From rags to riches : On constant proportions investment strategies

In this paper we study the performance of self-financing constant proportions trading strategies, i.e. dynamic asset allocation strategies that keep a fixed constant proportion of wealth invested in each asset in all periods in time, in a stationary financial market. We prove that any mixed constant proportions trading strategy yields a strictly positive exponential rate of growth of investors wealth if prices are non-degenerated. This result can be regarded as being counterintuitive because any such strategy yields no increase of wealth under constant prices. We further show that the result also holds under small transaction costs, which is important for the viability of this approach because constant proportions strategies require frequent rebalancing of the portfolio.