Question

Consider that IBM is trading at $144 and Exxon Mobil is trading at $ 88. In your portfolio you own $2,000,000 of IBM and 7,000,000 of. Exxon Mobil has an annualized volatility of 43 % and IBM’s annualized volatility is 18%. The correlation between the two stocks is 33%

Calculate

a) The 10 day 99% Var for each stock

b) The 5 day 95 % Var for the two-stock portfolio

c) The diversification benefit of holding IBM stock at the 99% confidence interval for 10 days

Note: I need the correct solution to all the 3 sub-parts.

Answer 1

Lets assume there are 250 trading days in an year.

Ans a) 10 day 99% VaR for IBM = 2000000 * .18/root(250/10) * 2.33 = $167760

10 day 99% VaR for Exxon Mobil = 7000000 * .43/root(250/10) * 2.33 = $1402660

Ans b) 5 day 95% VaR for IBM = 2000000 * .18/root(250/5) * 1.645 = $83762.38

5 day 95% VaR for Exxon Mobil = 7000000 * .43/root(250/5) * 1.645 = $700240.74

5 day 95% VaR for two stock portfolio = root(VaR of IBM^2 + VaR of Exxon ^2 + 2*var of IBM * VaR of Exxon * correlation.)

= $732164.39

Ans c) 10 day 99% VaR for portfolio = $1466595.72

Diversification Benefits = $167760 + $1402660 -  $1466595.72 = $103824.28