Financial Market Theory Tuesday, September 25, 2018 Professor Edwin T Burton

Harry Markowitz As a graduate student in Economics at University of Chicago in the 1950s, Harry wanted to know how to optimally construct a portfolio of stocks In order to make any headway, Harry had to decide how to describe (define) a stock. So, what to do? September 25, 2018

A Stock is a Probability Distribution of Returns according to Harry mean Returns September 25, 2018

MEAN September 25, 2018

Variance First Calculate the Mean Then take each observation and form [Xi – Mean(X)]2 Then calculate their average (or weight by the probability of each observation) September 25, 2018

Correlation Coefficient 1,2 1,2  12 -1 <= 1,2 <= 1 September 25, 2018

Standard Deviation  The square root of variance September 25, 2018

Mean-Variance (Harry Markowitz, 1955) Each asset defined as: Probability distribution of returns Mean and Variance of the distribution known Covariances of returns between any two assets are 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 25, 2018

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 25, 2018 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 25, 2018 September 15, 17, 2015

Portfolio Choice Mean More risk Less risk σ σ September 25, 2018