Decision tree analysis is a quantitative method that

Decision tree analysis is a quantitative method that shows
likely outcomes and consequences of a decision
§ Often used in business to decide between courses of
action between competing projects where there is
uncertainty in outcomes
§ The optimal decision rule is to choose the course of action
that has the highest expected value or payoff – but beware
that this only holds true if the decision maker is risk neutral!
Otherwise, we must adjust the decision for risk preference.

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Ro demonstrate individual risk preferences ….
Consider a gamble:
§ Heads you win $100
§ Tails you get $0
Let’s Vote by Show of Hands..
§ How much would you pay to enter the gamble? Hint:-
what certain amount do you think is equivalent to the
gamble?
a) $100?
b) $75-100, $50-75
c) $50?
d) $40-50, $30-40, $20-30, $10-20, $0-10?
e) zero?
• What is the most
common response?
• Is it below $50?
• What does this imply?

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Putting it onto a decision tree
Head. Win $100
Tail. Win nothing
P(Head)=50%
P(Tail)=50%
Don’t gamble. Win and lose nothing.
Choice 1 Enter the gamble:
E(v) = 50% x $100 + 50% x 0 = $50
Choice 2 Do nothing:
E(v) = 0
Choice 1
Choice 2
Choice
1 or 2?
What would we pay to entice us into Choice 1?

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Utility and risk aversion
§ If we plot utility against wealth then a
concave shape (upper right)
represents “risk-aversion”. ie. We
attach less change in utility to a
change in profit as we get wealthier.
– A constant line would be “risk-neutral”.
This implies indifference to equal sized
gains and losses.
– A convex shape would indicate “risk-
seeking”.
§ Note the line is steeper for losses
(lower left)
§