Exercise

# Rolling annualized mean and volatility

In previous exercises, you have already familiarized yourself with the `Return.annualized()`

and `StdDev.annualized()`

functions. In this exercise, you will also use the function SharpeRatio.annualized() to calculate the annualized Sharpe Ratio. This function takes the arguments `R`

, and `Rf`

. The `R`

argument takes an xts, vector, matrix, data.frame, timeSeries, or zoo object of asset returns. The `Rf`

argument is necessary in `SharpeRatio.annualized()`

, as it takes into account the risk-free rate in the same period of your returns. For this example, you can use the object `rf`

to fulfill the `Rf`

argument.

The function chart.RollingPerformance() makes it easy to visualize the rolling estimates of performance in R. Familiarize yourself first with the syntax of this function. It requires you to specify the time series of portfolio returns (by setting the argument `R`

), the length of the window (`width`

), and the function used to compute the performance (argument `FUN`

). To see all three plots together, PerformanceAnalytics provides a shortcut function charts.RollingPerformance(). Note the `charts`

instead of `chart`

. This function creates all of the previous charts at once and does not use the argument `FUN`

!

Instructions

**100 XP**

- Calculate the annualized returns, volatility, and Sharpe Ratio for
`sp500_returns`

. Assign these values to`returns_ann`

,`sd_ann`

, and`sharpe_ann`

respectively. Remember to supply the risk-free rate to the`Rf`

argument when calculating the Sharpe Ratio. - We provided the code for a plot of a rolling 12-month estimate of the annualized mean. Use this to help with the other plots!
- Plot the rolling 12-month estimates of the annualized volatility of the S&P 500 returns.
- Plot the rolling 12-month estimates of the annualized Sharpe ratio of the S&P 500 returns.