What is the Treynor ratio of a portfolio comprised of 45% Portfolio A and 55% Portfolio B?
$\begin{array}{lrr}
&\text{A}&\text{B}\
\text { Neight } & 45 \% & 55\% \
\text { Avg Return } & 13.60 \% & 8.40 \% \
\text { Std Dev } & 17.20 \% & 6.40 \%\
\text{Beta}&1.38&0.87
\end{array}$

The risk-free rate is 3.12% and the market risk premium is 8.5%.
A).041
B).058
C).069
D).114
E).136

Question

What is the Treynor ratio of a portfolio comprised of 45% Portfolio A and 55% Portfolio B?
$\begin{array}{lrr}
&\text{A}&\text{B}\
\text { Neight } & 45 \% & 55\% \
\text { Avg Return } & 13.60 \% & 8.40 \% \
\text { Std Dev } & 17.20 \% & 6.40 \%\
\text{Beta}&1.38&0.87
\end{array}$

The risk-free rate is 3.12% and the market risk premium is 8.5%.
A).041
B).058
C).069
D).114
E).136

Quizplus · Accepted Answer

First, we need to calculate the expected return of the portfolio. 
Expected return of portfolio = (0.45 x Expected return of Portfolio A) + (0.55 x Expected return of Portfolio B) 
Next, we need to calculate the portfolio beta using the weightages and betas of the individual portfolios. 
Portfolio beta = (0.45 x Beta of Portfolio A) + (0.55 x Beta of Portfolio B)

Using the given information: 
RF = 3.12% 
Market risk premium = 8.5%

Expected return of Portfolio A = RF + (Beta of Portfolio A x Market risk premium) 
= 3.12% + (1.3 x 8.5%) 
= 14.62%

Expected return of Portfolio B = RF + (Beta of Portfolio B x Market risk premium) 
= 3.12% + (0.9 x 8.5%) 
= 10.92%

Portfolio beta = (0.45 x 1.3) + (0.55 x 0.9) 
= 1.035

Treynor ratio = (Expected return of portfolio - Risk-free rate) / Portfolio beta 
= (0.45 x 14.62% + 0.55 x 10.92% - 3.12%) / 1.035 
= 6.89% / 1.035 
= 6.66%

Therefore, the Treynor ratio of the portfolio is 0.066 or 6.6% (rounded off to two decimal places). The closest choice is C).

What Is the Treynor Ratio of a Portfolio Comprised of 45