Q1. A UL student wants to invest $1 million for 1 year. After analyzing and elim
ID: 376489 • Letter: Q
Question
Q1. A UL student wants to invest $1 million for 1 year. After analyzing and eliminating numerous possibilities, he has narrowed his choice to one of three alternatives:
D1: Invest in a guaranteed income certificate paying 10% (GIC);
D2: Invest in a bond with a coupon value of 8%;
D3: Invest in a well-diversified portfolio of stocks.
He believes that the payoffs associated with the last two alternatives depend on a number of factors, foremost among which is interest rates. He concludes that there are three possible states of nature:
S1: Interest rates increase;
S2: Interest rates stay the same;
S3: Interest rates decrease.
After further forecasting analysis, he determines the amount of profit he will make for each possible combination of a decision and a state of nature. The profits from each alternative investment are summarized in the following payoff table:
PAYOFF TABLE ($)
S1
S2
S3
D1
1,100,000
1,100,000
1,100,000
D2
950,000
1,080,000
1,180,000
D3
1,150,000
1,090,000
1,040,000
Still based on forecasting techniques, he also determines the probabilities of the states of nature:
P (S1) = .2 P (S2) = .5 P (S3) = .3
a) Determine the optimal investment strategy.
b) Determine the expected value of perfect information.
However, after taking econ course, our student wants to improve his decision-making capabilities. He learns about Campus Consultants (CC), who, for a fee of $ 5,000, will analyze the economic conditions and forecast the behaviour of interest rates over the next 12 months. CC has been forecasting interest rates for many years and so provides him with various conditional probabilities:
I1: CCC predicts that interest rates will increase;
I2: CCC predicts that interest rates will stay the same;
I3: CCC predicts that interest rates will decrease.
We assume that the following assessments are available for these conditional probabilities:
CCC MARKET RESEARCH
S1
S2
S3
I1
P(I1|S1) = .6
P(I1|S2) = .1
P(I1|S3) = .1
I2
P(I2|S1) = .3
P(I2|S2) = .8
P(I2|S3) = .2
I3
P(I3|S1) = .1
P(I3|S2) = .1
P(I3|S3) = .7
c) Construct a decision tree for the complete investment decision problem.
d) Determine the expected value of sample information.
e) Determine the optimal investment strategy.
S1
S2
S3
D1
1,100,000
1,100,000
1,100,000
D2
950,000
1,080,000
1,180,000
D3
1,150,000
1,090,000
1,040,000
Explanation / Answer
a) optimal strategy will be the one which has the maximum expected returns:
expected returns D1 = 1100000.... since all have the same payoff
expected returns D2 = S1*P1 + S2*P2 + S3*P3
= 950000*0.2 + 1080000*.5 + 1180000*0.3
= 190000 + 540000 + 354000
= 1084000
expected returns D3 = S1*P1 + S2*P2 + S3*P3
= 1150000*0.2 + 1090000*.5 + 1040000*0.3
= 230000 + 545000 + 312000
= 1087000
Since expected value of D1 is the highest at 1100000, hence optimal strategy is to choose decision 1, guaranteed income certificate of 10%.
b) Expected value of perfect information will be the highest gain in all scenarios multiplied by probability
In S1, D3 has highest payoff at 1150000
In S2, D1 has highest payoff at 1100000
In S3, D2 has highest payoff at 1180000
Hence, expected value = 1150000*.2 + 1100000*.5 + 1180000*.3
= 230000 + 550000 + 354000
= 1134000
Expected value of perfect information = 1134000
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.