Risk and return metrics that matter

A strategy report that leads with “12% annual return” and stops there has told you almost nothing. Twelve percent earned with steady monthly gains and twelve percent earned with three quiet years and one violent 40% drawdown are different products, and the difference only shows up once return is paired with a measure of what it cost to get there. This article works through the metrics that make that pairing precise, and the assumption each one leans on.

Annualised return and the compounding trap

Two conventions exist for turning a series of periodic returns into an annual figure, and they disagree. Arithmetic annualisation multiplies the average periodic return by the number of periods per year: $\bar{r} \times 252$ for daily data. Geometric annualisation compounds: $(1 + \bar{r})^{252} - 1$ . For small, steady returns the two are close; for volatile return series they diverge substantially, because arithmetic annualisation ignores the fact that a 50% loss requires a 100% gain to recover — it overstates what an investor actually compounded.

Worked example. A strategy returns +20% in year one and -20% in year two. The arithmetic average is 0%, suggesting a flat outcome. The actual compounded result is $1.20 \times 0.80 = 0.96$ , a 4% loss over two years. Arithmetic annualisation would have reported the wrong sign entirely.

Volatility is annualised by scaling, not compounding: daily standard deviation $\sigma_d$ becomes annual volatility as $\sigma_d \sqrt{252}$ , under the assumption that returns are independent and identically distributed period to period. That assumption is routinely wrong — volatility clusters, so a calm quarter followed by a turbulent one produces a realised annual volatility higher than the square-root scaling predicts.

Sharpe ratio

The Sharpe ratio is the workhorse risk-adjusted return measure:

\text{SR} = \frac{\mu - r_f}{\sigma}

where $\mu$ is annualised return, $r_f$ the risk-free rate, and $\sigma$ annualised volatility. A strategy returning 14% annually with 18% volatility against a 4% risk-free rate has $\text{SR} = (0.14 - 0.04)/0.18 \approx 0.56$ — a modest figure by institutional standards, where a Sharpe above 1.0 over a multi-year sample is considered strong.

Sharpe’s structural weakness is that it penalises upside and downside deviations identically. A strategy with frequent small losses and one enormous gain has the same volatility penalty as one with frequent small losses and one enormous loss — the ratio cannot distinguish “good” volatility from “bad” volatility. It is also undefined when volatility is zero, and unreliable on short samples: a Sharpe ratio computed on 40 daily observations carries a standard error large enough to make most reported values statistically indistinguishable from each other.

Sortino ratio: penalising the downside only

The Sortino ratio replaces total volatility with downside deviation — the standard deviation computed only over returns below a minimum acceptable return (commonly zero or the risk-free rate):

\text{Sortino} = \frac{\mu - r_f}{\sigma_d}, \qquad \sigma_d = \sqrt{\frac{1}{n}\sum_{r_i < \text{MAR}} (r_i - \text{MAR})^2}

Because $\sigma_d \le \sigma$ by construction, Sortino is always greater than or equal to Sharpe for the same strategy. This is a feature when the return distribution is asymmetric — a strategy with a long right tail of gains and a tight cluster of small losses looks better under Sortino than under Sharpe, which is arguably the fairer picture. It breaks down the same way Sharpe does on short samples, and the downside-deviation estimate itself becomes noisy when very few observations fall below the minimum acceptable return threshold.

Calmar ratio

The Calmar ratio divides annualised return by the absolute value of maximum drawdown:

\text{Calmar} = \frac{\mu}{|\text{Max Drawdown}|}

It answers a question neither Sharpe nor Sortino addresses directly: how much return did the strategy generate per unit of its worst realised loss? A strategy returning 15% annually with a 25% maximum drawdown has a Calmar ratio of 0.6. The metric’s weakness is that it depends on a single event — the worst drawdown in the sample — so it is highly sensitive to sample length and can be dominated by one historical episode that may or may not recur.

Information ratio, beta and alpha

The information ratio measures active return relative to a benchmark, scaled by the volatility of that active return (tracking error):

\text{IR} = \frac{\mu_p - \mu_b}{\sigma(\mu_p - \mu_b)}

An information ratio of 0.5 or higher, sustained over several years, is considered a meaningfully skilled result in active management — the bar is lower than Sharpe because tracking error is typically smaller than absolute volatility.

Beta measures a portfolio’s sensitivity to benchmark moves, estimated as $\beta = \text{Cov}(r_p, r_b)/\text{Var}(r_b)$ via linear regression. Alpha is the annualised return left over after beta exposure is accounted for — the intercept of that regression, annualised. A portfolio with $\beta = 1.2$ and a benchmark that returned 10% “explains” 12% of the portfolio’s return through market exposure alone; alpha is whatever the portfolio earned above or below that. Both estimates depend on the regression window: beta measured over one year and beta measured over five years on the same asset routinely differ by 0.2 or more, because sensitivity to the benchmark is not actually constant through time.

VaR and CVaR

Value at Risk states a loss threshold: the loss that will not be exceeded with a given probability over a given horizon. A one-day 95% VaR of $50,000 on a portfolio means a loss larger than $50,000 is expected on roughly 5% of trading days, not that it cannot happen. Four estimation methods are in common use — historical (empirical quantile of past returns), parametric (assumes a normal distribution), Cornish-Fisher (adjusts the normal quantile for observed skew and kurtosis), and Monte Carlo (simulates paths from a fitted model) — and they can disagree substantially on the same portfolio when returns are fat-tailed, because the parametric method in particular understates tail risk under a normal-distribution assumption.

Conditional VaR (also called expected shortfall) answers the question VaR leaves open: given that the loss exceeds the VaR threshold, how large is it on average? CVaR is a coherent risk measure — it satisfies subadditivity, meaning the CVaR of a combined portfolio never exceeds the sum of its parts’ CVaRs — a property VaR does not have. This is the primary reason CVaR has displaced VaR as the preferred tail-risk measure in institutional practice, even though VaR remains the more commonly quoted headline number.

Capture ratios

Upside and downside capture measure participation in benchmark moves separately: upside capture is the portfolio’s average return during benchmark-positive periods divided by the benchmark’s average return in those same periods, and downside capture is the analogous ratio during benchmark-negative periods. A portfolio with 90% upside capture and 60% downside capture participates less in benchmark declines than in benchmark advances — a favourable asymmetry that neither Sharpe nor beta reports directly, because both compress the full return distribution into a single number.

No single metric substitutes for the others: Sharpe and Sortino describe risk-adjusted return under different assumptions about which volatility matters, Calmar ties return to the worst realised outcome, information ratio isolates skill relative to a benchmark, VaR and CVaR describe the tail, and capture ratios describe asymmetry in participation. A portfolio allocation should be judged on several of these together, and the allocation methods that produce the weights being judged are covered in portfolio optimisation from first principles.

Key takeaways

Geometric annualisation reflects actual compounding; arithmetic annualisation overstates it whenever returns are volatile, and the gap widens with volatility.
Sharpe penalises upside and downside volatility identically, while Sortino penalises only downside deviation — the two can rank the same strategies differently when returns are asymmetric.
Calmar ratio ties return to the single worst drawdown in the sample, which makes it informative but highly sensitive to sample length.
VaR states a loss threshold and CVaR states the average loss beyond it; CVaR is coherent and VaR is not, which is why CVaR is the preferred tail-risk measure in institutional practice.
No individual metric is sufficient on its own — each rests on an assumption (normality, constant beta, a fixed minimum acceptable return) that fails in identifiable, specific circumstances.