- Exercise 2 An investor who maximizes a linear mean-variance utility, U(µp, σp) μpaσ, optimally invests half of her wealth in asset 1, having expected re- turn μ₁ = 10% and standard deviation σ1 10%, and half of her wealth in a risk-free asset, having return FR = 4%. = (a) Find the efficient frontier and represent it in the plane (σp, μP) (assuming that the investor feasible portfolios can include a short position in the risk- free asset). (b) Find the risk-aversion parameter a of the investor. (c) Using the same efficient frontier, for which levels of risk-aversion parameter the investor has a negative position in the risk-free asset? =

- Exercise 2 An investor who maximizes a linear mean-variance utility, U(µp, σp) μpaσ, optimally invests half of her wealth in asset 1, having expected re- turn μ₁ = 10% and standard deviation σ1 10%, and half of her wealth in a risk-free asset, having return FR = 4%. = (a) Find the efficient frontier and represent it in the plane (σp, μP) (assuming that the investor feasible portfolios can include a short position in the risk- free asset). (b) Find the risk-aversion parameter a of the investor. (c) Using the same efficient frontier, for which levels of risk-aversion parameter the investor has a negative position in the risk-free asset? =

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

See similar textbooks

Similar questions

Exercise Exercise 1. Consider the Cournot game G = (I, (Ai, Ti)i≤1) such that: 1. I = {1,2} is the set of firms. 2. AR+ is the set of firm i's strategies. 3. TAR is firm i's payoff function defined by, for some c ≥ 0, Ti(Qi, 9−i) = max{1 − (qi + q−i), 0}qi — cqi. Answer the following questions: 1. Find all (pure-strategy) Nash equilibria in the case of c = = 0. 2. Find all (pure-strategy) Nash equilibria in the case of c = (0, 1). 3. Find all (pure-strategy) Nash equilibria in the case of c = [1,∞). Exercise 2. Consider the Braess's paradox G 1. I = {1,2,. , 10} is the set of people. ... 2. A = {1,0} is person i's strategy space. = (I, (Ai, ui)i≤1) such that: 3. u AR is person i's payoff function defined by -11-Σjel aj if ai =1 ui (a) = -11-Σje(1a) if a = 0, where Σ;a; is the number of people choosing strategy 1 and Σ; (1 - a;) is the number of people choosing strategy 0. Show that every (pure-strategy) Nash equilibrium has five people choosing route SAG and five players choosing route…
Given the following probability distribution, what is the expected return and the standard deviation of returns for Security J? The answer choice lists expected return and standard deviation in the respective order. State 1 2 3 Pri 0.2 O 12%; 5.18% O 15%; 3.16% O 15%; 6.50% 0.6 0.2 O 20%; 5.00% 15%; 10.00% rj 10% 15 20
3.1 Show that for any portfolio w = equal to (wi,..., wn) the Beta of the portfolio is Bw = wiB1 + + wn Bn, !! ... where B; for i = 1,...,n are Betas of individual assets.
n is the number of periods of an investment, PV is the starting value, FVn is the future value n periods ahead, and ^ means 'to the power of'. What is the correct formula for calculating return? a)(PV/FVn)^n - 1 b)(FVn/PV)^n c)1 - (FVn/PV)^n d)(FVn/PV)^n - 1
Which of the following regression outcomes indicates the asset with the greatest total risk? • large beta, small R² • small beta, large R² • small beta, small R² large beta, large R² .
An investor has preferences represented by the utility function U = E(r) - 20². What is her certainty equivalent return for a portfolio with an expected return of 10% and a standard deviation of 15%? Oa. 1.0% O b. 2.5% O c. 0.5% O d. 5.5% O e. 10.0%
What is the Variance of returns for Security XYZ?
man.1
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
Given the following probability distribution of returns: Probability Return 0.1 -15.0% 0.25 0.0% 0.3 8.5% 0.25 12.0% 0.1 32.0% what is the expected return?
Mean and Variance of Discrete Random Variable and the Characteristics of Normal Random Variable Example 1: Suppose that you are given the option of two investment portfolios, A and B, with potential profits and the associated probabilities displayed below. PORTFOLIO A Profit X -2,000 -4,000 3,000 5,000 PROBABILITY P(x) 0.3 0.1 0.3 0.3 PORTFOLIO B Profit X -3,000 -2,000 4,000 5,000 Probability P(X) 0.2 0.2 0.4 0.2 Calculated Mean and Standard Deviation for Portrollo A: Mean = 1,400 and standard deviation = 3,322.65 Calculated Mean and Standard Deviation for Portrollo B: Mean=1,600 and standard deviation= 3,882.31 A. using the mean and variance of portfolio A, interpret the result B.Based on the expected profits, which portfolio will you choose?
Show that for an initial wealth w and a linear utility function u(w) = w, then P= E[X].

Recommended textbooks for you

Essentials Of Investments

Finance

ISBN:

9781260013924

Author:

Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:

Mcgraw-hill Education,

FUNDAMENTALS OF CORPORATE FINANCE

Finance

ISBN:

9781260013962

Author:

BREALEY

Publisher:

RENT MCG

Financial Management: Theory & Practice

Finance

ISBN:

9781337909730

Author:

Brigham

Publisher:

Cengage

Foundations Of Finance

Finance

ISBN:

9780134897264

Author:

KEOWN, Arthur J., Martin, John D., PETTY, J. William

Publisher:

Pearson,

Fundamentals of Financial Management (MindTap Cou…

Finance

ISBN:

9781337395250

Author:

Eugene F. Brigham, Joel F. Houston

Publisher:

Cengage Learning

Corporate Finance (The Mcgraw-hill/Irwin Series i…

Finance

ISBN:

9780077861759

Author:

Stephen A. Ross Franco Modigliani Professor of Financial Economics Professor, Randolph W Westerfield Robert R. Dockson Deans Chair in Bus. Admin., Jeffrey Jaffe, Bradford D Jordan Professor

Publisher:

McGraw-Hill Education

Essentials Of Investments

Finance

ISBN:

9781260013924

Author:

Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:

Mcgraw-hill Education,

FUNDAMENTALS OF CORPORATE FINANCE

Finance

ISBN:

9781260013962

Author:

BREALEY

Publisher:

RENT MCG

Financial Management: Theory & Practice

Finance

ISBN:

9781337909730

Author:

Brigham

Publisher:

Cengage

Foundations Of Finance

Finance

ISBN:

9780134897264

Author:

KEOWN, Arthur J., Martin, John D., PETTY, J. William

Publisher:

Pearson,

Fundamentals of Financial Management (MindTap Cou…

Finance

ISBN:

9781337395250

Author:

Eugene F. Brigham, Joel F. Houston

Publisher:

Cengage Learning

Corporate Finance (The Mcgraw-hill/Irwin Series i…

Finance

ISBN:

9780077861759

Author:

Stephen A. Ross Franco Modigliani Professor of Financial Economics Professor, Randolph W Westerfield Robert R. Dockson Deans Chair in Bus. Admin., Jeffrey Jaffe, Bradford D Jordan Professor

Publisher:

McGraw-Hill Education

SEE MORE TEXTBOOKS