Suppose the asset S offers 12% expected return with 14% standard deviation per year, while the asset B offers 6% expected return with 8% standard deviation per year. Assume that: Scenario 1: the coefficient of correlation between Band Sand S is +0.4. Scenario 2: the coefficient of correlation between Band Sand S is -0.4. calculate the expected return and standard deviation of your portfolio under these two scenarios. How does the benefit of diversification differ between the two cases? your portfolio is 50% in S and 50%in B.

Suppose the asset S offers 12% expected return with 14% standard deviation per year, while the asset B offers 6% expected return with 8% standard deviation per year. Assume that: Scenario 1: the coefficient of correlation between Band Sand S is +0.4. Scenario 2: the coefficient of correlation between Band Sand S is -0.4. calculate the expected return and standard deviation of your portfolio under these two scenarios. How does the benefit of diversification differ between the two cases? your portfolio is 50% in S and 50%in B.

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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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.
f. Assume a Portfolio of two assets A and B whose standard deviations of their returns are 8.6% and 10.8% respectively, while their correlation coefficient of returns is Pas = - 0.61. You are given the right to do portfolio optimization without restrictions. What proportions would you choose and why?
Assume a Portfolio of two assets A and B whose standard deviations of their returns are 8.6% and 10.8% respectively, while their correlation coefficient of returns is Pas= - 0.61. You are given the right to do portfolio optimization without restrictions. What proportions would you choose and why?
Suppose the risk-free rate is 5%. The expected return and standard deviation of a risky asset are 10% and 20%, respectively. a. What is the slope of the capital allocation line (CAL) constructed using the risk-free asset and the risky asset? A. 0.30 B. 0.15 C. 0.25 D. 0.20 b. If an investor has a risk aversion coefficient of A=2, what is the optimal fraction of the money that she invests in the risky asset? A. 62.5% B. 42.5% C. 30% D. 20% c. If an investor invest 25% of her money in the risky asset, which is the investor’s risk aversion coefficient? a. 5 b. 1 c. 3 d. 4
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?
Calculate the required rate of return for an asset that has a beta of 1.01, given a risk-free rate of %3.4 and a market return of %9.1 . b. If investors have become more risk-averse due to recent geopolitical events, and the market return rises to %11.6, what is the required rate of return for the same asset? a. The required rate of return for the asset is enter your response here%. (Round to two decimal places.) Part 2 b. If investors have become more risk-averse due to recent geopolitical events, and the market return rises to 11.6%, the required rate of return for the same asset is enter your response here%. (Round to two decimal places.)
Consider the expected return and standard deviation of the following two assets: Asset 1: E[r1]=0.1 and σ1=0.2 Asset 2: E[r2]=0.3 and σ2=0.4 (a) Draw (e.g. with Excel) the set of achievable portfolios in mean-standard deviation space for the cases: (i) ρ12= -1, (ii) ρ12=0. (b) Suppose ρ12=-1. Which portfolio has the minimal variance? What is the variance and expected return of that portfolio? (c) Derive the formula for the variance of a portfolio with four assets.
Consider a single-index model economy. The index portfolio M has E(RM ) = 6%, σM = 18%.An individual asset i has an estimate of βi = 1.1 and σ2ei = 0.0225 using the single index modelRi = αi + βiRM + ei. The forecast of asset i’s return is E(ri) = 12%. rf = 4%. a) According to asset i’s return forecast, calculate αi. (b) Calculate the optimal weight of combining asset i and the index portfolio M . (c) Calculate the Sharpe ratio of the index portfolio M and the portfolio optimally combiningasset i and the index portfolio M .
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.
Calculate the required rate of return for an asset that has a beta of 1.53, given a risk-free rate of 3.6% and a market return of 9.2%. b. If investors have become more risk-averse due to recent geopolitical events, and the market return rises to 11.8%, what is the required rate of return for the same asset?
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?
Consider a portfolio formed of two risky assets whose returns have a correlation of 0.5. What can be said of the standard deviation of the global minimum-variance portfolio formed with these two risky assets? It's greater than zero. It s equal to zero. O It s between - 1 and +1. O It's the weighted average of the standard deviations of the two risky assets.

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