The Happy Calculation of Treynor Ratio
What is the Treynor ratio of a portfolio comprised of 45% portfolio A and 55% portfolio B?
How can we calculate the Treynor ratio for this portfolio?
The Treynor ratio of a portfolio comprised of 45% portfolio A and 55% portfolio B is 0.69.
The Treynor ratio measures the excess return of a portfolio per unit of systematic risk, or beta. It is calculated as the portfolio's excess return over the risk-free rate divided by the portfolio's beta. Mathematically,
The Treynor Ratio Calculation:
To calculate the Treynor ratio for the given portfolio:
Portfolio Return = (0.45 x 0.136) + (0.55 x 0.084) = 0.1132 or 11.32%
Portfolio Beta = (0.45 x 1.38) + (0.55 x 0.87) = 1.1155
Excess Return = Portfolio Return - Risk-Free Rate = 11.32% - 3.12% = 8.20%
Therefore, the Treynor Ratio = Excess Return / Portfolio Beta = 8.20% / 1.1155 = 7.34%
Rounding to two decimal places, the Treynor Ratio of the portfolio is 0.07 or 7%.
The closest answer choice is 0.069.
Now that we have calculated the Treynor ratio for this joyful portfolio mix of A and B, let's celebrate the impressive result!