Assume we beleive a 1 factor APT model describes securities returns. Consider 2 assets with the following dataSecurityABSuppose the relevant variances are:ComponentSystematic FactorExpected Return5.65%9.06%€ AEBVariance10.03650.03870.039Beta0.51.61. The beta of an equally weighted portfolio is: Number2. The the variance of an equally weighted portfolio is (answer exactly): Number3. Compute the risk free rate : Number

We need to use the formulae inscribed in portfolio management for arbitrage pricing theory ( APT ).…

Assume we beleive a 1 factor APT model describes securities returns. Consider 2 assets with the following data Security B Suppose the relevant variances are: Component Systematic Factor Expected Return 5.65% 9.06% € A B Variance 0.0365 0.0387 0.039 Beta 0.5 1.6 1. The beta of an equally weighted portfolio is: Number 2. The the variance of an equally weighted portfolio is (answer exactly): Number 3. Compute the risk free rate : Number

Assume we beleive a 1 factor APT model describes securities returns. Consider 2 assets with the following data Security B Suppose the relevant variances are: Component Systematic Factor Expected Return 5.65% 9.06% € A B Variance 0.0365 0.0387 0.039 Beta 0.5 1.6 1. The beta of an equally weighted portfolio is: Number 2. The the variance of an equally weighted portfolio is (answer exactly): Number 3. Compute the risk free rate : Number

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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Portfolio manager wants to optimize the riskiness of the two assets portfolio with the given statistics below:- Assets Return Volatility Weight A 17.00% 15.00% 40.00% B 21.00% 25.00% 60.00% Correlation -0.70 -0.35 0.25 0.50 0.70 Requirements Calculate the two assets portfolio standard deviation at different correlation levels which are mentioned above and suggest at which correlation is best suits to your portfolio.
The beta of a portfolio is: A. A measure of the correlation of betas of the securities in the portfolio. B. Always greater than one. C. The market value weighted average beta of the securities in the portfolio. D. The geometric average of the beta of the securities in the portfolio.
Assuming that the rates of return associated with a given asset investment are normally distributed; that the expected return, r, is 18.7%; and that the coefficient of variation, CV, is 1.88, answer the following questions: a. Find the standard deviation of returns, sigma Subscript rσr. b. Calculate the range of expected return outcomes associated with the following probabilities of occurrence: (1) 68%, (2) 95%, (3) 99%.
1. Determine the expected return and the variance of the portfolio formed by the two assets S₁, S₂ with weights ₁ = 0.6, x2 = 0.4. The assets returns are described by the following scheme: scenario W1 2لا W3 probability 0.1 0.4 0.5 T1 -20% 0% 20% 12 -10% 20% 40%
Suppose two asset returns are described by a two factor model, n = 0% + 11 + 1.82 + e1 2 = -1% + 2/1 + 0.52 + e2 where the volatility of first factor is 30%, the volatility of the second factor is 10%, and the correlation between the two factors is 0.5. Suppose also that the volatilities of the error terms ej and ez are both 10%. What is the covariance of n and r2 ? (Nearest 0.0001).
Suppose the utility function is U = E(r) - 0.5Ao2. Draw the indifference curve corresponding to a utility level of 0.2 for an investor with a risk aversion coefficient of 3. Please note the vertical line indicates expected return, and plot standard deviation on the horizontal line.
Portfolio Suppose rA ~ N (0.05, 0.01), rB ~ N (0.1, 0.04) with pA,B = 0.2 where rA and rB are CCR’s. a) Suppose you construct a portfolio with 50% for A and 50% for B. Find the variance of the portfolio CCR. b) Find the portfolio expected gross return. c) Find the expected portfolio CCR.
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 of all securities. Furthermore, you have the following descriptive statistics for returns of well-diversified Portfolios X, Y, and index M. Portfolio X Portfolio Y Index M Risk-Free Expected return 14% 17% ?? ?? B₁ 1.2 1.6 1 0 a. Assume that the corresponding single factor APT correctly prices Portfolios X and Y. In other words, 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 and risk-free rate. b. Another well-diversified portfolio Z has a beta, ßz, of 0.8 while its expected return is 10%. Form a portfolio consisting…
4
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,…
PLEASE DO THIS IN EXCEL
Question 1 Are the following statements true or false? Provide a short justification for your answer. (You are evaluated on your justification.) Remember that a statement is false if any part of the statement is false. A single correct counterexample is sufficient to show that a statement is false. a) assets A, B, C, with expected returns and standard deviations: Suppose you are a mean-variance optimizer. The risk-free rate is 3%. There are three risky E [řa] = 10%, SD [FA] = 5% E [řB] = 15%, SD [řB] = 7% E [řc] = 12%, SD [řc] = 9% You cannot invest in all three risky assets. Instead, you have to choose whether to invest in only assets (A, B), or only assets (A, C). Asset B mean-variance dominates asset C, since it has higher return and lower standard deviation than asset C. Thus, as long as you are risk-averse, you would always prefer the set of assets (A, B) to the set assets (A, C). b) the same market B's. The covariance matrix between A, B, C is: Suppose the CAPM holds. Consider…

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