Multifactor Models of Risk and Return

Résumé du document

The assumptions about the capital market theory expands on to that of the Markowitz portfolio model, and includes consideration of the risk-free rate of return. The correlation and covariance of any asset with a risk-free asset is zero, so that any combination of an asset or portfolio with the risk-free asset generates a linear return and risk function. Therefore, when you combine the risk-free asset with any risky asset on the Markowitz efficient frontier, you derive a set of straight-line portfolio possibilities. The dominant line is the one that is tangential to the efficient frontier. This dominant line is referred to as the capital market line (CML), and all investors should target points along this line depending on their risk preferences. Since all investors want to invest in the risky portfolio, this portfolio, referred to as the market portfolio, must contain all risky assets in proportion to their relative market values. Moreover, the investment decision and the financing decision can be separate because, although everyone will want to invest in the market portfolio, investors will make different financing decisions about whether to lend or borrow based on their individual risk preferences. Given the CML and the dominance of the market portfolio, the relevant risk measure for an individual risky asset is its covariance with the market portfolio, that is, its systematic risk. When this covariance is standardized by the covariance for the market portfolio, we derive the well-known beta measure of systematic risk and a security market line (SML) that relates the expected or required rate of return for an asset to its beta measure.

Extraits

[...] Hence, the only difference between the alternative portfolios is the proportion of the risky asset portfolio in the total portfolio. To attain a higher expected return than is available at point M (in exchange for accepting higher risk) you can either invest along the efficient frontier beyond point such as point or, add leverage to the portfolio by borrowing money at the risk-free rate and investing in the risky portfolio at point M The Market Portfolio: Because portfolio M lies at the point of tangency, it has the highest portfolio possibility line Everybody will want to invest in Portfolio M and borrow or lend to be somewhere on the CML Therefore this portfolio must include ALL RISKY ASSETS Because the market is in equilibrium, all assets are included in this portfolio in proportion to their market value Because it contains all risky assets, it is a completely diversified portfolio, which means that all the unique risk of individual assets (unsystematic risk) is diversified away Systematic Risk : Only systematic risk remains in the market portfolio. [...]

[...] If the alpha is zero, the stock is on the SML and is properly valued in line with its systematic risk. Calculating Systematic Risk: The Characteristic Line : The systematic risk input for an individual asset is derived from a regression model, referred to as the asset's characteristic line with the market portfolio: R it = a i + b i R Mi + The characteristic line (Equation 8.7 ) is the regression line of best fit through a scatter plot of rates of return for the individual risky asset and for the market portfolio of risky assets over some designated past period. [...]

[...] In their study, the most significant variables were book-to-market value (BE/ME) and size. Subsequent studies both supported their findings and differed with them because some more recent authors have found a significant relationship between beta and rates of return on stocks. Another problem has been raised by Roll, who contends that it is not possible to empirically derive a true market portfolio, so it is not possible to test the CAPM model properly or to use the model to evaluate portfolio performance. [...]

[...] Relaxing the Assumptions Differential Borrowing and Lending Rates (heterogeneous Expectations and Planning Periods) Zero Beta Model (does not require a risk-free asset) Transaction Costs (with transactions costs, the SML will be a band of securities, rather than a straight line ) Heterogeneous Expectations and Planning Periods (will have an impact on the CML and SML) Taxes (could cause major differences in the CML and SML among investors) IV. Empirical Tests of the CAPM When testing the CAPM, there are two major questions. First, How stable is the measure of systematic risk (beta)? Because beta is our principal risk measure, it is important to know whether past betas can be used as estimates of future betas. Second, Is there a positive linear relationship as hypothesized between beta and the rate of return on risky assets? [...]

[...] When we relax several of the major assumptions of the CAPM, the required modifications are reasonably minor and do not change the overall concept of the model. Empirical studies have indicated stable portfolio betas, especially when enough observations were used to derive the betas and there was adequate volume. Although the early tests confirmed the expected relationship between returns and systematic risk (with allowance for the zero-beta model), several subsequent studies indicated that the univariate beta model needed to be supplemented with additional variables that considered skewness, size, leverage, and the book value/market value ratio. [...]