x=20. Assume that your utility is U(R) = x E(R) -5x var(R), where R denotes the annual return on your portfolio. You identified 3 assets you want to invest in and estimated their annual expected returns and standard deviations to be as follows: Expected return St. deviation Risky asset 1 100 Risky asset 2 200 Risk-free asset 250 100 250 0 Therefore, if your student ID number ends with 25, then your utility function is U(R) = 25 E(R) 125 var(R), and the three assets you want to invest in have the following expected values and standard deviations: Expected return St. deviation Risky asset 1 Risky asset 2 Risk-free asset 0.25 0.125 0.1 0.25 0.1 0 The correlation between the two risky assets is assumed to be 0.25 (irrespective of what your x is). 1. Compute your optimal portfolio of the three assets, assuming that short selling is allowed. 2. You want to invest $1,000 in the optimal portfolio you found in part (1) and you want to hold that portfolio for 1 year. The annual returns on the two risky assets are normally distributed with the means and standard deviations listed in the table above (correspond- ing to your x) and therefore the return on your optimal portfolio will also be normally distributed with the mean and variance as found in part (1). (a) Run a Monte Carlo simulation (with 500 iterations) to generate a set of possible returns on your optimal portfolio. For each case, compute how much money you will have at the end of the year, if you realized that return.
x=20. Assume that your utility is U(R) = x E(R) -5x var(R), where R denotes the annual return on your portfolio. You identified 3 assets you want to invest in and estimated their annual expected returns and standard deviations to be as follows: Expected return St. deviation Risky asset 1 100 Risky asset 2 200 Risk-free asset 250 100 250 0 Therefore, if your student ID number ends with 25, then your utility function is U(R) = 25 E(R) 125 var(R), and the three assets you want to invest in have the following expected values and standard deviations: Expected return St. deviation Risky asset 1 Risky asset 2 Risk-free asset 0.25 0.125 0.1 0.25 0.1 0 The correlation between the two risky assets is assumed to be 0.25 (irrespective of what your x is). 1. Compute your optimal portfolio of the three assets, assuming that short selling is allowed. 2. You want to invest $1,000 in the optimal portfolio you found in part (1) and you want to hold that portfolio for 1 year. The annual returns on the two risky assets are normally distributed with the means and standard deviations listed in the table above (correspond- ing to your x) and therefore the return on your optimal portfolio will also be normally distributed with the mean and variance as found in part (1). (a) Run a Monte Carlo simulation (with 500 iterations) to generate a set of possible returns on your optimal portfolio. For each case, compute how much money you will have at the end of the year, if you realized that return.
Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
14th Edition
ISBN:9781305506381
Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Chapter2: Fundamental Economic Concepts
Section: Chapter Questions
Problem 6E
Related questions
Question
Substitute X=20. Can you show me how to do question 1 please
Transcribed Image Text:x=20.
Assume that your utility is U(R) = x E(R) -5x var(R), where R denotes the annual
return on your portfolio. You identified 3 assets you want to invest in and estimated their
annual expected returns and standard deviations to be as follows:
Expected return St. deviation
Risky asset 1
100
Risky asset 2
200
Risk-free asset
250
100
250
0
Therefore, if your student ID number ends with 25, then your utility function is U(R) =
25 E(R) 125 var(R), and the three assets you want to invest in have the following expected
values and standard deviations:
Expected return St. deviation
Risky asset 1
Risky asset 2
Risk-free asset
0.25
0.125
0.1
0.25
0.1
0
The correlation between the two risky assets is assumed to be 0.25 (irrespective of what your x
is).
1. Compute your optimal portfolio of the three assets, assuming that short selling is allowed.
2. You want to invest $1,000 in the optimal portfolio you found in part (1) and you want
to hold that portfolio for 1 year. The annual returns on the two risky assets are normally
distributed with the means and standard deviations listed in the table above (correspond-
ing to your x) and therefore the return on your optimal portfolio will also be normally
distributed with the mean and variance as found in part (1).
(a) Run a Monte Carlo simulation (with 500 iterations) to generate a set of possible
returns on your optimal portfolio. For each case, compute how much money you will
have at the end of the year, if you realized that return.
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