confusing VaR calculation method

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Information from question given: Portfolio value $150, annual return 12%, annual return volatility 25%, calculate VaR using 3 standard deviation.

my answer is = 150( 12%-3*25%)= 94.5

but solution given is 150*3*25%

it is very confusing, when we should include the annual return of 12% to calculate VaR?

Anyone know this? thank you.

 

[David Harper CFA FRM]

Hi cheeseng,

You are right to be confused. Without a specific qualification, your answer is not incorrect. The problem, as stated, is flawed for leaving open the ambiguity. (This item is on my list for GARP's specific attention. It has arisen several times). In this case,

Relative VaR$= $150 * 25% sigma * 3 deviate = $112.50; i.e., loss versus future expected value
Absolute VaR$ = $150 * (-12% + 25% sigma * 3 deviate ) = $94.5; i.e., loss versus current value

The reason that, strictly speaking, neither is incorrect is:
* Interpretation of Jorion would favor, inconclusively, the relative VaR for its conservatism and consistency with UL. I say inconclusively because the horizon is long (one year) which favors an argument for absolute.
* Dowd, consistent with my impression of most practitioners (e.g., I get a lot of pushback from real-world experts when I omit the return and use the relative VaR without specifying a return), clearly uses the absolute VaR. (i.e., your answer).

The reason the absolute VaR is a better default (IMO) is simply that absolute VaR is a general case of the relative VaR: for shorter horizons, we apply the absolute VaR but just assume the return is effectively zero. When the timeframe is longer--one year, in this case--if the question does not say, then your answer is the better "default" answer. Bottom line, the question needs to be more specific.

Btw, for what it's worth, the reason I prefer to follow Dowd with:
-12% + 25% * 3, rather than
12% - 25%*3, although they give the same answer is …

When you go to add a liquidity cost (LC), by keeping the habit of the first, you avoid the error we've seen often (even in sample questions!) of adding this way:
12% - 25%*3 + LC. Wrong! In favor of:
-12% + 25% * 3 + LC. Correct!

David