1. A single-factor model of the economy classifies sources of uncertainty as systematic (macroeconomic) factors or firm-specific (microeconomic) factors. The index model assumes that the macro factor can be represented by a broad index of stock returns. 2. The single-index model drastically reduces the necessary inputs into the Markowitz portfolio selection procedure. It also aids in specialization of labour in security analysis. 3. If the index model specification is valid, then the systematic risk of a portfolio or asset equals b^{2}s^{2}_{m}, and the covariance between two assets equals b_{i}b_{j}s^{2}_{m}. 4. The index model is estimated by applying regression analysis to excess rates of return. The slope of the regression curve is the beta of an asset, whereas the intercept is the asset’s alpha during the sample period. The regression line also is called the security characteristic line. 5. Multifactor models seek to improve the explanatory power of single-factor models by explicitly accounting for the various systematic components of security risk. These models use indicators intended to capture a wide range of macroeconomic risk factors. 6. Once we allow for multiple risk factors, we conclude that the security market line also ought to be multidimensional, with exposure to each risk factor contributing to the total risk premium of the security. 7. A risk-free arbitrage opportunity arises when two or more security prices enable investors to construct a zero net investment portfolio that will yield a sure profit. Rational investors will want to take infinitely large positions in arbitrage portfolios regardless of their degree of risk aversion. 8. The presence of arbitrage opportunities and the resulting large volume of trades will create pressure on security prices. This pressure will continue until prices reach levels that preclude arbitrage. 9. When securities are priced so that there are no riskfree arbitrage opportunities, we say that they satisfy the no-arbitrage condition. Price relationships that satisfy the no-arbitrage condition are important because we expect them to hold in real-world markets. 10. Portfolios are called well diversified if they include a large number of securities and the investment proportion in each is sufficiently small. The proportion of a security in a well-diversified portfolio is small enough so that, for all practical purposes, a reasonable change in that security’s rate of return will have a negligible effect on the portfolio rate of return. 11. In a single-factor security market, all well-diversified portfolios have to satisfy the expected return–beta relationship of the security market line in order to satisfy the no-arbitrage condition. If all well-diversified portfolios satisfy the expected return–beta relationship, then all but a small number of securities also satisfy this relationship. 12. The APT does not require the restrictive assumptions of the CAPM and its (unobservable) market portfolio. The price of this generality is that the APT does not guarantee this relationship for all securities at all times. 13. A multifactor APT generalizes the single-factor model to accommodate several sources of systematic risk. The multidimensional security market line predicts that exposure to each risk factor contributes to the security’s total risk premium by an amount equal to the factor beta times the risk premium of the factor portfolio that tracks that source of risk. 14. A multifactor extension of the single-factor CAPM, the ICAPM, is a model of the risk–return tradeoff that predicts the same multidimensional security market line as the APT. The ICAPM suggests that priced risk factors will be those sources of risk that lead to significant hedging demand by a substantial fraction of investors.

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