Financial liability stress tests: an approach based on the use of a rating migration matrix

Kleszcz, Klaudia; Nehrebecka, Natalia

doi:10.2478/ceej-2020-0002

Figures & Tables

PD distribution according to the Hadasik method for 2004. Source: Own study.

Distribution of the market concentration ratio for 2004. Source: Own study.

Distribution of the variable obtained from the optimal mixed ratio model for PD Hadasik and HHI for 2004. Source: Own study.

Variables of a one-notch upgrade transition of enterprises in Poland. Source: Own study.

Variables of a one-notch downgrade transition of enterprises in Poland. Source: Own study.

Principal component obtained from the PCA and the variable obtained from median mapping on the migration matrix variable for a one-notch upgrade transition. Source: Own study.

Principal component obtained from the PCA and the variable obtained from median mapping on the migration matrix variable for a one-notch downgrade transition. Source: Own study.

Time series of macroeconomic variables. (a) Unemployment rate and export variables: raw series and stationary form. (b) Share prices and consumption variables: raw series and stationary form. (c) Import and retail trade variables: raw series and stationary form. Source: Own study.

Stress tests for a one-notch upgrade transition. Source: Own study based on NOTORIA data.

Stress tests for a one-notch downgrade transition. Source: Own study based on NOTORIA data.

Model estimation results using probit models

Variable	Model 3		Model 4

	Coefficient	[statistics;p-value]	Coefficient	[statistics;p-value]
SHARE PRICES	−0.035	[−1.9; 0.057]

EXport	0.066	[2.27; 0.023]

Δ (UNEMPLOYMENT RATE)	5.151	[1.13; 0.260]

QUARTER II	0.044	[0.10; 0.921]	0.9295	[1.98; 0.048]

QUARTER III	0.563	[1.25; 0.212]	1.3360	[2.77; 0.006]

QUARTER IV	0.582	[1.29; 0.199]	0.8352	[1.77; 0.076]

CONSTANT	−0.425	[−1.28; 0.202]	−1.1117	[−2.89; 0.004]

Retail Trade			0.1610	[2.22; 0.027]

Import			0.0898	[1.89; 0.064]

Pseudo R^2	0.1089		0.1853

StatISTICS F	[10.71; 0.0976]		[18.50; 0.0024]

Linktest	_hat [3.19; 0.001]		_hat [3.81; 0.000]
	_hatsq [1.71; 0.088]		_hatsq [0.51; 0.608]

Hosmer Lemeshow	[6.49; 0.5920]		[6.9; 0.5472]

R^2 MZ	0.215		0.368
NUMERICAL R^2	0.620		0.708
CORRECTED NUMERICAL R^2	0.229		0.417

Test results for stationary variables and seasonality

	Dickey-Fuller		Breusche-Godfrey		KPSS		Seasonality test JDemetra

	Test Statistics	Critical Statistics	Test Statistics	p-value	Test Statistics	Critical Statistics	Test Statistics	p-value
Stock prices	−6,380	−2,907	0,256	0,6129	0,0576	0,146	2,119	0,3466
			0,356	0,8371
			0,393	0,9418
			1,772	0,7776

Export	−3,147	−2,911	0,386	0,5343	0,1	0,146	0,000	1,000
			0,394	0,8212
			1,298	0,7296
			1,406	0,8432

Δ (Unemployment rate)	−3,951	−3,477	2,447	0,1177	0,128	0,146	63,537	0,000
			2,449	0,2940
			2,610	0,4557
			6,679	0,1539

The retail trade	−8,911	−2,907	0,738	0,3903	0,0456	0,146	0,634	0,9831
			0,887	0,6417
			2,286	0,5152
			2,287	0,6832
Import	−8,621	−2,907	0,030	0,8617	0,0436	0,146	0,000	1,000
			0,581	0,7479
			3,283	0,3500
			9,925	0,0417

Results of estimation of VAR models

Variables	Model 1		Model 2

Share prices

L1. SHARE PRICES	0.2020	[1.61; 0.113]

