Assignment 3: Decision Analysis, Value of Information, Monte Carlo Simulation

1
Subject code:
Subject name:
Student’s name:
Student number:
Assessment item number:

2
Assignment 3
QUESTION 1 Decision Analysis
(a) Discuss how a utility function can be assessed. What is a standard gamble and how is it
used in determining utility values?
Utility functions are assessed by:
a. Identifying the worst and best attribute levels
b. Assigning utility of zero to worst outcome and 1 to best outcome
c. Naming the desirable outcome at 50:50
The Standard Gamble (SG) measures the preference of an individual under uncertainty. It is used
to express the outcome of different choices in utility values. Standard gamble determines the
mean probability when a respondent is indifferent between accepting a gamble and continuing
with the current situation.
(b) Alan Barnes invests primarily in the share market. Recently he has become concerned
about the share market as a good investment. During the next year he must decide whether
to invest $10,000 in the share market or in a government bond at an interest rate of 9%.
Alan expects the share market to be good, fair or bad, giving a return of 14%, 8% or 0%
respectively on his money.

3
1. Develop a decision matrix showing the two possible strategies, the three states of the
share market and the monetary gains or losses under the six possible action-state scenarios.
Table 1: Data
Profit Shares Bonds
Probability 50% 50%
Good 14% 9%
Fair 8% 9%
Poor 0% 9%
Table 2: Results
EMV Minimum Maximum
0.115 0.09 0.14
0.085 0.08 0.09
0.045 0 0.09
Maximum 0.115 0.09 0.14
Table 3: Criterion of regret
Regret
Shares Bonds Expected Maximum
Probability 0.5 0.5

4
Good 0% 0 0 0
Fair 0.06 0 0.03 0.06
Poor 0.14 0 0.07 0.14
Minimum 0 0
2. Which alternative would an optimist choose? The share market
3. Which alternative would a pessimist choose? The bonds market
4. Which alternative is indicated by the criterion of regret? There is no alternative
indicated under the criterion of regret.
5. Assuming probability of a good market = 0.4, a fair market = 0.4 and a bad market = 0.2,
using expected monetary values what is the optimum action?
Data Results
Profit Shares Bonds EMV Minimum Maximum
Probability 50% 50%
Good 40% 9% 0.245 0.09 0.4
Fair 40% 9% 0.245 0.09 0.4
Poor 20% 9% 0.145 0.09 0.2
Maximum 0.245 0.09 0.4
The optimum action would be to invest wholly in the share market.
6. What is the expected value of perfect information?