Utility Formula: U = E(r) – 0,5 x A x σ2
where, E(r) = Expected Return ;=12%
σ2 = Standard Deviation;= 25%
A = Risk Aversion Coefficient
Since standard deviation of T-bills is 0.
Utility for T-bills:-
Utility = 0.07 - 0.5A(0)2
= 0.07 - 0
= 0.07
Utility for portfolio:-
Utility = 0.12 - 0.5A(0.25)2
= 0.12 - 0.03125A
Setting the utility values of T-bills & portfolio equal and calculating A:
0.07 = 0.12 - 0.03125A
0.03125A = 0.05
A = 1.6
So, risk aversion(A) more than 1.6 means an investor would derive less utility from the risky portfolio and vice-versa.
Therefore, risk aversion (A) must be less than 1.6 for the risky portfolio to be preferred to T-bills.
If you need any clarification regarding this solution, then you can ask in comments
If you like my answer then please Up-vote as it will be motivating.
Consider a portfolio that offers an expected rate of return of 12% and a standard deviation...
Consider a portfolio that offers an expected rate of return of 12% and a standard deviation of 22%. T-bills offer a risk-free 5% rate of return. What is the maximum level of risk aversion for which the risky portfolio is still preferred to T-bills? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Consider a portfolio that offers an expected rate of return of 10% and a standard deviation of 24%. T-bills offer a risk-free 6% rate of return. What is the maximum level of risk aversion for which the risky portfolio is still preferred to T-bills?
Problem 6-5 Consider a portfolio that offers an expected rate of return of 11% and a standard deviation of 21%. T-bills offer a risk-free 6% rate of return What is the maximum level of risk aversion for which the risky portfolio is still preferred to T-bills? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Maximum level of risk aversion must be
A risky portfolio has an expected return of 12% and standard deviation of 25%. Given a risk free rate of 3%, what percentage of a clients portfolio should be allocated to the risky portfolio if the client has a risk aversion of 4?
You manage a risky portfolio with an expected rate of return of 18% and a standard deviation of 28%. The T-bill rate is 8%. Your client's degree of risk aversion is A= 3.5, assuming a utility function U=EU - VAо. a. What proportion, y, of the total investment should be invested in your fund? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Investment proportion y b. What is the expected value and standard deviation of the...
You manage a risky portfolio with an expected rate of return of 20% and a standard deviation of 37%. The T-bill rate is 7%. Your client's degree of risk aversion is A2.5, assuming a utility function U = E) - VAO? a. What proportion, y. of the total investment should be invested in your fund? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Investment proportion y 1% b. What is the expected value and standard deviation...
Arisky fund has an expected return of 9% and standard deviation of 15%. The T-Bill rate is 3%. An investor allocates 125% of her retirement portfolio to the risky fund and -25% to T-Bills (recall the negative allocation to T-Bills indicates borrowing at risk free rate). What is the investor's risk aversion coefficient (A)? 0.47 2.13 -2.13 1.40
You manage a risky portfolio with an expected return of 12% and a standard deviation of 24%. Assume that you can invest and borrow at a risk-free rate of 3%, using T-bills. a. Draw the Capital Allocation Line (CAL) for this combination of risky portfolio and risk-free asset. What is the Sharpe ratio of the risky portfolio? b. Your client chooses to invest 50% of their funds into your risky portfolio and 50% risk-free. What is the expected return and...
Assume that you manage a risky portfolio with an expected rate of return of 14%and a standard deviation of 38%. The T-bill rate is 4%. A client prefers to invest in your portfolio a proportion (y) that maximizes the expected return on the overall portfolio subject to the constraint that the overall portfolio's standard deviation will not exceed 25%.a. What is the investment proportion, y ? (Do not round Intermediate calculations. Round your answer to 2 decimal places.)b. What is the...
A risky portfolio has an expected return of 12% and standared deviation of 25% given a risk free rate of 3% what is the expected return on the complete portfolio for a client with a risk aversion of 4?