The Role Of LearnIng In Dynamic Portfolio Decisions

European Finance Review 1: 295–306, 1998. © 1998 Kluwer Academic Publishers. Printed in the Netherlands.

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The Role of Learning in Dynamic Portfolio Decisions
M. J. BRENNAN
The Anderson School at UCLA, 110 Westwood Plaza, Los Angeles, CA 90095-1481, U.S.A.

Abstract. This paper analyzes the effect of uncertainty about the mean return on the risky asset on the portfolio decisions of aninvestor who has a long investment horizon. Building on the earlier work of Detemple (1986), Dothan and Feldman (1986), and Gennotte (1986), it is shown that the possibility of future learning about the mean return on the risky asset induces the investor to take a larger or smaller position in the risky asset than she would if there were no learning, the direction of the effect depending onwhether the investor is more or less risk tolerant than the logarithmic investor whose portfolio decisions are unaffected by the possibility of future learning. Numerical calculations show that uncertainty about the mean return on the market portfolio has a significant effect on the portfolio decision of an investor with a 20 year horizon if her assessment of the market risk premium is based solely onthe Ibbotson and Sinquefield (1995) data.

1. The Role of Learning in Dynamic Portfolio Decisions A central stylized fact about capital markets is that the equity risk premium is of the order of 8 5%. This figure, which is derived from the average annual stock market returns over the period beginning in 1926, is often treated as a parameter, rather than as an estimate. Thus Mehra and Prescott(1985) take the premium (which they estimate at around 6%) as a datum which gives rise to the “equity premium puzzle”.1 However, there are dissenting views: Brown et al. (1995) have argued recently that use of the realized mean return on the equity market as an estimate of the expected return is likely to involve a survival bias which, they suggest, could be as high as 400 basis points per year.Blanchard (1993), using a forward looking econometric approach, concludes that the premium is around 2–3%, and Scott (1992) places it even lower at 1–2%. Finally, of course, use of the realized historical average excess return on stocks as an estimate of the current risk premium
Inaugural Lecture at the First Annual Meeting of Fame, Geneva, 1997. Irwin and Goldyne Hearsh Professor of Banking andFinance, University of California, Los Angeles, and Professor of Finance, London Business School. I am grateful to Nicholas Barberis, Jerome Detemple, Rajna Gibson, Andrew Kaplin, Eduardo Schwartz, Stephanie Winhart, and the Editor, Simon Benninga, for helpful comments. 1 An interesting aspect of this puzzle is that few economists who recognize the puzzle hold the highly levered stock positions thatthey would hold if they behaved according to their own criteria for rationality.

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presumes that the risk premium is constant over time. Without taking a position on the magnitude of the equity market risk premium, this paper explores some implications of uncertainty about the risk premium for optimal dynamic portfolio strategies. Portfolio theory was originally developed toanalyze the problem of an investor who faced a single period horizon, and a known investment opportunity set. Subsequent extensions have generalized the theory to allow both for a multi-period horizon, and for incomplete information about the investment opportunity set. Thus, the basic single-period theory was extended by Hakansson (1970), Merton (1971), Samuelson (1969), Breeden (1979) and othersto allow for a multi-period horizon in which investment opportunities might either be constant, time-dependent, or even stochastic – in the latter case, these early authors assumed that the investment opportunity set is observable and that the parameters of the stochastic process governing its evolution are known by the investor. Brennan, Schwartz and Lagnado (1996) and Brennan and Schwartz...