An aggressive equity growth fund delivers an annualized return of 19.2% with a Standard Deviation of 14.5%. If the risk-free rate is 6.0%, what is the Sharpe Ratio of the scheme?

[ A ]1.36

[ B ]13.20%

[ C ]1.32

[ D ]0.91[ CORRECT ]

Takeaway

The scheme's Sharpe Ratio is 0.91, calculated by dividing the fund's excess return over the risk-free rate by its standard deviation.

Derivation

Step 1: Excess return = Fund return - risk-free rate = 19.2% - 6.0% = 13.2%. Step 2: Sharpe Ratio = Excess return / Standard Deviation = 13.2% / 14.5% = 0.91. Sharpe measures return earned per unit of total risk taken (as opposed to Sortino, which isolates only downside risk), and a ratio of 0.91 means the fund generated roughly 0.91 units of excess return for every unit of volatility endured. The two most common calculation errors this question is designed to catch are: forgetting to subtract the risk-free rate before dividing, and dividing raw return by volatility without adjusting for risk-free rate at all.

Why the others fail

A — 1.36

1.36 does not correspond to (19.2-6.0)/14.5 or any correctly-derived ratio from the given inputs — it is an unsupported figure not produced by the Sharpe Ratio formula.

B — 13.20%

13.20% is simply the excess return figure (19.2% - 6.0%) quoted on its own, without being divided by the fund's standard deviation of 14.5% to convert it into a risk-adjusted ratio.

C — 1.32

1.32 comes from dividing the fund's gross 19.2% return by 14.5% volatility directly, skipping the required step of first subtracting the 6.0% risk-free rate.