Optimum portfolio and VaR based on MVAR

[NNath]

Hi @David Harper CFA FRM

https://forum.bionicturtle.com/threads/marginal-var.6008/

Refer to the post above and your reply below

https://forum.bionicturtle.com/threads/marginal-var.1365/#post-5001

If the MVAR (X) is greater than MVAR (Y) then in-order to get optimal portfolio increase the allocation of X and in-order to get lower VaR increase the allocation of Y. This makes option C and D both correct. Is this right?

 

[David Harper CFA FRM]

@NNath do you know the source of this question? I can't find the source (I just prefer to ensure I see the whole source). Is this a previous GARP Practice question?

 

[David Harper CFA FRM]

Hi @NNath I modified my Jorion Portfolio VaR spreadsheet to address this tricky question, see here at http://trtl.bz/jorion-portfolio-var-optimal

And here is the question, although I'd like to know the source to ensure it's fully specified:

n a two-position portfolio consisting of positions X and Y, it is found that the marginal VAR of X is greater than that of Y. Using this information, which of the following is most likely to be TRUE? Increasing the allocation to:
Choose one answer.
a. X and/or reducing the allocation to Y will move the portfolio toward the optimal portfolio
b. Y and/or reducing the allocation to X will lower the VAR of the portfolio,
c. Y and/or reducing the allocation to X will move the portfolio toward the optimal portfolio
d. X and/or reducing the allocation to Y will lower the VAR of the portfolio

.The correct answer is X and/or reducing the allocation to Y will move the portfolio toward the optimal portfolio.

My question is Marginal VAR of A is more than B. So the optimal portfolio will be to reduce the alloation to A and increase allocation to B. So answer B should be the right one.

In my opinion:

• The correct answer is (b): if ΔVaR(y) < ΔVaR(x) then per Jorion, to move toward the risk-minimizing portfolio, we increase the allocation to the position with the lower ΔVaR
• Per my previous answer, I do not think we have enough information to address the optimal portfolio as we don't know expected returns (see row 37 of the XLS for the decision, if we do have the information). So I don't see how we can decide about choices (a) or (c). @ShaktiRathore 's solution (at https://forum.bionicturtle.com/threads/marginal-var.6008/#post-19097 ) is elegant, however, he assumes the expected return is determined by CAPM. If we assume that, then both positions are already efficient as their Treynor ratios will equal the market's equity risk premium; in which case, the ratio E[R(i)]/ β(i) will already match. I hope that's helpful. Interesting question ...

 

[NNath]

In Schweser notes, thanks for the clearification