Backtest a Value at Risk model against realized returns.

A Value at Risk estimate is only useful if it is actually well-calibrated against reality. This method builds a rolling, out-of-sample VaR path (each VaR estimate uses only the window_size returns preceding it, never the return it is compared against) and tests it with Kupiec’s Proportion of Failures test (is the overall breach rate consistent with alpha?) and/or Christoffersen’s independence test (are breaches spread out over time, or do they cluster together?).

For more information about the methods, see the following papers:

  • Kupiec, P.H. (1995). “Techniques for Verifying the Accuracy of Risk Measurement Models.” The Journal of Derivatives, 3(2), 73-84.
  • Christoffersen, P.F. (1998). “Evaluating Interval Forecasts.” International Economic Review, 39(4), 841-862.

Also known as: VaR validation, VaR backtest, POF test.

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Calculate the Value at Risk Backtest in Python

The Value at Risk Backtest is available in the Risk module of the open-source Finance Toolkit. Install it with:

pip install financetoolkit -U

Then call get_var_backtest as shown below.

from financetoolkit import Toolkit

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

toolkit.risk.get_var_backtest(window_size=252)

Which returns:

  AMZN TSLA Benchmark
Kupiec Statistic 0.0817 1.6459 0.0018
P-Value 0.7749 0.1995 0.9662
Christoffersen Statistic 0.0631 0.4302 1.0847
P-Value 0.8017 0.512 0.2977

Parameters

get_var_backtest accepts the following parameters:

  • period (str, optional): The data frequency for returns (daily, weekly, quarterly, or yearly). Defaults to “daily”, since window_size is expressed in return observations of this frequency (252 only means “about one year” when period is daily).
  • distribution (str, optional): The distribution to use for the rolling VaR estimates, one of “historic”, “gaussian”, “studentt” or “evt”. Defaults to “historic”.
  • alpha (float, optional): The confidence level for the VaR estimates (e.g., 0.05 for 95% confidence). Defaults to 0.05.
  • window_size (int, optional): The rolling window size (in number of return observations) used to estimate each VaR value. Defaults to 252 (approximately one trading year of daily returns).
  • test (str, optional): Which test(s) to run, one of “kupiec”, “christoffersen” or “both”. Defaults to “both”.
  • rounding (int | None, optional): The number of decimals to round the results to. Defaults to None.
EWMA Volatility Autocorrelation (ACF) Hurst Exponent Marginal Value at Risk (mVaR) Component Value at Risk (cVaR) CoVaR Acerbi-Szekely Test GARCH Parameters GJR-GARCH Volatility Model GJR-GARCH Volatility Forecast GJR-GARCH Parameters EGARCH Volatility Model

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

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