Resolution of a Financial Puzzle

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. ∗Goldyne and Irwin Hearsh Professor of Banking and Finance, University of California, Los Angeles, and Professor of Finance, London Business School. †University of California, Los Angeles. In a recent article, Canner, Mankiw and Weil (1997) have pointed out that the portfolio recommendations of popular financial advisors are apparently inconsistent with the Tobin (1958) separation theorem that, if the distribution of returns belongs to the elliptical class, then the proportions in which different risky assets are held in the optimal portfolio of risky assets is independent of the investor’s risk aversion. The authors report that the financial advisors they study recommend that the ratio of bonds to stocks increase as the investor’s risk aversion increases. They consider several possible explanations for this phenomenon, including the absence of a real riskless asset, non mean-variance preferences, differences between the historical and the subjective distribution of returns, constraints on short sales, and considerations raised by the fact that investors have multi-period horizons, but conclude that these explanations are unsatisfactory, leaving an apparent puzzle. In this paper we show that the variation in the ratio of bonds to stocks recommended by the financial advisors is quite consistent with a model of portfolio optimization in a dynamic context. The reason for the violation of the separation principle is that bonds are not just any risky asset but have the particular property that their returns covary negatively with expectations about future interest rates. This covariation, which plays no role in the one period context of the Tobin separation theorem, is important for an investor with a multi-period horizon, as the classic paper of Merton (1973) recognizes. The model of time varying interest rates and expected stock returns is presented in Section I and some representative calculations are offered in Section II. Tobin originally stated the theorem for mean variance preferences. The necessary condition for investors to have mean-variance preferences for arbitrary utility functions is that the distribution of returns belong to the elliptical class of which the normal distribution is a member. Canner et al (1997) recognize the possible importance of the dynamic considerations induced by a multi-period horizon, but attempt to model the dynamic portfolio decision in a static fashion by considering only a buy and hold policy, adjusting the mean vector and covariance matrix for the length of the horizon: they conclude that “it appears impossible to reconcile the advice of financial advisors with the textbook CAPM by changing the time horizon”.