This question is from the back of the textbook of GARP and about VaR of a USD 1 million investment in 2 funds.

Fund Expected Return Volatility

Alpha 5% 20%

Omega 7% 25%

Assuming the returns follow the normal distribution and that there are 252 trading days per year, which of the following is the closest to the maximum possible daily 95% value-at-risk (VaR) estimate for the portfolio?

Fund Alpha volatility: 0.20 / sqrt of 252 = 1.260%

Fund Omega volatility: 0.25 / sqrt of 252 =1.575%

Portfolio variance:

0.5*0.5 * 0.01260^2 + 0.5*.5 * 0.01575^2 + 2 * 0.5 * 0.5 *0.01260 * 0.01575 * r

Maximum variance = 0.00004 + 0.000062 + 0.000099 = 0.000201 for r = 1

Maximum volatility = square root of 0.000201 = 1.4177%

Therefore, 95% VaR maximum is 1.6449 * 0.014177 * 1,000,000 approximately = USD 23,320

The answer above of GARP is USD 23,320, without considering the expected return from USD 1 million investment. I think the expected return must be subtracted in VaR calculation,

so the answer must be less than this value.

**Question 5.**Consider a USD 1 million portfolio with an equal investment in two funds, Alpha and Omega. with the following annual return distributions:Fund Expected Return Volatility

Alpha 5% 20%

Omega 7% 25%

Assuming the returns follow the normal distribution and that there are 252 trading days per year, which of the following is the closest to the maximum possible daily 95% value-at-risk (VaR) estimate for the portfolio?

**A.**USD 16,590**B.**USD 23,320**C.**USD 23,460**D.**USD 32,970**Answer: B**

Explanation:From the table, we can get daily volatility for each fund:Explanation:

Fund Alpha volatility: 0.20 / sqrt of 252 = 1.260%

Fund Omega volatility: 0.25 / sqrt of 252 =1.575%

Portfolio variance:

0.5*0.5 * 0.01260^2 + 0.5*.5 * 0.01575^2 + 2 * 0.5 * 0.5 *0.01260 * 0.01575 * r

Maximum variance = 0.00004 + 0.000062 + 0.000099 = 0.000201 for r = 1

Maximum volatility = square root of 0.000201 = 1.4177%

Therefore, 95% VaR maximum is 1.6449 * 0.014177 * 1,000,000 approximately = USD 23,320

The answer above of GARP is USD 23,320, without considering the expected return from USD 1 million investment. I think the expected return must be subtracted in VaR calculation,

so the answer must be less than this value.

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