LVaR holding period

[shanlane]

Hello,

From the constant-spread LVaR adjustment formula, we see that when we increase the holding period, we decrease the adjustment. When you (or Dowd) says "holding period" what exactly are you referring to? I assume this means the time over which you liquidate the position, because this would make sense from a real world perspective: If you liquidate a position over the period of a week it will have less of an effect on the market than if you get rid of it in 10 minutes (hence, less of an adjustment is needed). Then again, that seems to take an endogeneous view of the spread, so I am not really sure why it works that way. Is my interpretation of this correct? If not, could you please point out the flaw in my reasoning?

Thanks!

Shannon

 

[David Harper CFA FRM]

Hi Shannon,

Excellent point: to make an adjustment based on the timing (time to liquidate) of the exit/sale/reduction of the position is indeed an endogenous liquidity adjustment. In fact, this suggests methods discussed by Dowd that are in the book but clearly out of FRM scope; e.g., endogenous + exogenous.

Or, put another way: If the point is to increase the VaR to account for liquidity risk, then we could actually increase the horizon input to account for this; e.g., say the daily vol = 1%, such that the 99% daily VaR = 1%*2.33. If the position might take 1.5 days to liquidate we could (this is not strickly FRM, okay) say the liquidity-adjusted 1-day VaR = SQRT(1.5/1)*1%*2.33; i.e., extend the horizon input to adjust the VaR for liquidity. But with respect to Dowd's statement:

"Holding period" is meant, along with "confidence level" as one of the two inputs ("design decisions") into the VaR. The exogenous constant spread LVaR approach, although it sounds fancy, is not fancy at all, it just adds one-half the bid-ask spread; i.e.,

LVaR = [-drift*T + sigma*deviate*SQRT(T) + 0.5*spread] * Value; or as %
LVaR% = [-drift*T + sigma*deviate*SQRT(T)+ 0.5*spread]; Dowd's LVaR is lognormal, but it does not matter here

Here is Dowd's statement:

"It is easy to show that the liquidity adjustment (a) rises in proportion with the assumed spread, (b) falls as the confidence level increases, and (c) falls as the holding period increases. The first and third of these are obviously ‘correct’, but the second implication is one that may or may not be compatible with one’s prior expectations."

He is referring to the ratio of LVaR/VaR (14.4 p 311). All he is saying is that, as the holding period increases (an increase in T), the "basic" VaR (as we already know) is increasing (to a point!) but the 0.5* spread is not, so the ratio (LVaR/VaR) falls as holding period increases. I guess an intuitive interpretation is something like, the ~ fixed cost of our exit (1/2 the spread) diminishes relative to the VaR as our holding period increases. I hope that explain, I think you started with a very interesting observation! Thanks,

 

[shanlane]

Yes it did.

Thanks!

Shannon