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.
36 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 mostcommon response?•Is it below $50?•What does this imply?
37 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?
40 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) §
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