Comments on: Arbitrary CAPM

By: dsquared

dsquared — Sat, 30 Jan 2010 21:38:40 +0000

unless I’ve forgotten or misremembered (which is entirely possible), mean-variance optimisation is optimal for a) anyone who has a quadratic utility function whatever the distribution of returns or b) anyone of any sort of utility function if returns are lognormally distributed.

By: ian_db

ian_db — Sat, 30 Jan 2010 13:32:00 +0000

The linearity comes from investors being mean-variance optimizers. there’s no normality or log-normality anywhere in the model. nevertheless, i agree with others that this is silly.

By: sgibson

sgibson — Fri, 29 Jan 2010 21:05:27 +0000

The misuse of the word simplistic is almost Freudian.

By: dsquared

dsquared — Fri, 29 Jan 2010 19:47:46 +0000

… adding some intuition to the above, if you have a portfolio of securities X, Y and Z, what is the return on the portfolio? It’s the sum of the returns on X, Y and Z, isn’t it? It’s basically a linear problem (unless you start assuming very complicated things indeed) which is why it’s modelled with a linear model.

By: dsquared

dsquared — Fri, 29 Jan 2010 19:38:30 +0000

I’m seconding Alex R – that’s actually quite an ignorant comment and I’m really surprised that Derman passed it on approvingly. The “linear” relationship of the CAPM isn’t imposed on the model – it’s a consequence of the quadratic programming, the assumption of a lognormal distribution (or alternatively the assumption of quadratic utility IIRC). There are all sorts of reasons to dislike the one-period CAPM, and I blog about them intermittently, but someone who thinks you could just randomly substitute in a cubic relationship is not really someone I want on “team anti-CAPM”.

By: Lilguy

Lilguy — Fri, 29 Jan 2010 19:25:52 +0000

AlexR–As an MBA grad myself from a quant grad school many years ago, the simplicity of the CAPM was confused by many as “elegance.” And it certainly isn’t science by any metric, then or now. It doesn’t even meet most criteria for being “statistics.”

You may not know it, but I think you’ve been absorbed by the bankonomics borg. Beware!

By: AlexR

AlexR — Fri, 29 Jan 2010 17:54:10 +0000

I’m a little puzzled by Derman’s student’s comment: the linearity in the CAPM is just a consequence of efficient markets/no-arbitrage and the ability of large banks and investors to lend or borrow freely at the risk-free rate. Now both of these are certainly not exactly correct, but they are either almost correct or at least a standard economic assumption.

On the broader question of whether what financial economists and analysts do is “science” is the sense of “reflecting reality” — well, it is as long as it works. But I guess I don’t get how that’s all that different from any other kind of science — especially social science.

By: KenInIL

KenInIL — Fri, 29 Jan 2010 16:11:55 +0000

I had somewhat the same reaction to Black-Scholes after reading the 1997 not-really-a-Nobel economics announcement. It is certainly more complicated than a linear equation, but the model is explicitly based on several not-true-in-reality assumptions. It seemed that the only reason it worked to price options was that everyone had decided to adopt the formula to price their options!

By: Uncle_Billy

Uncle_Billy — Fri, 29 Jan 2010 15:16:23 +0000

Nonsense. Gauge theory is your friend in the financial business.