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# GARP 2016 Sample Exam Question Q.5

#### Kenji

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

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

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

Last edited:

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @Kenji

Yes, this question has been observed as problematic several times (it's actually several years old) and reported to GARP, see https://www.bionicturtle.com/forum/threads/2012-practice-part-2-18.5908/
The "maximum" in "maximum VaR" is ambiguous; in addition to the fact the question wants relative VaR but includes expected returns such that absolute VaR is a perfectly acceptable inference.

#### Kenji

##### New Member
Subscriber
David, thank you very much. I was surprised to see that it was 2012.

#### Kavita.bhangdia

##### Active Member
Hi David,
If we leave the mean, the VAR will be maximum with correlation = 1.
When correlation is 1, total VAR = VAR1+ VAR2.

Why can't we solve it this way?

Why do we have to compute portfolio variance and then calculate Var?
Thanks
Kavita

Staff member
Subscriber