IPM - utility theory
Investment Decisions Under Uncertainty
7.1 Investor preferences and expected utility
-If there is no uncertainty then we just need to determine how much we want to consume now and how much later i.e. assets are risk free with return certain across all states of the world
-A risky asset is one whose cash flows are not certain across all possible states of the world. In finance it is commonly assumed that investors are risk averse, rational and have unlimited demand for wealth (nonsatiated)
-This means investors dislike variance, rank investments in a consistent matter and always prefer more to less of a good in any comparison
-Utility is a measure of preferences or investor wellbeing and investors aim to maximise this and provides a means to rank alternatives
-The best ranking function is expected utility and it is underpinned by five assumptions:
1. Comparability: Investors can state a preference among all alternative certain outcomes
2. Transitivity: If A>B and B>C then A>C i.e. are consistent in ranking of outcomes
3. Independence: Ranking will hold no matter what other assets are held
I.e. If indifferent between X and Y then will be indifferent between X with probability P, Z with probability 1-P and Y with probability P, Z with probability 1-P
4. Measurable: You need to assign a value to the ranking
5. Certainty Equivalent: This means that everything has a price i.e. the price at which the investor is indifferent between the gamble and CE
-These assumptions are restrictive as the choice between alternatives is not independent of shares held
(e.g. if aim to diversify), ranking may not be consistent and some individuals do not always want more
-Expected utility is found by the sum of: Utility from the outcome x Probability of that value (weighting function) and investors aim to maximise this i.e. E(U)=ΣW U(W)P(W)
*NOTE: This differs from the utility of the expected value i.e. U(E[W]) as the expected utility takes into account the
7.1 Investor preferences and expected utility
-If there is no uncertainty then we just need to determine how much we want to consume now and how much later i.e. assets are risk free with return certain across all states of the world
-A risky asset is one whose cash flows are not certain across all possible states of the world. In finance it is commonly assumed that investors are risk averse, rational and have unlimited demand for wealth (nonsatiated)
-This means investors dislike variance, rank investments in a consistent matter and always prefer more to less of a good in any comparison
-Utility is a measure of preferences or investor wellbeing and investors aim to maximise this and provides a means to rank alternatives
-The best ranking function is expected utility and it is underpinned by five assumptions:
1. Comparability: Investors can state a preference among all alternative certain outcomes
2. Transitivity: If A>B and B>C then A>C i.e. are consistent in ranking of outcomes
3. Independence: Ranking will hold no matter what other assets are held
I.e. If indifferent between X and Y then will be indifferent between X with probability P, Z with probability 1-P and Y with probability P, Z with probability 1-P
4. Measurable: You need to assign a value to the ranking
5. Certainty Equivalent: This means that everything has a price i.e. the price at which the investor is indifferent between the gamble and CE
-These assumptions are restrictive as the choice between alternatives is not independent of shares held
(e.g. if aim to diversify), ranking may not be consistent and some individuals do not always want more
-Expected utility is found by the sum of: Utility from the outcome x Probability of that value (weighting function) and investors aim to maximise this i.e. E(U)=ΣW U(W)P(W)
*NOTE: This differs from the utility of the expected value i.e. U(E[W]) as the expected utility takes into account the