Question

Your portfolio which consists of 40% of stock T, and 60% of stock Q. T has daily Standard Deviation 2% while Q has daily Standard Deviation 3%. The correlation of two stocks is 0.4. What is the 1 day and 1 month 95% absolute VaR given 20 trading days per month?

Answer 1

Given about a portfolio,

Weight in stock T, Wt = 40%

Weight in stock Q Wq = 60%

daily standard deviation of Stock T SDt = 2%

daily standard deviation of Stock Q SDq = 3%

correlation of two stocks Corr(t,q) = 0.4

So, standard deviation of portfolio is

SD(p) = SQRT((Wt*SDt)^2 + (Wq*SDq)^2 + 2*Wt*Wq*SDt*SDq*Corr(t,q))

= SQRT((0.4*0.02)^2 + (0.6*0.03)^2 + 2*0.4*0.6*0.02*0.03*0.4) = 0.0224 or 2.24%

For 95% VAR, Z = 1.65

So, 1 day 95% VAR = Z*SD(p) = 1.65*2.24 = 3.70%

For 1 month, standard deviation = daily standard deviation*t^(0.5) = 2.24*20^0.5 = 10.03%

So, 1 month 95% VAR = 1.65*10.03 = 16.55%