CExercise 529) P Morgan Asset Management publishes i r at on about financial inv

Question

CExercise 529) P Morgan Asset Management publishes i r at on about financial investments. Over the past 10 years the expected return for the S&P; 500 was 4% with a standard devotion of 19.45% andthe expected retum over that same perod for·Core Bonds Md was ues ati·tandare deltion enin u g Mpen Asset Management Gulde to the Markets, 1 Quarter, 2012). The publication also reported that the correlation between the S8P 500 and Core Bonds is-0.32. You are considening portfolio Investments that are composed of an S&P; 500 index fund and a Core Bonds fund. Using the ieformation provided, determine the covarlance between the values as negative numbers SAP 500 and Core Bonds. Round your answer to two decimal places. if required enter negative 154 Construct a portfolo that 10% rvested in an S&P; 500tndex fund and RISan a Core Bond fnd. Round your answers to one decanal place. b. 5.419.78 In percentage terms, what is the expected return and standard deviation for such a portfolia? Round your answers to two decimal places Expected return In percentage terms, what is the expected retum and standard deviation for such a portolle? Round your answers to teg decimal Expected renum MacBook Pro otion command command option

Explanation / Answer

let x=SP500 and mean(x)=5.04 and sd(x)=19.45 and

y=core bonds, mean(y)=5.78 and sd(y)=2.13

corr(x,y)=-0.32

corr(x,y)=cov(x,y)/(sd(x)*sd(y))

(a) cov(x,y)=corr(x,y)*sd(x)*sd(y)=-0.32*19.45*2.13=-13.2571

(b)portfilio z=0.5*x+0.5*y

%return of z=0.5*mean(x)+0.5*mean(y)=0.5*5.04+0.5*5.78=5.41

sd of return=9.44

var(z)=var(0.5*x+0.5*y)=0.25*var(x)+0.25*var(y)+2*0.5*0.5*cov(x,y)=

=0.25*19.45*19.45+0.25*2.13*2.13-2*0.5*0.5*13.2571=89.0813

sd(z)=sqrt(var(z))=sqrt(89.0813)=9.44

(c)portfilio z=0.2*x+0.8*y

%return of z=0.2*mean(x)+0.8*mean(y)=0.2*5.04+0.8*5.78=5.63

sd of return=3.71

var(z)=var(0.2*x+0.8*y)=0.04*var(x)+0.64*var(y)+2*0.2*0.8*cov(x,y)=

=0.04*19.45*19.45+0.64*2.13*2.13-2*0.2*0.8*13.2571=13.79

sd(z)=sqrt(var(z))=sqrt(13.79)=3.71

(d)portfilio z=0.8*x+0.2*y

%return of z=0.8*mean(x)+0.2*mean(y)=0.8*5.04+0.2*5.78=5.19

sd of return=15.43

var(z)=var(0.8*x+0.2*y)=0.64*var(x)+0.04*var(y)+2*0.2*0.8*cov(x,y)=

=0.64*19.45*19.45+0.04*2.13*2.13-2*0.2*0.8*13.2571=238.05

sd(z)=sqrt(var(z))=sqrt(238.05)=15.43

(e) highest return (c)5.63

lowest sd (c)3.71

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