Excursions in the Martingale Hypothesis

We introduce a methodology for testing the martingale-hypothesis from time-series observations of a continuous asset process. Fixing the risk premium, the tests considered return the significance level at which a sample path belongs to a continuous martingale. Conversely, if the martingale hypothesis is assumed, we obtain the significance level of the particular risk premium. Using a time-change technique, we present tests which are independent of the continuous process driving the price process. This means that results are robust to any form of heteroskedasticity in asset returns. We show that the power against mean-reverting alternatives is higher than that of variance-ratio tests, at least for levels below 20%. We address estimation issues from discretely sampled data, and apply the tests to US stock indices. We conclude that for the S&P 500 index, the martingale hypothesis cannot be rejected at 15% level for a range of equity premia between 3.3% and 6.5%.