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Subject 4. Applications of the CAPM PDF Download
Estimate of Expected Return. Apply the CAPM formula to calculate the expected return of an asset or project.
Ri - Rf = αi - βi (Rm - Rf)
If we compare the SML and the SCL:
Portfolio Performance Evaluation. Four ratios are commonly used for this purpose.
- Sharpe Ratio
- It uses standard deviation, not beta, as a measure of volatility.
- The ratio itself is not very informative.
- Treynor Ratio
- M-Squared (M2)
- Jensen's Alpha
If an investor holds a portfolio that is not fully diversified, total risk matters. Sharpe ratio and M-squared are appropriate performance measures in such cases. On the other hand, if the portfolio is well-diversified, Treynor ratio and Jensen's alpha are relevant, as only the systematic risk of the portfolio matters.
Security Characteristic Line. A security characteristic line (SCL) graphs the relationship between the excess market return and excess security return.
While there is only one SML, there are many different SCLs for securities with different betas.
Security Selection. Overvalued and undervalued securities are those securities that do not lie on the SML line. By definition, securities that are efficiently priced should fall directly on the (calculated) SML line. If a security is above the line it is deemed undervalued since it is providing more expected return than what is demanded for that risk level. Securities falling below the SML line, on the other hand, provides less return than the market demands. Securities that fall below the SML are considered overvalued. In the former case, the security price will be bid up, such that the expected return declines and the security falls back to the SML line. In a situation where the security is overvalued, the security price declines until the expected return rises.
All assets and all portfolios should plot on the SML.
- Stock C has an estimated rate of return equal to its systematic risk or required rate of return.
- Stock B is expected to provide a rate of return above the required rate of return.
- Stock A is expected to provide a rate of return below the required rate of return.
- Investors should buy B (undervalued).
- Investors should sell A (overvalued).
Constructing a Portfolio
As the number of securities increases, the portfolio manager can eliminate unsystematic risk (or diversifiable risk) and focus on systematic or undiversifiable risk. As you can see, much of the unsystematic risk can be diversified away in as few as 30 securities.
To construct a market portfolio you can start with a portfolio of securities like the S&P 500. You can then evaluate the α of any security, using the CAPM and the S&P 500 as the market portfolio. If the α is positive, add the security to the portfolio. If a security's α is negative and it is already included in the portfolio, remove it. You can also use the information ratio of each individual security to determine the relative weight of the security in the portfolio.
Learning Outcome Statementsh. describe and demonstrate applications of the CAPM and the SML;
i. calculate and interpret the Sharpe ratio, Treynor ratio, M2, and Jensen's alpha.
CFA® 2022 Level I Curriculum, , Volume 5, Reading 50
User Contributed Comments 6
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|Allen88||ut doesn't a positive alpha comes from most recent returns and thus we still have uncertainty about its future returns???|
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