Question

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%.† The publication also reported that the correlation between the S&P 500 and core bonds is −0.32.
J.P. Morgan Asset Management also reported that the expected return for real estate investment trusts (REITs) was 13.07% with a standard deviation of 23.17%. The correlation between the S&P 500 and REITs is 0.74 and the correlation between core bonds and REITs is −0.04. (Past performance is no guarantee of future results.)
You are considering portfolio investments that are composed of an S&P 500 index fund and REITs as well as portfolio investments composed of a core bonds fund and REITs.

Using the information provided, determine the covariance between the S&P 500 and REITs and between core bonds and REITs. (Round your answers to three decimal places.)
S&P 500 and REITs
core bonds and REITs

Construct a portfolio that is 50% invested in an S&P 500 fund and 50% invested in REITs. In percentage terms, what are the expected return and standard deviation for such a portfolio? (Round your answer for the standard deviation to two decimal places.)
expected return
standard deviation

Construct a portfolio that is 50% invested in a core bonds fund and 50% invested in REITs. In percentage terms, what are the expected return and standard deviation for such a portfolio? (Round your answer for the standard deviation to two decimal places.)
expected return
standard deviation

Construct a portfolio that is 80% invested in a core bonds fund and 20% invested in REITs. In percentage terms, what are the expected return and standard deviation for such a portfolio? (Round your answer for the standard deviation to two decimal places.)
expected return
standard deviation

Answer 1

Answer:

.033348581

-.000197408

9.055%

.19887955

9.425%

.115913507

7.238%

.048729731

Step-by-step explanation:

a.)  Correlation= Covariance/(stdx*stdy)

which means that covaraince= correlation*stdx*stdy

Covariance of S&P and REIT= .74*.1945*.2317= .033348581

Covaraince of core bonds and REIT=  -.04*.2317*.0213=  -.000197408

b.) The expected return of a portfoilio is just the weighted average

so the expected return would be

.5*.0504+.5*.1307= .09055 or 9.055%

The variance of ax+by= a²var(x)+b²var(y)+2*a*b*cov(x,y)

So the varaince of .5x+.5y= .5²var(x)+.5²var(y)+2*.5*.5*cov(x,y)

(note: the standard deviation squared is equal to the variance)

so for this question we would have something like

.5²*.1945²+.5²*.2317²+2*.5*.5*.033348581= .039553076 which means the standard deviation is .19887955

(the .033348581 is the covariance that we calculated earlier)

c.)

Same deal as B, just with different numbers

The Expected return is :

.5*.0578+.5*.1307= .09425 or 9.425%

The volatility (or standard deviation) is

.5²*.0213²+.5²*.2317²+2*.5*.5*-.000197408 = .013435941 which means the standard deviation is .115913507

d.)

same deal as the questions before but the weights are different

expected return:

.8*.0578+.2*.1307 = .07238 or 7.238%

Volatility:

.8²*.0213²+.2²*.2317²+2*.8*.2*-.000197408= .002374587 which means the standard deviation is .048729731