Capital Asset Pricing Model

The capital asset pricing model (CAPM) is a theoretical framework predicts equilibrium expected returns on risky assets. CAPM is a one-factor model.

Assumptions

Here are the assumptions of the CAPM:

1. Individual behavior
a. Investors are rational, mean-variance optimizers.
b. Their common planning horizon is a single period.
c. Investors all use identical input lists, an assumption often termed homogeneous expectations. Homogeneous expectations are consistent with the assumption that all relevant information is publicly available.

2. Market structure
a. All assets are publicly held and trade on public exchanges.
b. Investors can borrow or lend at a common risk-free rate, and they can take short positions on traded securities.
c. No taxes.
d. No transaction costs.

The CAPM is based on two sets of assumptions, listed above. The first set pertains to investor behavior and allows us to assume that investors are alike in most important ways, specifically that they are all mean-variance optimizers with a common time horizon and a common set of information reflected in their use of an identical input list. The second set of assumptions pertains to the market setting, asserting that markets are well-functioning with few impediments to trading. Even a cursory consideration of these assumptions reveals that they are fairly strong, and one may justifiably wonder whether a theory derived from them will withstand empirical tests. Therefore, we will devote considerable attention later in the chapter to how the predictions of the model may change when one or more of these restrictive assumptions are relaxed.

Still, the simple version of the CAPM is a good place to start. While the appropriate quantification of risk and the prediction for the exact risk–return trade-off may differ across more sophisticated variants of the model, the central implication of the basic model, that risk premia will be proportional to exposure to systematic risk and independent of firm-specific risk, remains generally valid in its extensions. In part because of this commonality, the simple CAPM remains in wide use despite its empirical shortcomings.

Therefore, we begin by supposing that all investors optimize their portfolios á la Markowitz. That is, each investor uses an input list (expected returns and covariance matrix) to draw an efficient frontier employing all available risky assets and identifies an efficient risky portfolio, P, by drawing the tangent CAL (capital allocation line) to the frontier as in Figure 9.1, Panel A. As a result, each investor holds securities in the investable universe with weights arrived at by the Markowitz optimization process. Notice that this framework employs Assumptions 1(a) (investors are all mean-variance optimizers), 2(a) (all assets trade and therefore can be held in investors’ portfolios), and 2(b) (investors can borrow or lend at the risk-free rate and therefore can select portfolios from the capital allocation line of the tangency portfolio).

The CAPM asks what would happen if all investors shared an identical investable universe and used the same input list to draw their efficient frontiers. The use of a common input list obviously requires Assumption 1(c), but notice that it also relies on Assumption 1(b), that each investor is optimizing for a common investment horizon. It also implicitly assumes that investor choices will not be affected by differences in tax rates or trading costs that could affect net rates of return (Assumptions 2[c] and 2[d]).

Not surprisingly in light of these assumptions, investors would calculate identical efficient frontiers of risky assets. Facing the same risk-free rate (Assumption 2[b]), they would then draw an identical tangent CAL and naturally all would arrive at the same risky portfolio, P. All investors therefore would choose the same set of weights for each risky asset. What must be these weights?

A key insight of the CAPM is this: Because the market portfolio is the aggregation of all of these identical risky portfolios, it too will have the same weights. (Notice that this conclusion relies on Assumption 2[a] because it requires that all assets can be traded and included in investors’ portfolios.) Therefore, if all investors choose the same risky portfolio, it must be the market portfolio, that is, the value-weighted portfolio of all assets in the investable universe. We conclude that the capital allocation line based on each investor’s optimal risky portfolio will in fact also be the capital market line, as depicted in Figure 9.1, Panel B. This implication will allow us to say much about the risk–return trade-off.

History

Harry Markowitz laid down the foundation of modern portfolio management in 1952. The CAPM was published 12 years later in articles by William Sharpe, John Lintner, and Jan Mossin. The time for this gestation indicates that the leap from Markowitz’s portfolio selection model to the CAPM is not trivial.

Risks in CAMP

In the CAPM, total risk can be broken into two components: systematic risk and unsystematic risk. Systematic risk is the portion of risk that is related to the market and that cannot be diversified away. Unsystematic risk is non-market risk, risk that is idiosyncratic and that can be diversified away. Diversified investors can demand a risk premium for taking systematic risk, but not unsystematic risk.

In the CAPM, investors are only rewarded for taking systematic risk.

The Model

Required rate of return = risk-free rate + risk premium

The formula is:

required return = risk-free rate + beta * (expected market return – risk-free rate)

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