Risk budgeting

[shanlane]

Hello,

There is another example in Jorion where he seems to pull something out of thin air.

If you look at the risk budgeting problem on p 444, there is something fishy going on.

The particular step I am talking about it where he says the $525 million is split evenly betweent the two traders. The risk budget allocated to each of them being $98MM is fine, but then their correlation just happens to be the exact amount it would need to be in order for the total VaR based risk budget to be $184MM, which was sloved for in the preceeding section on p 443. If the correlation between the managers was anything but 0.78, this would not have worked out, yet the 0.78 did not come into play in any other part of the problem.

Am I missing something? It just seem like if the correlation was anything else, the rest of the example would blow up because the total risk budget would be greater than (or less than) 184 and therefore a different amount would be allocatied to each of them and then this number would not add to the $525MM that is supposed to be allocated to US equities.

Sorry for all of the questions today, but as you said, this text is DENSE and a lot of it comes out of left field.

Thank you!!!!

Shannon

 

[ibrahim-1987]

hi shannon,
i will lnik this one to TAA & SAA
let say in this way, there are three levels in this example:
1. trustee ( the SAA ) with VaR of 233 m, for the whole pension fund.
2. then an invetment manager has 4 assets to invest in, but with no more than 233m as a risk measure for the entire portofolio, & he decides the weights to achieve this VaR. "TAA" page444.
3. two traders are given 98 m (risk) each to achieve the (target return) separately in investment in Us equities. "Active Manager".

both managers work separately, but when they report to invetment manager, he calulates their correlation.
and then calculate the risk of the two managers TOGETHER, which will be equal to 184.

so, 98 is trade manager VaR alone.
184 Investment manager VaR for equities.

to make things more clear, look at table 17-3 page 444, and sums Risk Budgets for each invetment categories = 309.
but the entire portoflio AFTER considering correlation is 233.

hope this help.

 

[shanlane]

What you said makes perfect sense, but what I am saying is that the correlation of 0.78 just happens to make everything work out nicely. It was not taken into account at all when the allocation decision was being made. No matter what the correlation between them was they still would have been allocated the same amount of $ and risk capital. If they happened to be perfectly correlated, the combined VaR between them would have been too large.

Does that make sense?

Thanks,
Shannon

 

[ibrahim-1987]

I agree with y, but correlation is calculated through time on an ongoing process, not at a point in time, and it is monitored by the manager, to ensure both trader work in line with his VaR.
But in this example he assumed imprecisely that he took a sample from the trades at a point in time, which has correlation of .78, but if he took another sample it may or may not be different.

As a risk manager y can control risk or limit risk in situation like this in two ways;
1. Y specify a correlation coefficient between traders, and order yr traders to change their combinations, if correlation is changed or about to change. But this method is not effective.
2. Y allow correlation to change, but specify VaR, and letting portfolio combinations and correlation to change.

 

[shanlane]

Agreed on all counts, I just wanted to make sure that his use of the the .78 correlation was a little too convenient. On one hand, it is a way to set a maximum level of correlation betweent the two traders. I just think it would have been more realistic if ANY other correlation was used and then to show how adjustments could be made. As you said, this correlation could change. If it gets lower, then we will stay well below our risk budget. If the correlations increase, we either have to scale back on the amount allocated to each or to reverse some trades so that there is less concentration risk.

Thanks again!

Shannon

 

[ibrahim-1987]

Exactly, shannon

 

[shanlane]

Perfect.

Thanks!

Shannon