Mulakan

Analysis: Sortino ratio

Definition:

The Sortino Ratio is a modification of the Sharpe Ratio developed by Frank Sortino. Unlike the Sharpe Ratio, it ignores positive volatility, focusing only on drawdowns that are dangerous for the investor.

Interpretation:

It shows how well the return compensates for risk. The final value directly indicates how many percent of return corresponds to 1% of downside deviation.

The generally accepted target value of the indicator is ≥ 2, but the ratio with the benchmark and the market situation should always be taken into account.

Example:

Portfolio:

  • Risk Free Rate (RFR) = 2%
  • 2025-01-01 deposit of 1000
  • 2025-03-03 purchase of NASDAQ:AAPL (qty:1, price: 190, commission: 0)
  • 2025-04-11 Sortino Ratio calculation date. Last price of AAPL = 198.15

Sortino ratio portfolio 0.047%:

  • Downside risk is poorly compensated by return
  • Each percent of accepted downside deviation brought only 0.047% of excess return

Sortino ratio benchmark -0.817%:

  • For each unit percent of downside deviation, the portfolio lost 0.817% of return relative to the risk-free rate

Note: The short-term nature of the observed period, taken for simplification of the calculation, should be considered.

Calculation:

Sortino Ratio = (Rp − RFR) / DD

  • Rp (Return of portfolio) — portfolio performance in percent, calculated monthly for the period using the TWR method

  • RFR (Risk Free Rate) — taken from the portfolio settings. Since the annual rate is set in the settings, it must be converted to the rate for the period before calculation

  • DD (Downside Deviation) — standard deviation among the negative values of performance for the period

Example of Sortino Ratio calculation from interpretation:

  1. Monthly RFR calculation:
     2 / 12 = 0.167%
  2. Rp calculation:
     Performance by periods:
    1. January: 0
    2. February: 0
    3. March: 3.2% (obtained: pv on March 31 → ((1032.13 − 1000) / 1000) * 100 )
    4. April: −2.3% (obtained: ((1008.15 − 1032.13) / 1032.13) * 100 )

Rp = (0 + 0 + 3.2 − 2.3) / 4 = 0.225

  1. DD calculation:
    1. January: min(0, 0 − 0.167)² = 0.0279
    2. February: min(0, 0 − 0.167)² = 0.0279
    3. March: min(0, 3.2 − 0.167)² = 0
    4. April: min(0, −2.3 − 0.167)² = 6.1009

DD = ((0.0279 + 0.0279 + 0 + 6.1009) / 4)^(1/2) = 1.24%

  1. Sortino Ratio calculation:
    SR = (Rp − RFR) / DD = (0.225% − 0.167%) / 1.24% ≈ 0.047%

Reference in Pine:

//@version=6
indicator("Sortino ratio example")
method downsideDeviation(array<float> returns, series float targetReturn) =>
    float sum = 0.0
    for r in returns
        if r >= targetReturn
            continue
        sum += math.pow(r - targetReturn, 2)
    sum /= returns.size()
    float result = math.sqrt(sum)

method sortinoRatio(array<float> returnsArray, series float annualBenchmark) =>
    var int numberOfperiods = 12
    if barstate.islast
        float fixedPeriodReturn = annualBenchmark / numberOfperiods
        float downsideDev       = returnsArray.downsideDeviation(fixedPeriodReturn)
        float avgReturn         = returnsArray.avg()
        float result            = (avgReturn - fixedPeriodReturn) / downsideDev

array<float> arr = array.from(0, 0, 3.2, -2.3)
float sortino = sortinoRatio(arr, 2)
plot(sortino, precision = 3)

Note:

If all transactions were made in the current month relative to the indicator's calculation date, the indicator will not be calculated, since there is not a single completed calendar month.

Links:

Analysis: Sharpe ratio
Analysis: Holdings performance