This paper proposes a new tractable approach to solving asset allocation problems in situations with a large number of risky assets which pose problems for standard numerical approaches. Investor preferences are assumed to be deÞned over moments of the wealth distribution such as its skew and kurtosis. Time-variations in investment opportunities are represented by a ßexible regime switching process. We develop analytical methods that only require solving a small set of difference equations and can be applied even in the presence of large numbers of risky assets. We Þnd evidence of two distinct bull and bear states in the joint distribution of equity returns in Þve major regions with correlations that are much higher in the bear state. Ignoring regimes, an unhedged US investor's optimal portfolio is strongly diversiÞed internationally. Regimes in the return distribution leads to a large increase in the investor's optimal holdings of US stocks as does the introduction of predictability in returns from a short US interest rate. Our paper therefore offers a new explanation of the strong home bias observed in US investors' asset allocation, based on regime switching, skew and kurtosis preferences and predictability from the short US interest rate.

One key stylized fact in the empirical option pricing literature is the existence of an implied volatility surface (IVS). The usual approach consists of Þtting a linear model linking the implied volatility to the time to maturity and the moneyness, for each cross section of options data. However, recent empirical evidence suggests that the parameters characterizing the IVS change over time. In this paper we study whether the resulting predictability patterns in the IVS coefficients may be exploited in practice. We propose a two-stage approach to modeling and forecasting the S&P 500 index options IVS. In the Þrst stage we model the surface along the cross-sectional moneyness and time-to-maturity dimensions, similarly to Dumas et al. (1998). In the second-stage we model the dynamics of the cross-sectional Þrst-stage implied volatility surface coefficients by means of vector autoregression models. We Þnd that not only the S&P 500 implied volatility surface can be successfully modeled, but also that its movements over time are highly predictable in a statistical sense. We then examine the economic signiÞcance of this statistical predictability with mixed Þndings. Whereas proÞtable delta-hedged positions can be set up that exploit the dynamics captured by the model under moderate transaction costs and when trading rules are selective in terms of expected gains from the trades, most of this proÞtability disappears when we increase the level of transaction costs and trade multiple contracts off wide segments of the IVS. This suggests that predictability of the time-varying S&P 500 implied volatility surface may be not inconsistent with market efficiency.

This paper presents evidence of persistent 'bull' and 'bear' regimes in UK stock and bond returns and considers their economic implications from the perspective of an investor's portfolio allocation. We find that the perceived state probability has a large effect on the optimal asset allocation, particularly at short investment horizons. If ignored, the presence of such regimes gives rise to substantial welfare costs. Parameter estimation uncertainty, while clearly important, does not overturn the conclusion that predictability in the return distribution linked to the presence of bull and bear states has a significant effect on investors' strategic asset allocation.Returns in financial markets are difficult to predict and the absence of predictability served historically as one of the corner stones of financial economics. This proposition was largely supported by empirical studies. As recent as in the mid1970s, the consensus among researchers was that, to a good approximation, returns in stock, bond and foreign exchange markets were unpredictable and prices were well characterised by a random walk. Following a string of papers that documented limited predictability of returns across different predictor variables, sample periods and asset classes, the earlier consensus has largely been replaced by a view that -although predictability may be over-stated because of data-snooping effects and small sample distortions -returns are predictable, particularly at longer horizons.Predictability of returns does not, on its own, reject the notion that financial markets are efficient. In fact, because the predictable component in asset returns tends to be very small and uncertain, it is important to carefully consider how useful predictability really is to risk averse investors. Only recently have the economic implications of return predictability been explored by authors such as Barberis (2000), Brandt (1999), Campbell and Viceira (1999 and Kandel and Stambaugh (1996). These studies find that, faced with time-varying investment opportunities, it is optimal for investors to vary their portfolio weights both as a function of a set of predictor variables and as a function of their investment horizon. Although predictability of returns is generally weak from a statistical perspective, it is often found to have large effects on optimal portfolio holdings.So far the literature has almost invariably explored the asset allocation implications of return predictability in the context of simple linear models designed to characterise predictability in the conditional mean of returns. However, for asset allocation purposes it is important to go beyond this and correctly model the full probability distribution of returns. Unless investors have very restrictive

This paper studies asset allocation decisions in the presence of regime switching in asset returns. We find evidence that four separate regimes-characterized as crash, slow growth, bull and recovery states-are required to capture the joint distribution of stock and bond returns. Optimal asset allocations vary considerably across these states and change over time as investors revise their estimates of the state probabilities. In the crash state, buy-and-hold investors allocate more of their portfolio to stocks the longer their investment horizon, while the optimal allocation to stocks declines as a function of the investment horizon in bull markets. The joint effects of learning about state probabilities and predictability of asset returns from the dividend yield give rise to a non-monotonic relationship between the investment horizon and the demand for stocks. Welfare costs from ignoring regime switching can be substantial even after accounting for parameter uncertainty. Out-of-sample forecasting experiments confirm the economic importance of accounting for the presence of regimes in asset returns. * We are grateful to John Campbell, Wouter den Haan, and two anonymous referees for comments and also thank seminar participants at Caltech, the Innovations in Financial Econometrics conference at NYU

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