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Unformatted text preview: Chapter Thirteen Risky Assets Mean of a Distribution ◆ A random variable (r.v.) w takes values w 1 ,…, w S with probabilities π 1 ,..., π S ( π 1 + · · · + π S = 1). ◆ The mean (expected value) of the distribution is the av. value of the r.v.; E [ ] . w w w s s s S = = = ∑ μ π 1 Variance of a Distribution ◆ The distribution’s variance is the r.v.’s av. squared deviation from the mean; ◆ Variance measures the r.v.’s variation. var [ ] ( ) . w w w s w s s S = = = ∑ σ μ π 2 2 1 Standard Deviation of a Distribution ◆ The distribution’s standard deviation is the square root of its variance; ◆ St. deviation also measures the r.v.’s variability. st. dev [ ] ( ) . w w w w s w s s S = = = = ∑ σ σ μ π 2 2 1 Mean and Variance Probability Random Variable Values Two distributions with the same variance and different means. Mean and Variance Probability Random Variable Values Two distributions with the same mean and different variances. Preferences over Risky Assets ◆ Higher mean return is preferred. ◆ Less variation in return is preferred (less risk). Preferences over Risky Assets ◆ Higher mean return is preferred. ◆ Less variation in return is preferred (less risk). ◆ Preferences are represented by a utility function U( μ , σ ). ◆ U ↑ as mean return μ ↑ . ◆ U ↓ as risk σ ↑ . Preferences over Risky Assets Preferred Higher mean return is a good. Higher risk is a bad. Mean Return, μ St. Dev. of Return, σ Preferences over Risky Assets Preferred Higher mean return is a good. Higher risk is a bad. Mean Return, μ St. Dev. of Return, σ Preferences over Risky Assets ◆ How is the MRS computed? Preferences over Risky Assets ◆ How is the MRS computed? dU U d U d U d U d d d U U = + = ⇒ =  ⇒ =  ∂ ∂μ μ ∂ ∂σ σ ∂ ∂μ μ ∂ ∂σ σ μ σ ∂ ∂σ ∂ ∂μ / / . Preferences over Risky Assets Mean Return, μ St. Dev. of Return, σ Preferred Higher mean return is a good. Higher risk is a bad. d d U U μ σ ∂ ∂σ ∂ ∂μ =  / / Budget Constraints for Risky Assets ◆ Two assets. ◆ Riskfree asset’s rateorreturn is r f . ◆ Risky stock’s rateorreturn is m s if state s occurs, with prob....
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This note was uploaded on 01/06/2012 for the course ECON 102 taught by Professor Goodhart during the Spring '11 term at Abu Dhabi University.
 Spring '11
 GOODHART

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