Sortino ratio: what downside deviation measures and misses

The Sortino ratio is a volatility-adjusted measure: average return above a target divided by downside deviation, so only returns below the target enter the denominator. Large gains do not lower the score, as they do with the Sharpe ratio. That makes it a useful second reading for skewed returns, but it captures less of the cost that volatility imposes on compounded wealth. Like Sharpe, it does not measure risk in the sense of permanent loss or a catastrophic fall; drawdowns and recovery describe that better.

Our articles comparing investor portfolios with MSCI World report it next to the Sharpe ratio. Here we define it, test it on seven histories and measure how much the definition matters.

Key takeaways

• Sortino divides average excess return by downside deviation; returns above the target do not enter the denominator.
• In seven fund and model histories against MSCI World, Sortino was 1.43 to 1.66 times Sharpe and changed no fund-versus-index ranking.
• Definitions vary: target, averaging and sampling moved one fund's figure from 0.89 to 2.45 over broadly the same period.
• Compounded growth is reduced by swings in both directions, so read Sortino alongside Sharpe, CAGR and drawdowns.

The formula

For monthly returns r and a target T for each month, here the same-currency cash return:

Downside deviation = sqrt[sum of min(r − T, 0)² ÷ n]

Sortino ratio = mean(r − T) ÷ downside deviation × sqrt(12)

Every month counts in n, but months at or above the target add zero to the sum. The numerator is Sharpe's; only the denominator differs, as Sharpe uses the standard deviation of all excess returns.

Same Sharpe, different Sortino

Take two hypothetical 12-month paths with a 0% target, so returns equal excess returns:

• A: +4% in eight months, −5% in four.
• B: −2% in eight months, +7% in four.

B is A reflected around their shared 1% monthly mean, so both have a 4.431% monthly standard deviation and an annualised Sharpe ratio of 0.782.

A's four −5% months give a downside deviation of sqrt(4 × 0.05² ÷ 12) = 2.887% and a Sortino ratio of 1.200. B's eight −2% months give sqrt(8 × 0.02² ÷ 12) = 1.633% and 2.121. A has frequent small gains and rare large losses (skewness −0.81); B has the reverse (+0.81).

Yet £10,000 becomes £11,147 along A and £11,152 along B. A 77% higher Sortino ratio comes with about £5 more wealth, because both paths have the same mean and variance. These are teaching sequences, not forecasts.

Seven histories: Sortino tracks Sharpe

We applied the formula to monthly total returns for seven fund and model series and MSCI World Net in the same currency, with Treasury bills (USD) or SONIA (GBP) as cash. Skew is of the series' monthly excess returns.

Across the eleven distinct fund and index calculations, Sortino is 1.43 to 1.66 times Sharpe, and no fund-versus-index order changes.

That multiple is mostly arithmetic, not evidence of downside protection. If monthly excess returns were normally distributed with these means and volatilities, Sortino would be 1.57 to 1.80 times Sharpe. Every calculation except ARKK comes in below its normal-distribution multiple, consistent with negative skew: losses arrived in fewer, larger months.

ARKK is the case Sortino is designed for. Its skew is +0.23, against −0.35 for MSCI World over the same months, with 13 months of +15% or more against 5 of −15% or worse. Its multiple, 1.66, is above its normal-distribution value of 1.59, and Sortino narrows the gap: ARKK's Sharpe ratio is 74% of MSCI World's, its Sortino ratio 79%.

It still trails at 0.81 against 1.02: its average excess return was 1.8 times the index's, but its downside deviation of 21.7% a year was 2.3 times the index's 9.4%.

Definitions change the number

There is no single standard Sortino ratio. The target can be zero, cash or a chosen minimum acceptable return, and squared shortfalls can be averaged over all months or only those below the target. Holding Fundsmith's 152 months (I Acc, GBP) fixed:

The annual version rests on eleven observations, only two of them below cash for each series.

Fundsmith's January 2026 annual letter publishes an FE Analytics Sortino ratio of 0.75 for the fund against 0.48 for MSCI World, from launch to 31 December 2025 with a 3.5% risk-free rate. Rebuilding that window from the factsheet's monthly T Acc returns, rounded to 0.1 point, our method gives 1.46 against 1.22.

With window and rate matched, our figures are about two to two and a half times FE's (1.94 and 2.54 times), so the level gap comes mainly from FE's calculation, whose frequency and downside definition the letter does not state. The ranking reversal comes from the window: from launch to September 2026 with SONIA, the figures are 1.64 against 1.61.

Our February 2014 start omits the fund's first 39 months, when it gained 56.6% against 36.4%, and within our window the fund scores 3.11 against 2.00 to December 2021, then −0.19 against 1.06. A Sortino ratio is comparable only with one calculated on the same window, target and method.

Compounding counts swings in both directions

Compounded growth depends on the log of each monthly wealth factor, and log(1 + r) is approximately r − r²/2. The squared term penalises a large gain as well as a large loss, so the drag on geometric growth comes from total variance.

ARKK's annualised arithmetic mean was 19.60%, against annual log growth of 13.18%, or a 14.08% CAGR. Half its total variance, 6.50 points, approximates that 6.42-point gap. Half its squared downside deviation is only 2.36 points; up months supplied 65% of its squared monthly returns. A ratio that ignores upside swings therefore misses most of the compounding cost in this history.

Read Sortino with the Sharpe ratio, CAGR and maximum drawdown from the same data. For any quoted figure, check its target, frequency, denominator and window, including the cash rate and annualisation.