Consider the following single factor specification: R₁ = a¡ + ßi, Rµ + €i.Where R; is the return on security i, RM is the return on index M (a broad market index) and e, is a zero-mean white noise random variable not correlated with anything.Assume that the single factor specification above correctly describes the return generating processes ofall securities. Furthermore, you have the following descriptive statistics for returns of well-diversifiedPortfolios X, Y, and index M.Portfolio XPortfolio YIndex MRisk-FreeExpected return14%17%????B₁1.21.610a. Assume that the corresponding single factor APT correctly prices Portfolios X and Y. In otherwords, the expected returns of Portfolios X and Y shown above - 14% and 17% respectively -are equal to their APT-predicted expected returns. Calculate the expected return of Index M andrisk-free rate.b. Another well-diversified portfolio Z has a beta, ßz, of 0.8 while its expected return is 10%. Form aportfolio consisting of Portfolios and Z (excluding Index M and risk-free asset) that"generates an arbitrage profit. Scale all weights by the investment in Z - either 1 for buying Z or -1 for short-selling Z. Show your workings.

Required return on a stock or portfolio with single factor model is calculated as shown below.

here R₁ is the return on security i, RM is the return on index M (a broad market index) and e, is a zero- an white noise random variable not correlated with anything. sume that the single factor specification above correctly describes the return generating processes of securities. Furthermore, you have the following descriptive statistics for returns of well-diversified rtfolios X, Y, and index M. Portfolio X Expected return 14% Bi 1.2

here R₁ is the return on security i, RM is the return on index M (a broad market index) and e, is a zero- an white noise random variable not correlated with anything. sume that the single factor specification above correctly describes the return generating processes of securities. Furthermore, you have the following descriptive statistics for returns of well-diversified rtfolios X, Y, and index M. Portfolio X Expected return 14% Bi 1.2

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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. The following questions are related to modern portfolio theory. • Assume there are only two stocks in the equity market. •The risk-free rate is 1.00%. Stock Return Volatility Correlation Matrix Y 0.7 1.0 X Y X 15.00% 20.00% 1.0 10.00% 15.00% 0.7 (a) Make an investment portfolio using the risky assets that has an expected return 12%. (b) Calculate the volatility of the portfolio in (a).
Baghiben
Baghiben
You are given the following information concerning three portfolios, the market portfolio, and the risk-free asset: Op 1.45 1.20 0.75 1.00 Portfolio: X Y Z Market Risk-free Rp 11.00% 10.00 8.10 10.40 5.20 Information ratio Op 33.00% 28.00 18.00 23.00 0 Assume that the tracking error of Portfolio X is 9.10 percent. What is the information ratio for Portfolio X? Note: A negative value should be indicated by a minus sign. Do not round intermediate calculations. Round your answer to 4 decimal places. 02148 0
The following expected return and the standard deviation of current returns are known: Security (i) Expected Return Standard Deviation βi A 0.20 0.12 1.1 B 0.12 0.10 0.8 T-Bills 0.05 0 0 Market Portfolio 0.20 0.15 1 Required: Determine which of A or B is over-valued or undervalued.
Q1: Suppose there are (N) securities in the market and it is Expected return for each security = 10%. It was a contrast For any security = 0.0144 and the deviation was The common (covariance) between any two cards = 0.0064 Required: 1-Determine the expected return and variance of a portfolio consisting of... (N) paper, note that the relative weight of all papers equal = 1-N? 2- Explain what happens to the variance of this portfolio as it increases value(N)?
E(FAssume that using the Security Market Line (SML) the required rate of return (RA) on stock A is found to be half of the required return (Rs) on stock B. The risk-free rate (R;) is one-fourth of the required return on A. Return on market portfolio is denoted by RM. Find the ratio of beta of A (BA) to beta of B (BB). a o
Assume CAPM holds. What is the correlation between an efficient portfolio and market portfolio? a. 1 b.-1 c.0 d. Not enough information Assume CAPM holds. The risk-free rate is 1% and the expected return on the portfolio is 5%. What is the expected return of a stock with a beta of 2? 70%
Portfolio theory with two assets E(R1)=0.15 E(01)= 0.10 W1=0.5 E(R2)=0.20 E(02) = 0.20 W2=0.5 Calculate the expected return and the standard deviation of the two portfolios if r1,2 = 0.4 and -0.60 respectively.
2. Consider the following expected returns, volatilities, and correlations: Expected Standard Stock Return Deviation Correlation with Vital Correlation with Mital Correlation with Pital Vital 14% 6% 1.0 -1.0 0.0 Mital 44% 24% -1.0 1.0 0.7 Pital 23% 14% 0.0 0.7 1.0 a. Imagine a portfolio comprising solely of Vital and Mital. What portion of should be allocated to Vital stock to ensure a risk-free investment? your investment b. What is the portfolio's volatility when holding a $10,000 long position in Pital and a $2000 short position in Mital? wwwww c. In a market, there are two securities, Artis and Brotis. Currently, the price of Artis stands at £50. Looking ahead, the price of Artis next year will be £40 during a recession, £55 in normal economic times, and £60 in an expanding economy. The probabilities associated with recession, normal times, and expansion are 0.1, 0.8, and 0.1, respectively. Artis does not pay dividends and has a correlation of 0.8 with the market. On the other…
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Considering the attached set of securities and portfolio returns: Find the combination of the weights that minimizes CV of the portfolio. How does the CV of the optimal portfolio compare with the CVs of its constituents?

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