# Capital Asset Pricing Model (CAPM)

The Capital Asset Pricing Model is the keystone of the academic Modern Portfolio Theory developed in the Fifties and Sixties.  Its leading lights, Harry Markowitz, William Sharpe and Merton MIller, received the Nobel Prize in Economics for their role in developing this theory.

Taking a very simple view, the main difference between the CAPM and what I described in my Alpha and Beta post is the explicit introduction of a “risk-free” asset, normally thought of as being treasury bills.

Here’s the Alpha and Beta equation:

stock return = α + β(index return) + ε,

where α is a constant, β is the multiplier that links stock return and market return, and ε is a random error term.  (Although the theory doesn’t require it, the “index” has typically been interpreted as a stock market index, like the S&P 500.)

If we argue that the stock return has two components, the risk-free return (rf)  + the return for taking risk, then the equation can be rewritten as:

stock return = rf + α + β(index return – rf) + ε,

where β (a slightly different β from the first equation, but the same general idea) is a measure of the volatility of a stock vs the market, and α (a different α, sometimes called Jensen’s alpha) is any return that remains, positive or negative.

Another way of putting this is to say that the stock return consists of two elements:  the risk-free return plus a risk premium.  The stock return can, in turn, be broken down into two components: β, or systematic return, the return from owning a stock of a certain volatility; and α, the extra or non-systematic reward for owning this particular stock.  Non-systematic risk can be diversified away; systematic risk cannot.

If one assumes, as CAPM does, that everybody:

1.  has exactly the same information

2.  has the same skill in assessing information

3.  has the same ability and desire to put an investment plan into action, and

4.  has the same investment objectives and tax situation

then, according to CAPM, it follows that there can be no positive α.  α can be at best zero and is most likely a negative number.  Thus, the best one can do is, a la Markowitz, to create one or more portfolios of stocks where as much α as possible is diversified away.  All other things being equal, the more stocks in the portfolio, the greater the chance that the αs will cancel each other out.

Therefore, the “best” portfolio out of the collection of “efficient” portfolios–greatest return for a given level of risk– turns out to be the index itself.  An investor can do no better than to hold treasury bills and an index fund, varying the proportions according to one’s risk preferences.

There have been a number of criticisms of CAPM, including:

1.  The actual working of the stock market doesn’t follow the theory particularly well.  (Strictly speaking, the market portfolio could be understood to contain all risky assets, including real estate, fine art, intellectual property…If so,one might argue that the stock market isn’t a good proxy for the optimal portfolio of risky assets–hence the mismatch between theory and the real world.  But then another issue emerges–that you can’t get your arms around what the market portfolio actually is).

2.  The simplifying assumptions I mentioned above about the actions and beliefs of market participants are really sweeping.  It’s not clear (to me, anyway) how they could be modified to make them more realistic without losing all ability to get to the results that CAPM wants.

3.  The statistical methods only work under the assumption that risky-asset returns are arranged in an orderly “normal” pattern.  At least as far as the stock market is concerned, they’re not.

4.  The advocates of the theory are not disinterested observers.  They make their living by teaching theories of this sort.  If there were such a thing as α, it would make more sense for a  budding investor to apprentice himself to a practicing portfolio manager than to learn academic theory in business school.  So in a sense academics are marketing what they have in their own inventories.

There is one thing to be said, if not for the theory, then for its conclusions.  Where are the managers achieving positive alpha?  Studies seem to show that in the US stock market at least, they are few and far between.