Jorion, Foundation 1.a

[orit]

hello David,
Im studying for the FRM exam part 1, and I would appreciate if you elaborate on the two topics below taken for foundation 1.a:
1. compare and contrast valuation and risk management using Var as an example
2. describe advantage and disadvantage of Var relative to atop-loss, notional and exposure limit

Thanks,
Orit Waisman

 

[David Harper CFA FRM]

Hi Orit,

Both are from Jorion's VaR (book 3rd Ed) Chapter 1. I placed a snapshot from our notes below.

In regard to (2) advantages/disadvantages of VaR, this is frankly one of those precursor frameworks that points to future sub-topics (some of the Yes/Nos are densely packed). Further, since Jorion has published this, his "argument" can be debated, so it's not as straightforward as it looks (e.g., notionals and exposures are more favored post-crisis). Still, Jorion's argument is simply that VaR is better than the others risk management techniques (a debatable assertion). Stop-loss is flawed because it is ex ante ex post (activated after a loss incurred); and we need to know stop-loss as an order type. So, this makes the best candidates notional, exposures and VaR. Setting aside some interim detail, Jorion's primary argument in favor of VaR is that it aggregates: this is the huge advantage of VaR that (eg) manifests in Basel, various risk types can be summed into a single yardstick.

In regard to (1), this is the more important topic of the two (imo). If I could ask you to read my post explaining the Merton model here at http://forum.bionicturtle.com/threads/merton-model-a-summary-of-the-issues.5646/
... because the Merton model is a wonderful illustration of the essential difference between the two ideas. We don't even need the full Merton, we can see it in a single stock option: if you go to price (value) a stock option with Black-Scholes-Merton, you invoke a risk-free rate (risk neutrality) in a PRECISE calculation to determine the price (present value) of the option. On the other hand, if you ask, what is my potential loss on this option position?, you exit the precision of derivatives valuation and (most likely) are attempting to ROUGHLY ESTIMATE a potential future loss based on a presumed actual (physical) distribution. It's a big difference, in the question, and in the means to generate an answer. I hope that helps, thanks,

 

[orit]

Thanks David

 

[skoh]

Hi David,

For P1.T1.Jorion Chapter 1, question 7ii), how can we derive the $12,620 for continuous return = LN[($12,620 + $12,000)/12,000] = 71.9%?

Also you mentioned ".. please note: a geometric return which discounts 1/2 variance is also fine, alternative answer!" How do calculate the geometric return?

Thanks

 

[David Harper CFA FRM]

Hi skoh,

I just mentioned it to allow for somebody who might have computed an expected return (x) = drift (i.e., mu) - variance^2/2. In this case, 10% - 10% volatility^2/2= 9.5%. Maybe I should not have inserted it, only b/c the point of the question is merely to compare leverage versus non-leverage. But the "problem" is that "expected return" allows for a definitions either without volatility or eroded by volatility (and this particular question is not well-written to suss out that distinction). I hope that helps,

 

[skoh]

thanks david. How about question 10.1c? Why is Notional not able to aggregate?

 

[David Harper CFA FRM]

Hi skoh,

Jorion's reference to notional as a risk measure which does not lend itself to aggregation (see the chart above) refers primarily to the idea that notionals do not (easily) incorporate diversification effects when positions are aggregated. Using notionals, a derivatives portfolio will tend be the sum of individual position notionals; which assumes perfect correlations.

That's the primary meaning ("aggregation" is often, not always of course, a keyword that leads to a diversification point). I think Jorion's secondary point may be lack of practical (quasi-) netting, which I would tend to view as a sub-type of diversification anyway; e.g., portfolio holds a long and short position in same currency; the notionals are (absolute) positives, so summing them is incorrect aggregation. Thanks,

 

[skoh]

Thanks!

 

[Backwardation]

Hi Orit,

Both are from Jorion's VaR (book 3rd Ed) Chapter 1. I placed a snapshot from our notes below.

In regard to (2) advantages/disadvantages of VaR, this is frankly one of those precursor frameworks that points to future sub-topics (some of the Yes/Nos are densely packed). Further, since Jorion has published this, his "argument" can be debated, so it's not as straightforward as it looks (e.g., notionals and exposures are more favored post-crisis). Still, Jorion's argument is simply that VaR is better than the others risk management techniques (a debatable assertion). Stop-loss is flawed because it is ex ante (activated after a loss incurred); and we need to know stop-loss as an order type. So, this makes the best candidates notional, exposures and VaR. Setting aside some interim detail, Jorion's primary argument in favor of VaR is that it aggregates: this is the huge advantage of VaR that (eg) manifests in Basel, various risk types can be summed into a single yardstick.

In regard to (1), this is the more important topic of the two (imo). If I could ask you to read my post explaining the Merton model here at http://forum.bionicturtle.com/threads/merton-model-a-summary-of-the-issues.5646/
... because the Merton model is a wonderful illustration of the essential difference between the two ideas. We don't even need the full Merton, we can see it in a single stock option: if you go to price (value) a stock option with Black-Scholes-Merton, you invoke a risk-free rate (risk neutrality) in a PRECISE calculation to determine the price (present value) of the option. On the other hand, if you ask, what is my potential loss on this option position?, you exit the precision of derivatives valuation and (most likely) are attempting to ROUGHLY ESTIMATE a potential future loss based on a presumed actual (physical) distribution. It's a big difference, in the question, and in the means to generate an answer. I hope that helps, thanks,

Good morning,

you wrote: "Stop-loss is flawed because it is ex ante (activated after a loss incurred)" .... I would therefore call is an ex post (=after a loss) risk measure; the VaR would rather be an ex-ante (=before a loss occurs) risk measure.

The basic fatures can be summarized as following:

- stop loss: can be helpful if markets are trending or if traders try to double their bets in order to turn losses to profits.
-VaR: big benefit is that it is easy to understand and communicate, it can be aggregated accros portfolios, divisions and risks; disadvantages are that traders can "game" the VaR by creating P/Ls with spikes beyond the VaR, it doesn't tell anything about the distributino beyond the VaR, it is not subadditive (except for certain VaR types) and is subject to some measurement error

 

[David Harper CFA FRM]

Hi backwardation, nice catch, yes, I should have written ex post rather than ex ante, thanks for your careful attention (fixed above), thanks