Exercise

# Historical simulation

Suppose that a UK investor has invested 30% of her wealth in the FTSE index, 40% in the S&P 500 index, and 30% in the SMI index.

For different vectors of log-returns for the 5 risk factors, the function `lossop()`

computes the loss or gain incurred by the investor when her total wealth is 1. The function can also be applied to a 5-dimensional time series of log-returns to obtain a time series of historically-simulated losses and gains corresponding to each vector of log-returns in the time series.

The function `lossop()`

is the so-called **loss operator** for the portfolio and has been specially written for this exercise. In general, for each new portfolio, a specific function has to be written to compute portfolio losses and gains.

In this exercise, you will form historically simulated losses and examine them. This is a necessary prelude to using these data to estimate VaR and ES.

Instructions

**100 XP**

- Calculate the loss that would result from a log-return of -0.1 for all five risk factors (this has been done for you).
- Create the object
`hslosses`

by applying`lossop()`

to`returns`

, and then plot`hslosses`

. - Form a Q-Q plot of
`hslosses`

against the normal distribution. - Plot the sample acf of
`hslosses`

and of then of the absolute values in`hslosses`

.