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

2. 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

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

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

5. 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

6.  = √ 2 1,2 1,2  12 Some Definitions (Xi1- µi )
1,2 
12
September 9, 2014

7. Harry Markowitz
September 9, 2014

8. 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

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

10. 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

11. 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

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

13. Sept 27, 2016