portfolio Var calculation (daily/annual shift)

[southeuro]

hi all,

here's a question from FRM 2012:

1 million portfolio with equal investment in alpha and omega (annual).
Alpha -- expected return and volatility 5% and 20% respectively.
Omega -- expected return and volatility 7% and 25% respectively.

Assuming 252 trading days what's the daily max VAR?

The way I tackle this is I take 1.645 for 95% deviate, I also take correlation as equal to 1 as that's what maximises. Equal weight means 0.5 in the calculation of volatility of portfolio.

the question i have is this: I tweeked the annual volatility to daily at that point (after finding the volatility annual) with squared (1/252) but apparently it's wrong. The answer they give is that they make that tweek (annual to daily) in the beginning.

Conceptually they both should yield same but I suppose mathematically it'd be different. If so, what is the reason why we choose to tweek in the beginning rather than in the end.

Thanks

 

[David Harper CFA FRM]

Hi @southeuro

It should not matter. The answer finds a daily volatility of 1.471% after starting with the down-scaling, but you should get the same if you save it for last

• Annual volatility = sqrt(50%^2*20%^2 + 50%^2*25%^2 + 2*50%*50%*20%*25%) = 22.50%, such that
• daily volatility = 22.50%*sqrt(1/250) = 1.417%

Please note I submitted this particular problem to GARP, two years ago: we identified two problems with it. The more important (imo) is that returns (drifts) are given but not used, so it's really asking for relative VaR so it should say that. It is completely understandable for a current candidate to want to utilize the drifts (and therefore get a lower answer than given). I hope tha helps, thanks!