B.1 Risk and Reward-2-1.pptx

B.1 Risk and Reward-2-1.pptx - Venti Risk and reward 1...

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Venti Risk and reward 1 Introduction to Risk and Reward What is risk? Utility analysis of risky choices certainty equivalent risk premium degree of risk aversion (A) Sharpe Ratio Measuring the historical mean and variance of returns Historical record More on risk and risk premiums
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Venti Risk and reward 2 What is Risk? Certainty : Expectations are single valued Uncertainty : Many possible outcomes, each with some probability Given a choice between $C for sure, or a risky gamble with expected payoff $C, a risk averse individual will prefer the sure payoff. Individuals are generally risk averse in situations in which a large fraction of their wealth is at risk: insurance investing
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Venti Risk and reward 3 Risk, Return, and Uncertainty What does this imply about the relationship between wealth and utility? Attitudes toward risk: Risk averse U’(W)>0, U’’(W)<0 Risk neutral U’(W)>0, U’’(W)=0 Risk lover U’(W)>0, U’’(W)>0
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Venti Risk and reward 4 Risk, Return, and Uncertainty 0 $1,000 $2,000 Wealth of investor U($1,000) U(W) U($0) U($2,000) Concave utility → risk-averse investor Utility of wealth 0 $1,000 $2,000 Wealth of investor U($1,000) U(W) U($0) U($2,000) Utility of wealth A $1,000 increment Another $1,000 increment A given increase in utility A smaller increase in utility
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Venti Risk and reward 5 0 $1,000 $2,000 wealth U(W) U(certain) U(W) Compare utility of two “investments” – one certain and one risky: $1,000 with certainty or $0 with p=1/2 and $2,000 with p=1/2 Note: expected wealth is the same, but which has greater expected utility? U($0) U($2,000 ) U(risky) Risk, Return, and Uncertainty
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Venti Risk and reward 6 Risk, Return, and Uncertainty Certainty Equivalent : investor indifferent between $CE with certainty and the risky investment: U($CE) = U(risky) = 1/2U($0) + 1/2U($2,000) Risk Premium : the difference between the expected return and the certainty equivalent, i.e. it is how much a security must be priced below expected return to get the investor to buy it.
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Venti Risk and reward 7 Risk, Return, and Uncertainty 0 $1,000 $2,000 wealth U(W) U(W) U($0) U($2,000) risk premium certainty equivalent U(certain) U(risky)
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Venti Risk and reward 8 Risk, Return, and Uncertainty What affects the discount rate “r”? : a certain $ in the future is worth less than a certain $ in the present.
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