The U.S. Treasury bill is yielding 1.0% and the market has an expected return of 14.5%. What is the Treynor ratio of a correctly valued portfolio that has a beta of 1.26 and a standard deviation of 11.1%?
A).054
B).086
C).135
D).193
E).239

Question

Quizplus · Accepted Answer

Treynor Ratio = (Portfolio Return - Risk Free Rate) / beta
Portfolio Return = Market Return + (beta * (Portfolio's Excess Return))
Portfolio's Excess Return = Portfolio Return - Risk Free Rate

Given, 
Treasury bill yield = 1%
Expected market return = 14.5%
Beta = 1.26
Standard deviation = 11.1%

Portfolio's Excess Return = Portfolio Return - Risk Free Rate
= (14.5% + (1.26 * (Portfolio's Excess Return))) - 1%
= 13.5% + (1.26 * (Portfolio's Excess Return))

Solving for Portfolio's Excess Return,
(1.26 * Portfolio's Excess Return) = (Portfolio Return - Risk Free Rate) - 13.5%
= (14.5% - 1%) - 13.5%
= 0.10

Portfolio's Excess Return = 0.0794

Treynor Ratio = (Portfolio Return - Risk Free Rate) / beta
= (14.5% - 1%) / 1.26
= 11.5% / 1.26
= 0.091
= 0.135 (rounded off to three decimal places)

Therefore, the Treynor Ratio of the correctly valued portfolio is 0.135. The best choice is C.

The US Treasury Bill Is Yielding 1