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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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,…
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?
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?
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 expected return and standard deviation of the following two assets: Asset 1: E[r1]=0.1 and σ1=0.2 Asset 2: E[r2]=0.3 and σ2=0.4 (a) Draw (e.g. with Excel) the set of achievable portfolios in mean-standard deviation space for the cases: (i) ρ12= -1, (ii) ρ12=0. (b) Suppose ρ12=-1. Which portfolio has the minimal variance? What is the variance and expected return of that portfolio? (c) Derive the formula for the variance of a portfolio with four assets.
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
There are two assets 1 and 2, with returns X and Y correspondingly. Return X is a random variable with mean 1 and variance 1; return Y is a random variable with mean 1 and variance 3. We know that the expectation of X*Y is equal to 0. Find the share of asset 1 in the risk-minimizing portfolio.
Mean-variance expected utility is given by Eu = e-, where e is expected return, v is the variance of the portfolio and tis risk tolerance. Suppose an investor has risk-loving preferences. What can we say about the value of t? Select one: Ot1 O. t>0 O t=0
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?
Consider a portfolio formed of two risky assets whose returns have a correlation of 0.5. What can be said of the standard deviation of the global minimum-variance portfolio formed with these two risky assets? It's greater than zero. It s equal to zero. O It s between - 1 and +1. O It's the weighted average of the standard deviations of the two risky assets.
3. Consider a portfolio where equal investment is made in each of the n stocks. Thus, the proportion invested in each stock is 1/n. Prove that the portfolio variance will be: Portfolio V ariance = LAverage V ariance (1-) Average Covariance 4. By using the equation above, discuss the power and limits to diversification.
III. 1. The average variance of financial assets on a market is 0.4% and the average covariance between assets is 0.1%. Compute the variance of a portfolio composed of a. 5 assets: b. 100 assets. a. V(Rpf)=.. b. V(Rpf)=.. 2. On a market at equilibrium the effcient frontier has the following equation: E(Rp)=4%+1.2 opf The standard deviation of the market portfolio equals 5%. a. The expected return on a portfolio A with a beta of 1,2 equals .%. b. How much of the total risk of portfolio B is explained by the market if the correlation between A and B equals 0,5? Answer: R? =. %

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