# P1.T4.27. Normal value at risk (VaR) fundamentals (K. Dowd)

Discussion in 'Today's Daily Questions' started by Suzanne Evans, Apr 12, 2012.

AIMs: Describe the mean-variance framework and the efficient frontier. Explain the limitations of the mean-variance framework with respect to assumptions about the return distributions.

Questions:

27.1. Dowd defines an arithmetic, absolute value at risk (VaR) given by VaR(%) = -drift + volatility*deviate. For a portfolio with current value of $1.0 million, expected return of 15.0% and volatility of 40% per annum, which of the following is nearest to the 99.0% confident 20-day absolute VaR (assume T = 250 days per year)? a.$88,750
b. $103,500 c.$188,400
d. $251,200 27.2. A portfolio with a current value of$1.0 million has an expected return of 12.0% with volatility of 50.0% per annum. Dowd distinguishes between the more familiar value at risk (VaR) that assumes normally distributed arithmetic returns, given by VaR(%) = -drift + volatility*deviate, and a lognormal VaR that assumes geometric means are normally distributed, given by lognormal VaR(%) = 1 - exp[drift - volatility*deviate]. Both are absolute, not relative VaRs, as they incorporate the drift. For this portfolio, which of the following is nearest to the dollar difference produced by the two VaRs (i.e., normal VaR versus lognormal VaR), with respect to a 95% confident 10-day VaR (assume T = 250 days per year)?

a. $650 b.$8,600
c. $12,100 d.$143,700

27.3. With respect to the mean-variance framework, Dowd asserts EACH of the following as true EXCEPT for:

a. The mean-variance framework assumes that standard deviation (or variance, the second central moment) is the primary risk measure
b. If a distribution has a mean of zero (0) and a variance of 1.0, it must be the standard normal distribution
c. The family of elliptical distributions includes the normal as a special case
d. Levy distributions are stable, and the normal is stable because it is a Levy (with alpha parameter = 2.0)