4. Suppose there are three uncorrelated assets. Each has a variance of 1.0 and expectedrates of return are 1, 2, and 3, respectively. For this example, short sales are allowed.Do the following:a. Find the minimum variance portfolio for the following desired expected portfoliorates of return: 1.0, 1.5, 2.0, 2.5, and 3.0.b. Sketch these on the return versus risk plot (you will need to use the standarddeviation of the portfolio, which clearly equals sqrt(w1^2+w2^2+w3^3), wherewi are the weights).c. Suppose we have a risk-free asset with a return of 2%. Modify your plot for b.

Minimum variance portfolio is one that has the specific proportions of its assets such that it…

Suppose there are three uncorrelated assets. Each has a variance of 1.0 and expe rates of return are 1, 2, and 3, respectively. For this example, short sales are allow Do the following: a. Find the minimum variance portfolio for the following desired expected pe rates of return: 1.0, 1.5, 2.0, 2.5, and 3.0. b. Sketch these on the return versus risk plot (you will need to use the standa deviation of the portfolio, which clearly equals sqrt(w1^2+w2^2+w3^3), w

Suppose there are three uncorrelated assets. Each has a variance of 1.0 and expe rates of return are 1, 2, and 3, respectively. For this example, short sales are allow Do the following: a. Find the minimum variance portfolio for the following desired expected pe rates of return: 1.0, 1.5, 2.0, 2.5, and 3.0. b. Sketch these on the return versus risk plot (you will need to use the standa deviation of the portfolio, which clearly equals sqrt(w1^2+w2^2+w3^3), w

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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Consider two assets. Suppose that the return on asset 1 has expected value 0.05 and standard deviation 0.1 and suppose that the return on asset 2 has expected value 0.02 and standard deviation 0.05. Suppose that the asset returns have correlation 0.4.Consider a portfolio placing weight w on asset 1 and weight 1-w on asset 2; let Rp denote the return on the portfolio. Find the mean and variance of Rp as a function of w.
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.
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.
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
Chose one of the options below The Mean-Variance Optimization (MVO) model finds the portfolio weights with the smallest variance for a given level of expected return, given the individual assets' expected returns, variances and correlations. The Black-Litterman model is the mean-variance optimization model run backwards, that is, the MVO model solved for variables other than the weights. The Black-Litterman model solves for the A. asset pairwise correlations B. asset standard deviations C. portfolio weights D. asset expected returns
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
assume that every asset has the same expected return and variance. furthermore, all assets have the same covariance with each other. as number of assets in a portfolio grows, which becomes more important: variance or covariance? clarify your answer using words, diagrams, formulae or a practical example.
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
What is the expected return on a two asset portfolio and what are its variance and standard deviation. What is R squared? Please keep it short and simple but making lots of sense. thanks
Consider the following linear regression model: (R₁-r)= a; + b(RMkt - rf) + e; The b; in the regression: O measures the deviation from the best fitting line and is zero on aver- measures the sensitivity of the security to market risk. measures the diversifiable risk in returns.
Expected return 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 of each asset? c. What is the expected return of a portfolio with 12% in asset J, 52% in asset K, and 36% in asset L? d. What is the portfolio's variance and standard deviation using the same asset weights from part (c)? Hint: Make sure to round all intermediate answers you will type. a. What is the expected return of asset J? (Round to four decimal places.) Data table (Click on the following icon in order to copy its contents into a spreadsheet.) Return on Asset J in State of Economy Boom Growth Stagnant Recession Probability of State 0.24 0.36 0.21 0.19 State 0.050 0.050 0.050 0.050 Return on Asset K in State 0.230 0.120 0.020 -0.060 Return on Asset L in State 0.250 0.190 0.065 - 0.190
There are three assets with the rates of return r1 = 214 +2 18+1, r2 = -314+61B –2, r3 = 514 – 1B+4, respectively, where A and B are two independent random events. Find the portfolio of the three assets with the minimum variance and determine its expected return rate.

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