You are considering an investment in a portfolio P with the following expected returns in three different states of nature: Recession Steady Expansion Probability 0.10 0.55 0.35 Return on P -15% 20% 40% The risk-free rate is currently 4%, and the market portfolio M has an expected return of 16% and standard deviation of 20%, and its correlation with P is .7. Is P an efficient portfolio relative to the market?
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INV2 P1 1
You are considering an investment in a portfolio P with the following expected returns in three different states of nature:
|
Recession |
Steady |
Expansion |
Probability |
0.10 |
0.55 |
0.35 |
Return on P |
-15% |
20% |
40% |
The risk-free rate is currently 4%, and the market portfolio M has an expected return of 16% and standard deviation of 20%, and its correlation with P is .7.
- Is P an efficient portfolio relative to the market?
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- INV2 P1 3b You are considering an investment in a portfolio P with the following expected returns in three different states of nature: Recession Steady Expansion Probability 0.10 0.55 0.35 Return on P -15% 20% 40% The risk-free rate is currently 4%, and the market portfolio M has an expected return of 16% and standard deviation of 20%, and its correlation with P is .7. Would you characterize P as a buy or sell and why?INV2 P1 2 You are considering an investment in a portfolio P with the following expected returns in three different states of nature: Recession Steady Expansion Probability 0.10 0.55 0.35 Return on P -15% 20% 40% The risk-free rate is currently 4%, and the market portfolio M has an expected return of 16% and standard deviation of 20%, and its correlation with P is .7. What is the portfolio P’s beta?INV 2 -1c You are considering an investment in a portfolio P with the following expected returns in three different states of nature: Recession Steady Expansion Probability 0.10 0.55 0.35 Return on P -15% 20% 40% The risk-free rate is currently 4%, and the market portfolio M has an expected return of 16% and standard deviation of 20%, and its correlation with P is .7. c. Does portfolio P have a positive or negative alpha relative to its required return given its level of risk? Would you characterize P as a buy or sell, and why?
- INV 2 -1 You are considering an investment in a portfolio P with the following expected returns in three different states of nature: Recession Steady Expansion Probability 0.10 0.55 0.35 Return on P -15% 20% 40% The risk-free rate is currently 4%, and the market portfolio M has an expected return of 16% and standard deviation of 20%, and its correlation with P is .7. Is P an efficient portfolio relative to the market?INV 1 4b You have invested in a portfolio of 60% in risky assets (Portfolio R) and 40% in T-bills. The risky portfolio is described below: E(rR)=12% σR =15% T-bill rate 3% Expected Return on Overall Portfolio is 8.4% What is the standard deviation of your overall portfolio?Problem 13-10 Returns and Standard Deviations [LO1] Consider the following information: State of Economy Probability of State of Economy Rate of Return if State Occurs Stock A Stock B Stock C Boom .15 .37 .47 .27 Good .45 .22 .18 .11 Poor .35 −.04 −.07 −.05 Bust .05 −.18 −.22 −.08 a. Your portfolio is invested 20 percent each in A and C, and 60 percent in B. What is the expected return of the portfolio? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b-1. What is the variance of this portfolio? (Do not round intermediate calculations and round your answer to 5 decimal places, e.g., .16161.) b-2. What is the standard deviation? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
- A4 a. Suppose we have two risky assets, Stock I and Stock J, and a risk-free asset. Stock I has an expected return of 25% and a beta of 1.5. Stock J has an expected return of 20% and a beta of 0.8. The risk-free asset’s return is 5%. a. Calculate the expected returns and betas on portfolios with x% invested in Stock I and the rest invested in the risk-free asset, where x% = 0%, 50%, 100%, and 150%.Q No 3 Assume you are a portfolio manager at JS Global Capital Ltd. Recently you came across three attractive stocks and want to create a portfolio investment in these three stocks. The details of the stocks are given below: Company name Volatility (Standard deviation) Weight in Portfolio Correlation with the market portfolio Engro Ltd 25% 0.30 0.40 Lucky Cement Ltd 12% 0.30 0.60 FFC Ltd 13% 0.40 0.50 The expected return on the market portfolio is 8% and its volatility is 10%. The risk-free rate based on central bank’s discount rate is 3%. Calculate each of the stock’s expected return and risk (beta) as compared to the market What should be the expected return of the portfolio based on values calculated in part a. Calculate the beta of the portfolio? what does it tells regarding the riskiness of the portfolio?. E(RI) = .15(.11) + .55(.18) + .30(.08) Using CAPM to determine the expected rate of return for risky assets, consider the following example stocks, assuming that you have already compute the betas Stock Beta WND 0.80 STA 1.35 CTE 1.15 DUY 1.20 EVN -0.20 Stock WND the economy’s RFR to be 6 percent (0.06) and the expected return on the market portfolio (E(RM)) to be 8 percent (0.08) Stock STA, the economy’s RFR to be 5percent (0.05) and the expected return on the market portfolio (E(RM)) to be 7 percent(0.07) Assume that all the other stocks is as follows since we expect the economy’s RFR to be 5 percent (0.05) and the expected return on the market portfolio (E(RM)) to be 9 percent (0.09),
- INV 1 4b You have invested in a portfolio of 60% in risky assets (Portfolio R) and 40% in T-bills. The risky portfolio is described below: E(rR)=12% σR =15% Compute the standard deviation of your overall portfolio.A4 5a Consider the following information on three stocks in four possible future states of the economy: Rate of return if state occurs State of economy Probability of state of economy Stock A Stock B Stock C Boom 0.3 0.35 0.45 0.38 Good 0.3 0.15 0.20 0.12 Poor 0.3 0.05 –0.10 –0.05 Bust 0.1 0.00 –0.30 –0.10 a. Your portfolio is invested 30% in A, 50% in B, and 20% in C. What is the expected return of your portfolio?7. Portfolio Risk and Return. Suppose that the S&P 500, with a beta of 1.0, has an expected return of 10% and T-bills provide a risk-free return of 4%. (LO12-1) How would you construct a portfolio from these two assets with an expected return of 8%? Specifically, what will be the weights in the S&P 500 versus T-bills? How would you construct a portfolio from these two assets with a beta of .4? Find the risk premiums of the portfolios in parts (a) and (b), and show that they are proportional to their betas.