Economics 434
Theory of Financial Markets
Professor Edwin T Burton
Economics Department
The University of Virginia
Economics 434 – Financial Market Theory
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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
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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
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The risk free asset
Mean
The one with the highest mean
Standard Deviation
Economics 434 – Financial Market Theory
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Combine with Risky Assets
Mean
?
Risky Assets
Risk Free
Asset
Standard Deviation
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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
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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
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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
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Combine with Risky Assets
Mean
Risk Free
Asset
Standard Deviation
Economics 434 – Financial Market Theory
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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
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Tobin’s Result
Mean
Use of Leverage
E
Risk Free
Asset
Standard Deviation
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The End
Economics 434 – Financial Market Theory
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