Monday, May 12, 2008

VaR, Capital, and Default Rates

I was reading the Jorion's book Value at Risk, and was struck by the little note where he pointed out that, say, if you want to target a BBB default rate, you merely look at the capital sufficient so that the probability of hitting this extreme event is equal to an annualized default rate of 0.3% or so (the BBB annual default rate). I see this mentioned a lot, and I think it is pretty silly. VaR has its purposes, but setting top-down capital allocations is not one of them.

My problem here is that he implicitly assumes people are looking at the issue as a Master Trust versus like a set of static pools of debt. In a master trust, you have a sequence of new business coming on, and so the value of the master trust, if ever below liabilities, implies default. But no businesses have their present value calculated like a master trust. Instead, it is like a static pool: assets that are market to market are not the present value of the future strategy, but merely the value of the particular assets on the book at this time. You can mark to market various vintages of assets: those put on in various months, each with its own vintage. The present value of this strategy is not a direct function of those static pools, because you change your underwriting strategy over time, often because over time a strategy becomes obsolete. Even a true Master Trust might have an endogenously shifting underwriting standards.

Or to use a different example, lets say I were to buy low volatility assets with positive momentum. This is what I did in the Falken Fund from 1996-2001, which outperformed the S&P by 10% per year, and which Telluride tried to get me to never do again (one would think prior use allows one to use this idea going forward, but this might take a jury of my peers). Now lets say this strategy of longs had a mark-to-market below the value of my liabilities. Does that mean I'm bankrupt? Only if I am stuck with these specific longs forever. In that case, my current negative NPV means my strategy's NPV is also negative. But if I can adjust my algorithm, this just means that iteration of the strategy is a loser. Or, maybe this is only a temporary setback for my current strategy applied to this particular set of longs. When I throw on the next batch of new longs, it might work in the next period, and I might use a new variation that throws out longs beginning with the letter X.

The key is that one never marks to market a strategy, but merely its current constituents. Thus it is not the algorithm itself that is being marked to market because it is always in flux. Thus, there is really no relation between bankruptcy, the Value-at-Risk number, and capital.

1 comment:

Anonymous said...

This post was lonely, with nobody commenting on it. Just here to offer support.