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Week 5 Notes

by: D S

Week 5 Notes FIN 501

Financial Economics
Tatyana Deryugina

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Financial Economics
Tatyana Deryugina
Class Notes
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This 3 page Class Notes was uploaded by D S on Thursday October 1, 2015. The Class Notes belongs to FIN 501 at University of Illinois at Urbana-Champaign taught by Tatyana Deryugina in Summer 2015. Since its upload, it has received 30 views. For similar materials see Financial Economics in Finance at University of Illinois at Urbana-Champaign.

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Date Created: 10/01/15
Financial Economics Week 5 Professor Tatyana Derugvina University of Illinois Urbana Champaign Text 1 Choice Under Uncertainty Lotteries L 1117 X H2 Know expected value EX 725132 Just know that states have to be mutually exclusive and exhaustive Uncertainty Game Flip coin until head comes up Expected value of the Lottery inf What is the most you would pay to play this game Should be willing to put in your full wealth but yet you don t St Petersburg Paradox Indicates that we care more about risk instead of expected value thus use a value called EU expected utility that denotes a person s utility function for money as uw ua gtIlt m7 y gtIlt now based upon state 513 Definition Risk Averse always prefer the certain outcome as opposed to an uncertain lottery with the same expected value Risk Neutral indifferent between a certain outcome and any lottery with the same expected value A risk neutral decision maker tries to maximize expected value Risk Loving take the risky situation Risk characteristics and types of curve risk averse strictly concave uw risk neutral linear uw risk loving convex uw Note that the concavity can change across different regions in that it s not one or another Example was done with strictly increasing and concave uw lnw What amount of money for sure makes person indifferent between otter money certainty equivalent of the lottery Cce 2 EU De nition Risk Premium difference between the CE and EV what individual would pay to have EV instead of lottery Arrow Pratt measures absolute risk average 734w Zlg works for linear and non linear note this only works when you are comparing the same cfass of utility functions De nitions of different risk aversions Constant Absolute Risk Aversion CARA utility not depend on current wealth Decreasing Absolute Risk Average DARA risk aversion decreases as current wealth increases Portfolio Choice rf risk free asset7 always pay te same excluding the market basically covered the entire rst month of portfolio maximization from Adam s class sample problem in the notes follow the proof if interested 2 Choice Under Uncertainty continued Investing in risky assets reason somon wants to invest at least a little bit in risky assets whenever the return is positive is that hte risk premium of the rst little bit of risk is small compared to the mean return examples shown the cost of risk was like 1 of amount invested Discussion on Readings Target Date Retirement Why target date funds reduce investors exposure They reduce exposure because the number of expected working years shortens and thus people are unable to make up the money from the loss Why is it not optimal to have 0 exposure When you have a little money t risk there is a larger amount of payout Putting in a small percent still gives you some return Note that within different funds there was large uctuations in the target optimal allocation If you were risk neutral put all in the market Gold Hedging Hedging gold prices fallen out of favor Gold prices have kept increasing and hedgers make money on decreases Should companies act risk averse It depends Pro risk neutral compnies don t exist If investors can diversity their portfolios they should Maximizing pro t 2 risk neutral De nitions risk asset distribution of payoffs across states of the world or a bundle of commodities that each pay 1 in a particular state of the world Arrow Debreu asset and option pricing models Contingent Commodities good that is worth a positive amount if a particular state of the world occurs and is worth zero otherwise General idea if we can price contingent commodities we can price anything Utility with contingent commodities two states good and bad expected utility 39U39wg wb 7ru39wg 1 7ru39wb goal is to maximize 39U39wg wb given initial wealth w Similar to all the other problems for maximization pgwpbwb w individual s budget constraint actuarially fair price 2 underlying probabilities way important for insurance example given in slides and shows that pg 2 7r whenever you have a fair price then you re always on the w same level of consumption bc of MU of wealth Why is utility function considered state dependent MU of wealth is different if you have a broken leg Normally you would want more money to help with chores from the broken leg Also you may spend less in that one would not be doing helicotor skiing on a broken leg What happens with unfair pricing not full insured against a bad event Follow the example given for insurance in notes economists love derivatives because one can choose a pattern of consumption Options Bit demonstrates value of options to smooth out payouts or cause more difference Trick only use if different pay offs in differnt states


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