Marginal Expected Shortfall (MES)¶
Marginal Expected Shortfall (MES).
The firm's average return during the 5% worst days for the market.
MES measures how exposed a firm is to aggregate tail shocks and, interestingly, together with leverage, it has a significant explanatory power for which firms contribute to a potential crisis as noted by Acharya, Pedersen, Philippon, and Richardson (2010).
It is used to construct the Systemic Expected Shortfall.
firm_returns(np.ndarray) — (n_days,) array of the returns (equity or CDS) for the firm.
market_returns(np.ndarray) — (n_days,) array of the returns (equity or CDS) for the market as a whole.
q(float, optional) — The percentile. Range is [0, 1]. Deaults to 0.05.
The marginal expected shortfall of firm i at time t.
>>> from numpy.random import RandomState >>> from frds.measures import marginal_expected_shortfall
Let's simulate some returns for the firm and the market
>>> rng = RandomState(0) >>> firm_returns = rng.normal(0,1,100) >>> mkt_returns = rng.normal(0,1,100)
Compute the MES.
>>> marginal_expected_shortfall(firm_returns, mkt_returns) 0.13494025343324562
- Acharya, Pedersen, Philippon, and Richardson (2017), Measuring systemic risk, The Review of Financial Studies, 30, (1), 2-47.
- Bisias, Flood, Lo, and Valavanis (2012), A survey of systemic risk analytics, Annual Review of Financial Economics, 4, 255-296.