b.
Problems:
Spreadsheet problems
1. The expected value of investment A is ($4,000)(0.2) + ($5,000)(0.3) + ($6,000)(0.3) +
($7,000)(0.2) = $800 + $1,500 + $1,800 + $1,400 = $5,500.
The expected value of investment B is ($4,000)(0.3) + ($6,000)(0.4) + ($8,000)(0.3) =
$1,200 + $2,400 + $2,400 = $6,000.
(
a
) The standard deviation of investment A is $1,024.70. The standard deviation of
investment B is $1,549.19.
(
b
) Investment A is less risky than investment B because its standard deviation is smaller,
but it also provides a lower expected income.
(
c
) It is not clear, therefore, from the information given which investment is best. It
depends on whether the lower expected income from investment A is more than balanced
by its lower risk. This depends on the attitude of the individual toward risk.
2.
(
a
) From the spreadsheet, the expected value of project A of 2.8 is higher than 2.7 for
project B, so it is preferred.
(
b
) Project B has a higher expected utility of 2.315, however, so it is preferred under this
criterion.
(
c
) The individual is risk averse because the utility function of profit increases at a
decreasing rate or faces down so that the marginal utility of profit diminishes
Froeb and McCann’s chapter 17:
a.
Individual problems:
17-3
Boat Insurance = $2,150
Payment
Probability
$25,000
1 – (0.6+0.25+.12) = 0.03
$5,000
0.12
$0
0.25
$0
0.6
Expected payment = 0.03*25,000 + 0.12*5,000 + 0.25*0 + 0.6*0 = $1,350
Expected payment + $200 profit = $1,550