Chapter 5 Mini Case Continued Barney Smith Investment Advisors recently issued e

ID: 1226393 • Letter: C

Question

Chapter 5 Mini Case Continued

Barney Smith Investment Advisors recently issued estimates for the state of the economy and the rate of return on each state of the economy. Alta Industries, Inc. is an electronics firm; Repo Men Inc. collects past due debts; and American Foam manufactures mattresses and various other foam products. Barney Smith also maintains an "index fund" which owns a market-weighted fraction of all publicly traded stocks; you can invest in that fund and thus obtain average stock market results. Given the situation as described, answer the following questions.

Assume that you recently graduated and you just landed a job as a financial planner with the Cleveland Clinic. Your first assignment is to invest $100,000. Because the funds are to be invested at the end of one year, you have been instructed to plan for a one-year holding period. Further, your boss has restricted you to the following investment alternatives, shown with their probabilities and associated outcomes. State of Economy Probability T-Bills Alta Inds. Repo Men American Foam Market Port. Recession 0.1 8.00% -22.0% 28.0% 10.0% -13.0% Below Average 0.2 8.00% -2.0% 14.7% -10.0% 1.0% Average 0.4 8.00% 20.0% 0.0% 7.0% 15.0% Above Average 0.2 8.00% 35.0% -10.0% 45.0% 29.0% Boom 0.1 8.00% 50.0% -20.0% 30.0% 43.0%

f. Suppose you create a two-stock portfolio by investing $50,000 in Alta Industries and $50,000 in Repo Men. Calculate the expected return, standard deviation, coefficient of variation, and beta for this portfolio. How does the risk of this two-stock portfolio compare with the risk of the individual stocks if they were held in isolation?

Explanation / Answer

Expected return for Alta industry =0.1*(-0.22)+0.2*(-0.02)+0.4*(0.2)+0.2*(0.35)+0.1*(0.5)= 0.174

Expected return for Repo industry =0.1*(0.28)+0.2*(0.147)+0.4*(0)+0.2*(-0.1)+0.1*(-0.2)= 0.0174

Expected return for Market Portfolio =0.1*(-0.13)+0.2*(0.01)+0.4*(0.15)+0.2*(0.29)+0.1*(0.43)= 0.15

Expected return for T bill(Risk free rate)= 0.1*(0.08)+0.2*(0.08)+0.4*(0.08)+0.2*(0.08)+0.1*(0.08)=0.08

Expected return from two stock=weight* Expected return for Alta industry+ weight* Expected return for Repo industry

Expected return from two stock=0.5*0.174+0.5*0.0174=0.0957=9.57%

Standard deviation for Alta=(0.1*((-0.22-0.174)^2)+0.2*((-0.02-0.174) ^2)+0.4*((0.2-0.174) ^2)+0.2*((0.35-0.174) ^2)+0.1*((0.5-0.174) ^2))^0.5=0.2

Standard deviation for Repo=(0.1*((0.28-0.0174)^2)+0.2*((0.147-0.0174)^2)+0.4*((0-0.0174) ^2)+0.2*((-0.1-0.0174) ^2)+0.1*((-0.2-0.0174) ^2))^0.5=0.13

Standard deviation for market=(0.1*((-0.13-0.15)^2)+0.2*((0.01-0.15)^2)+0.4*((0.15-0.15)^2)+0.2*((0.29-0.15)^2)+0.1*((0.43-0.15)^2))^0.5=0.15

Covariance of portfolio =0.1*((-0.22-0.174)* (0.28-0.0174))+0.2*((-0.02-0.174)* (0.147-0.0174))+0.4*((0.2-0.174)* (0-0.0174))+0.2*((0.35-0.174)* (-0.1-0.0174))+0.1*((0.5-0.174)* (-0.2-0.0174))= -0.027

Portfolio Variance= w2A*2(RA) + w2B*2(RB) + 2*(wA)*(wB)*Cov(RA, RB)

Portfolio Variance =(0.5*0.2)^2+(0.5*0.13)^2+2*0.5*0.5*(-0.027) 0.000725

Portfolio standard deviation =portfolio variance^0.5=(0.000725)^0.5=0.0269

Coefficient of variance= S.D of portfolio/Expected return of portfolio=0.0269/0.0957=0.28

Expected return of portfolio=Risk free rate+(market rate-risk free rate)*beta

0.0957=0.08+(0.15-0.08)*beta

Beta=(0.0957-0.08)/(0.15-0.08)=0.22

Navigate

Chapter 5 Lecture Notes (5.7) One-Sample Inference body of water available for S

Chapter 5 Modern Ethernet 1. Which term refers to the 100-Mbps standards, even t

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.

Chapter 5 Mini Case Continued Barney Smith Investment Advisors recently issued e

Question

Explanation / Answer

Related Questions

Navigate