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Economics 434 Theory of Financial MarketsPowerPoint Presentation

Economics 434 Theory of Financial Markets

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Economics 434Theory 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”

- Harry Markowitz
- 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

- 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

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)212 + (2)222 + 2121,2

Recall the definition of the correlation coefficient:

1,2

1,2

12

= (1)212 + (2)222 + 2121,212

If 1 is zero

P2= (1)212 + (2)222 + 2121,212

If one of the standard deviations is equal to zero, e.g. 1 then

P2 =

(2)222

(2)2

P =

Which means that:

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

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