Sortino Ratio: formula, calculation, and how it improves on the Sharpe
Sortino Ratio: formula, worked example, and comparison with the Sharpe Ratio. How measuring only downside risk gives a clearer picture of your portfolio's true risk.
Saturday, 21 March 2026
Two portfolios, same Sharpe: but they are not the same
Consider two funds with identical average annual returns of 8%. Their Sharpe Ratios are both 0.58. On paper, they look interchangeable. Then you look at the individual years.
The first alternates between years of +22% and -16%, with deep drawdowns that take months to recover. The second grows more steadily: less dramatic positive years, but contained losses when markets fall. Same average return, near-identical total volatility, same Sharpe. Yet the risk profiles are very different.
The issue lies in how the Sharpe Ratio measures volatility: it treats an upward swing and a downward swing as equally bad. For most investors, this symmetry makes little sense. Nobody complains about earning more than expected. Losses are what matter.
The Sortino Ratio was developed to address this limitation. It penalises only downside volatility: the kind that actually erodes capital and tests the investor’s resolve.
What is the Sortino Ratio
The Sortino Ratio measures excess return over a minimum acceptable return (MAR) divided by downside deviation: the volatility of returns that fall below the MAR.
The formula is:
$$S = \frac{R_p - MAR}{\sigma_d}$$
where:
- $R_p$ is the portfolio’s average return over the period
- $MAR$ is the minimum acceptable return (often the risk-free rate, or simply 0%)
- $\sigma_d$ is the downside deviation, calculated only on periods where return falls below the MAR
The downside deviation is computed as:
$$\sigma_d = \sqrt{\frac{1}{N} \sum_{t=1}^{N} \left[\min!\left(R_t - MAR,; 0\right)\right]^2}$$
In practice: for each observation period, take the difference between the return and the MAR, keep only the negative values (the years where return was below the threshold), square them, average, and take the square root. Periods with returns above the MAR contribute zero to the downside deviation.
Step-by-step calculation: a worked example
Suppose a portfolio produces the following annual returns over five years:
| Year | Return |
|---|---|
| 1 | +14% |
| 2 | +9% |
| 3 | -3% |
| 4 | +18% |
| 5 | +12% |
Step 1: average return
$$\bar{R} = \frac{14 + 9 + (-3) + 18 + 12}{5} = \frac{50}{5} = 10%$$
Step 2: choose the MAR
We use 2% as an approximate risk-free rate, consistent with short-term eurozone government bond yields.
Step 3: downside deviation
Only periods with returns below 2% contribute to the calculation:
| Year | Return | Below MAR? | Squared contribution |
|---|---|---|---|
| 1 | +14% | No | 0 |
| 2 | +9% | No | 0 |
| 3 | -3% | Yes: -3% - 2% = -5% | $(-5)^2 = 25$ |
| 4 | +18% | No | 0 |
| 5 | +12% | No | 0 |
$$\sigma_d = \sqrt{\frac{0 + 0 + 25 + 0 + 0}{5}} = \sqrt{5} \approx 2.24%$$
Step 4: Sortino Ratio
$$S = \frac{10% - 2%}{2.24%} = \frac{8%}{2.24%} \approx 3.57$$
A value of 3.57 indicates a very high risk-adjusted return relative to downside risk. The reason is clear: over five years, only one produced a negative return, and the loss was contained at -3%.
How to interpret the Sortino Ratio
There is no universal threshold, but these practical benchmarks are widely used:
| Value | Interpretation |
|---|---|
| Below 1 | Poor: returns do not adequately compensate for downside risk |
| 1 to 2 | Acceptable: in line with a well-diversified balanced portfolio |
| Above 2 | Good: strong return per unit of downside risk |
| Above 3 | Excellent: rarely sustained over long periods |
A Sortino below 1 means the portfolio is not generating enough return to justify the losses it produces in down periods. Between 1 and 2, you are in the territory of a correctly constructed balanced portfolio. Above 2, the risk-return combination is genuinely favourable from a downside perspective.
As with all metrics calculated on historical data, past Sortino Ratio values do not guarantee future performance.
Sortino vs Sharpe: a practical comparison
Returning to the two funds described at the start. Here are their figures over a ten-year horizon (illustrative values designed to demonstrate the concept):
| Metric | Fund Alpha | Fund Beta |
|---|---|---|
| Average annual return | 8% | 8% |
| Total volatility ($\sigma$) | 10.4% | 10.3% |
| Sharpe Ratio (MAR = 2%) | 0.57 | 0.58 |
| Years below 2% return | 4 (small losses) | 2 (deep losses) |
| Downside deviation ($\sigma_d$) | 4.1% | 5.8% |
| Sortino Ratio (MAR = 2%) | 1.46 | 1.03 |
The Sharpe Ratios are almost identical: 0.57 versus 0.58. An investor relying on Sharpe alone would conclude the two funds are equivalent.
