Download Markowitz and Tobin, October 2, 2012

Economics 434
Theory of Financial Markets
Professor Edwin T Burton
Economics Department
The University of Virginia
Economics 434 – Financial Market Theory
Tuesday,
Tuesday,
September
August
21,2010
2010
Tuesday,
Oct
2, 201224,
Tuesday,
August
25,
2009
Modern Portfolio Theory
 Three Significant Steps to MPT
 Harry Markowitz
 Mean Variance Analysis
 The Concept of an “Efficient Portfolio”
 James Tobin
 What Happens When You Add a “Risk Free Asset” to
Harry’s story
 Bill Sharpe (Treynor Lintner, Mossin, etal)
 Put Tobin’s Result in Equilbrium
 The Rise of Beta
 The Insignificance of “own variance”
Economics 434 – Financial Market Theory
Tuesday,
Tuesday,
September
August
21,2010
2010
Tuesday,
Oct
2, 201224,
Tuesday,
August
25,
2009
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
Economics 434 – Financial Market Theory
Tuesday,
Tuesday,
September
August
21,2010
2010
Tuesday,
Oct
2, 201224,
Tuesday,
August
25,
2009
The risk free asset
Mean
The one with the highest mean
Standard Deviation
Economics 434 – Financial Market Theory
Tuesday,
Tuesday,
September
August
21,2010
2010
Tuesday,
Oct
2, 201224,
Tuesday,
August
25,
2009
Combine with Risky Assets
Mean
?
Risky Assets
Risk Free
Asset
Standard Deviation
Economics 434 – Financial Market Theory
Tuesday,
Tuesday,
September
August
21,2010
2010
Tuesday,
Oct
2, 201224,
Tuesday,
August
25,
2009
Recall the definition of the variance of a Portfolio
with two assets
 P2 =  (P - P)2
n
= {1(X1- 1) + 2(X2 - 2)}2
n
Economics 434 – Financial Market Theory
Tuesday,
Tuesday,
September
August
21,2010
2010
Tuesday,
Oct
2, 201224,
Tuesday,
August
25,
2009
Variance with 2 Assets - Continued
= (1)212 + (2)222 + 2121,2
Recall the definition of the correlation coefficient:
1,2 
1,2
12
= (1)212 + (2)222 + 2121,212
Economics 434 – Financial Market Theory
Tuesday,
Tuesday,
September
August
21,2010
2010
Tuesday,
Oct
2, 201224,
Tuesday,
August
25,
2009
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:
Economics 434 – Financial Market Theory
 P = (2)2
Tuesday,
Tuesday,
September
August
21,2010
2010
Tuesday,
Oct
2, 201224,
Tuesday,
August
25,
2009
Combine with Risky Assets
Mean
Risk Free
Asset
Standard Deviation
Economics 434 – Financial Market Theory
Tuesday,
Tuesday,
September
August
21,2010
2010
Tuesday,
Oct
2, 201224,
Tuesday,
August
25,
2009
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
Economics 434 – Financial Market Theory
Tuesday,
Tuesday,
September
August
21,2010
2010
Tuesday,
Oct
2, 201224,
Tuesday,
August
25,
2009
Tobin’s Result
Mean
Use of Leverage
E
Risk Free
Asset
Standard Deviation
Economics 434 – Financial Market Theory
Tuesday,
Tuesday,
September
August
21,2010
2010
Tuesday,
Oct
2, 201224,
Tuesday,
August
25,
2009
The End
Economics 434 – Financial Market Theory
Tuesday,
Tuesday,
September
August
21,2010
2010
Tuesday,
Oct
2, 201224,
Tuesday,
August
25,
2009