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Economics 434 Theory of Financial Markets. Professor Edwin T Burton Economics Department The University of Virginia. Modern Portfolio Theory . Three Significant Steps to MPT Harry Markowitz Mean Variance Analysis The Concept of an “Efficient Portfolio” James Tobin

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Economics 434 theory of financial markets
Economics 434Theory of Financial Markets

Professor Edwin T Burton

Economics Department

The University of Virginia


Modern portfolio theory
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”


Tobin s result
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
The risk free asset

Mean

The one with the highest mean

Standard Deviation


Combine with risky assets
Combine with Risky Assets

Mean

?

Risky Assets

Risk Free

Asset

Standard Deviation


Recall the definition of the variance of a portfolio with two assets
Recall the definition of the variance of a Portfoliowith two assets

 P2 =  (P - P)2

n

= {1(X1- 1) + 2(X2 - 2)}2

n


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


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

(2)2

 P =

Which means that:


Combine with risky assets1
Combine with Risky Assets

Mean

Risk Free

Asset

Standard Deviation


Combine with risky assets2
Combine with Risky Assets

Mean

The New Feasible Set

E

Always combines the risk free asset

With a specific asset (portfolio) E

Risk Free

Asset

Standard Deviation


Tobin s result1
Tobin’s Result

Mean

Use of Leverage

E

Risk Free

Asset

Standard Deviation



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