Economics 434: The Theory of Financial Markets Professor Burton Fall 2016 Sept 27, 2016

The Capital Asset Pricing Model Markowitz – mean, variance analysis Tobin – the role of the risk free rate Sharpe (and others) – beta and the market basket September 15, 17, 2015

Today: Markowitz on Mean-Variance Theory Sept 27, 2016

Need Mathematical Concepts Mean Variance Covariance Correlation Coefficient September 15, 17, 2015

Correlation coefficient ≡ ρx,y Symbols Mean [x] ≡ µ(x) ≡ µx Variance [x] ≡ σ2(x) ≡ σx2 Covariance [x,y] ≡ σx,y If x and y are the same variable, then σy,y ≡ σx,x ≡ σx2 ≡ σy2 Correlation coefficient ≡ ρx,y September 15, 17, 2015

 = √ 2 1,2 1,2  12 Some Definitions (Xi1- µi ) 1,2  12 September 9, 2014

Harry Markowitz September 9, 2014

Mean-Variance (Harry Markowitz, 1955) Each asset defined as: Probability distribution of returns Mean and Variance of the distribution known Assume no riskless asset (all variances > 0) Portfolio is A collection of assets with a mean and a variance that can be calculated Also an asset (no difference between portfolio and an asset) September 15, 17, 2015

Diagram with 2 Assets Asset 2 (μ2, σ2) Asset 1 (μ1, σ1) Mean Standard Deviation = √(Variance) September 15, 17, 2015

Now combine asset 1 and 2 into portolios consisting only of assets 1 and 2 Mean Asset 2 (μ2, σ2) Asset 2 (μ2, σ2) Portfolio (μP, σP) Portfolio (μP, σP) Asset 1 (μ1, σ1) Asset 1 (μ1, σ1) σ σ Where should the portfolio be in the diagram? September 15, 17, 2015

Investors will Choose some portfolio among those on the efficient frontier Those who wish less risk choose portfolios that are further to the left on the efficient frontier. These portfolios are those with lower mean and lower standard deviation Investors desiring more risk move to the right along the efficient frontier in search of higher mean, higher standard deviation portfolios September 15, 17, 2015

Portfolio Choice Mean More risk Less risk σ σ September 15, 17, 2015

Sept 27, 2016