- 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

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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
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
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%
man.1
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?

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