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lec1new2

# lec1new2 - Financial Data Analysis Professor S Kou...

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Financial Data Analysis Professor S. Kou, Department of IEOR, Columbia University Lecture 1.b Review of Mean Variance Analysis 1 Review of The Mean Variance Analysis Consider a one period economy as before with N risky assets, and a money market account with the risk-free rate r > 0 being a °xed constant. The trading strategy is denoted by ° = ( ° 0 , ° 1 , ..., ° N ), where ° 0 is the number of shares invested in the money market account, and ° n is the number of shares invested in the n th risky asset. Let R be the return of such a strategy ° at time 1. The mean-variance analysis assumes that an investor attempts to solve the following prob- lem: min ° V ar [ R ] subject to E [ R ] = ±; ± > r: The intuition is that for the same return, the investor prefers a portfolio with a smaller variance. Note that the mean variance problem does not take consideration of any distribution properties (e.g. skewness, kurtosis etc.) other than the mean and variance. This is a signi°cant drawback of the mean variance analysis. Let w n = ° n S n (0) =V (0) , w = ( w 1 ; :::; w n ) > , where S n (0) is the values of the n th risky asset at time 0 and V (0) is the total initial amount of money at time 0. In other words,

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