7-28 Select the INCORRECT the following: statement from among a. Under the Markowitz formulation, a portfolio of 30 securities would have 870 covariances. b. Under the Markowitz formulation, a portfolio of 30 securities would have 30 variances in the variance-covariance matrix. c. Under the Markowitz formulation, a portfolio of 30 securities would have 870 terms in the variance-covariance matrix. d. Under the Markowitz formulation, a portfolio of 30 securities would require 435 unique covariances to calculate portfolio risk.

7-28 Select the INCORRECT the following: statement from among a. Under the Markowitz formulation, a portfolio of 30 securities would have 870 covariances. b. Under the Markowitz formulation, a portfolio of 30 securities would have 30 variances in the variance-covariance matrix. c. Under the Markowitz formulation, a portfolio of 30 securities would have 870 terms in the variance-covariance matrix. d. Under the Markowitz formulation, a portfolio of 30 securities would require 435 unique covariances to calculate portfolio risk.

EBK CONTEMPORARY FINANCIAL MANAGEMENT

14th Edition

ISBN:9781337514835

Author:MOYER

Publisher:MOYER

Chapter8: Analysis Of Risk And Return

Section: Chapter Questions

Problem 21P

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3) i) Calculate the average returns, variance and standard deviation for three securities X, Y and Z that have performed as follows. Returns % Year X Y Z 1 11 36 -3 2 6 -7 0 3 -8 21 5 4 28 -12 9 5 13 43 5 ii) Is there any basis for preferring one of these securities over the others? iii) Calculate the covariances between X, Y and Z.
17. The purpose of computing a minimum variance hedge ratio is to minimize the variance of the: (a) hedging instrument. (b) correlation estimator. (c) instrument to be hedged. (d) combined underlying and hedging instrument portfolio. 7
3) If two securities are perfectly negatively correlated then the global-minimum variance portfolio has a standard deviation that is always A) greater than zero. B) equal to zero. C) equal to the sum of the securities' standard deviations. D) equal to −1. Choose the correct answer and justify it.
Portfolios A and B are both well-diversified. The risk-free rate is 8%. The return for the market is 10%. Portfolio A has an expected return of 15% and beta of 1.1. Portfolio B has an expected return of 9% and beta of 0.20. Portfolio A's variance is 9%, whilst Portfolio B's variance is 5.5%. Calculate for Portfolio A and Portfolio B the following: 1. Sharpe's Measure, 2. Treynor's Measure, 3. Jensen's Measure. Which is the better portfolio according to each measure?
5. Consider the portfolios constructed from the two risky securities with expected returns, standard deviations of returns, and correlation between returns given in the following table. |1=0.10 M2 = 0.15 01 = = 0.28 02 = 0.24 P12 = -0.10 Find the equation of the minimum variance line w = μa + b.
The market has three risky assets. The variance-covariance matrix of the risky assets are as follows: r1 r2 r3 r1 0.25 0 -0.2 r2 0 4 0.1 r3 -0.2 0.1 1 Assume the market portfolio is M = 0.2 ◦ r1 + 0.5 ◦ r2 + 0.3 ◦ r3. Further assume E(rM) = 0.08. (1) What is the variance of M?(2) What is the covariance of r2 and M?(3) What is β2?(4) If the rate of return of the risk-free asset is 0.02. Then what is the fair expected rate of return of security 2?(5) An investor wants to invest in a portfolio P = 0.4◦r1+0.6◦r3. What is its “fair” expected rate of return?
Exercises: a. The standard deviation of returns is 0.30 for Stock A and 0.20 for Stock B. The covariance between the returns of A and B is 0.006. The correlation of returns between A and B is: b. Explain the differences between systemic risk and unsystematic risk, give additional examples c. Compare and contrast the Capital Market Line and Security Market Line d. The covariance of the market's returns with the stock's returns is 0.008. The standard deviation of the market's returns is 0.08, and the standard deviation of the stock's returns is 0. 11. What is the correlation coefficient of the returns of the stock and the returns of the market? e. According to the CAPM, what is the required rate of return for a stock with a beta of 0.7, when the risk-free rate is 7% and the expected market rate of return is 14%
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
4) Which of the following statement(s) is(are) true regarding the variance of a portfolio of two risky securities? 1.I) The higher the coefficient of correlation between securities, the greater the reduction in the portfolio variance. 2.II) There is a linear relationship between the securities' coefficient of correlation and the portfolio variance. 3.III) The degree to which the portfolio variance is reduced depends on the degree of correlation between securities. A) I only B) II only C) III only D) I and II E) I and III Justify the correct answer.
QUESTION 1 Which of the following statements is true regarding the variance or standard deviation of a portfolio of two risky securities? a. The portfolio variance is independent of the correlation between securities. b. If the two securities are perfectly negatively correlated, the minimum variance portfolio has a standard devaition that is greater than zero. C. The degree to which the portfolio variance is reduced depends on the degree of correlation between securities. d. There is a linear relationship between the securities' coefficient of correlation and the portfolio's standard deviation. e. If the two securities are not correlated, the minimum variance portfolio has a standard devaition that equals zero.
a) The covariance between stocks A and B is 0.0014, standard deviation of stock A is 0.032, and standard deviation of stock B is 0.044. Which of the following is the most appropriate to depict the risk- return characteristics of a portfolio consisting of only stocks A and B, and explain why? E(R) E(R) E(R) A A A (A) (B) (C) b) found to be half of the required return (Rs) on stock B. The risk-free rate (R) is one-fourth of the required Assume that using the Security Market Line (SML) the required rate of return (RA) on stock A is return on A. Return on market portfolio is denoted by RM. Find the ratio of beta of A (DA) to beta of B (OB). c) Assume that the short-term risk-free rate is 3%, the market index S&P500 is expected to pay returns of 15% with the standard deviation equal to 20%. Asset A pays on average 5%, has standard deviation equal to 20% and is NOT correlated with the S&P500. Asset B pays on average 8%, also has standard deviation equal to 20% and has correlation of 0.5 with…
Calculate the standard deviation of a portfolio with 0.24 invested in Asset A, 0.33 invested in Asset B, and the rest invested in Asset C. Express your answer as a decimal with four digits after the decimal point (e.g., 0.1234, not 12,34%). Std Dev(A) = 0.43, Std Devirg) = 0.67. Std Dev(rc)=0.53 Correlation(A) =-0.24, Correlation(Arc)-0.32, Correlationirere)=0.09 Type your answer.....