CHAPTER 2-4

Exercise 2.24 In this exercise, we examine the effect of combining investmentswith positively correlated risks, negatively correlated risks, anduncorrelated risks. A firm is considering a portfolio of assets.The portfolio is comprised of two assets, which we will call ''A\"and \"B.\" Let X denote the annual rate of return from assetA in the following year, and let Y denote the annual rateof return from asset B in the following year. Suppose that E(X) = 0.15 and E(Y) =0.20, SD(X) = 0.05 and SD(Y) =0.06, and CORR(X, Y) = 0.30.

	(a) What is the expected return of investing 50% of theportfolio in asset A and 50% of the portfolio in asset B? What isthe standard deviation of this return?

	(b) Replace CORR(X, Y) = 0.30 byCORR(X, Y) = 0.60 and answer the questions inpart (a). Do the same for CORR(X, Y) = 0.60,0.30, and 0.0.

	(c) (Spreadsheet Exercise). Use a spreadsheet to perform thefollowing analysis. Suppose that the fraction of the portfolio thatis invested in asset B is f, and so the fraction of theportfolio that is invested in asset A is (1 f). Lettingf vary from f = 0.0 to f = 1.0 inincrements of 5% (that is, f = 0.0, 0.05, 0.10, 0.15, . .. ), compute the mean and the standard deviation of the annual rateof return of the portfolio (using the original data for theproblem). Notice that the expected return of the portfolio varies(linearly) from 0.15 to 0.20, and the standard deviation of thereturn varies (non-linearly) from 0.05 to 0.06. Construct a chartplotting the standard deviation as a function of the expectedreturn.

	(d) (Spreadsheet Exercise). Perform the same analysis as in part(c) with CORR (X, Y) = 0.30 replaced byCORR(X, Y) = 0.60, 0.0, 0.30, and 0.60.

Exercise 2.38

Ninety percent of residential gas customers in Illinois use gasfor residential heating. Sixteen residential gas customers arerandomly selected to participate in a panel discussion for a stateenergy fair. A gas industry executive is hopeful that at leasttwelve of the panel members, i.e., 75%, will come from homes inwhich gas is used for residential heating. If you were theexecutive's assistant, what degree of assurance could you give theexecutive that her 75% goal might be reached or exceeded?