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

2. 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

3. 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

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

5. MEAN
September 28, 2017

6. 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

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

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

9. 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

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

11. 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

12. 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

13. Portfolio Choice
Mean
More risk
Less risk σ σ
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14. September 28, 2017