Download Tuesday, September 27,2016

Economics 434: The Theory of
Financial Markets
Professor Burton
Fall 2016
Sept 27, 2016
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
Today: Markowitz on Mean-Variance Theory
Sept 27, 2016
Need Mathematical Concepts
•
•
•
•
Mean
Variance
Covariance
Correlation Coefficient
September 15, 17, 2015
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
i 1
Some Definitions
 2  i 1
n
xi
 x 

x
   x 
n
i
n
n
2
 = √ 2
(Xi1- µi )
n
  x, y  
 x   ( x)  y   ( y ) 
i 1
n
1,2 
September 9, 2014
1,2
12
Harry Markowitz
September 9, 2014
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
Diagram with 2 Assets
Mean
Asset 2 (μ2, σ2)
Asset 1 (μ1, σ1)
Standard Deviation = √(Variance)
September 15, 17, 2015
Mean
Portfolio (μP, σP)
Asset 2 (μ2, σ2)
Asset 1 (μ1, σ1)
σ
Where should the portfolio be in the diagram?
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 15, 17, 2015
Portfolio Choice
Mean
More risk
Less risk
σ
September 15, 17, 2015
Sept 27, 2016