Why is it so difficult to outperform the random walk? An application of the Meese-Rogoff puzzle to stock prices

Some economists suggest that the Meese-Rogoff puzzle is equally applicable to the stock market, in the sense that no model of stock prices can outperform the random walk in out-of-sample forecasting. We argue that this is not a puzzle and that we should expect nothing, but this result if forecasting accuracy is measured by the root mean square error (RMSE) and similar metrics that take into account the magnitude of the forecasting error only. We demonstrate by using two models for dividend-paying and nondividend-paying stocks that as price volatility rises, the RMSE of the random walk rises, but the RMSE of the model rises even more rapidly, making it unlikely for the model to outperform the random walk.