon and risk aversion.

A simple valuation model that allows for time variation in investment opportunities is developed and estimated. The model assumes that the investment opportunity set is completely described by two state variables, the real interest rate and the maximum Sharpe ratio, which follow correlated Ornstein- Uhlenbeck processes. The model parameters and time series of the state variables are estimated using data on US Treasury bond yields and expected in- flation for the period January 1952 to December 2000, and, as predicted, the estimated maximum Sharpe ratio is shown to be related to the equity premium. In cross-sectional asset pricing tests using the 25 Fama-French size and book-to-market portfolios, both state variables are found to have significant risk premia, which is consistent with the ICAPM of Merton (1973). In contrast to the CAPM and the Fama-French 3-factor model, the simple ICAPM is not rejected by cross-sectional tests using the 25 Fama-French size and B/M sorted portfolios. Returns on the 30 industrial portfolios do not discriminate clearly between the three models. When both sets of portfolios are included as test assets all three models are rejected, but the estimated risk premia for both ICAPM state variables are significant while those associated with the Fama-French arbitrage portfolios are insignificant.

We provide a novel method for extracting estimates of realized pure price inflation from stock returns. The key is recognizing that pure price inflation should a®ect nominal returns of all traded assets by exactly the same amount. The popular Fama- French three-factor model is employed to purge stock returns of real economic factors. We uncover evidence that purchasing power parity holds quite well using the extracted inflation measures.

We estimate the parameters of pricing kernels that depend on both aggregate wealth and state variables that describe the investment opportunity set, using FTSE 100 and S&P 500 index option returns as the returns to be priced. The coefficients of the state variables are highly significant and remarkably consistent across specifications of the pricing kernal, and across the two markets. The results provided further strong evidence, which is consistent with Merton's (1973a) Intertemporal Capital Asset Pricing Model, that state variables in addition to market risk are priced.