You are considering investing $1,000 in a complete portfolioin a T - bill that pays a rate of return of 0.06and a risky portfolio, P, constructed with two risky securities A and B. The weights of A and B in P are 60% and 40%, respectively. Stock A has an expected rate of return of 0.13 and a variance of 0.01, and Stock B has an expected rate of return of 0.2 and a variance of 0.0081. If you want to form a complete portfolio with an expected rate of return of 0.08, what percentages of your money must you invest in the T - bill, A, and B, respectively, if you keep A and B in the sameAA

You are considering investing $1,000 in a complete portfolioin a T - bill that pays a rate of return of 0.06and a risky portfolio, P, constructed with two risky securities A and B. The weights of A and B in P are 60% and 40%, respectively. Stock A has an expected rate of return of 0.13 and a variance of 0.01, and Stock B has an expected rate of return of 0.2 and a variance of 0.0081. If you want to form a complete portfolio with an expected rate of return of 0.08, what percentages of your money must you invest in the T - bill, A, and B, respectively, if you keep A and B in the sameAA

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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You are considering investing $1,000 in a T-bill that pays 0.05 and a risky portfolio, P, constructed with two risky securities, X and Y. The weights of X and Y in P are 0.60 and 0.40, respectively. X has an expected rate of return of 0.14 and variance of 0.01, and Y has an expected rate of return of 0.10 and a variance of 0.0081.What would be the dollar values of your positions in X and Y, respectively, if you decide to hold 40% of your money in the risky portfolio and 60% in T-bills? A. $100; $240 B. $360; $240 C. $240; $160 D. Cannot be determined. E. $240; $360
You are considering investing $1,000 in a T-bill that pays 0.06 and a risky portfolio, P, constructed with two risky securities, X and Y. The weights of X and Y in P are 0.40 and 0.60, respectively. X has an expected rate of return of 0.14 and variance of 0.01, and Y has an expected rate of return of 0.10 and a variance of 0.0081. If you want to form a portfolio with an expected rate of return of 0.11, what percentages of your money must you invest in the T-bill and P, respectively
You are considering investing $1,000 in a T-bill that pays 0.05 and a risky portfolio, P, constructed with two risky securities, X and Y. The weights of X and Y in P are 0.60 and 0.40, respectively. X has an expected rate of return of 0.14 and variance of 0.01, and Y has an expected rate of return of 0.10 and a variance of 0.0081. What would be the dollar value of your positions in X, Y, and the T-bills, respectively, if you decide to hold a portfolio that has an expected outcome of $1,120?
You manage a risky portfolio with an expected rate of return of 17% and a standard deviation of 28%. The T-bill rate is 7%. Your client's degree of risk aversion is A = 2.0, assuming a utility function u E(r) = A0². a. What proportion, y, of the total investment should be invested in your fund? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Investment proportion y Expected return Standard deviation - % b. What are the expected value and standard deviation of the rate of return on your client's optimized portfolio? (Do not round intermediate calculations. Round your answers to 2 decimal places.) % %
. Assume that you manage a risky portfolio with an expected rate ofreturn of 18% and a standard deviation of 28%. The T-bill rate (risk-free rate) is 7%. Yourclient chooses to invest 70% in the risky portfolio in your fund and 30% in a T-bill moneymarket fund. We assume that investors use mean-variance utility: U = E(r) − 0.5 × Aσ2,where E(r) is the expected return, A is the risk aversion coefficient and σ2is the variance ofreturns.a) What is the expected value and standard deviation of the rate of return on your client’sportfolio? b) What is the reward-to-volatility ratio (Sharpe ratio) of your risky portfolio? What isthe reward-to-volatility ratio (Sharpe ratio) of your client’s risky portfolio? Commenton the relationship between these two Sharpe ratio calculated and explain the intuitionbehind. c) Draw the Capital Allocation Line (CAL) of your portfolio on an expected returnstandard deviation diagram. What is the slope of the CAL? Show the position ofyour client on your fund’s CAL.…
You manage a risky portfolio with an expected rate of return of 17% and a standard deviation of 36%. The T-bill rate is 6%. Your client's degree of risk aversion is A = 3.1, assuming a utility function u = E(r) A02. a. What proportion, y, of the total investment should be invested in your fund? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Investment proportion y % b. What are the expected value and standard deviation of the rate of return on your client's optimized portfolio? (Do not round intermediate calculations. Round your answers to 2 decimal places.) Expected return % Standard deviation %
Asset A offers an expected rate of return of 25%, with a standard deviation of 20%. Asset B offers an expected return of 15% with a standard deviation of 30%. The risk-free asset offers 5%. Suppose that the correlation coefficient between asset A and asset B equals 1. Please specify the portfolio weight on asset A in the optimal risky portfolio. Your answer should be a entered as a decimal rounded to two decimal places, e.g., enter 63% as 0.63.
Consider a T-bill with a rate of return of 5 percent and the following risky securities. From which set of portfolios, formed with the T-bill and any one of the 4 risky securities, would a risk averse investor always choose his portfolio? Security A: E(r) = 0.15; Variance = 0.04 Security B: E(r) = 0.10; Variance = 0.0225 Security C: E(r) = 0.12; Variance = 0.01 Security D: E(r) = 0.13; Variance = 0.0625 A) The set of portfolios formed with the T-bill and security A. B) The set of portfolios formed with the T-bill and security B. C) The set of portfolios formed with the T-bill and security C. D) The set of portfolios formed with the T-bill and security D.
c. Suppose the risk-free rate is 4.2 percent and the market portfolio has an expected return of 10.9 percent. The market portfolio has a variance of .0382. Portfolio Z has a correlation coefficient with the market of .28 and a variance of .3285. According to the capital asset pricing model, what is the expected return on Portfolio Z?
You manage a risky portfolio with an expected rate of return of 18% and a standard deviation of 30%. The T-bill rate is 6%. Your client’s degree of risk aversion is A = 3.4, assuming a utility function U = E(r) - ½Aσ². a. What proportion, y, of the total investment should be invested in your fund? (Do not round intermediate calculations. Round your answer to 2 decimal places.) b. What is the expected value and standard deviation of the rate of return on your client’s optimized portfolio? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
Consider the following two portfolios. Portfolio A has an expected return of 9%, a standard deviation of returns is 32%, and a beta of 1.5. Portfolio B has an expected return of 7.5%. The risk-free rate is 3%. Assuming the CAPM holds, and Portfolio A and B are fairly priced, then Portfolio B has a beta of? a. 0.61 ○ b. 0.98 ○ c. 1.13 ○ d. 1.09 ○ e. 1.18
Suppose you are given stocks A and B. Stock A has an expected return of 11% and a standard deviation of 4%. Stock B has an expected return of 21% and a standard deviation of 10%. The correlation between them is -1. Suppose it is possible to borrow at the risk-free rate, rf. What must be the value of the risk-free rate? (Hint: Think about constructing a risk-free portfolio from stocks A and B.) (Round answer to 3 decimal places.)

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