Marginal Expected Shortfall¶

Introduction¶

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 (2017).

It is used to construct the Systemic Expected Shortfall.

References¶

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.

API¶

class frds.measures.MarginalExpectedShortfall(firm_returns: ndarray, market_returns: ndarray)[source]¶

Marginal Expected Shortfall

__init__(firm_returns: ndarray, market_returns: ndarray) → None[source]¶

Parameters:

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.

estimate(q: float = 0.05) → float[source]¶

estiamte

Parameters:: q (float, optional) – The percentile. Range is [0, 1]. Deaults to 0.05.
Returns:: The marginal expected shortfall of firm \(i\) at time \(t\).
Return type:: float

Examples¶

>>> from numpy.random import RandomState
>>> from frds.measures import MarginalExpectedShortfall

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.

>>> mes = MarginalExpectedShortfall(firm_returns, mkt_returns)
>>> mes.estimate()
0.13494025343324562