Compare valuation and risk management using VAR as an example

[edmundkan]

Dear,

On Powerpoint Page 23 of Foundations 1, there is a table for comparison between Derivatives Valuation and Risk Management, I am not fully understand the "precision" column. What is precision means and why high precision under derivatives valuation and less precision required under risk management? Can you explain mroe in detail, please? Thanks.

 

[David Harper CFA FRM]

Hi Edmund - The table copies from Jorion 1, where he means that valuation strive to be precise to a point estimate; e.g., the bond has a value of $98. He says that is needed for trading. But risk measures are rarely precise: they are rough approximations; e.g., the bond may lose at least $10 with 95% confidence. But we know that is both probabilistic and imprecise. I think it also acknowledges that we cannot know the downside with precision, where there is less data by definition; it is more realistic to be approximate or range-bound. (It bugs me that he commingles "precision" and "accuracy." I think he really means: both should be accurate but risk is less precise. See this. But that is useless editorial on my part).

He also relates to distributions: valuation prefers the precise mean of the distribution; e.g., the expected (mean) FV payoff is $X, therefore the discount PV price is $Y today. But risk is concerned with approximate dispersion (standard deviation). That is, valuation = 1st moment, risk = 2nd, 3rd, and 4th moments.

David

 

[scorpiomanoj]

Hi friend,

I think Derivatives valuation needs to be highly accurate as it impacts the holders P & L. (All valuation and pricing of derivatives are done on the basis of `no arbitrage' concept.), whereas risk management is a kind of process implemented to minimise the future loss of the asset / portfolio, which naturally cannot be accurate as it is based on certain assumptions. For eg, VAR is a risk management tool and is based on certain assumptions like the type of distribution of returns. Another example is Modified duration, a risk management tool for fixed income products, assumes parallel shifts of yield curve.

With respect to derivatives valuation, the simplest eg is forward contract valuation, which is the present value of difference between the delivery price of the forward contract booked originally (K) and the current forward price (F0) of the contract. Obviously the valuation needs to be precise as it affect the P&L.

David, please correct me if im wrong.

Thanks
Regards
Manoj Kumar Halan.

 

[David Harper CFA FRM]

Manoj -

I *agree* with your comments, and I think you speak to an even more relevant and practical aspect of the valuation: that marking positions to market (mark-to-market) requires "precise" point estimates (as does trading itself, so this is true of both the trade and untraded positions in the trading/banking book). Whether that needed valuation precision is warranted is perhaps another question (i think some of the pushback against M2M includes the notion that illiquid instruments are "hard to value" hard to make precise).

I think your point about distributions is key, too: that's is Jorion's more subtle point. In risk-neutral valuation, the distribution of returns is not needed (e.g., the black-scholes does not include a projection of the stock's future price, as Manoj says, it is based on a no-arbitrage idea and the knowledge that the replicating portfolio will always have the same payoff renders useless the need for a distribution, in a valuation only!). But estimating losses needs some view of a distribution. So, concretely: to price an option via Black-Scholes, we don't need stock distribution; to estimate our downside exposure, we do (even if simulated).

David