Homework Answers
As a result, any combination of two assets (the risk-free asset and a portfolio of risky assets) will be a straight line, the Capital Allocation Line (CAL) or the Capital Market Line (CML). The figure above shows how this touches the efficient frontier
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II. Essays/Calculations (60%) 1. (a) Please draw the efficient frontier for a portfolio of N>2 risky...
3. (a) In the case of multiple risky assets, explain the concepts of efficient frontier and...
3. (a) In the case of multiple risky assets, explain the concepts of efficient frontier and feasible region. 5 points] (b) Suppose there are n risky assets (e.g. stocks) and a risk-free asset in the market. Explain how a mean-variance investor allocates his wealth across these assets. [10 points
Which of the following is a TRUE statement? A The tangent portfolio is the risky portfolio...
Which of the following is a TRUE statement? A The tangent portfolio is the risky portfolio on the efficient frontier whose tangent line cuts the horizontal axis at the risk-free rate. B The new (or super) efficient frontier represents the portfolios composed of the risk-free rate and the tangent portfolio that offers the highest expected rate of return for any given level or risk. C The separation theorem states that the investment decision, (how to construct the portfolio of risky...
4. Investor equilibrium The following graph shows the set of portfolio opportunities for a multiasset case....
4. Investor equilibrium The following graph shows the set of portfolio opportunities for a multiasset case. The point Pre corresponds to a risk-free asset, the red curve BME is the efficient frontier, the shaded area under the efficient frontier represents the feasible set of portfolios of risky assets, and the yellow curves 11 and 12 are indifference curves for a particular investor. EXPECTED RATE OF RETURN (Percent) 10 RISK (Portfolio's standard deviation) Point A, where the line PRF MZ is...
2. (Understanding optimal portfolio choice) Consider two risky assets, the expected return of asset one is...
2. (Understanding optimal portfolio choice) Consider two risky assets, the expected return of asset one is μ-0.1, the expected return of asset two is μ2-0.15, the risk or standard deviation of asset one is σ1-0.1, the risk or standard deviation of asset two is σ2-02. The two assets also happen to have zero correlation. An investor plans to build a portfolio by investing w of his investment to asset one and the rest of his investment to asset two. Calculate...
4. Investor equilibrium The following graph shows the set of portfolio opportunities for a multiasset case....
4. Investor equilibrium The following graph shows the set of portfolio opportunities for a multiasset case. The point RF corresponds to a risk-free asset, the red curve BME is the efficient frontier, the shaded area under the efficient frontier represents the feasible set of portfolios of risky assets, and the yellow curves II and I2 are indifference curves for a particular investor. EXPECTED RATE OF RETURN (Percent) 10 RISK (Portfolio's standard deviation) The points on the line PRF MZ represent:...
The following graph shows the set of portfolio opportunities for a multiasset case. The point rrr...
The following graph shows the set of portfolio opportunities for a multiasset case. The point rrr corresponds to a risk-free asset, the red curve BME is the efficient frontier, the shaded area under the efficient frontier represents the feasible set of portfolios of risky assets, and the yellow curves I and I 2 are indifference curves for a particular investor. EXPECTED RATE OF RETURN Percent) RISK IPortfolio's standard deviation The points on the line PREMZ represent: Portfolios that are dominated...
3 Question 3 In a market are listed two risky assets whose returns are described by the following parameters...
3 Question 3 In a market are listed two risky assets whose returns are described by the following parameters HA=0.01. MB = 0.07, 01 = 0.2 and op = 0.12. The correlation among the securities is constant and equal to p=0.1. 1. Derive the equation for the frontier 2. Derive the minimum variance portfolio and the equation for the efficient frontier 3. Let's add a risk free asset among the possible investments with return r = 0.03 and derive the...
3. You have a risky portfolio that yields an expected rate of return of 15% with...
3. You have a risky portfolio that yields an expected rate of return of 15% with a standard deviation of 25%. Draw the CAL for an expected return/standard deviation diagram if the risk free rate is 5%. a. What is the slope of the CAL? b. If your coefficient of risk aversion is 5, how much should you invest in the risky portfolio? 4. A pension fund manager is considering three mutual funds. The first is a stock fund, the...
