Elton, Gruber, Brown, and Goetzmann
Modern Portfolio Theory and Investment Analysis, 7th Edition
Solutions to Text Problems: Chapter 1
Chapter 1: Problem 1
A. Opportunity Set
With one dollar, you can buy 500 red hots and no rock candies (point
A), or 100 rock candies and no red hots (point B), or any combination of red
hots and rock candies (any point along the opportunity set line AB).
Algebraically, if X = quantity of red hots and Y = quantity of rock
candies, then:
0.2X 1Y 100
,That is, the money spent on candies, where red hots sell for 0.2 cents a piece
and rock candy sells for 1 cent a piece, cannot exceed 100 cents ($1.00).
Solving the above equation for X gives:
X 500 5Y
which is the equation of a straight line, with an intercept of 500 and a slope
of 5.
,B. Indifference Map
Below is one indifference map. The indifference curves up and to the
right indicate greater happiness, since these curves indicate more
consumption from both candies. Each curve is negatively sloped, indicating a
preference of more to less, and each curve is convex, indicating that the rate
of exchange of red hots for rock candies decreases as more and more rock
candies are consumed. Note that the exact slopes of the indifference curves
in the indifference map will depend an the individual’s utility function and
may differ among students.
Chapter 1: Problem 2
A. Opportunity Set
The individual can consume everything at time 2 and nothing at time
1, which, assuming a riskless lending rate of 10%, gives the maximum time-2
consumption amount:
, $20 + $20 (1 + 0.1) = $42.
Instead, the individual can consume everything at time 1 and nothing
at time 2, which, assuming a riskless borrowing rate of 10%, gives the
maximum time-1 consumption amount:
$20 + $20 (1 + 0.1) = $38.18
Modern Portfolio Theory and Investment Analysis, 7th Edition
Solutions to Text Problems: Chapter 1
Chapter 1: Problem 1
A. Opportunity Set
With one dollar, you can buy 500 red hots and no rock candies (point
A), or 100 rock candies and no red hots (point B), or any combination of red
hots and rock candies (any point along the opportunity set line AB).
Algebraically, if X = quantity of red hots and Y = quantity of rock
candies, then:
0.2X 1Y 100
,That is, the money spent on candies, where red hots sell for 0.2 cents a piece
and rock candy sells for 1 cent a piece, cannot exceed 100 cents ($1.00).
Solving the above equation for X gives:
X 500 5Y
which is the equation of a straight line, with an intercept of 500 and a slope
of 5.
,B. Indifference Map
Below is one indifference map. The indifference curves up and to the
right indicate greater happiness, since these curves indicate more
consumption from both candies. Each curve is negatively sloped, indicating a
preference of more to less, and each curve is convex, indicating that the rate
of exchange of red hots for rock candies decreases as more and more rock
candies are consumed. Note that the exact slopes of the indifference curves
in the indifference map will depend an the individual’s utility function and
may differ among students.
Chapter 1: Problem 2
A. Opportunity Set
The individual can consume everything at time 2 and nothing at time
1, which, assuming a riskless lending rate of 10%, gives the maximum time-2
consumption amount:
, $20 + $20 (1 + 0.1) = $42.
Instead, the individual can consume everything at time 1 and nothing
at time 2, which, assuming a riskless borrowing rate of 10%, gives the
maximum time-1 consumption amount:
$20 + $20 (1 + 0.1) = $38.18
