CONFIDENCE-BASED MEASURE OF BANK SOLVENCY

Transcription

1 CONFIDENCE-BASED MEASURE OF BANK SOLVENCY Davide Mare University of Edinburgh, UK Fernando Moreira University of Edinburgh, UK Roberto Rossi University of Edinburgh, UK 1-Day Conference Credit Risk Models - December 15 th 2014

2 2/17 Motivation he measurement of financial stability in banking aims at assessing the degree of institution solvency In this exercise, it is paramount to explicitly account for the degree of uncertainty in the estimations Existing accounting-based indicators do not include estimation error in the evaluation of banks financial health/soundness

3 Risk Measures 15/12/ Day Conference Credit Risk Models 3/17 Existing measures Volatility of stock prices Distance to default CDS Spread Credit ratings Z-Score Marginal expected shortfall Equity beta Equity return volatility Asset return volatility ail risk Miscellaneous risk measures Source of information Market Accounting based based We focus on the Z-Score as it is the most used accounting based measure for non-listed institutions to assess the overall risk of bank solvency

4 Existing measures Z-Score exploits the following accounting information Return on assets (ROA) After-tax profits divided by total assets Capital to asset ratio (CAR) otal equity divided by total assets After-tax profits are assumed to be random Capital and total assets are given he Z-Score is defined, under mild assumptions, as the number of the standard deviations of the return on assets necessary to wipe out equity capital (Boyd and Graham, 1986) 15/12/ Day Conference Credit Risk Models 4/17

5 5/17 Existing measures Z-Score exploits the following accounting information Return on assets (ROA) After-tax profits divided by total assets Capital to asset ratio (CAR) otal equity divided by total assets Lower Z-Score indicates higher probability of insolvency Z CAR ( ROA) ( ROA)

6 6/17 Existing methods A variety of options to compute the Z-Score has been surveyed in Lepetit and Strobel (2013) k CAR, k Boyd et al. (2006) Z1 Yeyati and Micco (2007) Hesse and Cihák (2007) Boyd et al., 2006 Lepetit and Strobel (2013) Z Z2 k k CAR k ROA CAR 3 t ROA CAR Z4 ROA Z5 k={-2,-1, } n=3 t t t CAR t={1.} =last period

7 7/17 Existing methods - Limitations Z3 considers the current ROA and the standard deviation over the whole horizon therefore it is not clear which is the random variable Z4 sigma instantaneous is a non-standard measure of variability and therefore we cannot use it in a probabilistic analysis, i.e. it is not clear the link with the probability of default

8 8/17 Existing methods - Limitations Z5 does not reflect the fact that the magnitude of returns can be associated with higher variance (heteroscedasticity)

9 9/17 Motivating example Example I Data: σ ROA =standard deviation of ROA over the sample period μ ROA =mean of ROA over the sample period CV=Coefficient of variation / t t t={1.} =last period ime series Random Variables ROA 1 ROA 2 ROA ( ) ( ) Z-Score 1 2 Z5 Z6 ROA ROA CV

10 10/17 Existing methods - Limitations No existing methods reflects the degree of estimation error associated with the available data

11 11/17 Motivating example Example II ROA Bank S S S S S S S S ROA Bank 2 Mean (ROA) St. Dev. α LO Bound Average UP Bound Bank Bank

12 12/17 Contribution t={1.} =last period o address the limitation illustrated in the example I, we introduce a new method (Z6) based on the coefficient of variation of the ROA Z6 CV CAR o address the limitation illustrated in the example II, we complement existing methods (Z1, Z2, Z5) and Z6 by building confidence intervals around mean (ROA) and the standard deviation (ROA) to reflect the degree of estimation error

13 13/17 Motivating example Example III t={1.} =last period Lower Z-Score indicates higher probability of insolvency ROA 2005 S S S S S S S S S Bank1 μ(roa) σ(roa) CV Z3-2008S2 Z5-2008S2 Z6-2008S CAR

14 Contribution t={1.} =last period o address the limitation illustrated in the example II, we complement existing methods (Z1, Z2, Z5) and Z6 by building confidence intervals around mean (ROA) and the standard deviation (ROA) to reflect the degree of estimation error 1 1 tn 1, /2 s, tn 1,1 /2 s L, U n n ( n 1) s ( n 1) s 2 2,, 2 2 L U n 1,1 /2 n1, /2 CB CAR Z5, CAR t, L t, U t, U t, L 15/12/ Day Conference Credit Risk Models 14/17

15 15/17 Preliminary results (I) We classify the observations into the deciles of the distributions of the confidence based Z5 and Z6 and the non-confidence based indicators In principle, being equal the measurement error for all banks, we should obtain the same classification Difference in deciles base method vs confidence based Diff Z ,134 2,050 6,574 61,476 Z ,549 72,228 Difference in deciles base method vs confidence based Diff Z ,130 Z ,283 7,349

16 16/17 Preliminary results (II) For each Z-score, when confidence intervals overlap, we can t distinguish banks in terms of their risk So, the smaller the number of overlaps the better (i.e. risk rankings are more conclusive) Year Average number of overlaps (per institution) # of institutions Z1 Z2 Z5 Z Global average In any year, Z6 has the smallest number of overlaps

17 17/17 Conclusions We introduce a new method to compute bank solvency (Z6) based on the coefficient of variation of the Return on Assets We complement existing methods by building confidence intervals around them to reflect the degree of estimation error Our preliminary results show the importance of including estimation error while assessing risk exposures We also argue that data availability is a key element whilst drawing comparisons between point estimates