L2. SHARE PRICES	0.0954	[0.76; 0.453]

L1. EXport	0.1622	[0.67; 0.508]

L2. EXport	−0.8204	[−3.41; 0.001]

L1. UNEMPLOYMENT RATE	30.5003	[0.91; 0.366]

L2. UNEMPLOYMENTRATE	−16.7610	[−0.49; 0.627]

CONSTANT	−33.3054	[−2.35; 0.022]

EXport

L1. SHARE PRICES	0.0545	[0.82; 0.414]

L2. SHARE PRICES	0.1183	[1.78; 0.081]

L1. EXport	0.3884	[3.02; 0.004]

L2. EXport	−0.3914	[−3.08; 0.003]

L1. UNEMPLOYMENT RATE	3.3631	[0.19; 0.850]

L2. UNEMPLOYMENT RATE	5.0669	[0.28; 0.780]

CONSTANT	−19.9736	[−2.67; 0.010]

Import

L1. Import			0.1817	[1.49; 0.141]

L2. Import			−0.1262	[−1.04; 0.305]

L3. Import			0.1074	[0.90; 0.370]

L4. Import			−0.3177	[−2.64; 0.010]

L1. Retail Trade			0.0994	[0.58; 0.562]

L2. Retail Trade			0.4579	[2.78; 0.007]

L3. Retail Trade			−0.1223	[−0.74; 0.459]

L4. Retail Trade			0.3918	[2.33; 0.023]

CONSTANT			0.9983	[1.58; 0.120]

Retail Trade

L1. Import			0.1541	[1.57; 0.122]

L2. Import			0.1742	[1.77; 0.082]

L3. Import			0.0693	[0.72; 0.473]

L4. Import			0.0036	[0.04; 0.970]

L1. Retail Trade			−0.0547	[−0.4; 0.692]

L2. Retail Trade			−0.0515	[−0.39; 0.699]

L3. Retail Trade			−0.1656	[−1.25; 0.216]

L4. Retail Trade			−0.0344	[−0.25; 0.801]

CONSTANT			0.9983	[1.32; 0.191]

R^2	0.2917		0.2931
	0.3998		0.1346
	0.9985

STATISTICS F	[4.32; 0.001]		[3.05; 0.006]
	[6.99; 0.000]		[1.147; 0.346]
	[7005.84; 0.000]

B-G	[0.540; 0.4625]		[3.812; 0.0509]
	[0.946; 0.6231]		[6.728; 0.0346]
	[1.573; 0.6655]		[7.059; 0.0701]
	[1.947; 0.7456]		[7.180; 0.1267]

J-B	[4.23; 0.1205]		[4.71; 0.0947]

L-B	[27.99; 0.7145]		[22.89; 0.9057]
ROOTS FOR UNIT CIRCLE	0.89		−0.56
	0.25		−0.03
	0.25		−0.03
	−0.38

List of variable definitions used in the study

Variable	Definition of the variable	Data source
	Response variables

PD	2.41753 – 2.62766 (total liabilities/balance sheet total) + 0.0013463(net sales revenues/average receivables) – 0.009225(inventories365/sale) + 0.0272307*(net profit/total capital)	NOTORIA

HHI	Herfindahl-Hirschman index	NOTORIA

	Explanatory variables

Import	Increase in import of goods and services compared to the previous period	OECD

Retail trade	Increase in retail trade compared to the previous period	OECD

Share prices	Increase in share prices compared to the previous period	OECD

Export	Growth in export of goods and services compared to the previous period	OECD

Consumption	Increase in consumption compared to the previous period	OECD
Unemployment rate	Δ (unemployment rate)	OECD

Financial liability stress tests: an approach based on the use of a rating migration matrix

Figures & Tables

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Model estimation results using probit models

Test results for stationary variables and seasonality

Results of estimation of VAR models

List of variable definitions used in the study

Paradigm

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