Return and Risk: The Capital Asset Pricing Model (CAPM)
Return and Risk: The Capital Asset Pricing Model (CAPM)
This chapter sets forth the fundamentals of modern portfolio theory. Our basic points are these:
This chapter shows us how to calculate the expected return and variance for individual securities, and the covariance and correlation for pairs of securities. Given these statistics, the expected return and variance for a portfolio of two securities A and B can be written as
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In our notation, X stands for the proportion of a security in one's portfolio. By varying X, one can trace out the efficient set of portfolios. We graphed the efficient set for the two asset case as a curve, pointing out that the degree of curvature or bend in the graph reflects the diversification effect: The lower the correlation between the two securities, the greater the bend. The same general shape of the efficient set holds in a world of many assets.
A diversified portfolio can only eliminate some, but not all, of the risk associated with individual securities. The reason is that part of the risk with an individual asset is unsystematic, meaning essentially unique to that asset. In a well-diversified portfolio, these unsystematic risks tend to cancel out. Systematic, or market, risks are not diversifiable.
The efficient set of risky assets can be combined with riskless borrowing and lending. In this case, a rational investor will always choose to hold the portfolio of risky securities represented by point A in Figure 11.8. Then he can either borrow or lend at the riskless rate to achieve any desired point on line II in the figure.
The contribution of a security to the risk of a large, well-diversified portfolio is proportional to the covariance of the security's return with the market's return. This contribution, when standardized, is called the beta. The beta of a security can also be interpreted as the responsiveness of a security's return to that of the market.
The CAPM states that
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In other words, the expected return on a security is positively (and linearly) related to the security's beta.
