Exercise

# Annualized mean and volatility

The mean and volatility of monthly returns correspond to the average and standard deviation over a monthly investment horizon. Investors annualize those statistics to show the performance over an annual investment horizon.

To do so, the package `PerformanceAnalytics`

has the function Return.annualized() and StdDev.annualized() to compute the (geometrically) annualized mean return and annualized standard deviation for you.

Remember that the *Sharpe ratio* is found by taking the mean excess returns subtracted by the risk-free rate, and then divided by the volatility!
The packages `PerformanceAnalytics`

and `sp500_returns`

are preloaded for you.

Instructions

**100 XP**

- Use the function
`Return.annualized()`

to compute the annualized mean of`sp500_returns`

. - Use the function
`StdDev.annualized()`

to compute the annualized standard deviation of`sp500_returns`

. - Calculate the annualized Sharpe Ratio using commands from the
`PerformanceAnalytics`

package, assign it to`ann_sharpe`

. Assume the risk free rate is 0. - Obtain all the above results at once using the function table.AnnualizedReturns().