Which of the following is approximately the Value at Risk at 5 percent of a portfolio of $10 million of asset A,whose expected return is 15 percent and volatility is 35 percent,and $15 million of asset B,whose expected return is 21 percent and volatility is 30 percent,where the correlation between the two assets is 0.2.
A)$5.6 million
B)$10 million
C)$15 million
D)$1.25 million
E)none of the above

Question

Quizplus · Accepted Answer

To calculate the Value at Risk (VaR) at 5 percent, we need to use the following formula:

VaR = (Portfolio Value) x (Z-score) x (Portfolio Volatility)

Z-score for a 5 percent VaR is -1.645 (lookup table value).

Let's first calculate the portfolio volatility:

Portfolio Volatility = sqrt[(weight A)^2 x (volatility A)^2 + (weight B)^2 x (volatility B)^2 + 2 x weight A x weight B x (volatility A) x (volatility B) x (correlation AB)]

We have weight A = 10/(10+15) = 0.4 and weight B = 15/(10+15) = 0.6

Plugging in the values, we get:

Portfolio Volatility = sqrt[(0.4)^2 x (0.35)^2 + (0.6)^2 x (0.30)^2 + 2 x 0.4 x 0.6 x (0.35) x (0.30) x (0.2)] = 0.2662

Now, we can calculate the VaR:

VaR = ($10m + $15m) x (-1.645) x (0.2662) = $5.58 million ≈ $5.6 million

Therefore, the best choice is A ($5.6 million).

Which of the Following Is Approximately the Value at Risk