Problem 1 Consider the following information about three stocks: Rate of Return if State Occurs State of Economy Probability of State of Economy Stock A Stock B Stock C Boom Average Poor 0.2 40% 15% 7% 0.3 15% 30% 7% 0.3 5% -5% 7% Recession 0.2 -20% 5% 7% Your portfolio manager has invested 30% of your money in Stock A, 50% in Stock B, and 20% in Stock C. a) What is the expected return of your portfolio? b) What is the covariance between Stocks A and B? c) What is the correlation coefficient between Stocks B and C? d) What is the standard deviation of your portfolio? Hint: Instead of using the portfolio variance formula for three stocks, you can save time by calculating the return on the portfolio for all four states of the economy, and then calculate the standard deviation of these portfolio returns.

Problem 1 Consider the following information about three stocks: Rate of Return if State Occurs State of Economy Probability of State of Economy Stock A Stock B Stock C Boom Average Poor 0.2 40% 15% 7% 0.3 15% 30% 7% 0.3 5% -5% 7% Recession 0.2 -20% 5% 7% Your portfolio manager has invested 30% of your money in Stock A, 50% in Stock B, and 20% in Stock C. a) What is the expected return of your portfolio? b) What is the covariance between Stocks A and B? c) What is the correlation coefficient between Stocks B and C? d) What is the standard deviation of your portfolio? Hint: Instead of using the portfolio variance formula for three stocks, you can save time by calculating the return on the portfolio for all four states of the economy, and then calculate the standard deviation of these portfolio returns.

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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1. Consider the following states of outcomes, probabilities, and expected returns on only stocks three stocks in your portfolio; X, Y, and Z. State Probability X Y Boom 0.15 16% 10% 22% Semi-Boom ?? 14% 8% 18% Normal 0.50 10% 6% 14% Mild-Recession 0.10 5% 4% -10% Full-Recession 0.10 -3% 2% -12% a. What is the expected return of the portfolio if $25,000 is invested in X, $35,000 in Y, and $30,000 invested in stock Z? b. What are the standard deviations of stocks X, Y, and Z?
Assume you have created a 2-stock portfolio by investing $30,000 in stock X with a beta of 0.8, and $70,000 in stock Y with a beta of 1.2. Market risk premium is 8% and risk-free rate is 6%. The followings are the probability distributions of Stocks X and Y’s future returns: State of Economy Probability rx rY Recession 0.1 -10% -35% Below average 0.2 2% 0% Average 0.4 12% 20% Above average 0.2 20% 25% Boom 0.1 38% 45% Calculate the portfolio’s expected rate of return and the standard deviation of its future returns Calculate the required rate of return of your portfolio. Which stock in…
Question 3 You are trying to develop a strategy for investing in two different stocks. The anticipated annual return for a ¢1,000 investment in each stock under four different economic conditions has the following probability distribution: Returns Probability Economic Condition Stock X Stock Y 0.1 Recession -50 -100 0.3 Slow Growth 20 50 0.4 Moderate Growth 100 130 0.2 Fast Growth 150 200 (a) Which of the investments has a better return and why? (b) Which of the investments is relatively less risky and why? (c) What type of association exists between the two-investment options X and Y? Interpret your results.
Consider the following information on two stocks: P(State) Stock A Stock B Boom 20% 30% 20% Normal 50% 12% -5% Slow 15% 4% 8% Recession 15% -10% 10% $Investment Beta Asset A $35,000 1.45 Asset B $15,000 0.85 Q1. Calculate the weight of A in the portfolio. (Enter percentages as decimals and round to 4 decimals) Q2. Calculate the expected return on the portfolio. (Enter percentages as decimals and round to 4 decimals) Q3. Calculate the standard deviation of the portfolio. (Enter percentages as decimals and round to 4 decimals).
Quantitative Problem: You are given the following probability distribution for CHC Enterprises: State of Economy Probability Rate of return Strong 0.25 18 % Normal 0.55 8 % Weak 0.20 -6 % Using excel: What is the stock's expected return? Do not round intermediate calculations. Round your answer to two decimal places. % What is the stock's standard deviation? Do not round intermediate calculations. Round your answer to two decimal places. % What is the stock's coefficient of variation? Do not round intermediate calculations. Round your answer to two decimal places.
Aa.5
You have been given this probability distribution for the holding-period return for a stock: Stock of the Economy Probability HPR Boom 0.40 22 % Normal growth 0.35 11 % Recession 0.25 – 9 % What is the expected standard deviation for the stock? Multiple Choice 7.04% None of the options are correct. 2.07% 9.96% 1.44%
What is the expected return of a portfolio consisting of $6,000 stocks G and $4,000 stock H ? State of Probability of Returns if State Occurs Economy State of Economy Stock G (" Stock H ")/(11%) Boom 22% 14% 1% Normal 78% 7% 9% a. 7.2% b. 7.6% c. $7.9% d. 8.3% e. $8.9% 33. Joel Foster is the portfolio manager of the SF Fund, a $1 million hedge fund that contains the following stocks. The required rate of return on the market is 10% and the risk-free rate is 4%. What rate of return should investors expect (and require) on this fund? Stoo Amount bar(A) 270,000 B 330,000 1.4 bar(C) 400,000 0.7 $1,000,000 a. 8.756% b. 9.382% c. 9.921%
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Consider the following data State of Nature Prob. Stock A Return Boom 0.3 16.00% Normal 0.6 14.20% Recession 0.1 8.00% If the current rate on a treasury bill is 4%, what is the risk premium on the stock? (Note: treasury bill rate is generally regarded as risk free rate) Group of answer choices 10.12% 8.14% 14.12% 11.12%
Consider the following information: Rate of Return if State Occurs State of Probability of State of Economy Stock A Stock B Stock C Economy Boom 0.15 0.32 0.42 0.33 Good 0.45 0.19 0.13 0.12 Poor 0.30 -0.05 -0.08 -0.06 Bust 0.10 - 0.16 -0.28 0.09 a. Your portfolio is invested 30 percent each in A and C, and 40 percent in B. What is the expected return of the portfolio? (Round your answer to 2 decimal places. (e.g., 32.16)) Expected return % b-1What is the variance of this portfolio? (Do not round intermediate calculations and round your answer to 5 decimal places. (e.g., 32.16161)) Variance b-2What is the standard deviation? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16)) Standard deviation %
Accounting Use the following information: Stock A B Good state 12% 17% Bad state 0% -1% Assume there is 60% probability that the good state occurs and 40% chance the bad state occurs. What is the expected return of a portfolio that is 9% invested in stock A and 1-9% invested in B? (Please use 5 decimal places, this should be written in percentage return, so an answer of 23.143% should be written at .23143)

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