A Note on Constant Proportion Trading Strategies

16 Pages Posted: 15 Jun 2010 Last revised: 10 Mar 2011

Martin Haugh

Columbia University - Department of Industrial Engineering and Operations Research (IEOR)

Date Written: March 2011

Abstract

We study constant proportion (CP) trading strategies when there are multiple underlying securities that follow general diffusion dynamics. We focus in particular on a recently derived expression for the terminal wealth of a CP strategy and use this expression to address two issues. First we compare the performance of a CP strategy with the performance of the corresponding buy-and-hold strategy. Our main result here is that when no-short sales and no-borrowing constraints are imposed the exposure of the CP strategy to realized variances and covariances can be interpreted as a (multiplicative) premium paid to the follower of the CP strategy. This premium is the reward for accepting a final wealth that is proportional to the geometric mean of the terminal security prices rather than the arithmetic mean. While this result follows from a simple application of the geometric-mean inequality we have not seen it elsewhere in the literature. The second issue we address is the performance of leveraged ETFs (LETFs) which have recently been criticized for not performing as `advertised', particularly during the financial crisis of 2008. While not the first to explain the performance of LETFs, we make the very obvious connection between LETFs and CP strategies and show that LETF performance is easily explained by our expression for the terminal wealth of a CP strategy when there is just one risky security. We argue that this connection between LETFs and CP strategies was not widely understood because until very recently, the expression for the terminal wealth of a CP strategy, though easy to derive, was not known in the literature. Finally, we propose a class of ETFs, {\em Constant Proportion ETFs} (CPETFs), that should be more suitable for less sophisticated investors. Moreover, because these CPETFs would sell high and buy low they should help to dampen market volatility at the close, a property not shared by LETFs.

Keywords: Leveraged ETFs, constant-proportion trading strategies

JEL Classification: G11

Suggested Citation

Haugh, Martin, A Note on Constant Proportion Trading Strategies (March 2011). Available at SSRN: https://ssrn.com/abstract=1625063 or http://dx.doi.org/10.2139/ssrn.1625063

Martin Haugh (Contact Author)

Columbia University - Department of Industrial Engineering and Operations Research (IEOR) ( email )

331 S.W. Mudd Building
500 West 120th Street
New York, NY 10027
United States

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