Why is a return meaningless without its risk?
Two portfolios both finished the year at +12%. The first drifted upward with an annualised volatility of 8%. The second lurched between +9% and −7% months, with a volatility of 30%, and spent a stretch of the summer down a quarter from its high.
Same destination. Very different roads. Reporting only the destination throws away most of what happened — including everything that determines whether the holder could have stayed in the seat.
Every risk-adjusted measure has the same shape
Once you see the pattern, the whole family becomes readable:
Something you earned ÷ something you endured
What changes between the metrics is only which earning and which enduring:
| Measure | Numerator: earned above… | Denominator: endured… |
|---|---|---|
| Sharpe ratio | the risk-free rate | total volatility |
| Sortino ratio | a target (often zero) | downside volatility only |
| Information ratio | the benchmark | tracking error |
| Calmar ratio | nothing (raw annual return) | the worst drawdown |
Four questions, four different definitions of "risk". None of them is the correct one; each is correct about a different worry. The next three lessons build the first three properly, and Unit 3 builds the fourth.
Why the ratio, and not the return, is the comparable number
There is a hard-nosed reason professionals compare ratios rather than raw returns. Risk can be dialled up or down far more easily than skill can. A portfolio delivering 6% at 6% volatility and one delivering 12% at 24% volatility do not merely differ in ambition — the first produces more return per unit of turbulence, and the arithmetic of scaling exposure is a well-understood mechanical exercise.
This is not a suggestion to use leverage, which introduces financing costs, forced-sale risk and path dependence that the tidy arithmetic ignores. It is the reason the ratio, rather than the headline, is the number that carries information about how the return was produced.
The honest caveat, stated once and meant throughout
Every measure in this unit is computed from history. A high ratio describes a period that has already happened, using a definition of risk chosen by whoever did the computing. It does not identify a good investment, does not rank the future, and does not persist reliably. Treat these numbers as descriptions of a past experience — precise, useful, and silent about what comes next.
Try it now
- Two funds are below, one broad and one concentrated. Measure the same three-year span on each and write down both total returns and both CAGRs.
- Now the denominator. Switch both to Daily and measure a dozen ordinary sessions on each to get a feel for the typical daily move, then compute each series' daily standard deviation and annualise by × √252.
- Line the four numbers up. Which delivered more return per unit of volatility? State it as an observation about that window only — and note that the concentrated fund almost certainly won on the numerator and lost on the denominator, which is exactly why neither number is reportable alone.