Download R=My+Z*Sigma

Comments on
“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=0.03
K=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 simulations
Model 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 simulations
Kernel density functions for actual and estimated Zbs
0.12
actual
Zb=4.0
0.10
Model 1
average estimated Zb=7.0
median of estimated Zb=4.8
0.08
0.06
0.04
Model 2
average estimated Zb=11.1
median of estimated Zb=7.5
0.02
0.00
-20
0 4
20
40
60
80
100
120
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.