Assuming no arbitrage opportunities exist, the risk premium on the factor portfolios F1 and F2 should be: O a. 12.14%, 9.29% O b. 9.29%, 12.14% O c. 5%,4% O d. 4%,5%
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- APT An analyst has modeled the stock of Crisp Trucking using a two-factor APT model. The risk-free rate is 6%, the expected return on the first factor (r1) is 12%, and the expected return on the second factor (r2) is 8%. If bi1 = 0.7 and bi2 = 0.9, what is Crisp’s required return?Consider the following information on the estimated factor loadings for a two-factor APT model for three well-diversified portfolios. Beta1 Beta2 E(r) Port A 1.5 .3 .15 Port B .75 .65 .15 Port C 0 1.0 .21 The risk-free rate is 1% per annum. Beta1 is the factor loading on Factor 1 and Beta2 is the factor loading for factor 2; E(r) denotes the expected return. Assume there are no transactions costs and that you can short the portfolios and borrow and lend at the risk-free rate (you can obviously go long in the portfolios too). This question has you determine whether or not there exists an arbitrage opportunity with…Consider the one-factor APT. Assume that two portfolios, A and B, are well diversified. The betas of portfolios A and B are 1.0 and 1.5, respectively. The expected returns on portfolios A and B are 19% and 24%, respectively. Assuming no arbitrage opportunities exist, the risk-free rate of return must be 14% 9% 16.5% 4%
- Suppose that you use Arbitrage Pricing Theory (APT) to evaluate well-diversified portfolios. The three factor portfolios used in an APT model, portfolios 1, 2, and 3, have expected returns E(r1) = 5%, E(r2) = 3%, and E(r3) = 8%. Suppose further that the risk-free rate (λ0) is 2%. Calculate the total return on a well- diversified portfolio with its beta on the first factor, βA1 = 1.1, beta on the second factor, βA2 = .9, and beta on the third factor, βA3 = 1.2.Assume that the following one-factor macroeconomic model describes the expected return for portfolios: Also assume that all investors agree on the expected returns and factor sensitivity of the three highly diversified Portfolios A, B, and C given in the following table: Portfolio Expected Return Factor Sensitivity A 0.09 0.50 B 0.13 0.75 C 0.17 1.50 If the model and the table are both correct, determine whether or not an arbitrage opportunity exists. If not, why not? If so, explain how to exploit it.Suppose that there are two independent economic factors, F1 and F2. The risk-free rate is 6%. The following are well-diversified portfolios: Portfolio Beta on F1 Beta on F2 Expected Return A 1.5 2.0 31% B 2.2 -0.2 27% [i]. What is the risk premium for F1?
- Consider the multifactor APT. There are two independent economic factors, F1 and F2. The following information is available about two well-diversified portfolios with risk free rate of 5%. Portfolio β on F1 β on F2 Expected Return A 1.0 2.0 17% B 2.0 0.5 14% What's the risk premium of Factor 2 portfolio? Group of answer choices 4% 3% 8% 9%We believe that the single factor model can predict any individual asset’s realized rate of return well. Both Portfolio A and Portfolio B are well-diversified: ri = E(ri) + βiF + Ei, where E(ei) = 0 and Cov(F, i) = 0 A B β 1.2 0.8 E(r) 0.1 0.08 (1) What is the rate of return of the risk-free asset? (2) What is the expected rate of return of the well-diversified portfolio C with βC = 1.6, which also exists in the market? (3) A fund constructs a well-diversified portfolio D. Studies show that βD = 0.6. The expected rate of return of D is 0.06. Is there an arbitrage opportunity? If so, construct a trading strategy to earn profits with no risk. If not, why?Assume the APT equation for portfolios A and B with the following system of equations: E[rA] = λ0 + (λ1)3 + (λ2)0.2 = 11.0 E[rB] = λ0 + (λ1)2 + (λ2)1 = 13.0 Assume the following: . The risk free rate is λ0 = Rf = 5 . The expected return on the market portfolio is RM = 10 . Expected returns are consistent with the CAPM. . (hint: note that λ1 = E[RA] − Rf and λ2 = E[RB] − Rf ). Answer the following: (a) What are λ1 and λ2? (b) What is the CAPM β associated with the pure portfolio associated with factor 1? (c) What is the CAPM β associated with the pure portfolio associated with factor 2?
- Consider the multifactor model APT with three factors. Portfolio A has a beta of 0.8 on factor 1, a beta of 1.1 on factor 2, and a beta of 1.25 on factor 3. The risk premiums on the factor 1, factor 2, and factor 3 are 3%, 5%, and 2%, respectively. The risk-free rate of return is 3%. The expected return on portfolio A is __________ if no arbitrage opportunities exist. A. 23.0% B. 16.5% C. 13.4% D. 13.5%A two-asset portfolio has the following characteristics. The correlation coefficient between the returns of the two assets is +0.1. Asset Expected Return Expected Standard Deviation Weight A 12% 3% 0.8 B 20% 7% 0.2 Calculate the expected return and the risk (i.e. standard deviation) of this two-asset portfolio. Comment on the risk of this portfolio relative to the two individual assets. Suppose the correlation coefficient between A and B was -1.0. How can an investor obtain a zero risk portfolio consisting of A and B?Suppose that there are two independent factors, F1 and F2. The risk-free rate is 3%, and all stocks have independent firm-specific components with a standard deviation of 42%. Portfolios A and B are both well-diversified with the following properties: Portfolio Beta on F1 Beta on F2 Expected Return A 1.8 2.1 32% B 2.7 -0.21 27% What is the expected return-beta relationship in this economy? Calculate the risk-free rate, rf, and the factor risk premiums, RP1 and RP2, to complete the equation below (write answers as percentages, rounded to two decimal places). E(rp) = rf + (BP1 X RP1) + (BP2 X RP2) (Note: B = Beta) rf ?% RP1 ?% RP2 ?%
