El desarrollo local en los Andes ecuatorianos

This section briefly defines the systemic risk measures (SRMs) implemented in this paper and elaborates on their econometric implementation.

2.3.1 Marginal Expected Shortfall

The Marginal Expected Shortfall (MES) proposed by Acharya et al. (2010) measures the

expected return (loss) of banki’s stock given that the banking system’s overall return is in its tail. More intuitively, the MES can be interpreted as the ”participation rate” of bank i within a financial crisis. Following Acharya et al. (2010), Brownlees and Engle (2015) introduce a time-dependent dynamic extension of the MES that is defined as bank

4

After its IPO in July 2011, Bankia S.A. requested a bailout ofe_{19bn in May 2012 and was partially}

nationalized by the Spanish government. As a consequence, the bank reported on average a negative balance for its book value of equity over the sample period.

2 Systemic risk measures and their viability for banking supervision 13

i’s expected cumulative h-day stock return – i.e., over time interval [t, t+h] – with the condition that the banking system’s cumulativeh-day return is falling below a predefined threshold C, indicating distress in the banking system:

MESi,ht (C) = −E Ri;[t,t+h] Rsys_;[t,t+h]≤C , (2.1)

with Ri;[t,t+h] denoting bank i’s cumulative stock return over h days:

Ri;[t,t+h] = exp h X τ=1 ri,t+τ ! −1. (2.2)

ri,t represents the one-day returns of bank i’s stock. The h-day banking system return

Rsys;[t,t+h] is defined analogously. Note that for the ease of interpretation, we switch the

sign for the risk measure. Thus, an increase in the measure indicates an increase in the level of systemic risk.

2.3.2 SRISK

Based on the MES, Acharya et al. (2012) directly model a bank’s expected undercapital- ization during a financial crisis. The proposed systemic risk measure, SRISK, therefore incorporates financial market data as well as balance sheet data. A bank’s capital shortfall or its undercapitalization, respectively, is defined as the amount of capital that a bank would have to raise during a financial crisis in order to prevent bankruptcy. Hence, a bank’s expected time-varying capital shortfall over the time interval [t, t+h] given the event of a financial crisis or severe distress in the banking system is calculated as follows:

SRISKi,h_t (C, k) = E

capital shortfall_i;[t,t+h] crisis

. (2.3a)

Applying the going concern loss absorbing capacity concept, Equation (2.3a) can be re- arranged:

SRISKi,h_t (C, k) = Eh{k_×(debt + equity)₋equity_}i;[t,t+h] crisis

i

, (2.3b)

In order to prevent bankruptcy, institution i’s equity cushion needs to be larger than a fractionk of the (market valued) total assets. Within the Basel III framework, parameter

kcan be considered to represent the absolute Tier I capital ratio of 3%, which is consistent with the Basel III maximum Leverage Ratio of 33.3 that must be satisfied even during a crisis. In that case,k can be interpreted as a Basel Capital Adequacy Ratio equivalent on

market valued total assets instead of risk-weighted assets. The market value of total assets is determined using current debt balance sheet data – assuming that the levels of debt remain relatively constant over the observed time interval [t, t+h] – and the market value of equity. The market value of equity within a future financial crisis can be expressed as a function of MES:

SRISKi,h_t (C, k) = k_×debti,t −(1−k)

1₋MESi,h_t (C)_×equity_i,t. (2.3c) The higher a bank’s SRISK, the higher its capital shortfall during a crisis period. A negative SRISK indicates that a bank’s equity cushion is sufficiently large in order to avoid bankruptcy.

2.3.3 Conditional Value at Risk

The bottom-up measure Conditional Value at Risk (CoVaR) proposed by Adrian and Brunnermeier (2016) explicitly allows the calculation of a bank’s contribution to systemic risk in the banking system measuring the value at risk return of the banking system conditional on institutioni being in severe financial distress. In analogy to the MES and SRISK measures we define a multi-period CoVaR measure that is in line with the CoVaR extension of Girardi and Erg¨un (2013). The ”distress CoVaR” CoVaRsyst |i≤VaR,h is defined

as the banking system’s h-day value at risk return, conditional on bank i’s h-day stock return being at orbelow banki’s h-day value at risk:

PRsys;[t,t+h]≤CoVaRtsys|i≤VaR,h (q)

Ri;[t,t+h]≤VaR i,h t,q =q, (2.4a)

with VaRi,ht,q denoting bank i’s h-day value at risk return. Parameter q indicates the

confidence level.5 _{The median state CoVaR is given by conditioning on the one standard}

deviation band around institution i’s median h-day return: PRsys;[t,t+h] ≤CoVaRsyst |i=median,h(q)

Ri_;[t,t+h]−ν_i,th ≤σh_i,t =q, (2.4b) 5

Whereas Adrian and Brunnermeier (2016) estimate CoVaR using a quantile regression approach, we employ a bivariate conditionally heteroskedastic model to account for the time-varying dependence structure between banks and the banking system, which enables the measure to better capture the tail events of distress (Girardi and Erg¨un, 2013). Furthermore, we are able to evaluate all three SRMs within a common statistical setup that improves the comparability and interpretability of our key results.

2 Systemic risk measures and their viability for banking supervision 15 whereσh

i,t andνi,th indicate the standard deviation and the median return of institutioni’s h-day cumulative stock return. Thus, institution i’s marginal systemic risk contribution to overall systemic risk in the banking system is defined as the difference between the system’s CoVaR conditional on bankibeing in financial distress and the system’s CoVaR conditional on banki being in its median state:

∆CoVaRi,ht (q) = −

h

CoVaRsyst |i≤VaR,h (q)−CoVaR

sys|i=median,h

t (q)

i