Portfolio Optimization When Expected Stock Returns are Determined by Exposure to Risk
Bernoulli, Vol. 15, No. 2, pp. 464-474, 2009
11 Pages Posted: 13 Oct 2009 Last revised: 26 Oct 2009
Date Written: October 8, 2009
It is widely recognized that when classical optimal strategies are applied with parameters estimated from data, the resulting portfolio weights are remarkably volatile and unstable over time. The predominant explanation for this is the difﬁculty of estimating expected returns accurately. In this paper, we modify the n stock Black-Scholes model by introducing a new parametrization of the drift rates. We solve Markowitz' continuous time portfolio problem in this framework. The optimal portfolio weights correspond to keeping 1/n of the wealth invested in stocks in each of the n Brownian motions. The strategy is applied out-of-sample to a large data set. The portfolio weights are stable over time and obtain a signiﬁcantly higher Sharpe ratio than the classical strategy.
Keywords: 1/ n strategy, Black–Scholes model, expected stock returns, Markowitz' problem, portfolio optimization, ranks
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