Decision Tree Analysis and Decision Making in Finance Problems

This assignment presents solutions to four problems involving decision tree analysis in a financial context. The solutions cover constructing and interpreting decision trees, identifying decision and event nodes, calculating expected values, and making optimal decisions based on the given data. The assignment utilizes the Analytics Solver Platform (ASPE) to construct and solve decision trees, demonstrating the application of these techniques. The solutions also explore risk-neutrality and its impact on decision-making, analyzing the expected value of assets and the expected utility to determine the best course of action. Finally, the assignment emphasizes the importance of decision trees in aiding informed financial decisions by evaluating different alternatives and their associated probabilities.

QUESTION 1
The circle node represents the event node while the square node represents the decision node.
The key difference between these two types of nodes is that the decision node extends to the
event node while the event node has the two possibilities. The analysis of the decision tree above
is done using the Analytics solver platform integrated in Microsoft Excel. Below is the procedure
applied:
I. First, go to the “Analytics Solver” and open decision tree and select the “Decision Tree”
options from there. It is represented as follows:

II. Select the “Add node” option and start building the decision tree. The following dialog
box would appear after clicking on the “Add Node” option:
If the node is represented as square, then it would be “Decision” node type and otherwise
it would be of “Event/Chance” type.
III. Fill the value of the “Decision 2” as 750. Hit enter and the decision tree with one node is
obtained as following:

IV. Add another node by selecting the upper triangle with the value zero. Fill the dialog box
as “Event” Type with the chances as 20%, 80%. The following decision tree would be
obtained:
V. Continuing in a similar fashion, the decision tree below is obtained.

Therefore, the estimated payoff is 820
QUESTION 2
Alternatives are represented by rectangles while random events are represented by circles. The
alternative with higher expected gain is chosen.
Starting from the last decision,
E ( C )= ( 0.4 × 2500 ) +0.6 (−700 )=100−420=580
E ( D ) =900i . e . constant
Choose D and thus,
E ( A ) = ( 0.2× 900 ) + ( 0.8 × 800 )=820
E ( B )=750
Thus choose A

Solution:
At the beginning (node 1), choose A. If the event with probability 0.2 occurs (node 2), choose D.
The decision tree is not always explicitly given and thus a decision tree must be made from the
table provided. Alternatives are called “Actions” and random events are called “state of nature”.
For a given problem, it should be kept in mind that the tastes of nature have probabilities. This
makes it easier to identify actions and state of nature and form a decision tree.
E ( A ) = ( 0.2× 900 ) + ( 0.8 × 800 )=820

QUESTION 3
Consider the excel model below which represents the states of nature, prior probabilities,

The decision tree is therefore as shown below,

QUESTION 4
a) Expected value of assets after 1 year in case of buying earthquake insurance is
¿ Current value of assets−Cost of insurance¿ 250000−180 ¿ 249820
Expected value of assets after 1 year in case of not buying earthquake insurance is
¿ Current value of assets− ( Probability of earthquake× Value of damage¿earthquake )
¿ 250000− ( 0.001× 160000 )¿ 249840Expected value of assets after 1 year is higher in case
of NOT buying insurance. Therefore, for a risk-neutral decision maker, the best
alternative is NOT to buy the insurance.
b) Expected utility of assets after 1 year in case of buying earthquake insurance is
¿ Current value of assets−Cost of insurance¿ √ 250000−180 ¿ 320
Expected utility of assets after 1 year in case of not buying earthquake insurance is
¿ Current value of assets− ( Probability of earthquake× Value of damage¿earthquake )
¿ √ 250000− ( 0.001× √ 16 0000 ) ¿ 499.6Expected value of utility after 1 year is higher in
case of NOT buying insurance. Therefore, for a risk-neutral decision maker, the best
alternative is NOT to buy the insurance.