Exercise

# Equity and implied volatility risk factors

To analyze the risk of a portfolio consisting of an option, it is necessary to consider changes in all three risk factors: stock price, volatility and interest rates. Here, you will focus on the first two of these risk factors and assume that interest rates do not change much over short time intervals. The daily risk-factor values for the period 1990-2010 are contained in `riskfactors`

and the corresponding log-returns in `returns`

; both multivariate datasets are loaded in your workspace.

Volatility is a new risk factor that hasn't been considered so far in this course. It is represented by the VIX index which is constructed from the implied volatilities of a wide range of options on the S&P 500 index:

```
> names(returns)
[1] "X.GSPC" "X.VIX"
```

In this exercise, you will be able to verify whether the log-returns of volatility behave like other return data you have encountered, and to see how they vary with the log-returns of the S&P 500 index.

Instructions

**100 XP**

- Use the appropriate function to plot the data in
`riskfactors`

and in`returns`

. - Use
`plot()`

and`as.matrix()`

in succession to create a scatterplot of`returns`

. - Use
`apply()`

to conduct the Jarque-Bera test on`returns`

, and then use`qqnorm()`

and brackets for indexing to make a Q-Q plot against normal for the log-returns of the series in`returns`

containing volatility data. - Create the sample acf plot of the data in
`returns`

and then the absolute returns of the data. - Use
`cor()`

to calculate the correlation between the log-returns of the two risk factors in`returns`

.