Question

A portfolio consists of two assets. $1 million is invested in Asset 1 and $2 million is invested in Asset 2. The estimated daily variance for Asset 1 is 0.01, for Asset 2 the daily variance is 0.005. The estimated covariance for the two assets is 0.002. What is the 10-day VaR at the 95% confidence level?

Answer 1

First we calculate the portfolio variance. Assuming the two assets are s1 , s2 with weights w1, w2 and risks σ1 and σ2. The formula for calculating portfolio variance is:

Portfolio variance=(W1σ1)2+W2σ22+2W1W2*covariance(S1S2)

To calculate weights. Asset 1 has 1 million , Asset 2 has 2 millions, the weights w1 and w2 are 1/3 and 2/3 respectively

Portfolio variance = 0.333²*0.01+0.667²*0.005+2*0.333*0.667*0.002 = 0.00422

Portfolio risk = sqrt(prortfolio variance) = 0.065

one day Var for portfolio risk = 0.065

10 day VaR at 95% confidence interval therefore = -1.65*0.065*sqrt(10) = -0.3391 which is approximately -33.4%

Reason why it is 1.65 is the z value of a one tail confidence interval is 1.65

Formula for calculating VaR for different periods = σ_{one day}*sqrt(T)*(Z value for confidence interval)