A diversified equity scheme delivers an annualized return of 15.0% and has a portfolio Beta of 1.20. If the risk-free rate of return is 6.0%, what is the Treynor Ratio of the scheme?

[ A ]12.50 percent

[ B ]9.00 percent

[ C ]7.50 percent[ CORRECT ]

[ D ]6.25 percent

Takeaway

Option C is correct: 7.50 percent

Derivation

The Treynor Ratio measures the excess return earned per unit of systematic risk (Beta). Formula: Treynor Ratio = (Scheme Return (Rs) - Risk-Free Rate (Rf)) / Beta. Substituting the values: Treynor Ratio = (15.0% - 6.0%) / 1.20 = 9.0% / 1.20 = 7.50% (or 0.075). Treynor Ratio evaluates how well a diversified equity portfolio compensates investors for market risk. This question tests the quantitative calculation of Treynor Ratio. The common error is dividing total return by Beta (15.0 / 1.20 = 12.50%) without deducting the risk-free rate.

Why the others fail

A — 12.50 percent

12.50% results from dividing total return (15.0%) by Beta (1.20) without subtracting the risk-free rate of 6.0%.

B — 9.00 percent

9.00% is the numerator (risk premium = 15.0% - 6.0%) but fails to divide by the portfolio Beta of 1.20.

D — 6.25 percent

6.25% is an arithmetic error resulting from mistakenly using a Beta of 1.44 instead of the stated 1.20.