Chapter Thirteen Risky Assets
Chapter Thirteen Risky Assets
Main issue Mean-Variance Utility Budget Constraints for Risky Assets Measuring risk Capital Asset Pricing Model
Main Issue Mean-Variance Utility Budget Constraints for Risky Assets Measuring Risk Capital Asset Pricing Model
Mean of a distribution A random variable(r v )w takes values Wi,,, Ws with probabilities ■■■ s=1) The mean(expected value) of the distribution is the average value of the r.v., Elw]=uw= 2WSIS
Mean of a Distribution A random variable (r.v.) w takes values w1 ,…,wS with probabilities 1 ,...,S (1 + · · · + S = 1). The mean (expected value) of the distribution is the average value of the r.v.; E[w] w w . s s s S = = = 1
Variance of a distribution The distrilbution's variance is the rv,'s av, squared deviation from the mean var[w]=ow=2(ws-UW)"IS ariance measures the rvs variation
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 = = − = 2 2 1
Standard deviation of a Distribution The distribution's standard deviation is the square root of its variance; st dev[w]=ow=v 2 ∑(s-12)2xs St deviation also measures the rvs variability
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 = = = − = 2 2 1
Mean and variance Two distributions with the same Probability variance and different means Random Variable values
Mean and Variance Probability Random Variable Values Two distributions with the same variance and different means
Mean and variance Two distributions with the same Probability mean and different variances Random Variable values
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 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个 as mean returnμ个 U↓ as risk o个
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(,). U as mean return . U as risk
Preferences over Risky assets Mean return, H Preferred Higher mean return is a good Higher risk is a bad St Dev of return, o
Preferences over Risky Assets Preferred Higher mean return is a good. Higher risk is a bad. Mean Return, St. Dev. of Return,
