This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Chapter Thirteen Risky Assets Mean of a Distribution â—† A random variable (r.v.) w takes values w 1 ,â€¦, w S with probabilities Ï€ 1 ,..., Ï€ S ( Ï€ 1 + Â· Â· Â· + Ï€ S = 1). â—† The mean (expected value) of the distribution is the av. value of the r.v.; E [ ] . w w w s s s S = = = âˆ‘ Î¼ Ï€ 1 Variance of a Distribution â—† The distributionâ€™s variance is the r.v.â€™s av. squared deviation from the mean; â—† Variance measures the r.v.â€™s variation. var [ ] ( ) . w w w s w s s S = = = âˆ‘ Ïƒ Î¼ Ï€ 2 2 1 Standard Deviation of a Distribution â—† The distributionâ€™s standard deviation is the square root of its variance; â—† St. deviation also measures the r.v.â€™s variability. st. dev [ ] ( ) . w w w w s w s s S = = = = âˆ‘ Ïƒ Ïƒ Î¼ Ï€ 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 â—† Higher mean return is preferred. â—† Less variation in return is preferred (less risk). Preferences over Risky Assets â—† Higher mean return is preferred. â—† Less variation in return is preferred (less risk). â—† Preferences are represented by a utility function U( Î¼ , Ïƒ ). â—† U â†‘ as mean return Î¼ â†‘ . â—† U â†“ as risk Ïƒ â†‘ . Preferences over Risky Assets Preferred Higher mean return is a good. Higher risk is a bad. Mean Return, Î¼ St. Dev. of Return, Ïƒ Preferences over Risky Assets Preferred Higher mean return is a good. Higher risk is a bad. Mean Return, Î¼ St. Dev. of Return, Ïƒ Preferences over Risky Assets â—† How is the MRS computed? Preferences over Risky Assets â—† How is the MRS computed? dU U d U d U d U d d d U U = + = â‡’ =  â‡’ =  âˆ‚ âˆ‚Î¼ Î¼ âˆ‚ âˆ‚Ïƒ Ïƒ âˆ‚ âˆ‚Î¼ Î¼ âˆ‚ âˆ‚Ïƒ Ïƒ Î¼ Ïƒ âˆ‚ âˆ‚Ïƒ âˆ‚ âˆ‚Î¼ / / . Preferences over Risky Assets Mean Return, Î¼ St. Dev. of Return, Ïƒ Preferred Higher mean return is a good. Higher risk is a bad. d d U U Î¼ Ïƒ âˆ‚ âˆ‚Ïƒ âˆ‚ âˆ‚Î¼ =  / / Budget Constraints for Risky Assets â—† Two assets. â—† Riskfree assetâ€™s rateorreturn is r f . â—† Risky stockâ€™s rateorreturn is m s if state s occurs, with prob....
View
Full Document
 Spring '11
 GOODHART
 Variance, Capital Asset Pricing Model, Financial Markets, risky assets

Click to edit the document details