The Sortino tells a different story. Fund Beta, despite having fewer negative years in absolute terms, concentrates its losses in much deeper drawdowns. Its downside deviation is 5.8% against Fund Alpha’s 4.1%. The result: Beta’s Sortino is 1.03 versus Alpha’s 1.46.
The difference does not show up in the Sharpe because total volatility is nearly identical: Beta offsets its deep losses with exceptionally strong positive years. But those strong positive years do not create problems for the investor. Deep losses do, and they can trigger selling at the wrong moment, disrupt a regular savings plan, or simply cause stress that leads to poor decisions.
When to use Sortino instead of Sharpe
The Sharpe Ratio remains useful for quick comparisons between portfolios with similar volatility profiles. The Sortino becomes the better tool in these cases:
Portfolios in the drawdown (decumulation) phase. Investors spending down their capital are far more exposed to bad early returns than those still accumulating. A very negative year early in retirement can dramatically shorten how long a portfolio lasts. The Sortino measures exactly the risk that matters most in this phase.
Comparing strategies with asymmetric return profiles. Options-based strategies, structured products, and alternative assets often produce very skewed return distributions. The Sharpe cannot capture this asymmetry; the Sortino at least measures it on the downside dimension.
Capital-preservation and low-volatility portfolios. Investors focused on protecting capital want to know how often and how severely the portfolio falls below an acceptable threshold, not how much it swings in both directions.
Evaluating funds with historically deep drawdowns. A fund manager with a high Sharpe but repeated deep loss episodes over time can have a much lower Sortino, revealing real risk that the better-known metric conceals.
The Sortino Ratio in Wallible
Wallible calculates the Sortino Ratio directly in the portfolio risk metrics panel, alongside the Sharpe Ratio, Calmar Ratio, maximum drawdown, and VaR. You can compare the Sortino Ratio across different portfolio configurations in the backtesting tool, using real historical data, to see which allocation produced the best downside-adjusted return over defined periods.
Try building two portfolios with the same average allocation but different components: often the Sortino surfaces differences that the Sharpe leaves invisible.
Analyse your portfolio’s Sortino Ratio on Wallible
Frequently asked questions
Is the Sortino Ratio better than the Sharpe Ratio?
Not in absolute terms: they are complementary metrics. The Sharpe is more widely used and enables quick comparisons against established benchmarks. The Sortino adds precision when you want to evaluate downside risk specifically, which is the primary concern for most investors. Reading both together gives the clearest picture.
What MAR should I use for the Sortino Ratio?
The most common choice is the risk-free rate (short-term government bond yield), representing the return available with no risk. Some investors use 0%, treating any loss as unacceptable, or expected inflation as the minimum real return threshold. The choice of MAR changes the Sortino value, so using the same reference when comparing different portfolios is essential.
What is downside deviation?
Downside deviation measures the volatility of returns that fall below the MAR only. Unlike standard deviation, it completely ignores positive periods: a year of +30% contributes nothing to the calculation. This makes it more representative of the risk investors actually experience, because concerns centre on losses, not gains.
Can the Sortino Ratio be negative?
Yes. A negative Sortino occurs when the portfolio’s average return is below the MAR, even accounting for volatility. It means the portfolio failed to reach the minimum return threshold over the period measured. For a fund, a negative Sortino is a significant warning sign.
How do Sharpe and Sortino compare for pure equity portfolios?
For a purely equity portfolio with roughly symmetrical return distributions, Sharpe and Sortino tend to tell similar stories. The divergence becomes meaningful when the portfolio includes assets with asymmetric returns: high-yield bonds, momentum strategies, commodities, or structured products. In those cases, the Sortino captures a dimension of risk that the Sharpe ignores.
Next steps
- Analyse your portfolio’s Sharpe, Sortino, and Calmar Ratios in the Wallible app
- Compare downside risk metrics with maximum drawdown and the Calmar Ratio
- Explore tail risk further with VaR and CVaR and Expected Shortfall
- Understand return distribution characteristics with skewness and kurtosis
- See how Monte Carlo simulation complements downside risk metrics in the Monte Carlo guide
