The Risk Management subject of CAPM Tutor lets you calculate the Value at Risk of a portfolio, using your own price data. In the following exercise we will use weekly data on 10 major US stocks to illustrate this use of CAPM Tutor.

Step 1: If from a previous subject you have stored portfolio weights (for up to 5-portfolios) you can now recall these weights to perform a VaR analysis. To do so first click on the Edit menu item in the main display window (titled Risk Management Display). Then select Portfolio Weights, Restore Weights and finally click on the set to be restored (from Set 1 to Set 5). These weights are then restored to the weight row. When you use portfolio weights the initial value of your portfolio is assumed to be $1,000,000. As a result, VaR is scaled relative to this value. You can then rescale this number relative to your own portfolio’s value.

If you have not stored any portfolio weights to be restored then you will have to enter portfolio weights directly or enter the number of stocks held in your portfolio (see step 3 below).

Note: If you restore weights, saved from another subject, you should check that they are properly aligned.

Click on the button VaR to perform the value at risk analysis.

This analysis is performed analytically assuming that returns are normally distributed. In addition, you can conduct a Monte Carlo simulation analysis of VaR by specifying how many simulations you want to perform and then clicking on the button Simulate. This will be approximately the same as the analytical VaR in most cases.

If you leave your data as is i.e., "Leave As Is" then the time horizon for both volatility and VaR is the same as the time horizon implied by your data. Thus, given the above data set is monthly then the time horizon for volatility and VaR is monthly. If you would like to convert this to daily you must first select Monthly for your data set and then select Horizon to equal 1-Day.

If you use portfolio weights, then the program allocates $1m across the assets given the portfolio weights. You can then rescale VaR to your own portfolio value.

Optional Step 3: In addition to weights you can also specify quantities. Let us start with quantities of the stocks, and suppose we buy 1 of each stock and then calculate the VAR of the portfolio. To do this, type in the number 1 in the row marked "Quantity" for each stock and click the button marked "VAR" to compute VaR for this specific portfolio.

Suppose now your portfolio value is 1115.375 and the VAR is 14.6112. This tells you that on your portfolio, you expect that over the next day, you will not lose more than $14.61 with 95% probability. Notice that your portfolio VaR is now scaled relative to the value of the portfolio specified in quantities not $1 million as is the case if you use portfolio weights.

Notes: If you specify quantities as opposed to weights the program calculates the portfolio value using the last prices in your data set. It computes the covariance matrix of returns using the entire data set, and uses this information to calculate the portfolio volatility and the VAR.

The results of your analytical or simulation study of VaR are automatically displayed. You can test the hypothesis of normality formally in Portfolio Statistics. In a frequency distribution display, the bars show you the frequency distribution of returns over the sample period. To obtain this, the program calculates the returns from your position assuming that you held it from the beginning of the date set to the end of the data set. It then calculates the frequency distribution of returns. Since the definition of VAR is based on normally distributed returns, it is important to see whether the return distribution over the period is approximately normal. The solid line on the picture is a plot of the normal density. You can therefore immediately see whether you think the normality assumption is violated for your portfolio.

In the next lesson, provided in the Applications Guide, you will learn how to calculate VAR for any traded mutual fund from the data provided by the Morningstar Web site.

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