J P Morgan Asset Management publishes information about fina

J. P. Morgan Asset Management publishes information about financial investments. Over the past 10 years, the expected return for the S&P 500 was 5.04% with a standard deviation of 19.45% and the expected return over that same period for a Core Bonds fund was 5.78% with a standard deviation of 2.13% (J. P. Morgan Asset Management, Guide to the Markets, 1st Quarter, 2012). The publication also reported that the correlation between the S&P 500 and Core Bonds is -.32. You are considering portfolio investments that are composed of an S&P 500 index fund and a Core Bonds fund.

a. Using the information provided, determine the covariance between the S & P 500 and Core Bonds. Round your answer to two decimal places.

b. Construct a portfolio that is 50% invested in an S&P 500 index fund and 50% in a Core Bond fund. Round your answers to one decimal place.

In percentage terms, what is the expected return and standard deviation for such a portfolio? Round your answers to two decimal places.

Expected return

Standard deviation

c. Construct a portfolio that is 20% invested in an S&P 500 index fund and 80% invested in a Core bond fund. Round your answers to one decimal place.
r =   

In percentage terms, what is the expected return and standard deviation for such a portfolio? Round your answers to two decimal places.

Expected return

Standard deviation

d. Construct a portfolio that is 80% invested in an S&P 500 index fund and 20% invested in a Core bond fund. Round your answers to one decimal place.
r =   

In percentage terms, what is the expected return and standard deviation for such a portfolio? Round your answers to two decimal places.

e. Which of the portfolios in parts (b), (c), and (d) above has the largest expected return?
- Select your answer

Which has the smallest standard deviation?

- Select your answer -

Which of these portfolios is the best investment alternative?
- Select your answer

Solution

Let \'X\' is S&P 500 and \'Y\' is corebond

Given : Mean of X =5.04%; SD of X =19.45%; Mean of Y = 5.78% and SD of Y = 2.13%; correlation = -0.32

Corr(X,Y) = COV(X,Y) / SD(X)*SD(Y) =-0.32

COV(X,Y) = -13.26

b) If 50% invested in X and 50% invested in Y

Expected return = E(0.5X+0.5Y) = 0.5*E(X)+0.5*E(Y) = 0.5*5.04 +0.5*5.78 =5.41

Standard deviation = sqrt Var(0.5X+0.5Y) = sqrt(0.25*Var(X)+0.25*Var(Y)+2*0.5*0.5*Cov(X,Y))=9.44

C)

a portfolio that is 20% invested in an S&P 500 index fund and 80% invested in a Core bond fund

Expected return = E(0.2X+0.8Y) = 0.2*E(X)+0.8*E(Y) = 5.63

Standard deviation = sqrt Var(0.2X+0.8Y) = sqrt(0.04*Var(X)+0.64*Var(Y)+2*0.2*0.8*Cov(X,Y))=3.71

d)

a portfolio that is 80% invested in an S&P 500 index fund and 20% invested in a Core bond fund.

Expected return = E(0.8X+0.2Y) = 0.8*E(X)+0.2*E(Y) = 5.12

Standard deviation = sqrt Var(0.8X+0.2Y) = sqrt(0.64*Var(X)+0.04*Var(Y)+2*0.2*0.8*Cov(X,Y))=15.43

e)

(C) has the largest expected return.

Smallest standard deviation is (C)

Option (C) is the best portfolio investment.