Assume that you are considering investing in two risky assets, namely PKX and XIY, with the following probability distribution. Assume that short selling is allowed. Stock РКХ XIY State of the world Probability Return (%) Return (%) 1 0.25 18 2 0.30 -3 0.20 12 4 0.10 4 12 0.15 1 1. Calculate the expected return and risk for each of these assets. Interpret. 2. Consider a portfolio that contains PKX and XIY. Note that XIY comprises 30% of the portfolio. What is the expected return and risk of this portfolio? 3. How will your answer in (2) change if XIY comprises 20% of the portfolio only? Comment on your findings. 15

Assume that you are considering investing in two risky assets, namely PKX and XIY, with the following probability distribution. Assume that short selling is allowed. Stock РКХ XIY State of the world Probability Return (%) Return (%) 1 0.25 18 2 0.30 -3 0.20 12 4 0.10 4 12 0.15 1 1. Calculate the expected return and risk for each of these assets. Interpret. 2. Consider a portfolio that contains PKX and XIY. Note that XIY comprises 30% of the portfolio. What is the expected return and risk of this portfolio? 3. How will your answer in (2) change if XIY comprises 20% of the portfolio only? Comment on your findings. 15

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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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?
Consider two perfectly negatively correlated risky securities A and B. A has an expected rate of return of 10% and a standard deviation of 16%. B has an expected rate of return of 8% and a standard deviation of 12%. An investor who wishes to form a portfolio that lies to the right of the optimal risky portfolio on the Capital Allocation Line must: A. lend some of her money at the risk-free rate. B. borrow some money at the risk-free rate and invest in the optimal risky portfolio C. invest only in risky securities D. such a portfolio cannot be formed E. both borrow some money at the risk-free rate and invest in the optimal risky portfolio and invest only in risky securities
Assume that you have a portfolio of two stocks, X and Y. If the risk of stock X is 1.2 and the risk of stock Y is 4 then the return on stock Y should be? If the portfolio is well diversified and stocks are strongly negatively related, then the risk for the portfolio will be?
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.
Suppose that stocks are exposed to systematic risks only so that stock i has the following return structure: Ri,t = mį + Si,t where mi is the average return, and si,t is the systematic risk. When we construct a portfolio including more and more stocks, which of the following would happen? The portfolio volatility gradually decreases and eventually converges to a certain positive value. ● The portfolio volatility gradually decreases and eventually converges to zero. The portfolio volatility stays unchanged.
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 14.5% R-squared 13.5 9.1 10.7 5.4 op 36% 31 21 26 0 6p 1.60 1.30 .80 1.00 0 Assume that the correlation of returns on Portfolio Y to returns on the market is 72. What percentage of Portfolio Y's return is driven by the market? (Enter your answer as a decimal not a percentage. Round your answer to 4 decimal places.)
An efficient portfolio is one that: Select one: a. maximises return for a given level of risk. b. maximises risk for a given level of return. c. minimises risk for a given rate of return. d. Both A and C. are efficient portfolios.
Consider the following portfolio choice problem. The investor has initial wealth w andutility u(x) = (x^n) /n. There is a safe asset (such as a US government bond) that has netreal return of zero. There is also a risky asset with a random net return that has onlytwo possible returns, R1 with probability 1 − q and R0 with probability q. We assumeR1 < 0, R0 > 0. Let A be the amount invested in the risky asset, so that w − A isinvested in the safe asset.i) What are risk preferences of this investor, are they risk-averse, riskneutral or risk-loving?ii) Find A as a function of w.
. The following questions are related to modern portfolio theory. • Assume there are only two stocks in the equity market. •The risk-free rate is 1.00%. Stock Return Volatility Correlation Matrix Y 0.7 1.0 X Y X 15.00% 20.00% 1.0 10.00% 15.00% 0.7 (a) Make an investment portfolio using the risky assets that has an expected return 12%. (b) Calculate the volatility of the portfolio in (a).
Consider a risky portfolio, A, with an expected rate of return of 0.15 and a standard deviation of 0.15, that lies on a given indifference curve. Which one of the following portfolios might lie on the same indifference curve? A. E(r) = 0.15; Standard deviation = 0.20 B. E(r) = 0.20; Standard deviation = 0.15 C. E(r) = 0.10; Standard deviation = 0.10 D. E(r) = 0.10; Standard deviation = 0.20 E. E(r) = 0.15; Standard deviation = 0.10
Consider the following portfolio choice problem. The investor has initial wealth w and utility u(x)=. There is a safe asset (such as a US government bond) that has net real return of zero. There is also a risky asset with a random net return that has only two possible returns, R₁ with probability 1-q and Ro with probability q. We assume R₁ 0. Let A be the amount invested in the risky asset, so that w - A is invested in the safe asset. 1) Does the investor put more or less of his portfolio into the risky asset as his wealth increases?
An investor has a portfolio of two assets A and B. The details are shown in the below table. Portfolio Details Asset Expectedreturn Standarddeviation Covariance (A, B) Expected Portfolio Return A 0.06 0.5 0.12 0.1 B 0.08 0.8 Which one of the following statements is NOT correct? a. The portfolio weight in asset A is -100%. b. The correlation of asset A and B’s returns is 0.3. c. The investor can benefit from a fall in the price of asset A. d. The variance of the portfolio is 2.33. e. The order of short selling is borrowing, buying, selling, and returning.

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