Value-at-Risk Theory and Practice

Chapter 1, Page 24
Exercise 7

Which of the following represent VaR metrics:

  1. conditional variance of a portfolio’s USD market value 1 week from today;
  2. conditional standard deviation of a portfolio’s JPY net cash flow over the next month.
  3. beta, as defined by Sharpe’s (1964) Capital Asset Pricing Model, conditional on information available at time 0.

Solution

  1. This is a function of the conditional distribution of the portfolio's market value 1P, so it is a VaR metric.

  2. Net cash flow is generally unrelated to portfolio market value. Accordingly, this cannot be expressed as a function of 0p and the conditional distribution of 1P. It is not a VaR metric.
  3. While beta is a function of 0p and the conditional distribution of 1P, additional information is required about the "market portfolio" in order to calculate beta. Accordingly, beta is not a VaR metric.
 

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