In: Statistics and Probability
CHAPTER 2-4
Exercise 2.24
In this exercise, we examine the effect of combining investments
with positively...
CHAPTER 2-4
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In this exercise, we examine the effect of combining investments
with positively correlated risks, negatively correlated risks, and
uncorrelated 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 asset
A in the following year, and let Y denote the annual rate
of return from asset B in the following year. Suppose that
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E(X) = 0.15 and E(Y) =
0.20,
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SD(X) = 0.05 and SD(Y) =
0.06,
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(a) What is the expected return of investing 50% of the
portfolio in asset A and 50% of the portfolio in asset B? What is
the standard deviation of this return?
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(b) Replace CORR(X, Y) = 0.30 by
CORR(X, Y) = 0.60 and answer the questions in
part (a). Do the same for CORR(X, Y) = 0.60,
0.30, and 0.0.
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(c) (Spreadsheet Exercise). Use a spreadsheet to perform the
following analysis. Suppose that the fraction of the portfolio that
is invested in asset B is f, and so the fraction of the
portfolio that is invested in asset A is (1 f). Letting
f vary from f = 0.0 to f = 1.0 in
increments of 5% (that is, f = 0.0, 0.05, 0.10, 0.15, . .
. ), compute the mean and the standard deviation of the annual rate
of return of the portfolio (using the original data for the
problem). Notice that the expected return of the portfolio varies
(linearly) from 0.15 to 0.20, and the standard deviation of the
return varies (non-linearly) from 0.05 to 0.06. Construct a chart
plotting the standard deviation as a function of the expected
return.
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(d) (Spreadsheet Exercise). Perform the same analysis as in part
(c) with CORR (X, Y) = 0.30 replaced by
CORR(X, Y) = 0.60, 0.0, 0.30, and 0.60.
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Exercise 2.38
Ninety percent of residential gas customers in Illinois use gas
for residential heating. Sixteen residential gas customers are
randomly selected to participate in a panel discussion for a state
energy fair. A gas industry executive is hopeful that at least
twelve of the panel members, i.e., 75%, will come from homes in
which gas is used for residential heating. If you were the
executive's assistant, what degree of assurance could you give the
executive that her 75% goal might be reached or exceeded?
orchestra answered 1 year ago