financial Market Theory

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
September
28, 2017
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?

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

5.  
n
x
x
i
n
i



1

MEAN September
28, 2017

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

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

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

11. and 2
September
28, 2017
September 15, 17, 2015
Mean
Asset 1 (μ1, σ1)
Asset 2 (μ2, σ2)
Portfolio (μP, σP)
σ
Where should the portfolio be in the diagram?
Asset 1 (μ1, σ1)
Asset 2 (μ2, σ2)
Portfolio (μP, σP)
σ

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 September
28, 2017
Mean
σ
σ
Less risk
More risk

14. September
28, 2017