Course2_Unit2_ST23_Questions

Rm-R is read as: O a. The return offered by the market over and above the risk-free rate O b. Market risk premium- Oc. Excess return on the market C. Od. All options are correct

As diversification increases, the firm-specific risk of a portfolio approaches A. 1. B. infinity. C. 0. D. (n – 1) × n.

* Consider the following portfolio II: long one call with exercise price E₁, long one put with exercise price E2, short one call with exercise price E, and short one put with exercise price E1+E2 E. Consider the case E₁ < E < E2 where E < 2 ⚫ (a) Write down the pay-off function A(S) for the portfolio II. • • (b) What is the value of the pay-off function when S < E₁? (c) What is the value of the pay-off function when E < S < E₂?

Solve it correctly

The CAPM states that the expected (required) return on an asset is : E(Ri)=Rf+βi[E(RM)−Rf] where the term in square brackets is the risk-premium earned by the market portfolio.  Therefore, the beta of the market portfolio (βM) must be equal to __________ . A) zero B) 0.5 C) 1.0 D) an unknown estimate

Assume that the return volatility for asset 1 and 2 is 0.2 and 0.3 respectively and the return correlation is 0.7. The portfolio volatility is a) 2.5 b) 3.0 c) 3.5 d) 4

Please advise

4. Suppose that there are 2 assets with ri 012 = 0.005. = 0.20, 01 = = 0.40, 2 = 0.10, 02 = 0.25 and (a) If ro = 0.02, what are the market portfolio return and variance? What are the corre- sponding weights (i.e. how much to invest in asset 1, asset 2, and the risk-free asset to get the market portfolio)? Answer. (b) If ro 0.05, what are the market portfolio return and variance? What are the corre- sponding weights? Answer.

2. Suppose that you have a riskfree asset and N risky assets for investment. The rate of return on the riskfree asset is r,, while the (Nx1) vector of the rate of return on the N risky assets is r, which is multivariate normal, i.e., r N(u, E). Your utility function for a portfolio that consists of the riskfree asset and the N risky asset is u(r,)=r,-=o, 2 Suppose that the sum of investment proportions on the riskfree and risky assets is one. Answer the following question. A. What is your optimal investment proportion in the risky assets? How is your investment on the riskfree asset affected by different values of 2? B. Suppose that there is only one risky asset i. Show the effects of the Sharpe ratio (4,/0, ) on the investment proportion in the risky asset.

vuunyiuunu assumption of "y. Q2. How portfolio return and risk is calculated? Explain the role of correlation among asset in portfolio? Why this correlation is important?

Please asap

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?

According to CAPM, the expected rate of return of a portfolio with a beta of 1.0 and an alpha of 0 is:a. Between rM and rf .b. The risk-free rate, rf .c. β(rM − rf).d. The expected return on the market, rM.

The market portfolio (M) has the expected rate of return E(rM) = 0.12. Security A is traded in the market. We know that E(rA) = 0.17 and βA = 1.5. (1) What is the rate of return of the risk-free asset (rf)? (2) Security B is also traded in the market. βB = 0.8. Then what is “fair” expected rate of return of security B according to the CAPM? (3) Security C is a third security traded in the market. βC = 0.6, and from the market price, investors calculate E(rC) = 0.1. Is C overpriced or underpriced? What is αC?

The optimal proportion of the risky asset in the complete portfolio is given by the equation below y*= E(Rp− Rf) A0² For each of the variables on the right side of the equation, discuss the impact of the variable's effect on y* and why the nature of the relationship makes sense intuitively. Assume the investor is risk averse

You are given the following information concerning three portfolios, the market portfolio, and the risk-free asset: Portfolio X Y Z Market Risk-free Rp 11.0% ор 33.00% 10.0 28.00 8.1 10.4 5.2 18.00 23.00 Ө вр 1.45 1.20 0.75 1.00 Ө Assume that the correlation of returns on Portfolio Y to returns on the market is 0.66. What percentage of Portfolio Y's return is driven by the market? Note: Enter your answer as a decimal not a percentage. Round your answer to 4 decimal places. R-squared

choose which one ? 3.Assume CAPM holds. What is the correlation between an efficient portfolio and the market portfolio?a.1b.-1c.0d.Not enough information

