Archive for the ‘General Finance’ Category

The Capital Asset Pricing Model

Wednesday, April 15th, 2009

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.

Is the capital pricing model flawed

Wednesday, April 15th, 2009

Is the capital asset pricing model flawed?  Is risk defined by volatility? Or is it something more of which the model cannot capture correctly?

For those of you without the technical knowledge. CAPM assumes that beta, or the volatility of a stock, is defined by how correlated that stock moves with the market as a whole. If the beta is 1, it perfectly matches the market, -1, it perfectly does opposite of what the market does, and so on. This is used to define the rate of return on equity, which estimates the cost of capital to the firm.

But is that really risk? I mean, you can have a very volatile security with an expected return of 1%-100%, and I bet you almost anyone out there would love to own it. It’s volatile, but not risky.

Should risk be redefined? Something such as the possibility of a negative utility towards the holder?

I’m not alone in this either. Warren Buffet (whom should be worshipped) agrees and doesn’t ahere to this definition of risk either. In his 2006 letter to his shareholder’s he criticizes the Efficient Market Theory.

quote:

Let me end this section by telling you about one of the good guys of Wall Street, my long-time
friend Walter Schloss, who last year turned 90. From 1956 to 2002, Walter managed a remarkably
successful investment partnership, from which he took not a dime unless his investors made money. My
admiration for Walter, it should be noted, is not based on hindsight. A full fifty years ago, Walter was my
sole recommendation to a St. Louis family who wanted an honest and able investment manager.

Walter did not go to business school, or for that matter, college. His office contained one file
cabinet in 1956; the number mushroomed to four by 2002. Walter worked without a secretary, clerk or
bookkeeper, his only associate being his son, Edwin, a graduate of the North Carolina School of the Arts.
Walter and Edwin never came within a mile of inside information. Indeed, they used “outside” information
only sparingly, generally selecting securities by certain simple statistical methods Walter learned while
working for Ben Graham. When Walter and Edwin were asked in 1989 by Outstanding Investors Digest,
“How would you summarize your approach?” Edwin replied, “We try to buy stocks cheap.” So much for
Modern Portfolio Theory, technical analysis, macroeconomic thoughts and complex algorithms.

Following a strategy that involved no real risk – defined as permanent loss of capital – Walter
produced results over his 47 partnership years that dramatically surpassed those of the S&P 500. It’s
particularly noteworthy that he built this record by investing in about 1,000 securities, mostly of a
lackluster type. A few big winners did not account for his success. It’s safe to say that had millions of
investment managers made trades by a) drawing stock names from a hat; b) purchasing these stocks in
comparable amounts when Walter made a purchase; and then c) selling when Walter sold his pick, the
luckiest of them would not have come close to equaling his record. There is simply no possibility that what
Walter achieved over 47 years was due to chance.

I first publicly discussed Walter’s remarkable record in 1984. At that time “efficient market
theory” (EMT) was the centerpiece of investment instruction at most major business schools. This theory,
as then most commonly taught, held that the price of any stock at any moment is not demonstrably
mispriced, which means that no investor can be expected to overperform the stock market averages using
only publicly-available information (though some will do so by luck). When I talked about Walter 23 years
ago, his record forcefully contradicted this dogma.

And what did members of the academic community do when they were exposed to this new and
important evidence? Unfortunately, they reacted in all-too-human fashion: Rather than opening their
minds, they closed their eyes. To my knowledge no business school teaching EMT made any attempt to
study Walter’s performance and what it meant for the school’s cherished theory.
Instead, the faculties of the schools went merrily on their way presenting EMT as having the
certainty of scripture. Typically, a finance instructor who had the nerve to question EMT had about as
much chance of major promotion as Galileo had of being named Pope.

Tens of thousands of students were therefore sent out into life believing that on every day the price
of every stock was “right” (or, more accurately, not demonstrably wrong) and that attempts to evaluate
businesses – that is, stocks – were useless. Walter meanwhile went on overperforming, his job made easier
by the misguided instructions that had been given to those young minds.

After all, if you are in the shipping business, it’s helpful to have all of your potential competitors be taught that the earth is flat. Maybe it was a good thing for his investors that Walter didn’t go to college.

Does CAPM assume that the efficent market hypothesis is correct? Or is it simply a religion?

Is Beta dead?