Consider the following information State of Economy Probability of State of Economy Boon Rate of Return If State Occurs Stock A Stock C .30 a. Expected return 419 04 a. What is the expected return on an equally weighted portfolio of these three stocks? Note: Do not round Intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16. b. What is the variance of a portfolio invested 27 percent each in A and B and 46 percent in C? Note: Do not round intermediate calculations and round your answer to 5 decimal places, e.g., 16161.

Consider the following information State of Economy Probability of State of Economy Boon Rate of Return If State Occurs Stock A Stock C .30 a. Expected return 419 04 a. What is the expected return on an equally weighted portfolio of these three stocks? Note: Do not round Intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16. b. What is the variance of a portfolio invested 27 percent each in A and B and 46 percent in C? Note: Do not round intermediate calculations and round your answer to 5 decimal places, e.g., 16161.

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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2. The following table gives information on the return and variance of assets A and B, whose covariance is 0.0003: A B 0} 0,0009 0,0012 E (R₂) 0,05 0,06 a. Does the portfolio (1/3 of A and 2/3 of B) dominate the portfolio (2/3 of A and 1/3 of B)? b. Does the portfolio (1/2, 1/2) belong to the efficient frontier? c. If there were the possibility of lending and borrowing at 2%, would the portfolio (1/2, 1/2) belong to the new efficient frontier?
Suppose the index model for stocks A and B is estimated with the following results: rA = 2% + 0.8RM + eA, rB = 2% + 1.2RM + eB, σM = 20%, and RM = rM − rf . The regression R2 of stocks A and B is 0.40 and 0.30, respectively. Answer the following questions. Total: (a) What is the variance of each stock? (b) What is the firm-specific risk of each stock? (c) What is the covariance between the two stocks?
3. Suppose the index model for stocks A and B is estimated with the following results:rA = 2% + 0.8RM + eA, rB = 2% + 1.2RM + eB , σM = 20%, and RM = rM − rf . The regressionR2 of stocks A and B is 0.40 and 0.30, respectively. Answer the following questions. (a) What is the variance of each stock? (b) What is the firm-specific risk of each stock? (c) What is the covariance between the two stocks?
a) Discuss the difference between a price-weighted index and a value-weighted index. Give one example for the price-weighted index and one example for the value-weighted index and discuss any problems/advantages associated with the specific indices. b) We assume that investors use mean-variance utility: U = E(r) – 0.5 × Ao², where E(r) is the expected return, A is the risk aversion coefficient and o? is the variance of returns. Given that the optimal proportion of the risky asset in the complete port- folio is given by the equation y* = E , where r; is the risk-free rate, E(rp) is the expected returm of the risky portfolio, o, is variance of returns, and A is the risk aversion coefficient. For each of the variables on the right side of the equation, discuss the impact of the variable's effect on y* and why the nature of the relationship makes sense intuitively. Assume the investor is risk averse. Ao
Suppose the index model for stocks A and B is estimated with the following results:rA = 2% + 0.8RM + eA, rB = 2% + 1.2RM + eB , σM = 20%, and RM = rM − rf . The regressionR2 of stocks A and B is 0.40 and 0.30, respectively.(a) What is the variance of each stock? (b) What is the firm-specific risk of each stock? (c) What is the covariance between the two stocks?
Calculate the correlation coefficient for the portfolio using the following information: Variance of Stock X 0.08 Variance of Stock Y 0.06 Covariance is 0.05 a. 0.1042 b. 0.7217 c. 0.00024 d. 0.0693
Suppose you have mean-variance utility function with a coefficient of risk Aversion-0, which stocks are preferred to P. E(r) III IP II IV Standard Deviation
Expected retun and standard deviation. Use the following information to answer the questions: a. What is the expected return of each asset? b. What is the variance and the standard deviation c. What is the expected return of a portfolio with 1 1 Data Table d. What is the portfolio's variance and standard de - X Hint Make sure to round all intermediate calculatio Swers yo (Click on the following icon D in order to copy its contents into a spreadsheet.) a. What is the expected return of asset J? (Round to four decimal places.) Return on Return on Return on Probability of State State of Asset J in Asset Kin State 0.200 0.140 0.040 Asset L in Economy State State Вoom 0.28 0.070 0.260 0.180 Growth 0.37 0.25 0.070 Stagnant 0.070 0.060 -0.210 Recession 0.10 0.070 -0.100 Print Done
The variance (risk) of an N-asset portfolio can be written as: o² = 2 + 2/11 -Cov where o² is the average variance of stocks in the portfolio and Cov is the average covariance between each pair of stocks in the portfolio. This result suggests that a well-diversified portfolio with a sufficiently large number of stocks will have O a zero total risk (variance) a zero covariance with other assets a zero diversifiable (nonsystematic) risk a zero market (systematic) risk
Consider the following information: State of Economy Boom Bust Probability of State of Economy a. Expected return b. Variance .60 .40 Rate of Return if State Occurs % Stock A Stock B .23 .08 .15 .18 a. What is the expected return on an equally weighted portfolio of these three stocks? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b. What is the variance of a portfolio invested 24 percent each in A and B and 52 percent in C? (Do not round intermediate calculations and round your answer to 6 decimal places, e.g., .161616.) Stock C .42 -.09
Suppose that there are four risky assets whose expected returns E(r) and variance- covariance matrix (S) are shown in the spreadsheet below. We also consider the portfolio weights of two portfolios x and y of risky assets (see Cells B8:E9): 1 8 Portfolio x 9 Portfolio y A FOUR-ASSET PORTFOLIO PROBLEM Variance-covariance, S 20 Portfolio variance, 21 Portfollo standard deviation o 0.10 0.01 0.03 0.05 11 Portfolio x and y statistics: Mean, variance, covariance, correlation 12 Mean, Ejr, 13 Variance, 14 Covariance() 15 Correlation P 16 17 Calculating returns of combinations of Portfolio x and Portfolio y 18 Proportion of x 19 Mean portfolio return, r 0.01 0.30 0.06 -0.04 0.20 0.20 10.50% 0.1216 0.0714 0.4540 ? ? ? 0.3 0.03 0.06 0.40 0.02 0.30 0.10 ? 0.05 0.02 0.50 0.40 0.10 0.10 0.60 Mean, Er Variance, 0.2014 Question il Question ili Mean returns E(r) ? 7% 9% 11% 20% Question i i. Write the Excel formula used to estimate the mean and variance of portfolio y in cells E12 and E13,…
Suppose that the index model for stocks A and B is estimated from excess returns with the following results: RA = 2.60% + 0.90RM + eA RB = -2.00% + 1.20RM + eB OM = 26%; R-squarea = 0.21; R-squareg = 0.12 Assume you create portfolio P with investment proportions of 0.70 in A and 0.30 in B.

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