Your client chooses to invest 40% in your portfolio (p) and 60% (f) in the risk-free asset. What is the standard deviation of your client’s portfolio?

You are a manager of a risky portfolio (consists of bonds and stocks) with an expected return E(rp) = 8% and standard deviation stdevp = 12%. The risk free rate rf = 2% and the standard deviation of the risk free asset is stdevf = 0% 7. Your client chooses to invest 40% in your portfolio (p) and 60% (f) in the risk-free asset. What is the expected return?

1. Your client chooses to invest 40% in your portfolio (p) and 60% (f) in the risk-free asset. What is the standard deviation of your client’s portfolio?

2. Your client chooses to invest 40% in your portfolio (p) and 60% (f) in the risk-free asset. What is the Sharpe ratio of your client’s portfolio?

3. Calculate the utility investors realize from investing 40% of their capital in your portfolio (p) and 60% (f) in the risk-free asset. Assume the following utility function: U = E(r) − 1 × A × stdev2, where A 2 (client’s risk aversion)=5.

4. Calculate the weight in the risky portfolio (p) that maximizes the utility of the client.

Expert Solution

1.
=proportion in risky portfolio*standard deviation of risky portfolio
=40%*12%=0.048

2.
=(Expected returns-risk free rate)/standard deviation
=(proportion in risky portfolio*returns of risky portfolio+proportion in riks free asset*returns of risk free asset-rsik free rate)/(proportion of risky portoflio*standard deviation of risky portfolio)
=(40%*8%+60%*2%-2%)/(40%*12%)=0.50

3.
=40%*8%+60%*2%-0.5*5*(40%*12%)^2=0.03824

4.
=(returns of risky portfolio-risk free rate)/(A*standard deviation of risky portfolio^2)
=(8%-2%)/(5*12%*12%)=0.833333333333333

jeff jeffy answered 2 years ago

An investor chooses to invest 60% of a portfolio in a risky fund and 40% in...

An investor chooses to invest 60% of a portfolio in a risky fund and 40% in a T-bill fund. The expected return of the risky portfolio is 17% and the standard deviation is 27%. The T-bill rate is 7%. What is the expected return and the standard deviation of the investor? What is the Sharpe ratio of the risky portfolio and the investor’s overall portfolio? Suppose the investor decides to invest a proportion (y) of his total budget in the...

1. Calculate the standard deviation of a portfolio consisting of 40 percent stock P and 60...

1. Calculate the standard deviation of a portfolio consisting of 40 percent stock P and 60 percent stock Q. Company Beta Expected Return Variance Correlation Coefficient P 1.3 28% 0.30 CORRP,Q = 0.3 Q 2.6 12% 0.16 Round to the nearset hundredth percent. Answer in the percent format. Do not include % sign in your answer (i.e. If your answer is 4.33%, type 4.33 without a % sign at the end.) 2. What is the beta of the following portfolio?...

Aasir can invest his money in risk-free asset and/or in a fund F. The risk-free asset...

Aasir can invest his money in risk-free asset and/or in a fund F. The risk-free asset provides a guaranteed return of 4%. The fund F provides expected return of 12% with volatility of 25%. If Aasir wants to limit his risk to no more than 20%, what is the highest expected return he can earn? If Aasir wants an expected return of at least 16%, what is the minimum possible volatility of his portfolio?

Your client would like to invest $15,000 in both the risk-free asset with return of rf...

Your client would like to invest $15,000 in both the risk-free asset with return of rf = 1% and the risky portfolio with expected return of μm = 8% and standard deviation of σm = 25%. Her utility function is U(μ,σ)=μ−ασ2, where her risk aversion is 1.5. a.How much should you invest in the risky portfolio so that she can receive the greatest utility? b. What is the expected return of this optimal portfolio? c. What is the standard deviation...

If you invest 40% of your money in A and 60% in B, what would be your portfolio's expected rate of return and standard deviation?

Consider the following probability distribution for stocks A and B: State Probability Return on Stock A Return on Stock B 1 0.10 10 % 8 % 2 0.20 13 % 7 % 3 0.20 12 % 6 % 4 0.30 14 % 9 % 5 0.20 15 % 8 % If you invest 40% of your money in A and 60% in B, what would be your portfolio's expected rate of return and standard deviation? 9.9%; 3% 9.9%; 1.1% 11%;...

In a portfolio consisting of the risk free asset and/or a risky asset, what is the...

In a portfolio consisting of the risk free asset and/or a risky asset, what is the expected return and standard deviation if you borrow 25% of your net worth by selling short the risk free asset and invest the proceeds in the risky asset, given the following? Rm = .15 Rf = .05 σm = .2

You proposed a portfolio for your client with 60% in stock A and 40% in stock...

You proposed a portfolio for your client with 60% in stock A and 40% in stock B. Stock A has an average weekly return of 0.88% and stock B has an average weekly return of 1.32%. Beta for stock A and B are 0.8 and 1.3 respectively. Now you want to deliver a performance report to the client regarding portfolio performance on a weekly basis. (a). What’s the portfolio average weekly return? (b). What’s the portfolio beta? (c). You have...

What is the standard deviation of the risk-free rate?

You expect the following set of possible outcomes for a stock:OutcomeProbabilityEnding Stock PriceHolding Period Return(Percent)Risk-free rate(Percent)Good35%$12044.54Neutral30%$100142Bad35%$70-16.5.5What is the standard deviation of the risk-free rate? Please enter your answer in percent rounded to the nearest basis point.

You invest all your money into a risky asset and a risk-free asset. The risky asset...

You invest all your money into a risky asset and a risk-free asset. The risky asset has an expected return of 0.065 and a standard deviation of 0.25, the risk-free asset returns 0.025. What is the return on your combined portfolio if you invest 0.4 in the risky asset, and the remainder in the risk-free asset? Round your answer to the fourth decimal point.

If the expected return on a risky asset is 13%, standard deviation is 25%, and the risk free asset 5%.

If the expected return on a risky asset is 13%, standard deviation is 25%, and the risk free asset 5%.Calculate the expected return , standard deviation, sharp ratio for the complete portfolio with y= .60

Question