Calculate the Downside Deviation of an investment portfolio or asset’s returns.

The Downside Deviation, also known as semi-deviation, is the standard deviation of only the returns that fall below a minimum acceptable return (MAR), isolating the volatility of negative outcomes from the volatility of the overall return distribution. It underlies risk-adjusted return measures such as the Sortino Ratio and the Omega Ratio.

Also known as: semi-deviation, downside risk, downside volatility.

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Calculate the Downside Deviation in Python

The Downside Deviation is available in the Risk module of the open-source Finance Toolkit. Install it with:

pip install financetoolkit -U

Then call get_downside_deviation as shown below.

from financetoolkit import Toolkit

toolkit = Toolkit(["AMZN", "TSLA"], api_key="FINANCIAL_MODELING_PREP_KEY")

toolkit.risk.get_downside_deviation()

Which returns:

  AMZN TSLA Benchmark
2021 0.0106 0.0215 0.0058
2022 0.0202 0.0283 0.0095
2023 0.0129 0.0217 0.005
2024 0.0118 0.0227 0.006
2025 0.0146 0.0257 0.0096
2026 0.0123 0.0165 0.0061

Parameters

get_downside_deviation accepts the following parameters:

  • period (str, optional): The data frequency for returns (daily, weekly, monthly, quarterly, or yearly). Defaults to “quarterly” if the Toolkit is initialised with quarterly=True, otherwise “yearly”.
  • minimum_acceptable_return (float, optional): The minimum acceptable return (MAR) used as the threshold below which returns are considered downside. Defaults to 0.0.
  • within_period (bool, optional): Whether to calculate the Downside Deviation within the specified period or for the entire period. Thus whether to look at the Downside Deviation within a specific year (if period = ‘yearly’) or look at the entirety of all years. Defaults to True.
  • rolling (int, optional): The rolling window size to use for the calculation. If set, the Downside Deviation is calculated over a rolling window of this many periods across the full return history instead of per period. Defaults to None.
  • rounding (int | None, optional): The number of decimals to round the results to. Defaults to 4.
  • growth (bool, optional): Whether to calculate the growth of the Downside Deviation values over time. Defaults to False.
  • lag (int | list[int], optional): The lag to use for the growth calculation. Defaults to 1.
  • standardize (bool, optional): Whether to standardize (Z-Score) the result. When combined with growth=True, standardizes the growth values instead of the raw values. Defaults to False.
Ulcer Index (UI) GARCH Volatility Model GARCH Volatility Forecast Variance Volatility Excess Volatility Skewness Kurtosis Mean Absolute Deviation (MAD) Coefficient of Variation (CV) EWMA Volatility Autocorrelation (ACF)

The Risk module page introduces the module, and the sidebar lists all of its functions.

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