Development of the Capital Asset Pricing Model
 
Markowitz (1952) began the modern age of Finance by showing how increasing diversification lowers portfolio’s standard deviation and variance. His work was based on the idea that stock returns are normally distributed and that people like returns and do not like risk. Thus they want a high mean, low standard deviation portfolio. The portfolios that have the highest return for a given level of risk are called the mean-variance efficient frontier(MVE).

When a Risk free asset is included in the model we can draw a line from the RF rate to the MVE we have what is called a capital allocation line (CAL). We obviously want to take the highest CAL. (the one with the highest return per unit of risk-also called the coefficient of variation). Thus, the optimal CAL will be just tangent to the old MVE frontier. If the CAL is tangent at the market portfolio, then the CAL is called the capital market line (CML).

From this big beginning step, Sharpe, Linter, and Treynor (some also say Mossien) helped to develop what has become known as the Capital Asset Pricing Model (CAPM). This MODEL is one of the most famous of all financial models. As a model it is useful if it helps to explain the world. We would also like it to be accurate, but it is not always the case.

Risk can be broken into market(systematic, undiversifiable etc.) and unique(firm specific, diversifiable, unsystematic) risk. Diversified investors are concerned with market risk...Beta is an asset’s contribution to the risk of a fully diversified portfolio. Beta is calculated by regressing the asset's return against the market portfolio. Thus the beta of T-Bills is zero (explain why) and the beta of the market portfolio is 1.00.


Expected return=RF+B(ERm - RF)

It is easy to play around with this and show that it is really just y=mx+b.

            where m=slope=Beta.

            Beta=cov(i,M)/var M If i=M, then beta=1.00.

            ERm-RF=slope of Security Market Line

The assumptions of the CAPM are important and numerous.
 

1. All investors are price takers.

2. All investors have the same time horizon.

3. All investors have the same information and interpret it in the same manner. (homogeneous expectations)

4. Markets are "perfect." i.e. no transaction costs, no taxes, short selling is allowed etc.

5. All investors are risk averse.

6. The market portfolio exists

 
a. exists

b. is measureable

c. is on the MVE frontier.


Implications of these asumptions are important. For example, if investors want to hold risky assets, the only risky asset they will hold is the market portfolio. (Which is usually assumed to be only tradeable public securities--this assumption may be important (see ROLL)).

Further, if borrowing and lending are allowed at the same rate, then efficient-set extends beyond the tangency point.

CAPM



Sorry about the drawing!

The resulting line is called the Security Market Line (SML) or the zero talent line. In a perfectly efficient market all assets should lie on this line. If CAPM is correct (a big "if" as we will soon see), we can determine the expected return on any asset.

Assets off the line are improperly priced.  Those assets that fall below the line are overpriced (they offer too low of return for their risk), while those above the line are underpriced.
 

Firms can also use CAPM to find the expected risk premium on there assets:
 

expected risk premium on an asset = beta * expected risk premium on market

(r-rf) = B*(Rm-Rf) (play around for other versions)


This allows us to estimate the investors required return or equivalently the firm's cost of capital.

 
When the assumptions hold, CAPM is the only measure of risk that is needed to determine the expected return of an asset.   Thus, firm specific risk factors are unnecessary.

The CAPM is one of the most widely tested models of all time.  Empirically CAPM held quite well in the early years of the model. Since then more and more anomalies have been discovered. For example the small firm anomaly which found that small stocks earned more than large firms did even after accounting for beta.  (Subsequent work has shown that much of this small firm effect can be traced to the tax loss trading that occurs in the end of the tax year.)

A bigger problem to CAPM advocate was voiced by Roll (1976) who claimed that the market portfolio was unmeasurable and thus we could never truly test CAPM.  A possible deathblow to CAPM was FAMA-FRENCH (1992) that concluded when size and the market to book value are included in the model, Beta becomes insignificant.

Finally the joint hypothesis problem is also a problem in the testing of any market model.  This is the idea that a test is simultaneously testing both the market and the model.  Because of these difficulties, we will never be able to say definitively whether CAPM is correct or not.

Currently there are several alternatives (for example APT, Consumption CAPM, Intertemporal CAPM)  to CAPM but not have been totally endorsed.  However, CAPM is still widely used as a model.

To see what some of the best minds in the field are saying (hey the agree with me ;-) ) check out interviews with William Sharpe and also an interview with Eugene Fama.

 
Summary:

We do know