Certainty equivalents in portfolio theory

Assuming your utility function U = E(r) - Ao². Consider the investments shown in the table. If your risk aversion coefficient is -2, which investment would you choose? Investment E[r] #1 #2 #3 #4 #2 #3 #4 #1 12% 15% 15% 24% σ 40% 40% 30% 40%

Baghiben

Problem 4. Consider tuo scenarios, wi with probability and w with probability Suppose that the return on sonie security is K retum on another security is K uch that the tu0 socurities hane the same risk = -2% in the first scenario and K = 6% in the second scenario. If the = -3% in the first scenario, find the return K in the other scenario

Suppose you have an investment portfolio with fraction x invested in a market portfolio and (1-x) in a risk- free asset. Increasing fraction x invested in the market portfolio and consequently decreasing (1-x) invested in the risk-free asset shall (select any correct answer, if there are multiple correct answers) Select one or more: O decrease the Sharpe ratio of the resulting portfolio O decrease the expected return of the resulting portfolio increase the Sharpe ratio of the resulting portfolio increase the expected return of the resulting portfolio Dincrease the risk of the resulting portfolio

Portfolio theory with two assets E(R1)=0.15 E(01)= 0.10 W1=0.5 E(R2)=0.20 E(02) = 0.20 W2=0.5 Calculate the expected return and the standard deviation of the two portfolios if r1,2 = 0.4 and -0.60 respectively.

The possible returns of a security I and research returns under three possible states are as follows. Probability % market % security 0.2 15 10 0.5 13 16 0.3 25 30 The risk free rate is 9%, determine the required rate of return of security I and sate whether it is correctly valued. 12-marks] 20 Ri= E(R) XW

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1. Portfolio Choice 1 Assume that .02 E(R)-.18 and market) portfolio. Suppose that an investor's preferences are given by 3 where T. denotes the tangency (or U-ER)-20; where P denotes the investor's portfolio choice which combines proportion W of the market portfolio and proportion 1-W of the risk-free asset. A. Is this investor risk loving or risk averse? Please explain your reasoning. B. If the investor wants to maximize utility by allocating her wealth between the market portfolio and the risk-free asset, what proportion of wealth should she hold in the risk- free asset (1-W)? What is the risk and expected return of this utility-maximizing portfolio? Please explain your answers and illustrate graphically, being careful to label all axes.

6. Equilibrium pricing: Let the subscripts: j = 0 denote the risk-free asset, j = 1,...,n the set of available risky securities, and M the market portfolio. For the questions that follow, assume that CAPM provides an accurate description of reality. a. b. C. d. State the CAPM equation. (1) Use the CAPM equation to show that the following condition is true s; ≤ SM for any j. What is the significance of this condition when interpreted in the context of the capital market line? (5) Assume that B = 0.8, μM = 0.1 and r = 0.05. Using the CAPM, determine the expected return from holding one unit of asset j for one period. (2) Given your answer to c.), what could you conclude (from the perspective of the security market line) if a market survey indicated that the forecasted one- period return on asset j was 8 percent? Describe and motivate the rational trading response that is consistent with your conclusion. (4)

Assume that security returns are generated by the single-index model,Ri = αi + βiRM + eiwhere Ri is the excess return for security i and RM is the market’s excess return. The risk-free rate is 2%. Suppose also that there are three securities A, B, and C, characterized by the following data:  Security βi E(Ri) σ(ei) A 0.7 7 % 20 % B 0.9 9   6   C 1.1 11   15     a. If σM = 16%, calculate the variance of returns of securities A, B, and C.   b. Now assume that there are an infinite number of assets with return characteristics identical to those of A, B, and C, respectively. What will be the mean and variance of excess returns for securities A, B, and C? (Enter the variance answers as a percent squared and mean as a percentage. Do not round intermediate calculations. Round your answers to the nearest whole number.)