William Sharpe has written a lot about CAPM and its flaws. His book “Investors and Markets” talks a bit about it. Here’s an excerpt comparing Markowitz/CAPM to the Kenneth Arrow’s State Preference Approach:
William Sharpe posted:
Let me be careful, because I’ll get in trouble with Harry Markowitz because we have somewhat different approaches to this. But the crux of the matter is that Markowitz and the CAPM, in its original manifestation, assumed that people choose portfolios strictly on the mean and the variance of the portfolio return distribution-which is to say, you tell me two things about a portfolio an that’s all I need to know. What is its expected return and standard deviation? You give me those two numbers and I’ll choose my portfolio among a set of portfolios based on those two numbers for each portfolio. Markowitz assumes you are willing to do that and CAPM assumes everyone is willing to make portfolio decisions this way. Now why might that be true? There are two conditions under which it would be true. One is, every single portfolio you can even imagine has nice probability distribution, which, if you tell me the expected return and the standard deviation, I know the whole distribution, I know the probability of any possible outcome. And the easiest case for that is everything is the normal distribution we learned about in class.
So that’s one kind of world in which this would be a great assumption. The other kind of world in which it would be a great assumption is, “All I care about are those two numbers. I don’t care what the probability distribution looks like.” Now for this to be the case, I must have a particular kind of preference, which is called quadratic utility. So you have these two possible rationales for those approaches. But what we know is that people are increasingly coming up with investment products that have very non-normal distributions: hedge funds and protected products. You go down the list. And there are all these exotics, which, partly intentionally, have weird distributions, what’s called tail risk—small probability of a disastrous outcome. That’s the classic hedge fund approach. So the first rationalization doesn’t hold as well perhaps as it did 40 years ago, at least for some people in some cases. The second rationalization, the preference assumption, the quadratic utility, if you look at it, it doesn’t seem to conform with how most people really think about having bad things happen or good things happen.
For a number of years, I’ve tried to think about finance in terms of the State-Preference approach, to think of the future as one in which the world can be in a number of discrete states, and each one has a probability. An easy way to think about it is a spreadsheet. You’ve got a column in the spreadsheet, and each row is a different thing that could happen. Only one of them will happen, but you don’t know which one. The best you can do is say, “There’s a 10% chance it’ll be this row and an 8% chance it’ll be that row.”
“Tail risk” is obviously a major issue with CAPM, as he stated, as it assumes a normal distribution of returns. Really, most people are probably more worried about bubbles and geopolitical disasters than standard-deviation.
The state-preference approach doesn’t rely on a normal distribution, has simpler calculations (although it involves a LOT of calculations), and easier to relate to and understand the idea of risk.
A great book that goes over the theory of investments is A History of the Theory of Investments, by Mark Rubinstein.