Query - Culp's Method

[Avishek]

Hi David!

While I was revising Culp’s Method, I hit upon another doubt. You have provided with a good example in the Market Risk Video at 85:35 minutes. The time horizon is specified as 1 year. But, exactly how does it matter if the horizon is more than 1 interval or less? Is the calculation contingent on a timeline?

Say for example, the same question you specified as Time Horizon as 2 years or 1/2 an year. Then how does it impact the concept? Please explain.

Market Risk is indeed interesting!!!

Thanks, Avi.

 

[David Harper CFA FRM]

Hi Avi,

Great question. In a way, the calculation is not contingent on time horizon. We can go back to something about VaR; VaR only means something if we specify (i) a confidence/significance and (ii) a time horizon. (the confidence, of course, gives us the alpha to plug in)

Another way, that i like to view this, is: both confidence and horizon SCALE (+up or -down) volatility. And, in the case of Absolute VaR, horizon scales the expected return.

So, if we use Dowd's liquidity-adjusted VaR (per our other thread):

Value[-mean + (volatility)(critical value; e.g., 1.65, 2.33) + (0.5)(spread)] = LVAR

Then, the mean and volatility can be any time horizon; one year, one day, three years. Since

mean = (annual expected mean)(number of years in desired VaR/1 year), or
mean = (daily expected mean)(number of days in desired VaR/1 day)

and

volatility = (daily volatility)SQRT[(number of days in desired VaR/(1 day)]

That is the meaning of the square root of delta T ("square root rule"): it translates any volatility (daily, annual) to the desired timeframe.

Just two notes:

1. That's all for the so-called ABSOLUTE VAR used by Stulz (for CFaR) and Culp (For LVaR). For RELATIVE VaR, as Jyothi notes, the expected mean doesn't get included at all

2. [just for the technical purists, not for the testable FRM]: we typically scale mean with n-period mean = (1-period mean)(number of periods) but that is implicitly arithmetic. It is okay alternatively to do scale a geometric mean: n-period mean = (1-period mean - volatility/2)(number of periods)

Thanks for another good question!

David

 

[rahul.goyl]

Hi David,

That very well explained. Thanks a lot for you continous effort to resolve our queries in just fraction of minutes.

Thanks for helping us out.

Rahul