As we have seen, over the $1926-2020$ period, small$-$company stocks had the highest return and the highest risk, while U$.$S$.$ Treasury bills had the lowest return and the lowest risk. While we certainly hope you have a $95-$year holding period, it is likely your investment will be for fewer years. One way risk and return are examined over shorter investment periods is by using rolling returns and standard deviations. Suppose you have a series of annual returns, and you want to calculate a three$-$year rolling average return. You would calculate the first rolling average at Year $3$ using the returns for the first three years. The next rolling average would be calculated using the returns from Years $2,3,$ and $4,$ and so on$.$

a$.$ Using the annual returns for large$-$company stocks and Treasury bills, calculate both the $5-$ and $10-$year rolling average returns and standard deviations.

b$.$ Over how many $5-$year periods did Treasury bills outperform large$-$company stocks? How many $10-$year periods?

c$.$ Over how many $5-$year periods did Treasury bills have a larger standard deviation than large$-$company stocks? Over how many $10-$year periods?