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“Measuring Banks Insolvency Risk in
CEE Countries”
Ivicic, Kunovac, Ljubaj
by Neven Mates
Senior Resident Representative, IMF Moscow Office
The main conclusions: The stability of banking sector in all CEE countries is
improving:
• Favorable macroeconomic developments have resulted in higher and less volatile returns on assets;
• Stability increased: Risk of a systemic crisis only 0.1 percent;
• Increased concentration reduces stability;• Low inflation improves stability;• Rising loan provisions are a sign of increased
vulnerability.
The Method:
• Z-score as a measure of distance-to-insolvency.
• Let assume that the return on assets R is a random variable with mean My and standard deviation Sigma.
R=My+Z*Sigma
• The bankruptcy threshold: A border case when the return on assets is so negative that it would exhaust capital in one year:
R=-K
where K is the capital to asset ratio.
• Z-score triggering the bankruptcy Zb is then equal to:
Zb=-(My+K)/Sigma
Chebyshev theorem tell us that the following inequality applies, regardless of a specific distribution function of R:
P{R≤ -K} ≤ Sigma2/(My+K)2
Or
P{R≤-K} ≤ 1/Zb2
How far can the Z-scores bring us to?
• Intuitively, an attractive measure of a “distance to bankruptcy”;
• Can be used to compare various banks, or their groups;
• But can we make conclusions on the probability of the bankruptcy?
• The authors think that Chebyshev inequality allows them to establish a maximum probability, without specifying the underlying probability distribution.
• Indeed, Chebyshev produces the result that is not dependent on a specific probability function …
• … but it assumes that you exactly know the mean and variance of this function.
• If you do not know these, Chebyshev is of little help.
Monte Carlo simulations
How precisely can the authors’ procedure estimate parameters that enter into Z-score calculation, i.e. mean and standard deviation of return to assets variable?
Model 1: My=0.02 Stdev=0.03K=0.10 Zb=4 (true value)
Assuming R~iid N(0.02, 0.03), we generated 10,000 observations of Rs.
We used those Rs to estimate My, Sygma, and Zbs:
Average estimated Zb= 7.015 (almost twice as large)
Median of estimated Zb=4.765
Monte Carlo simulationsModel 2: The same, but we introduced a serial correlation between Rs.
Average estimated Zb= 11.08 (almost 3 times higher than the true value)
Median of estimated Zb=7.45 (twice as high)
Upper limit of the probability of default 1/Zb2 =0.063
Average of estimated 1/Zb2 =0.033 (about a half)
Median of estimated 1/Zb2 =0.018 (about a third).
But what if the sampling takes us 1 sd. from the sample mean?
Zb=28,
1/Zb2=0,1 percent .
Monte Carlo simulationsKernel density functions for actual and estimated Zbs
0.00
0.02
0.04
0.06
0.08
0.10
0.12
-20 0 20 40 60 80 100 120
Model 1average estimated Zb=7.0
median of estimated Zb=4.8
Model 2average estimated Zb=11.1median of estimated Zb=7.5
4
actualZb=4.0
Predicting Zs: Which factors matter?
• Regression of Z-s on macroeconomic and microeconomic variables for each of 7 CEE countries separately.
• Absence of robustness in the regressions for the whole period 1998-2006.
Predicting Zs: Which factors matter?Macroeconomic variables:• GDP growth is significant and has an expected sign in only 3 out of 7
countries;• Inflation is significant and has an expected sign in 5 countries;• Concentration index: In two countries the coeficient is positive and
significant, in two it is negative and significant; • Libor: The coeficient is significant with a right sign in 3 countries (but
large differences in the size), it has a wrong sign in one.
Microeconomic (banks-specific) variables:• Credit growth: Significant and right sign in 4 countries;• Total assets: Not significant in any country;• Loans to assets ratio: Negative and significant in 2 countries, positive
and significant in 1;• Loan provisions to net-interest income: Positive significant in one,
negative in one;• Liquid assets to customer and short-term funding: Not significant.
Predicting Zs: Which factors matter?
5-year Rolling regressions:
• Even less robustness;
• Wild gyrations of coefficients consecutive regressions;
• In one case, coefficient for GDP goes from -68 to +69 in two consecutive regressions (2004 and 2005), but in both cases it is significant at 1 percent.