Marginal VAR

[sarita]

A portfolio has an equal amount invested in 2 positions, x and y. the expected excess return of x is 9% and y is 12%. Their marginal vars are 0.06 and 0.075 respectivly. to move towards optimal portfolio, the manager should:
1) increase the allocation in y and lower that in x
2) increase the allocation in x and lower that in y

hi David, The answer is 1. increase the alloation to y. However, i don't understand why since i thought you must decrease allocation the one that has the hightest marginal VAR. in this case y has the highest marginal VAR; why should we increase alloction? is the answer wrong.

Very best,
SY

 

[David Harper CFA FRM]

Hi SY,

Can i ask you the source, just curious?

This confused me, too, and I've historically been imprecise (in the videos) on this point. FWIW. I think the answer is correct.

Part of the confusion is that, alternatively, if the question asked for the global minimum risk portfolio (lowest risk), then your rule would apply: reduce the position with higher marginal VaR (position Y); this will tend to lower its VaR and help get the marginal VaRs into equality.

However, Jorion's point is that rule (cut allocation with highest marginal VaR) is the risk management perspective. As opposed to the portfolio manager's (PM) perspective, where the PMs perspective is not to minimize risk but to seek the portfolio with the highest return/risk ratio (highest Sharpe ratio). So this goal is to seek the "optimal portfolio" and to get the ratio of excess returns/marginal VaRs into equality. So here you have:

X = 9%/0.06 = 1.5 excess/marginal VaR
Y = 12%/0.075 = 1.6

Now the rule is to increase allocation to the position with higher ratio (Y) as that will send it's ratio down because, now, marginal VaR is in the denominator (!); i.e., more of position w.r.t the portfolio will increase the marginal VaR/beta of the position. So i think the answer is correct. Thanks, David

 

[sarita]

Thanks David. The question is from Shweser's practice questions.

very best. SY