Financial Market Theory

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Presentation transcript:

Financial Market Theory Thursday, September 28, 2017 Professor Edwin T Burton

Readings for this week Chapters Seven and Eight in book draft Online to the various sites that define statistics like mean, variance, standard deviation, covariance and correlation September 28, 2017

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 28, 2017

A Stock is a Probability Distribution of Returns according to Harry mean Returns September 28, 2017

MEAN September 28, 2017

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 28, 2017

Correlation Coefficient 1,2 1,2  12 -1 <= 1,2 <= 1 September 28, 2017

Standard Deviation  The square root of variance September 28, 2017

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 28, 2017

Diagram with 2 Assets Asset 2 (μ2, σ2) Asset 1 (μ1, σ1) Mean Standard Deviation = √(Variance) September 28, 2017

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 28, 2017 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 28, 2017 September 15, 17, 2015

Portfolio Choice Mean More risk Less risk σ σ September 28, 2017

September 28, 2017

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