P2.T9. Risk Management & Investment Management: Jorion, Chapter 17: VaR and Risk Budgeting


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Hello @David Harper CFA FRM . Can you please explain how did you calculate weights for maximizing portfolio information ratio i,e 55%, 37% and 8% respectively in the example given on page 37 of Jorion, Chapter 17: VaR and Risk Budgeting. As per the formula provided before the example, we are required to input IR(p) in the formula to arrive at the w(i). However, the IR(p) itself depends on the calculation of weights to arrive at the active return before IR can be calculated.

Can you please guide where I am going wrong in my calculations.?



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David Harper CFA FRM

David Harper CFA FRM
Staff member
@mkaabb96 Please don't bump your post to me (I deleted it). This is a forum. You ask, "Can you please guide where I am going wrong in my calculations" but where are your calculations??

It's an optimization problem, here is the XLS at https://www.dropbox.com/s/n5s1ydimxdmhn20/jorian 17-4b.xlsx?dl=0

And, if you would try to search (rather than bump me) you might find that I explained it previously here (among other places like https://forum.bionicturtle.com/threads/equation-with-too-many-variables.5711/) at https://forum.bionicturtle.com/thre...ed-performance-measures-bodie.5549/post-72102 i.e.,
Hi @Marco.Musci Yes, in Jorion 17.5.2 (Budgeting across Active Managers), Jorion explains that if we maximize the portfolio information ratio subject to a fixed tracking error volatility (TEV), the relative risk budgets should be proportional to the information ratios. I wrote a practice question for this concept here at https://forum.bionicturtle.com/thre...isk-var-in-investment-management-jorion.5520/ which employs the formula to which you refer ...
Mathematically that is, if omega(.) is tracking error (TEV), IR(.) is the information ratio, and x(i) is the weight of the position, Jorion 17.7 gives: x(i)*omega(i) = IR(i)*[1/IR(portfolio)]*omega(portfolio). If the portfolio's maximum information ration is 0.82 subject to a TEV constraint of 5.0%, what is allocation to a manager with an information ratio of 0.50 and a TEV of 8.0%?

.... and the relevant Jorion text is below. Good luck tomorrow!