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Lecture 3 Uncertainty and Risk Robert A. Miller 45-978 November 2009 Robert A. Miller (45-978) Uncertainty and Risk November 2009 1 / 34
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Discounting for risk Consumer preferences One feature of trading that investors care about, that our analysis of auctions lacks, is the dispersion of payo/s about the mean return from bidding. If traders only cared about the mean return of an asset, it is hard to justify why assets would have di/erent mean returns. There is abundant evidence that assets have di/erent mean returns, suggesting that traders care about other moments of the probability distribution apart from the °rst. For example AAA bonds have lower mean returns than those on mining and oil stocks, but the latter experience much higher volatility. The di/erential in mean returns is inconsistent with EMH, and suggests that investors require a risk premium to buy stocks whose returns exhibit greater variance. Robert A. Miller (45-978) Uncertainty and Risk November 2009 2 / 34
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Discounting for time Consumer preferences Another feature our analysis of auctions lacks is the underlying trade o/ between current and future consumption. The primary reason for stock issues is to °nance the °rm±s operations. The stock±s dividend stream, from the date of issue to liquidation, ultimately determines its value, because that is all the successive owners receive in net. This compact between investor (or shareholder) and asset manager (or executive o¢ cer) embodies the trade o/ between present and future. Of course there are other reasons for issuing °nancial securities, such as swindling investors through Ponzi schemes for example. And many °nancial derivatives do not pay dividends. However these derivatives would have no value if the underlying stocks never paid dividends, and even Ponzi schemes exist only because some buyers believe they will be paid dividends. Robert A. Miller (45-978) Uncertainty and Risk November 2009 3 / 34
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Characterizing utility functions Consumer preferences We begin our study of consumer preferences begins with an inquiry into the attitudes people hold towards risk and their willingness to postpone consumption. Under relatively mild behavioral assumptions, each person reveals a utility function dictating their choices, which we denote by u ( c ) as a function of consumption c : 1 Every pair of outcomes ( c 1 , c 2 ) is (weakly) ranked. 2 No contradictions are encountered in ranking triplets ( c 1 , c 2 , c 3 ) . 3 Utility is weighted by the probability of occurrence. All three axioms have been challenged, especially the third, but almost all economics and °nance takes them as a unquestioned premise. Robert A. Miller (45-978) Uncertainty and Risk November 2009 4 / 34
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Inquiries into risk tolerance Consumer preferences Let ( c 1 , . . . , c J ) denote the consumption prizes associated for a lottery over J outcomes that occur with probabilities ( p 1 , . . . , p J ) .
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