Optimal Variance Forecasting in a Trading Context

In financial trading, the economic value of return and variance forecasts arises from three key components: an investor's risk preference, the quality of return predictions, and the accuracy of risk estimates. This study isolates the third component—risk knowledge—and demonstrates that its contribution is a non‐linear function of realized and predicted variance. We formulate the benefits of accurate risk estimation using a loss function framework and propose an optimal variance forecasting method that minimizes (maximizes) the expected loss (benefit). Empirical results show that traditional variance forecasts optimized for mean squared error (MSE) yield benefits that are generally statistically insignificant. In contrast, the proposed forecasting approach produces consistently large and significant gains.