I see rating agencies have downgraded Lehman and AIG today. Do you need further proof of their worthlessness? What I don’t get most about them is this: How a company’s capital requirement is depended upon a rating? (Such as having to raise such and such capital if their rating gets downgraded to a certain level.) I wonder going forward if companies are going to let ratings agencies have such power over their debt offerings?
I sincerely chuckle at people, especially at so called “professionals” at my firm, that tell others, especially clients, that investment grade credit spreads for example are the cheapest in 20years. Investment grade? Get a clue people. Rating agencies are a complete and utter joke. I also don’t understand why Wall Street uses Gaussian distributions to model risk when the model breaks each time there is a market crisis or dislocation. You got Portfolio Managers stating foolish things like “these spread movements are a 15 sigma event”. I just walk away shaking my head and saying “maybe you should consider fat tails” So a question for Joey - Why does the majority of Wall Street or the financial community model risk based on Gaussian distributions instead of Levy alpha-stable distributions? Isn’t the work of Benoit Mandelbrot held in high esteem? So why doesn’t Wall Street use it?
- Saying that spreads are a 15 sigma event doesn’t have anything to do with Gaussian anything until you start putting probabilities on it. 2) We like Mandelbrot and think he is smart. 3) Levy distributions would imply that securities don’t have variances, which causes a real philosophical issue. If the variance is infinite, then the risk is infinite and we have St. Petersburg paradoxes everywhere. We would need to think about the limits of risk differently and think that risk is actually limited because of utility or bankruptcy or finite wealth or something. 4) Levy distns are also wrong and they are intractable. Why substitute an intractable thing for tractable thing when they are both wrong? 5) No quant really believes in the sort of ubiquitous normal distn that you are talking about. If you throw out normal dist’ns, you throw out stochastic calculus which is a primary tool for pricing derivatives. Alas, you can’t just fix it up with Levy distns.
But you can still model risk with something other than a Gaussian. You could provide EVT estimates of risk in addition to VAR. You can just use a power law for the tail.
^ you bet. An excellent thing to do…
I’ve been thinking about this more and I had an interesting (maybe) thought. So we try to do lots of stuff with our model of stock price so that we can get it to be a decent reflection of what we observe about prices. For example, there is just no Gaussian model that explains the stock market crash. And above I wrote that “you can’t fix up stochastic calculus with Levy distns”. Actually, that’s BS. To fix this up, we just make the rate at which time moves to be stochastic. Imagine, for instance, that each tick of time happens with an exponential distribution and then allow the mean of that distribution to change. You can get a stochastic calculus with Levy distributions and explaining stck market crashes is easy. You can even say that you have a process with constant volatility, it’s just that we packed 25 years into 1 day. That means that the normal distn comes about by saying that time moves linearly and deterministically and you can get just about any other distribution by loosening up that restriction. You can get option smiles, stock market crashes, skews, and a fix for stochastic calc. What’s pretty interesting to me is that I have read a ton of stuff about changing the numeraire of the process, e.g., you don’t do risk neutral valuation in bank account terms but in zero coupon bond terms, but nowhere that I know of (which probably doesn’t meaan that much) does anyone change the numeraire of time. We get normality everywhere because time usually does move deterministically and linearly. We exxperience time moving deterministically and linearly so we impose it on our models. Cool, I think. BTW - I’m probably not the first person to think of this, but it’s exciting to me so I thought I would share it.