Thursday, 25 September 2008

On 'Fundamental Value'

There is a lot of talk at the moment about fundamental value. This mostly focusses on how good it would be if the market prices of assets rose back towards 'fundamental value', and what the government could do to assist that process.

There's only one problem. You can never know what the number is.

Consider a loan. Either it defaults, in which case you get some interest followed by recovery; or it doesn't, in which case you get scheduled P&I. In both cases the fundamental value is the PV of the cashflows. But you don't know whether it will default or not, so you can't combine the fundamental value on default with that for no default to get a single number.

In credit risk modelling we solve this problem by positing a probability of default, and then deriving that PD from spreads. But that's an argument that depends on the credit spread being fair compensation for default risk.

And of course ontologically it makes no sense to talk about a 'probability' of default. Either default happens or it doesn't and we only get one chance at finding out. Given that we can't take the same obligator, duplicate them a hundred times, and look at their performance on each occasion, we can never know that our 'probability' is correct. Thus there is literally no such thing as a 'fundamental value' in any scientific sense because we could never know whether we had such a thing.

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Blogger Timothy said...

Hi David, Presumably the point is even stronger regarding "correlation of default" which always looked to me to be so completely nebulous as to be a meaningless concept in many credit derivative models (although funnily enough somewhat more useful in mortgages than in corporate baskets). It is easy to posit situations were there are both positive and negative correlations between firms (the bankruptcy of a competitor my imply a distressed industry or the end of a price war), plus it says nothing about time as even if a correlation was 100% then it is possible for the default to occur at different times, one outside the life of a derivative.

7:16 am  
Blogger David Murphy said...

Absolutely. It makes sense to talk about a equity/equity return correlation because you can observe the actual returns and see if you were right. [Non-parametrically, of course - in reality the comovement of returns is not captured by something as simple as a single correlation, but that is another story. The point we can falsify the conjecture 'IBM and C have a return correlation of 0.3' because we can actually observe the returns and see if they do.]

Default correlations are another matter. The same two firms do not default repeatedly so 'default correlation', read as a statement about what happens, makes no sense. Of course they way it is actually used is as a statement about the price of tranches. That is, when I say 'default correlation = 0.3' what I mean is 'if I put a default correlation of 0.3 into a Gaussian Copula model, I recover the correct price of the tranche I am talking about'. To use the jargon, default correlation is an epi-phenomenon based on prices. It is not a statement about the world.

8:22 am  
Blogger Timothy said...

Hi David, There is however the problem that an set of equity prices is not really a proper time series so we still need to be wary, the equity price represents a share in a business which may change quite radically in both what it does and in how it structures it balance sheet even over quite short periods of time. This is not to say that the concept is not useful, just that we need to remain on guard.

8:30 am  
Blogger David Murphy said...

I agree completely. Similarly the volatility of the Dow is inherently problematic given that companies move in and out of it the whole time, change their business etc. Normally we gloss over this but exactly as you say it is worth remembering that we are assuming something in that process.

8:34 am  

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