adjusted_value_at_risk_score#

pymc_marketing.mmm.utility.adjusted_value_at_risk_score(confidence_level=0.95, risk_aversion=0.8)[source]#

Calculate adjusted Value at Risk (AVaR) score.

The adjusted Value at Risk (AVaR) score is a risk-adjusted metric that combines the mean and Value at Risk (VaR) based on a risk aversion parameter. It provides a single metric that accounts for both return and risk preferences.

The score is calculated as:

\[AVaR\ Score = (1 - \alpha) \cdot \mu + \alpha \cdot VaR\]

where:

\(\mu\) is the mean of the sample returns.
\(VaR\) is the Value at Risk at the specified confidence level.
\(\alpha\) is the risk aversion parameter.

Parameters:

confidence_levelfloat, optional: Confidence level for VaR (e.g., 0.95 for 95% VaR). Confidence level must be between 0 and 1.
risk_aversionfloat, optional: Risk aversion parameter (0 = low risk aversion, 1 = high risk aversion).

Returns:

UtilityFunctionType: A function that calculates the adjusted Value at Risk score given samples and budgets.

Raises:

ValueError: If the risk aversion parameter is not between 0 and 1. If confidence_level is not between 0 and 1.