IV Asset Allocation Decision (25 points) Suppose the economy can be in one of the following three states: (i) Boom or "good" state, (ii) Neutral state, and (iii) Recession or "bad" state. Each state can occur with an equal probability. The following two securities are available to you at the beginning of a month: Risky Security: It is currently trading at $50. At the end of the month, it is expected to yield a net payoff of $10 in the good state, a $5 payoff in the neutral state, and a $2 payoff in the bad state. Riskfree Security: It is currently trading at $4. At the end of the month, it is expected to yield a net payoff of $4 in all three states. 1. (5 points) Please draw the payoff trees for the risky and the riskfree securities. Please label the trees clearly. 2. (6 points) Combine the riskfree and the risky asset to construct a portfolio that gen- erates a positive payoff of $1 in the bad state. Compute the percentage of your total allocation that should be in the riskfree asset. 3. (6 points) Compute the mean/expected net payoff of the portfolio you constructed. 4. (8 points) Compute the risk (i.e., the standard deviation of the net payoff) of the portfolio you constructed. 5. (5 points) How will the shape of the minimum variance frontier change if the mean and the standard deviation of the second asset changes? The new mean and standard deviation estimates are p2 = 10% and 02 = 15%, respectively. Assume that the correlation between the two risky securities P12 is -0.50. Please show the new frontier and identify the new locations of the MVP and M. Again, you do not have to identify the locations of MVP and M exactly. Just show their approximate locations. V MVP and the Tangential Portfolio (25 points) Consider a simple economy with two risky securities and a riskfree security. The two risky securities have the following characteristics: Risky Security 1: Expected (or mean) annual return = M1 = 10%, Standard deviation = 0 = 10%. Risky Security 2: Expected (or mean) annual return = H2 = 6%, Standard deviation = 0 = 15% The correlation between the two risky securities is P12 = -0.50. Assume that the annual riskfree rate is 2%. You are not allowed to short the securities. 1. (5 points) Draw the minimum variance frontier. Identify the (i) minimum variance portfolio (MVP) and (ii) the tangential portfolio (i.e., the optimal risky portfolio or the market portfolio M). You do not need to identify the locations of MVP and M exactly. Just show their approximate locations. 2. (5 points) How will the shape of the minimum variance frontier change if the correlation between the two risky securities P12 is +1 instead? Please show the new frontier and identify the new locations of the MVP and M. Again, you do not have to identify the locations of MVP and M exactly. Just show their approximate locations. 3. (5 points) How will the shape of the minimum variance frontier change if the correlation between the two risky securities P12 is -1 instead? Please show the new frontier and identify the new locations of the MVP and M. Again, you do not have to identify the locations of MVP and M exactly. Just show their approximate locations. 4. (5 points) How will the shape of the minimum variance frontier change if the mean and the standard deviation of the second asset changes? The new mean and standard deviation estimates are M2 = 12% and 2 = 15%, respectively. Assume that the correlation between the two risky securities P12 is -0.50. Please show the new frontier and identify the new locations of the MVP and M. Again, you do not have to identify the locations of MVP and M exactly. Just show their approximate locations. IV Asset Allocation Decision (25 points) Suppose the economy can be in one of the following three states: (i) Boom or "good" state, (ii) Neutral state, and (iii) Recession or "bad" state. Each state can occur with an equal probability. The following two securities are available to you at the beginning of a month: Risky Security: It is currently trading at $50. At the end of the month, it is expected to yield a net payoff of $10 in the good state, a $5 payoff in the neutral state, and a $2 payoff in the bad state. Riskfree Security: It is currently trading at $4. At the end of the month, it is expected to yield a net payoff of $4 in all three states. 1. (5 points) Please draw the payoff trees for the risky and the riskfree securities. Please label the trees clearly. 2. (6 points) Combine the riskfree and the risky asset to construct a portfolio that gen- erates a positive payoff of $1 in the bad state. Compute the percentage of your total allocation that should be in the riskfree asset. 3. (6 points) Compute the mean/expected net payoff of the portfolio you constructed. 4. (8 points) Compute the risk (i.e., the standard deviation of the net payoff) of the portfolio you constructed. 5. (5 points) How will the shape of the minimum variance frontier change if the mean and the standard deviation of the second asset changes? The new mean and standard deviation estimates are p2 = 10% and 02 = 15%, respectively. Assume that the correlation between the two risky securities P12 is -0.50. Please show the new frontier and identify the new locations of the MVP and M. Again, you do not have to identify the locations of MVP and M exactly. Just show their approximate locations. V MVP and the Tangential Portfolio (25 points) Consider a simple economy with two risky securities and a riskfree security. The two risky securities have the following characteristics: Risky Security 1: Expected (or mean) annual return = M1 = 10%, Standard deviation = 0 = 10%. Risky Security 2: Expected (or mean) annual return = H2 = 6%, Standard deviation = 0 = 15% The correlation between the two risky securities is P12 = -0.50. Assume that the annual riskfree rate is 2%. You are not allowed to short the securities. 1. (5 points) Draw the minimum variance frontier. Identify the (i) minimum variance portfolio (MVP) and (ii) the tangential portfolio (i.e., the optimal risky portfolio or the market portfolio M). You do not need to identify the locations of MVP and M exactly. Just show their approximate locations. 2. (5 points) How will the shape of the minimum variance frontier change if the correlation between the two risky securities P12 is +1 instead? Please show the new frontier and identify the new locations of the MVP and M. Again, you do not have to identify the locations of MVP and M exactly. Just show their approximate locations. 3. (5 points) How will the shape of the minimum variance frontier change if the correlation between the two risky securities P12 is -1 instead? Please show the new frontier and identify the new locations of the MVP and M. Again, you do not have to identify the locations of MVP and M exactly. Just show their approximate locations. 4. (5 points) How will the shape of the minimum variance frontier change if the mean and the standard deviation of the second asset changes? The new mean and standard deviation estimates are M2 = 12% and 2 = 15%, respectively. Assume that the correlation between the two risky securities P12 is -0.50. Please show the new frontier and identify the new locations of the MVP and M. Again, you do not have to identify the locations of MVP and M exactly. Just show their approximate locations
