Investing equally in risk
Journal article, 2013

Classical optimal strategies are notorious for producing remarkably volatile portfolio weights over time when applied with parameters estimated from data. This is predominantly explained by the difficulty to estimate expected returns accurately. In Lindberg (Bernoulli 15:464-474, 2009), a new parameterization of the drift rates was proposed with the aim to circumventing this difficulty, and a continuous time mean-variance optimal portfolio problem was solved. This approach was further developed in Alp and Korn (Decis Econ Finance 34:21-40, 2011a) to a jump-diffusion setting. In the present paper, we solve a different portfolio problem under the market parameterization in Lindberg (Bernoulli 15:464-474, 2009). Here, the admissible investment strategies are given as the amounts of money to be held in each stock and are allowed to be adapted stochastic processes. In the references above, the admissible strategies are the deterministic and bounded fractions of the total wealth. The optimal strategy we derive is not the same as in Lindberg (Bernoulli 15:464-474, 2009), but it can still be viewed as investing equally in each of the n Brownian motions in the model. As a consequence of the problem assumptions, the optimal final wealth can become non-negative. The present portfolio problem is solved also in Alp and Korn (Submitted, 2011b), using the L 2 -projection approach of Schweizer (Ann Probab 22:1536-1575, 1995). However, our method of proof is direct and much easier accessible.

1/n strategy

Mean-variance

Black-Scholes model

Markowitz' problem

Portfolio optimization

Expected stock returns

Author

CARL LINDBERG

Chalmers, Mathematical Sciences, Mathematical Statistics

Decisions in Economics and Finance

1593-8883 (ISSN) 11296569 (eISSN)

Vol. 36 1 39-46

Subject Categories

Computational Mathematics

Probability Theory and Statistics

Control Engineering

DOI

10.1007/s10203-011-0121-3

More information

Latest update

11/22/2022