#08-41
A Martingale Test for Alpha
Dean P. Foster, Robert Stine and H. Peyton Young, February 2010
Abstract: This paper describes a new way of testing whether the returns from a financial
asset are systematically higher than a perfectly efficient market would allow.
Such an asset is said to have positive alpha. The standard way of estimating alpha
is to regress the asset’s returns against the market returns over an extended
period of time and to apply the t-test. The difficulty is that the residuals often
fail to satisfy independence and normality. In fact, portfolio managers may have
an incentive to employ strategies whose residuals depart by design from
independence and normality. To address these problems we propose a robust
test for alpha based on the martingale maximal inequality. Unlike the t-test, our
test places no restrictions on the distribution of returns while retaining
substantial statistical power. The method is illustrated for four assets: a stock, a
mutual fund, a hedge fund, and a fabricated fund that is deliberately designed to
fool standard tests of significance.
Keywords:
JEL classifications:
