Lecture_5_2010

Lecture_5_2010 - E4729 Financial Institutions, Markets, and...

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E4729 Financial Institutions, Markets, and Risk Lecture 5 Utility and Portfolio Theories & CAPM July 21, 2010 Leo M. Tilman L.M.Tilman & Co. & Columbia University
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Utility Theory
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3 E4729 Financial Institutions, Markets, and Risk Utility Theory Utility = relative enjoyment or satisfaction from an economic activity Investors maximize their utility associated with terminal wealth Unique utility of wealth function for each investor Marginal utility is the value of incremental $1 of wealth Common assumption: diminishing marginal utility of wealth function Nonsatiation investors always prefer higher levels of terminal wealth to lower levels of terminal wealth (all other factors being equal)
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4 E4729 Financial Institutions, Markets, and Risk Utility Theory Terminal wealth of two hypothetical portfolios Nonsatiation: if risks (standard deviations) were the same, investors would choose the portfolio with highest expected return But because of different risks and different expected returns, difficult to compare & choose. Therefore, an additional consideration (= risk preference) Cumulative probability density function of normal distributions
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5 E4729 Financial Institutions, Markets, and Risk Utility Theory Nonsatiation: curves are always upward sloping + diminishing marginal utility Risk aversion: investors dislike fair gambles (gambles with zero expected payoffs Heads: get $5, Tails: lose $5 Expected return 0 Would want to increase payout of heads or decrease losses in tails U(certain $105) > U(uncertain outcome with expectation of $105) Where outcomes are 100 and 110 w equal probabilities
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6 E4729 Financial Institutions, Markets, and Risk Utility Theory Certainty equivalent: return on certain investment whose utility is the same as that of an uncertain investment Certain $103 vs. expected $105 of a risky investment Risk premium: additional wealth $2 (or return 2%) required for a risky investment vs. the certainty equivalent More risk averse investors will have lower certainty equivalents and higher risk premia (prices or spreads )
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7 E4729 Financial Institutions, Markets, and Risk Utility Theory Indifference curves: sets of risk and return combinations that provide the same utility. S is level of utility associated with a particular curve Infinite number of curves that cannot intersect (possible final exam question) Farther northwest is more desirable 2 a S r
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8 E4729 Financial Institutions, Markets, and Risk Utility Theory
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9 E4729 Financial Institutions, Markets, and Risk Utility Theory
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Expected Returns and Standard Deviations
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11 E4729 Financial Institutions, Markets, and Risk Expected Returns Cash Flows Risks and Returns Overall Utility Terminal wealth (MV at horizon) and EROR are random variables Expected Rate of Return (EROR) MV (horizon) + FV of All Cash Flows Until Horizon – MV (today) EROR = ---------------------------------------------------------------------------------------------------------- MV (today) * MV denotes Market Value; FV denotes Future Value at Horizon; CF denotes cash flows
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12 E4729 Financial Institutions, Markets, and Risk Expected Returns EROR (no cash flows b/w now and horizon)
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Lecture_5_2010 - E4729 Financial Institutions, Markets, and...

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