Question

Consider a position consisting of a $120,000 investment in asset A and a $120,000
investment in asset B. Assume that the daily volatilities of both assets are 1% and that the
coefficient of correlation between their returns is 0.4. What are the five-day 95% VaR and
ES for the portfolio?

Answer 1

For Both Assets:

Standard Deviation of Daily change for each asset = 120,000 * daily volatilities = 120,000 * 0.01 = 1200

Variance of portfolio daily change = 1200² + 1200² + 2 * 0.4 * 1200 * 1200 = 4,032,000

Standard Deviation of portfolio daily change = 4,032,000^(1/2) = 2007.984 = 2007.98

standard deviation of portfolio of the 5-day change = 5^(1/2) * 2007.98 = 4489.99

Using the tables of N(x) normal table Z score at 95% VaR = 1.645

5-day 95 percent VaR = 4489.99 * 1.645 = $7386.03

Here, Mean = 0 X = 95% Y =1.645

ES = [4489.99 * e ^{(-1.645)^2/2}] / [ (2*3.14)^(1/2) * (1- 0.95) ]

= [4489.99 * 0.25846 ] / 0.12530

= 9261.6346 = $9261.64