September 18, 2020
SRISKv2 – A Note –
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Marco Migueis and Alexander Jiron
SRISK, introduced in Brownlees and Engle (2016), is one of the most influential systemic importance metrics for financial firms with over 500 citations according to Google Scholar as of this manuscript completion. However, the definition of capital shortfall employed in the calculation of SRISK is conceptually flawed. This note proposes a simple modification to the SRISK calculation that improves the logic of its definition and its usefulness as a systemic importance metric.
SRISK measures the systemic vulnerability of a financial firm as its expected capital shortfall conditional on a large market downturn. Brownlees and Engle (2016) define capital shortfall (CS) as the required capital given a firm’s assets minus the firm’s market equity. Specifically, the CS of a firm is defined as
where k is a prudential capital factor, Ai,T are the quasi assets of firm i at period T,2 and Wi,T is the market value of equity of firm i at period T.
The prudential capital factor is assumed to equal 8%. Building upon this definition of capital shortfall, SRISK is defined as
where h is the horizon over which SRISK is measured, Rm,T:T+h is market return between T and T+h, and C is the threshold level of the market return below which expect capital shortfall is measured.
The plain meaning of “capital shortfall” is the amount of capital by which a firm falls short of meeting a required level of capital. In the definition used in SRISK, a firm’s capital shortfall is positive when required capital is larger than its market equity and negative when required capital is smaller than its market equity. By the plain meaning of “capital shortfall,” when required capital is smaller than market equity there is no shortfall. Thus, a proper definition of capital shortfall is as follows:
Brownlees and Engle (2016) definition of capital shortfall weakens SRISK as a systemic importance metric. The negative portion of the “shortfall” domain lowers conditional expected shortfall and in some cases causes it to be negative. If SRISK aims to estimate the expected amount that the government would have to provide to support a systemically important firm upon a severe market shock – as it is argued in Brownlees and Engle (2016) – a reduction of expected shortfall due states of the world where shortfall is negative is only sensible if governments were to tax these negative shortfall amounts from firms. That is not a real world policy in any country, nor do the authors of SRISK advocate for such policy. Therefore, states of the world where a firm does not fall into shortfall upon a severe market shock do not offset the states of the world where a firm falls into shortfall. The authors minimize the incongruity of negative “expected shortfalls” by flooring SRISK at zero, but this does not change that SRISK is generally downward biased relative to a conditional expected shortfall measure based on a proper definition of capital shortfall.
Migueis, Marco, and Alexander Jiron (2020). ‘SRISKv2 – A Word,’ FEDS Notes. Washington: Board of Governors of the Federal Reserve System, September 18, 2020, https://doi.org/10.17016/2380-7172.2724.
Board of Governors of the Federal Reserve System revealed this content material on 18 September 2020 and is solely accountable for the data contained therein. Distributed by Public, unedited and unaltered, on 20 September 2020 19:09:03 UTC