Return for the risk taken

A return on its own says almost nothing. The exam wants you to read it against two things: the risk it took and the benchmark it should have beaten. Start with the idea that a 14% return earned on a stomach-churning ride can be worse than a 12% return earned calmly, because the calmer fund is the one an investor actually stays in.

The tool that captures this is the Sharpe ratio: the return above the risk-free rate, divided by standard deviation. In symbols, Sharpe = (return − risk-free rate) ÷ standard deviation, and higher is better because it means more reward per unit of total risk. Work an example: a fund returning 14% with a standard deviation of 8, against a 6% risk-free rate, scores (14 − 6) ÷ 8 = 1.0; a rival with the same 14% but a standard deviation of 16 scores only 0.5. Its close cousin, the Treynor ratio, uses the same excess return but divides by beta instead, rewarding return per unit of market risk rather than total risk.

Two more measures complete the toolkit. Alpha is the return a fund earns above its benchmark (or its risk-adjusted expectation), so a positive alpha is the mark of a manager who genuinely added value. And tracking error, the standard deviation of the fund’s returns minus its index’s, tells you how tightly a passive fund hugs its index, where lower is better. One caution ties it together: these ratios are relative tools, compare them only between funds of the same kind, never a debt fund’s Sharpe against an equity fund’s. Read return, risk and benchmark together, and you are reading a fund the way a professional does.