Economics 434
Financial Markets
Professor Burton
University of Virginia
Fall 2015
September 22, 2015
The Markowitz Assumptions
• Every asset is a probability distribution of
returns
•
•
•
•
•
Asset Xi has mean: μi
Asset Xi has variance: σ2i
Xi ~ (μi , σ2i )
Assume all assets are risky: σ2i > 0 for all I
Assume that correlation coefficients are all
less than one and greater than minus one
September 11, 2014
If   1
Then all the portfolios are here
September 11, 2014
This Means the “boundary”of the possible portfolios
looks like this:
September 11, 2014
This is very convenient
Mean
Maximizes
Utility
Standard Deviation
Tobin’s Result
Mean
Use of Leverage
E
Risk Free
Asset
Standard Deviation
Capital Asset Pricing Model
• Makes all the same assumptions as Tobin
model
• But Tobin’s model is about “one person”
• CAPM puts Tobin’s model in equilibrium, by
assuming that everyone faces the same
portfolio choice problem as in Tobin’s problem
• Only difference between people in CAPM is
that each has their own preferences (utility
function)
CAPM – two conclusions
• M – the “efficient” basket
• The pricing rule based upon “beta”
First Conclusion
Mean
M
Rf
What is M ?
Answer: contains all “positively”
priced assets, weighted by their
“market” values.
STDD
Second Conclusion:
After all the math is over
For every asset, i
i = Rf + i [M – Rf]
Where i =
Cov (i, M)
Var (M)

 I,M
2
M
This is often called the “Capital Asset Pricing Model”
Capital Market Line
Mean
M
Rf
What is M ?
Answer: contains all “positively”
priced assets, weighted by their
“market” values.
STDD
Security Market Line
i = Rf + i [M – Rf]
Mean
i
M
Rf
Security Market Line
1
Beta
Random Questions
• What is the beta of the market?
• Why not just buy one stock with the beta of
the market?
• Can betas be negative? What does it
mean?
• Is this model testable?
September 22, 2015