GARP 2016 Sample Exam Question Q.5

[Kenji]

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

Answer: B
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.

 

[David Harper CFA FRM]

Hi @Kenji

Yes, this question has been observed as problematic several times (it's actually several years old) and reported to GARP, see https://forum.bionicturtle.com/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]

David, thank you very much. I was surprised to see that it was 2012.

 

[Kavita.bhangdia]

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

 

[David Harper CFA FRM]

Hi @Kavita.bhangdia We can only add relative VaRs your way, we cannot add absolute VaRs thusly because the drift (the mean) scales proportionally with time but the volatility scales with the square root of time; e.g., https://forum.bionicturtle.com/thre...ersus-relative-var-versus-ul.6020/#post-41645 It's basically that we'd like to use a*(b+c) = ab + ac, but we can't because it's really a*b + sqrt(a)*c, and we can't easily reduce a*b + sqrt(a)+c. I hope that clarifies, thanks!