4. Suppose portfolio P's expected return in 12%, its volatility (standard deviation) is 20%, and the risk-free rate is 5%. Suppose further that a particular mix of asset i and P yields a portfolio P’with an expected return of 18% and a volatility of 30%. a. Compute for the Sharpe ratio of P. b. Compute for the Sharpe ratio of P'. Is adding asset i beneficial? Explain

4. Suppose portfolio P's expected return in 12%, its volatility (standard deviation) is 20%, and the risk-free rate is 5%. Suppose further that a particular mix of asset i and P yields a portfolio P’with an expected return of 18% and a volatility of 30%. a. Compute for the Sharpe ratio of P. b. Compute for the Sharpe ratio of P'. Is adding asset i beneficial? Explain

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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Supposing the return from an investment has the following probability distribution Return Probability R (%) 8 0.2 10 0.2 12 0.5 14 0.1 Required: What is the expected return of the investment? What is the risk as measured by the standard deviation of expected returns?
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?
The expected rate of return of an investment ________. a. equals one of the possible rates of return for that investment b. equals the required rate of return for the investment c. is the mean value of the probability distribution of possible returns d. is the median value of the probability distribution of possible returns e. is the mode value of the probability distribution of possible returns
On the basis of the utility formula below, which investment would you select if you were risk averse with A = 4? Investment Expected return E(r) Standard deviation σ 1 0.12 0.30 2 0.15 0.50 3 0.21 0.16 4 0.24 0.21
Think about whether a risk-free asset should earn a risk-premium beyond the risk-free rate. Thinking about that should give you an idea of the beta for a risk-free asset. Or, look again at the CAPM equation: E(Ri)=Rf+βi[E(RM)−Rf] Given this equation, what beta sets the E(R) of the risk free asset equal to the risk-free rate? A) zero B) 0.5 C) 1.0 D) its random
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.
a. Compute the expected rate of return on investment i given the following information: the market risk premium is 5%; Rf = 6%; βi = 1.2. b. Compute E(RM).
6. On the basis of the utility formula below, which investment would you select if you were risk averse with A = 4? Standard Expected return E(t) deviation Investment 0.12 0.30 0.15 0.50 0.21 0.16 0.24 0.21
Consider two assets. Suppose that the return on asset 1 has expected value 0.05 and standard deviation 0.1 and suppose that the return on asset 2 has expected value 0.02 and standard deviation 0.05. Suppose that the asset returns have correlation 0.4.Consider a portfolio placing weight w on asset 1 and weight 1-w on asset 2; let Rp denote the return on the portfolio. Find the mean and variance of Rp as a function of w.
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
Assume that the risk-free rate, RF, is currently 9% and that the market return, rm, is currently 16%. a. Calculate the market risk premium. b. Given the previous data, calculate the required return on asset A having a beta of 0.4 and asset B having a beta of 1.8.
There are two assets 1 and 2, with returns X and Y correspondingly. Return X is a random variable with mean 1 and variance 1; return Y is a random variable with mean 1 and variance 3. We know that the expectation of X*Y is equal to 0. Find the share of asset 1 in the risk-minimizing portfolio.

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