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# Handout+I - Handout I Risk Throughout this class the risk...

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Handout I Risk Throughout this class, the risk of any asset will be de…ned as its variance. Thus, an asset with variance ¾ 2 1 is riskier than an asset with variance ¾ 2 2 if and only if ¾ 2 1 > ¾ 2 2 . Where ¾ 2 i is the variance of the i-th asset. An investor is risk-averse if he or she has preferences over consumption represented by a concave utility function. That is, if an investor’s utility function u ( c ) exhibits diminishing marginal utility ( u 0 ( c ) > 0 and u 00 ( c ) < 0) as c increases we say this investor is risk-averse. As the name implies, a risk-averse investor views risk as a “bad” and is willing to pay to avoid it. For Example, suppose I were to o¤er the following game to a risk-averse investor. We will ‡ip a fair coin. If the coin comes up heads, I will pay x = ® dollars. If the coin comes up tails, I will pay x = ¯ dollars. ® > ¯: The expected payout of this game is E [ x ] = : 5 E [ x j h ]+ : 5 E [ x j t ] = : 5 ® + : 5 ¯ . If the investor

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Handout+I - Handout I Risk Throughout this class the risk...

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