A condition that entails that diversification, on which modern portfolio theory (MPT) is premised, will normally hold since a subadditive metric (risk metric in this context) would consistently generate a lower risk reading for a diversified portfolio than a non-diversified portfolio. According to the principle of subadditivity, the risk of a portfolio is always lower than or equal to the sum of the risks of its components.
In the context of internal risk management, subadditivity also implies that the aggregate risk of a financial institution is equal to or less than the sum of the risks of individual departments/ units/ sections of the institution.
Subadditive risk measures include volatility (standard deviation), expected shortfall, etc.
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