Using Daily Stock Returns to Estimate the Unconditional and Conditional Variances of Lower-Frequency Stock Returns

If intraday price data are unavailable, then using daily returns to construct realized measures of the variances of lower-frequency returns is a natural substitute for using high-frequency returns in this context. Notably, a suitable application of this approach yields realized measures that are unbiased estimators of the unconditional and conditional variances of holding period returns for any investment horizon. I use a long sample of daily S&P 500 index returns to investigate the merits of constructing realized measures in this fashion. First, I conduct a Monte Carlo study using a data generating process that reproduces the key dynamic properties of index returns. The results of the study suggest that using realized measures constructed from daily returns to estimate the conditional and unconditional variances of lower-frequency returns should lead to substantial increases in efficiency. Next, I fit a multiplicative error model to the realized measures for weekly and monthly index returns to obtain out-of-sample forecasts of their conditional variances. Using the forecasts produced by a generalized autoregressive conditional heteroskedasticity model as a benchmark, I find that the forecasts produced by the multiplicative error model always generate lower mean absolute errors. Furthermore, the improvements in forecasting performance are statistically significant in most cases.