Derivatives

CHAPTER 45 VaR: Other Portfolios

Aims

• To show how we can reduce the number of computations required to calculate VaR, while still retaining the linearity assumption and hence allowing the use of the variance-covariance (VCV) method.
• To show how the single index model (SIM) is used to simplify the calculation of the VaR for a portfolio containing a large number of stocks.
• To demonstrate how a portfolio of foreign stocks can be viewed as equivalent to holding the foreign market index and the foreign currency. This allows calculation of VaR in the domestic currency, using the VCV method.
• To show how representing a coupon paying bond as a series of zero-coupon bonds allows calculation of the VaR using the VCV method, for portfolios containing many bonds with different cash flows and durations.
• To show how the VCV method can be used to calculate the (approximate) VaR for a portfolio of options.

45.1 SINGLE INDEX MODEL

We use the single index model (SIM) to show how the volatility of a well-diversified portfolio of stocks can be measured by the volatility of the market return (e.g. the S&P 500) and the portfolio beta. This substantially reduces the computational burden when calculating VaR because the large number of correlations between individual stock returns can be encapsulated in the portfolio beta, and therefore do not have to be estimated. But it must be remembered that the SIM requires several simplifying assumptions – most notably that specific random events that affect ...