The CAPM equation is:
where βi = Cov (Ri, RM) / Var (RM)
CAPM is used to determine the required rate of return for any risky asset. It uses the SML or security market line to compare the relationship between risk and return. Unlike the CML, which uses standard deviation as a risk measure on the X axis, the SML uses the market Beta, or the relationship between a security and the marketplace.
The use of beta enables an investor to compare the relationship between a single security and the market return, rather than a single security with each and every security (as Markowitz did). Consequently, the risk added to a market portfolio (or a fully diversified set of securities) should be reflected in the security's beta.
E(RM) - RF is the market risk premium, while the risk premium of the security is calculated by β(E(RM) - RF).
The SML represents the required rate of return, given the systematic risk provided by the security. However, if the expected rate of return exceeds this amount, then the security provides an investment opportunity for the investor. The difference between the expected and required return is called the alpha (α) or excess rate of return. The alpha can be positive when the stock is undervalued (it lies above the SML), or negative when the stock is overvalued (it falls below the SML). The alpha becomes zero when the stock falls directly on the SML (properly valued).
Security Market Line vs. Capital Market Line:
I. a beta of zero.
II. a high yield.
III. a total risk of 1.
IV. no place in an efficient portfolio.
A. economic factors.
C. systematic risk.
A. Return on the market
B. Measure of risk
C. Risk-free rate
A. expected return to standard deviation.
B. expected return of securities to expected return of portfolios.
C. efficient sets of portfolios to the risk-free rate.
D. expected return to beta.
E. standard deviation to risk.
5 + 1.2(8 - 5) = 8.6%
A. He has 1.33 invested.
B. He has 0.67 invested.
C. He has 1.67 invested.
A. higher, higher.
B. lower, lower.
C. higher, lower.
I. The SML provides a benchmark for evaluating expected investment performance.
II. The SML leads all investors to invest in the same portfolio of risky assets.
III. The SML is a graphic representation of the relationship between expected return and beta.
IV. Properly valued assets plot exactly on the SML.
A. the simple relationship between risk and return
B. the theoretical relationship between systematic risk and expected return
C. the graphical depiction of the risk/return relationship.
The CAPM is the theoretical relationship between systematic risk and expected return, which when graphed gives us the SML.
A. shows the risk-return relationship of the CAPM in well-functioning markets
B. is kinked when there is borrowing at rates higher than RF
C. a graphical depiction of the CAPM
The SML is the graphical representation of the CAPM, not the same thing as the CAPM. It is not dependent on the markets functioning well. The SML is not affected by different borrowing rates.
A. Above the security market line.
B. On the Y-axis.
C. Below the security market line.
Slope = rise/run = (16% - 5%) / (24% - 0%) = 0.46
BetaQ = COVQ,M/VARM = 0.0750/0.242 = 1.30
A. Both A and B are overvalued.
B. A is overvalued and B is undervalued.
C. B is overvalued and A is undervalued.
According to the CAPM, a security with a beta of 1.1 has a required return = 6% + 1.1(16% - 6%) or 17%. Therefore, A (expected return = 14%) is overvalued, and B (expected return = 18%) is undervalued.
A. have positive betas.
B. have negative betas.
C. have zero alphas.
If your wealth is divided between the market portfolio and the risk-free asset, the portfolio beta equals the fraction invested in the market portfolio. It is instructive to prove this either by using the CAPM equation directly or by calculating the covariance between the portfolio and the market.
A. The expected risk premium on an investment is proportional to its beta
III. Standard deviation
A. I and II
Beta: a measurement of the volatility of a security with the market in general. A greater beta coefficient than 1 indicates systematic risk greater than the market, while a beta of less than 1 indicates systematic risk less than the market.
A. security market line
I. A portfolio that lies above the Security Market Line (SML) is under-priced.
II. The correlation between two portfolios on the SML equals +1.
III. Portfolios that lie on the Capital Market Line (CML) are as completely diversified as possible.
IV. Portfolios that lie on the SML are not necessarily completely diversified.
A. I, III and IV
The Capital Market line is a combination of the risk-free asset and the tangency portfolio that lies on the efficient frontier of risky assets. Hence, the CML consists entirely of efficient portfolios (and every single efficient portfolio must lie on the CML). Further, all the portfolios that lie on the CML are perfectly positively correlated. The SML, on the other hand, plots the expected return of a security against its beta. CAPM then implies that the SML is a straight line with the intercept representing the risk-free rate. Every single investment security that is fairly priced must lie on the SML. Thus, not every portfolio that lies on the SML is an efficient portfolio or completely diversified.
The Security Market Line (SML) is a plot of the expected returns on securities against their betas. CAPM implies that the slope of the SML equals the market risk premium and the intercept equals the risk-free rate. Hence, the data given in the problem imply that the market premium is 8.9%.
To calculate the expected return on the security using CAPM, we must first find its beta. The beta of the security equals the covariance between the security and the market divided by the market variance. Also, the covariance equals the product of the correlation coefficient and the individual standard deviations. Hence, the covariance between the security and the market equals 0.23 * 0.15 * 0.19 = 0.0066. Therefore, the beta of the security equals 0.0066/(0.152) = 0.29. Therefore, the CAPM expected return on the security equals 4.9% + 0.29 * 8.9% = 7.49%.
Since it is fairly priced and its expected rate of return is equal to that of the market portfolio, its beta must be 1.
0.5 x 1.6 + 0.5 x 0.7 = 1.15.
A. Short sell securities that have a beta of less than one and purchase the market portfolio.
Short selling is a form of borrowing . Therefore by borrowing to invest in the market portfolio, you increase the leverage in the portfolio and consequently, its beta. However, according to CAPM, this higher beta should lead to higher expected returns.
A. Since Stock A has an expected return of 11.41%, it must be overpriced.
Step 1. Calculate the expected return on Stock A: E(R) = (.10)(12%) + (.25)(15%) + (.40)(8%) + (.25)(-9%) = 5.9%
Step 2. Relative Comparison: Stock A's E(R) is 9.64%, and stock B's E(R) is 10.51%.
Step 3. Conclusion: Stock A is overpriced (this results a lower expected return.)