14. A portfolio is long bonds and short stocks. The bond position has an annual VaR of USD 20 million and stocks have an annual VaR of USD 15 million. If the correlation between bonds and stocks is 0.22, the annual VaR of the total portfolio is closest to

A. USD 22.20 million

B. USD 17.52 million

C. USD 6.55 million

D. USD 27.51 million

Correct answer is Afficeffice" />

A is correct: it results from this calculation: (20^2+(?15)^2*(?0.22)*20*15)^0.5 million USD = 22.26 million USD. The second term in parenthesis should have a minus.

B is incorrect: it results from this calculation: (20^2?15^2+0.22*2*20*15)^0.5 million USD = 17.52 million USD. The third term in parenthesis should have a minus.

C is incorrect: it is the result of the following calculation: (20^2?15^2?0.22*2*20*15)^0.5 million USD = 6.55 million USD. The second and third term have a minus because of the short position in stocks. 

D is incorrect: it results from this calculation: (20^2+15^2+0.22*2*20*15)^0.5 million USD = 27.51 million USD. The second and third term should have a minus.

Reference: . Philippe Jorion, Value at Risk, 2nd ed. (ffice:smarttags" />New York: McGraw?Hill, 2001), Chapter 5.

Type of Question: Market Risk