Download Tuesday, October 11, 2016

Economics 434: The Theory of
Financial Markets
Professor Burton
Fall 2016
Oct 11, 2016
Readings
• Chapters 8 and 9 – available on Collab
– Chapter 8 – Tobin
– Chapter 9 – CAPM
• So far, all 9 chapters plus “Random Walk Down
Wall Street”
Oct 11, 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
If σ < 1
P will lie to the left of the
Line joining the Assets
Mean
Asset 2 (μ2, σ2)
μ2
Asset 1 (μ1, σ1)
μ1
σ1
Oct 11, 2016
½ σ1 + ½ σ2
σ2
Main Conclusion of Markowitz Theory
Mean
Boundary of “feasible” portfolios
“Efficient” Portfolios
σ
September 15, 17, 2015
Today: Tobin Adds a Risk-Free Asset
Oct 11, 2016
Tobin’s Result
• If there is a riskless asset
• It changes the feasible set
• All optimum portfolios contain
– The risk free asset and/or
– The portfolio E
– …….in some combination….
• The Mutual Fund Theorem
James Tobin, Prof of Economics
Yale University
Winner of Nobel Prize in Economics
1981
The risk free asset
Mean
The one with the highest mean
Standard Deviation
Combine with Risky Assets
Mean
?
Risky Assets
Risk Free
Asset
Standard Deviation
If 1 is zero
 P2 = (1)212 + (2)222 + 2121,212
If one of the standard deviations is equal to zero, e.g. 1 then
 P2 = (2)222
Which means that:
 P = (2)2
Combine with Risky Assets
Mean
Risk Free
Asset
Standard Deviation
Combine with Risky Assets
Mean
The New Feasible Set
E
Risk Free
Asset
Always combines the risk free asset
With a specific asset (portfolio) E
Standard Deviation
Tobin’s Result
Mean
Use of Leverage
E
Risk Free
Asset
Standard Deviation
Tobin’s Result
Mean
Use of Leverage
E
Risk Free
Asset
Standard Deviation
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
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
Bill Sharpe
• M – the “efficient” basket
• The pricing rule based upon “beta”
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
Oct 11, 2016