Investment Performance Guy has a post “Periodicity of risk statistcs (and other measures)” in which it is wondered how valid volatility estimates are from a month of daily returns.
Here is a quick look. Figure 1 shows the variability (and a 95% confidence interval (gold lines) from a bootstrap) of the volatility estimate (black line) for the S&P 500 index in January 2011. Figure 2 is for the first quarter and Figure 3 is for the first half. All of these are with daily data.
It would be best if the culture changed to include confidence intervals as well as point estimates of volatility.
The bootstrapping is done like:
for(i in 1:1e4) spxvolQ1.boot[i] <- sd(spxret11Q1[sample(62,62, replace=TRUE)])
The plots are created like:
abline(v=quantile(spxvolM1.boot * 100 * sqrt(252), c(.025, .975)), lwd=2, col=”gold”)
abline(v=sqrt(252) * 100 * sd(spxret11M1), lwd=2, col=”black”)