2013 GARP exam practice quesiton

[shlobb13]

please confirm i'm not crazy and that they answers are off by a factor of 10. thx

The annual mean and volatility of a portfolio are 10% and 40%, respectively. The current value of the portfolio
is GBP 1,000,000. How does the 1-year 95% VaR that is calculated using a normal distribution assumption
(normal VaR) compare with the 1-year 95% VaR that is calculated using the lognormal distribution assumption
(lognormal VaR)?

a. Lognormal VaR is greater than normal VaR by GBP 13,040
b. Lognormal VaR is greater than normal VaR by GBP 17,590
c. Lognormal VaR is less than normal VaR by GBP 13,040
d. Lognormal VaR is less than normal VaR by GBP 17,590

Explanation: Normal VaR is calculated as follows:
Normal VaR = 0.1 – (1.645 * 0.4) = 0.558 (dropping negative sign)

and lognormal VaR is calculated as follows:
Lognormal VaR = 1 – exp [0.1 – (1.645 * 0.4)] = 0.4276

Hence, Lognormal VaR is smaller than Normal VaR by: 13.04% per year. With a portfolio of GBP 1,000,000 this translates to GBP 13,040.

 

[David Harper CFA FRM]

Hi @shlobb13 I agree with you, I get a difference of $130,327; my calcs here @ https://www.dropbox.com/s/rydssd9vxdib3nc/110315-garp-2013-p2-q2.xlsx?dl=0
I do not recall anybody catching this error, at least in this forum ...

 

[shlobb13]

thanks a lot David, a bit of my sanity has been restored

 

[afterworkguinness]

I'm short on sanity after 9 months of studying, so way to go getting some of yours back.