Financial Markets – Fall, 2019 – Sept 12, 2019

Tobin’s and the Risk-Free Asset What happens to “mean-variance” theory If there is a riskless asset? James Tobin, Prof of Economics Yale University Winner of Nobel Prize in Economics 1981

“The” risk free asset The one with the highest mean Mean Standard Deviation

Combine with Risky Assets Mean ? Risky Assets Risk Free Asset Standard Deviation

If 1 is zero  P2 = (2)222 (2)2  P = 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 Assets Mean Risk Free Asset Standard Deviation

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 Result Mean Use of Leverage E Risk Free Asset Standard Deviation

The End