Full valuation method for VaR

[liewpw05]

Hi David,

Reading Linda Ellen Chapter 3 and comparing with Jorion Value at Risk Chapter 10, have given rise to a source of confusion for me regarding what is the full valuation method for VaR?

Linda Ellen says "Full revaluation method calls for revaluation of the derivative at Var of the underlying" while Jorion says"Full valuation methods measure risk by full re-pricing the portfolio over a range of scenarios". This repricing could be done using risk factors generated by historical stimulation or Monte Carlo methods or Boot Strapping (as per your movie tutorial).

I notice your movie tutorial uses Jorion's definition which i think is the correct definition. Linda Ellen's version assumes linearity which is grossly misleading. What is your thoughts on this?


I have another question. It's related to the WCS measure which Linda Ellen called a complentary to VaR measure. From the reading, i understand that WCS measure is the expected worst case given a distribution of maximum losses. Is this WCS measure distinct or different from the Expected Shortfall measure which is conditional upon VaR?


Thanks. Look forward to your reply

Peggy

 

[David Harper CFA FRM]

Hi Peggy,

Really interesting! As I now read the Linda Allen on full revaluation (L.Allen has been in the cirriculm for several years, but not to my knowedge a source on this issue), I agree with your confusion, this 3.1.5. seems imprecise to me (compared to Jorion). Although after reading it three times, I finally think I see that she has same intent. My first observation (what confused me initially) is the potential confusion engendered by refering to instrument VaR compared to aggregated VaR (e.g., portfolio VaR, firm-wide VaR); I think it helps to treat the big, broad issue of aggregation as a separate matter. In that issue, linear/non-linear is a different dimension (IMO) than local/full revaluation. Here, as Jorion says or implies, local approaches include non-linear, and on the other hand Monte Carlo (full revaluation) techniques can assume linearity.

I read L.Allen as refering to instrument VaR, and in this respect she appears consistent with Jorion (but, don't get me wrong, we should just use Jorion). In the case of a bond, Allen is making this difference:

1. Delta-normal: estimate bond price change with duration and convexity. To agree with your point, it is imprecise of her to call this linear: of course, the convexity (like gamma for options) is adding non-linearity. Her contrast is simply: we aren't re-pricing the instrument. In this context, the portfolio equivalent would be "let's not re-price the whole portfolio for a interest-rate shock, let's use duration-convexity to estimate the change.

2. Compared to full-repricing: shock the interest rate, then re-price the bond.

In my view, the key instrument-based difference here is: the first operates on the risk factor (e.g., yield shock) to *estimate* the risk exposure (bond price change), while the second takes the trouble to get directly at the risk exposure (e.g., what is the new bond price?)

So, i agree Allen is imprecise and Jorion (as usual) is precise. I think the difference here is really "approximately (based on Taylor Series)" versus "full pricing" rather than linear/nonlinear. For example, I note that Jorion (handbook p 360) writes "To take into account nonlinear relationships, one would have to reprice the bond under different scenarios for the yield" and this appears to contradict himself (because, as noted: convexity and gamma introduce non-linearities). But what he *means* is: analytical methods (delta normal, duration convexity, delta gamma) are approximations based on derivatives and if we want to be accurate we need to reprice. Both of the authors in various places are using "linear" as a proxy for 2nd-term taylor series (duration +, delta +) approximations; Allen has also given us confusion previously by ruling out Taylor Series for MBS due to extreme "non-linearities" (after she just showed it can be used for non linear optoins!) and, in that place too, I think the "linear" is imprecise...

Re: Allen's WCS

I don't like her term worst-case scenario, I think it suggests the worst possible loss (which, e.g., doesn't exist in a normal distribution). Setting aside some minor technical differences (which are footnoted, more or less in the L2 Kevin Down reading on ES), yes, you are correct:

Linda's Allens WCS is an *expected* (average!) value of the losses in the tail (i.e., conditional on losses exceeding the VaR) = Dowd's Expected Shortfall (ES) = conditional VaR

all of these refer to the average loss condition on exceeding the VaR. Technically, further distinctions can justify a difference in these terms (e.g., contiuous/discrete distributions; loss relative to benchmark or not) but, for FRM purposes, she is referring to expected shortfall and that's the only conditional VaR we are really looking at. And, as you suggest, it's not the "worst thing that can happen" - that is worse even that the average *expected* worst loss.

Thanks, David