Modern Portfolio Theory and Capital Asset Pricing Model

What are the major assumptions needed to establish CAPM (as made by Sharpe, Litner, and Mossin)?

- Investments are perfectly divisible; - They are no transaction costs and/or taxes; - Full and costless information is available to all investors; - The lending and borrowing rates are equal, and are the same for all investors; and - Each investor can borrow or lend any amount at the market rate.

What is the two-fund separation theorem?

According to capital market theory, all investors will invest in two assets: the risk-free asset and the market portfolio.

The approximate tracking error for a fund that is indexed is equal to A. -12% B. 0% C. 4% D. Greater than 20%

B. 0%

The risk-free rate of interest is r = 5% and the market portfolio is characterized by E(R_M) = 13%. The betas for stocks A, B, and C are 0.5, 1.0, and 2.0, respectively. According to CAPM, what are the expected returns of the three stocks? A. E(R_A) = 5%, E(R_B) = 11%, E(R_C) = 21% B. E(R_A) = 9%, E(R_B) = 13%, E(R_C) = 21% C. E(R_A) = 14%, E(R_B) = 22%, E(R_C) = 26% D. None of the above.

B. E(R_A) = 9%, E(R_B) = 13%, E(R_C) = 21% In equilibrium, all three stocks are on the same security market line: E(R_i) = r + [E(R_M) - r)*Beta_i

In the CAPM, what is the expected return for a stock with a beta of 1? A. E(R_i) B. E(R_M) - r C. r + (E(R_M) - r) D. E(R_M)

C. r + E(R_M) - r According to the CAPM, the expected return is r + Beta[E(R_M) - r] Since the question says that the stock has a beta of 1, substituting 1 for beta gives the answer above.

If r = 4% and E(R_M) = 10%, then a stock with a beta of 1.3 is expected to return A. 10.0% B. 6.0% C. 7.8% D. 11.8%

D. 11.8%

What does beta measure? A. The volatility of the security. B. The joint volatility of any two securities in a portfolio. C. The volatility of a security divided by the volatility of the market index. D. The relative co-movement of a security with the market portfolio.

D. The relative co-movement of a security with the market portfolio.

What is the CAPM formula?

E(R_i) = R_f + Beta_i*[E(R_M) - R_f]

The Sharpe ratio and the Treynor ratio evaluate performance relative to a customized benchmark. A. True B. False

False

The realized rate of return on a stock A and stock B will be the same each month if they have the same beta. A. True B. False

False The realized return is random. CAPM predicts that the expected rates of return for Stocks A and B should be the same.

According to CAPM, the higher the variance of a security, the higher its expected return. A. True B. False

False: A security may have a higher variance of returns but still have a lower expected return because of its low beta.

Is the market portfolio the only efficient portfolio that can be formed?

No.

Define systematic risk and nonsystematic risk.

Systematic, or undiversifiable, risk is that portion of the risk that is associated with market fluctuations and therefore cannot be reduced by diversification. Non-systematic, or diversifiable, risk is that portion of risk that can be eliminated by combining the security in question with others in a diversified portfolio.

What is the difference between the Capital Market Line and the Security Market Line?

The CML shows the relationship between expected returns on an efficient portfolio and its standard deviation (See Figure 5.2). Another important relation-ship can be developed from the CML called the security market line (SML). The SML gives the relationship between the expected return for individual assets (not portfolios) and risk. However, in the SML the risk measure is systematic risk as proxied by beta, not by standard deviation as in the CML.

In the Sortino ratio, is performance compared to the performance of a risk-free asset or a client-designated benchmark?

The Sortino ratio compares a portfolio's performance to that of a client-designated benchmark which is a minimum return that the client specifies.

Here are the betas for three stocks: 3M ----------------------- 1.14 IRobot Coproration ---- 1.49 Applied Materials Inc. -- 1.64 The stock of which company is the most aggressive?

The most aggressive stock is the one with the largest beta, Applied Materials, Inc.

What is the relationship between CAPM and the market model?

These models are frequently confused because they both demonstrate a relationship between every asset and the market portfolio. The market model is an empirical model based on realized rates of return, whereas CAPM is based on expected and unobserved variables. The market model also provides a method of decomposing asset returns into two components: a systematic (or market) component and a residual (or non-market) component: r_P = a_P + b_P*r_M + e_P where r_P = R_P - r (or the excess return of the portfolio return RP over the risk-free rate r), and r_M = R_M - r (or the excess return of the market portfolio RM over the risk-free rate r). The residual component e_P is uncorrelated with the market excess return r_M. The systematic component is beta multiplied by the market excess return. The market model thus appears to be a natural framework for estimating beta. CAPM is an equilibrium pricing model, which suggests that each asset is priced so that its expected return compensates for its contribution to the risk of the market portfolio. The asset's expected return is thus found to be proportional to its beta. For a well-diversified portfolio, an asset's risk contribution will approximate its risk contribution to the market portfolio.

The beta of a security estimated from historical returns is equal to the true beta of the security. True or false? Discuss

This statement is false. The beta of a security obtained from past data is only an estimate of the true beta, which is unknown. The estimate is subject to statistical estimation errors and the true beta, at best, can be said to fall within a confidence interval with a given probability (the confidence level).

The Capital Market Line dominates the efficient frontier once a risk-free asset is introduced. A. True B. False

True