| Lo & Mackinlay established the Variance Ratio test in 1988 to test for random walk behaviour in asset returns. The test has been extensively used in finance to dispute the Efficient Market Hypothesis (EMH). We suggest a non-parametric variant of the Variance Ratio test that addresses certain shortcomings of the test---namely the poor small sample approximation of the asymptotic distribution of the test statistic, the model's sensitivity to the presence of heteroskedasticity and the lack of adjustment made for multiple testing. Using locally permuted return series and an exponential moving average, we construct a null distribution which is used to test the random walk hypothesis on both a lag-by-lag (marginal) and overall (simultaneous) basis. We establish that the rejection/acceptance of random walk behaviour is sensitive to both the exponential decay factor and lag size. We also construct a distribution-based strategy to equity pairs trading. Given the implicit Gaussian assumptions in market-neutral trading strategies, we construct portfolios using the Shapiro-Wilks statistic for stock pairs listed on both the FTSE index in London and NSE in Mumbai. Our strategy compares favourably when compared with both an established distance-based model and the top three deciles in the mutual fund universe. |
