P2.T5.R36 If model underestimates risk why would too little capital be allocated?

[Karim_B]

Hi @David Harper CFA FRM
Regarding P2.T5.R36 on page 3 of the Jorion Chapter 6 Study Notes about Backtesting & Exceptions I'm a bit confused by:

"When too many exceptions are observed, the model is “bad” and underestimates risk. This is a major problem because too little capital may be allocated to risk-taking units;"

If the model understimates risk, wouldn't you allocate more capital to the unit?

Intuitively I'd allocate more capital to a less risky activity assuming the same expected return as a more risky activity.

Or is this taking the perspective that the allocation is made after the backtesting results are in, and you can see that the model underestimates risk, so you'll allocate less capital to it than you would have if the model were correctly estimating risk since you can't trust the current model?

Thanks
Karim

 

[David Harper CFA FRM]

Hi @Karim_B

Right, good point. There is a before versus after perspective. Using Jorion's example, imagine now at the beginning of 2018, we develop a 99.0% VaR model and allocate capital according to our model. However, we are currently unaware that it is a "bad model" such that our VaR level (say, $1.0 million daily P&L) is actually a 97.0% VaR; i.e., we actually should expect to exceed the daily loss of $1.0 million on 3%*250 = 7.5 days rather than the 2.5 days we expect because we think the model is "good" or accurate. So we allocate capital accordingly.

Then at the end of the year, we "observe too many exceptions" above our $1.0 mm VaR, maybe we observe 11 because that's very plausible in our actual situation, but has a very very low p-value under our 99.0% hypothesis. In hindsight, at the end of the year, our backtest has revealed our model was actually bad (we observe too many exceptions such that we reject the null hypothesis that the model is good) and we realize that we allocated too little capital. Our VaR should have been higher, we should have allocated more. I'm confident that is the meaning if only because I've read this chapter about 583 times over the last ten years, lol I hope that's helpful!