Capital Asset Pricing Model

William Sharpe and others asked the follow up question: If rational investors follow the Markowitzian prescription, what kind of relationship exists between risk and return? Essentially, the capital asset pricing model (CAPM) developed by them is an exercise in positive economies. It is concerned with two key questions:

1. What is the relationship between risk and return for an efficient portfolio?
2. What is the relationship between risk and return for an individual security?

The CAPM, in essence predicts the relationship between the risk of an asset and its expected return. This relationship is very useful in two important ways. First, it produces a benchmark for evaluating various investments. For example when we are analyzing a security we are interested in knowing whether the expected return from it is in line with its fair return as per the CAPM. Second, it helps us to make an informed guess about the return that can be expected from an asset that has not yet been traded in the market. For example, how should a firm price its initial public offering of stock?

Although the empirical evidence on the CAPM mixed, it is widely used because of the valuable insight it offers and its accuracy is deemed satisfactory for most practical applications. No wonder the CAPM is a centerpiece of modern financial economics and William Sharpe, its principal originator, was awarded the Nobel Prize in Economics.

This article discusses various aspects of the CAPM; in addition, it explains the basics of arbitrage pricing theory (APT) which has been proposed as an alternative to the CAPM. It is organized into six sections as follows:

1. Basic assumptions
2. Capital market line
3. Security market line
4. Inputs required for CAPM
5. Empirical evidence on CAPM
6. Arbitrage piercing theory

Basic Assumptions:

The CAPM is based on the following assumptions

1. Individuals are risk averse
2. Individuals seek to maximize the expected utility of their portfolio over a single period planning horizon.
3. Individuals have homogeneous expectations and they have identical subjective estimates of the means, variances, and covariance’s among returns.
4. Individuals can borrow and lend freely at a risk less rate of interest.
5. The market is perfect; there are no taxes; there are no transactions costs; securities are completely divisible; the market is competitive.
6. The quantity of risky securities in the market is given.

Looking at these assumptions, one may feel that CAPM is unrealistic. However the value of a model depends not on the realism of its assumption but on the validity of its conclusions. Extensive empirical analysis suggests that there is a lot of merit in the CAPM.

Capital Market Line:

In the discussion of portfolio theory, it is learnt that rational investors would choose a combination of Rf and S (S represents the point on the efficient frontier of risky portfolio were the straight line emanating from Rf is tangential to the efficient frontier). If all investors attempt to purchase the securities in S and ignore securities not included in S, prices of securities would be revised. On the one hand, prices of securities included in S would rise and hence their expected returns will fall. This would shift S, along with other points which share securities with S, to the right of its initial position. On the other hands, prices of securities not included in S will fall, leading to an increase in their expected return. Consequently points reporting portfolios in which these securities are included will shift leftward. Finally, the set of prices reached would be such that every security will enter at least one portfolio on the linear segment KML. Of course, the market portfolio would itself be a point on that linear segment.

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