Expected return impact of the trade..-Question 20 from Round 1-Market Risk

[mudge2008]

Hi there,
The formula for the expected return impact = -[E(Ri)-E(Rj)]*delta(w)*W
=-(12%-15%)*0.01*1,000,000=$300
My answer followed your notes. Why did you multiply by 2%? Do I miss anything?

Does it matter how we treat asset i and asset j? or it's just a matter of interpretation. for example, if the purchased asset has a larger expected return, the resulting increase in portfolio expected return tends to decrease portfolio VaR. And the other way around.

Your answer is the following:
The expected return impact = (15% - 12%)(.02)($1 million) = $600

Thanks
Mudge

 

[David Harper CFA FRM]

Hi Mudge,

The question is bad, it can't be answered (a key sentence was truncated). I fixed it, the question is supposed to be: "what is return impact of a 2% trade, selling the 12% return asset and buying the 15% return asset." So your $300 is correct, if it were a 1% trade (but the question was unanswerable because there is nothing magic about a 1% trade).

To your question, no, you are quite right: there is no need to be mechanical here. Trading into (buying) the higher return will increase portfolio expected return, and vice versa.

And, yes further, an increase in portfolio's expected return decreases portfolio VaR. But please note two things about this statement:

1. It refers to absolute VaR, which counts the loss from zero. Stulz implictly refers to absolute VaR. Here is the example from another thread: if you start today with portfolio value of $100, expected annual return of 10% and (annualized) standard deviation (of returns) of 10%, the one-year 95% RELATIVE VAR = ($100)(10%)(1.645) = $16.45. The one-year 95% ABSOLUTE VAR = ($100)[(1.645)(10%)-10%] = $6.45. If the question is, does an increase in return decrease VaR, the answer is: Yes, for absolute VaR an increase will decrease VaR. But, for relative VaR, no it will not. There is no correct answer, the issue is: do we mean VaR relative to the initial portfolio or its expected value at the end of the VaR period?

2. Because Stulz implicitly assume absolute VaR, the expected return impact is only half of the final equation. The VaR impact of the trade includes two components: 1. The change to expected return (as above) and 2. The change to portfolio volatility/VaR. So, for example, the 2% trade above, trades into a higher expected return, so that part decreases VaR. However, presumably this also trades into a higher volatility asset (actually, a higher beta asset). So, that dynamic will increase VaR.

(after you totally get the above - that is, that the trade impacts risk and return, and that absolute VaR is a function of both, then take the final step: Stulz expected net gain on the trade does not simply net the higher (lower) return on the trade against the lower (higher) VaR because $1 of VaR does not cost exactly a $1. He subtracts (VaR impact of trade x Marginal cost of VaR) from the expected return. That's the net-net number, in words: the dollar expected gain minus the dollar cost of increased VaR)

 

[mudge2008]

Hi David,
Thanks for elaborating further on this topic.
Mudge