1. Let's assume you live in a world where there are only 2 risky assets, asset A and asset B. The...
1. Let's assume you live in a world where there are only 2 risky assets, asset A and asset B. There is also a risk free asset. You have the following information about the assets: Asset A 10% 5% Asset B 20% 25% Risk free (F) 5% 09% Expected Return Standard Deviation Let's assume the correlation between the returns of asset A and B is +1. Make a portfolio Pl that invests 50% in A and 50% in B. Calculate...
A. Capital Allocation Lines The optimal CAL is found as the ray from the risk free...
A. Capital Allocation Lines The optimal CAL is found as the ray from the risk free rate that is tangent to the _____________ and is called the ________________. efficient frontier; CML minimum variance portfolio; high range CAL indifference curve; SML lower half of the investment opportunity set; CAPM B. Capital Allocation Portfolio 1 has a standard deviation of 35% and a Sharpe ratio of 0.48. Portfolio 2 has a standard deviation of 29% and a Sharpe ratio of 0.44. Portfolio...
3. (a) In the case of multiple risky assets, explain the concepts of efficient frontier and feasible region. 5 points] (b) Suppose there are n risky assets (e.g. stocks) and a risk-free asset in the market. Explain how a mean-variance investor allocates his wealth across these assets. [10 points
4. Investor equilibrium The following graph shows the set of portfolio opportunities for a multiasset case. The point Pre corresponds to a risk-free asset, the red curve BME is the efficient frontier, the shaded area under the efficient frontier represents the feasible set of portfolios of risky assets, and the yellow curves 11 and 12 are indifference curves for a particular investor. EXPECTED RATE OF RETURN (Percent) 10 RISK (Portfolio's standard deviation) Point A, where the line PRF MZ is...
2. (Understanding optimal portfolio choice) Consider two risky assets, the expected return of asset one is μ-0.1, the expected return of asset two is μ2-0.15, the risk or standard deviation of asset one is σ1-0.1, the risk or standard deviation of asset two is σ2-02. The two assets also happen to have zero correlation. An investor plans to build a portfolio by investing w of his investment to asset one and the rest of his investment to asset two. Calculate...
4. Investor equilibrium The following graph shows the set of portfolio opportunities for a multiasset case. The point RF corresponds to a risk-free asset, the red curve BME is the efficient frontier, the shaded area under the efficient frontier represents the feasible set of portfolios of risky assets, and the yellow curves II and I2 are indifference curves for a particular investor. EXPECTED RATE OF RETURN (Percent) 10 RISK (Portfolio's standard deviation) The points on the line PRF MZ represent:...
The following graph shows the set of portfolio opportunities for a multiasset case. The point rrr corresponds to a risk-free asset, the red curve BME is the efficient frontier, the shaded area under the efficient frontier represents the feasible set of portfolios of risky assets, and the yellow curves I and I 2 are indifference curves for a particular investor. EXPECTED RATE OF RETURN Percent) RISK IPortfolio's standard deviation The points on the line PREMZ represent: Portfolios that are dominated...
3 Question 3 In a market are listed two risky assets whose returns are described by the following parameters HA=0.01. MB = 0.07, 01 = 0.2 and op = 0.12. The correlation among the securities is constant and equal to p=0.1. 1. Derive the equation for the frontier 2. Derive the minimum variance portfolio and the equation for the efficient frontier 3. Let's add a risk free asset among the possible investments with return r = 0.03 and derive the...
1. Let's assume you live in a world where there are only 2 risky assets, asset A and asset B. There is also a risk free asset. You have the following information about the assets: Asset A 10% 5% Asset B 20% 25% Risk free (F) 5% 09% Expected Return Standard Deviation Let's assume the correlation between the returns of asset A and B is +1. Make a portfolio Pl that invests 50% in A and 50% in B. Calculate...
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