Compute the expected value and the variance for x and y. Develop a probability distribution for x + y. Using the result of part (b), compute E(x + y) and Var (x + y). Compute the covariance and correlation for x and y. Are x and y positively related, negatively related, or unrelated?

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Exercises
Methods
25. Given below is a bivariate distribution for the random variables x and y.
SELF test
Ax, y)
2
50
80
.5
3
30
50
60
40
a. Compute the expected value and the variance for x and y.
b. Develop a probability distribution for x + y.
c. Using the result of part (b), compute E(x + y) and Var (x + y).
d. Compute the covariance and correlation for x and y. Are x and y positively related,
negatively related, or unrelated?
e. Is the variance of the sum of x and y bigger, smaller, or the same as the sum of the in-
dividual variances? Why?
Transcribed Image Text:Exercises Methods 25. Given below is a bivariate distribution for the random variables x and y. SELF test Ax, y) 2 50 80 .5 3 30 50 60 40 a. Compute the expected value and the variance for x and y. b. Develop a probability distribution for x + y. c. Using the result of part (b), compute E(x + y) and Var (x + y). d. Compute the covariance and correlation for x and y. Are x and y positively related, negatively related, or unrelated? e. Is the variance of the sum of x and y bigger, smaller, or the same as the sum of the in- dividual variances? Why?
30. In addition to the information in exercise 29 on the S&P500 and core bonds, J.P. Morgan
Asset Management reported that the expected return for real estate investment trusts
(REITS) was 13.07% with a standard deviation of 23.17% (J.P. Morgan Asset Manage-
ment, Guide to the Markets, 1st Quarter, 2012). The correlation between the S&P 500 and
REITS is .74 and the correlation between core bonds and REITS is – .04. You are consid-
ering 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.
a. Using the information provided here and in exercise 29, determine the covariance
between the S&P 500 and REITS and between core bonds and REITS.
b. 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?
c. 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?
d. 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?
e. Which of the portfolios in parts (b), (c), and (d) would you recommend to an
aggressive investor? Which would you recommend to a conservative investor?
Why?
Transcribed Image Text:30. In addition to the information in exercise 29 on the S&P500 and core bonds, J.P. Morgan Asset Management reported that the expected return for real estate investment trusts (REITS) was 13.07% with a standard deviation of 23.17% (J.P. Morgan Asset Manage- ment, Guide to the Markets, 1st Quarter, 2012). The correlation between the S&P 500 and REITS is .74 and the correlation between core bonds and REITS is – .04. You are consid- ering 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. a. Using the information provided here and in exercise 29, determine the covariance between the S&P 500 and REITS and between core bonds and REITS. b. 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? c. 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? d. 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? e. Which of the portfolios in parts (b), (c), and (d) would you recommend to an aggressive investor? Which would you recommend to a conservative investor? Why?
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