Do Asset Returns Follow a Random Walk? The Wald–Wolfowitz Runs Test (Spreadsheet)

Nope.

Well, we're 99.19% sure they don't.

Here I provide a simple spreadsheet to test whether asset returns follow a random walk.

Are future returns independent of current and past returns? Not according to the p-value of 0.0081 I calculated for the SPY ETF from 1/29/1993 to 9/29/2023.

There is one caveat here. You need to end the final state at some point, therefore, the last cell (I7725) is hard coded. If you model a different asset you need to update the range references and the last state.

Wald–Wolfowitz Runs Test.xlsx

Download XLSX • 650KB

Your test statistic is (observed runs - mean) / (Variance^(1/2)).