Basel II & the assumption of a zero mean

[stans]

Hallo,

I would like to ask whether Basel II assumes a zero mean for calculating a 10-day VaR. In other words, suppose I know the standard deviation of the returns, but I don't have any past data from which I could estimate the mean. Should I assume for a 10-day VaR computation that the mean return is 0? I would be grateful for help.

Regards,
Stan

 

[David Harper CFA FRM]

Hi Stan,

I don't *think* Basel II IMA is explicit but clearly a zero mean assumption is common and acceptable because it (relative VaR) is conservative (greater than) compared the same VaR deducted/offset for some expected gain (absolute VaR) when drift is positive.

Carol Alexander makes the case another way, where here "absolute VaR" (i.e., VaR that incorporates drift) is a PV such that we can assume a positive expected return at the riskless rate but it washes out anyhow in the DISCOUNTING: "Banking regulators often argue that the expected return on all portfolios should be equal to the risk free rate of return. In this case the discounted expected P&L will be zero or, put another way, the expected excess return will be zero." Source: Carol Alexander MRA, Vol IV

so I'm confident you are safe to assume zero, but i guess what i don't really know is if you could include a positive expected return over such a short period and thereby slightly lower the VaR...that seems like the ever-so-slightly more aggressive and atypical approach which i have not seen (arguably if i think of HS analogs, I perceive i have seen it both ways: I've seen short term HS VaR both that include and exclude the expected mean)

David

 

[stans]

Thank you very much for a precise answer.

Kindest regards,
Stan