Simple bank model. Document prepared by BSM Unit. May 2011

Transcription

1 Simple bank model Document prepared by BSM Unit May 11 Table of Contents 1. Summary of functional relationships.... Impairments Endownment estimate outline Non interest revenue Fee and commission income Total Non interest income not used currently pls see note above Margin income Operating expenditure Advances P age

2 1. Summary of functional relationships Impairments = f(debt service cost(t); average real house price growth(t); average USDZAR(t)) Endowment = f(rate sensitivity(t); change in rates(t)) Fee and commission income = f(nominal GDP(t )) Opex = cpi infl+% Margin =.1% Balance sheet growth for margin income = credit extension growth Margin income = (balance x margin). Advance Impairments growth = credit extension growth P age

3 .1. FRBG estimation model output Current impairment rate = 93bps as at 11 Change in impairment rate is modelled through the following function. Advances growth is assumed to be static in line with endowment balances Variable description for FRB Model Debt servicing cost Growth in House Price Index Average debtservice charge for quarter ended average annual growth rate in real ASAHPI (defalted by ECPI) aver_debtch=(debtservch+debtservch(-1)+debtservch(- )+debtservch(-3))/ USD/ZAR annual average USD/ZAR rate aver_usdzar=(usdzar+usdzar(-1)+usdzar(-)+usdzar(-3))/ Dum9 Dummy variable = 1 from 199 debtservch=rpor*nhddis(-1)/1 Dependent Variable: LOG(ODDS_FSR) Date: 8/5/1 Time: 1:35 Sample (adjusted): 198Q 9Q Included observations: 36 after adjustments LOG(AVER_DEBTCH(-)) LOG(AVER_USDZAR) C DUM9*LOG(AVER_RASAHPI/AVER_RASAHPI (-)) R-squared Mean dependent var Adjusted R-squared.813 S.D. dependent var.919 S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Prob(F-statistic). 3 P age

4 Q 86Q 88Q 9Q 9Q 9Q 96Q 98Q Q 1Q Q 3Q Q 5Q 6Q 7Q 8Q 9Q Sample 198Q 9Q Observations 36 Mean -3.7e-16 Median Maximum Minimum Std. Dev Skewness Kurtosis Jarque-Bera.8677 Probability.6983 Heteroskedasticity Test: Breusch-Pagan-Godfrey F-statistic Prob. F(3,3).15 Obs*R-squared Prob. Chi-Square(3).18 Scaled explained SS Prob. Chi-Square(3).97 P age

5 .. Industry estimation model output not used in model Variable description for Industry Model Debt servicing cost Growth in House Price Index Growth in real GDP USD/ZAR debtservch=rpor*nhddis(-1)/1 Annual growth in ASAHPI deflated by ECPI Real GDP growth (annualised GDP) annual average USD/ZAR rate Dependent Variable: LOG(ODDS) Date: 8/3/1 Time: 9: Sample (adjusted): 199Q 9Q Included observations: 63 after adjustments LOG(DEBTSERVCH(-)) C LOG(RASAHPI(-)/RASAHPI(-8)) LOG(RGDPA(-6)/RGDPA(-1)) LOG(AVER_USDZAR) R-squared.8653 Mean dependent var Adjusted R-squared.8966 S.D. dependent var.196 S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat.5665 Prob(F-statistic) P age

6 .3. Model comparisons Fundamental determinants: FRB Fundamental determinants: Industry Fundamental factors Coefficient size Lagged impact in months Coefficient size Lagged impact in months Relative coefficient size Debt servicing cost Collateral values* Real GDP growth NA USDZAR Overall macro factor sensitivity (R^) 8% 8% Beta estimate for positive movements in fundamental factor Beta estimate for negative movements in fundamental factor Fundamental factors FirstRand Industry FirstRand Industry Debt servicing cost.39%.3% -.1% -.33% Collateral values* -.118% -.8%.79%.7% Real GDP growth NA -.9% NA.198% USDZAR.9%.6% -.9% -.8% 6 P age

7 3. Endownment estimate outline 3.1. Income statement Current method this method is used because of the fact that the BS size is not observable on a regular basis: Income statement charge in quarter = (cumulative change in interest rates since beginning of financial year)*(t/)*(annual rate sensitivity of 1bps rate movement). o Where T = quarters remaining in the financial year. Rate sensitivity = 65 (as per Dec 1 results presentation ). (similarly, quarterly change in endowment = quarterly change in rates*(annual rate sensitivity/)*time to end of the year measured in quarters as per model) Growth rate in underlying asset is assumed to be directly related to credit extension growth Alternative method used previously uses rate sensitive BS size and rate change: 56*.8=5*i (1) 56*i 56(i*.) = 56(i i*.) = 56(i i*.) = 56(i i*.) =56(i(1.)) =56*i*.8 =5*i =(1) Cap+3i 3* NMD+56i+56i*. NRA+1* 1*i =65*i Then, income statement charge = change in above from t to t+1. 7 P age

8 3.. Balance sheet not used currently Shareholder s capital and reserves / Total Equity +Non maturity deposits (current savings and transmission accounts)*beta Non rate assets =Endowment assets Beta = rate sensitive portion of NMD Component analysis quarterly 65, 35, 1% 6, 3, 8% 9% 3% 6% 3% 3% 3% 9% 9% 3% 3% 3% 9% 55, 5,, 6% 6% 11% 5% 6% 15% 15% 1% 1% 1% 16% 5, 15, 1, % % 65% 7% 6% 65% 68% 63% 56% 56% 56% 56% 57% 55% 5, 5, % % % Jun7 Sep7 Dec7 Mar8 Jun8 Sep8 Dec8 Mar9 Jun9 Sept9 Dec9 Mar1, Jun7 Sep7 Dec7 Mar8 Jun8 Sep8 Dec8 Mar9 Jun9 Sept9 Dec9 Mar1 5, % NMDs Nett Non Rate assets (rhs) Total Equity NMDs Nett Non Rate assets (rhs) Total Equity Component analysis monthly 1% 7,, 6, 15, 8% 5, 1, 6%, 5, % 3,, % 1, 5, % 7M6 7M1 8M 8M6 8M1 9M 9M6 9M1 1M NMD Total Equity Nett Non Rate assets (rhs) 1, % 7M6 7M1 8M 8M6 8M1 9M 9M6 9M1 1M NMD Nett Non Rate assets Total Equity 8 P age

9 Component analysis focus on non rate assets and liabilities M6 7M1 8M 8M6 8M1 9M 9M6 9M1 1M 5 Jun7 Sep7 Dec7 Mar8 Jun8 Sep8 Dec8 Mar9 Jun9 Sept9 Dec9 Mar1 Non rate assets Non Rate Liabilities Nett Non Rate assets Non rate assets Non Rate Liabilities Nett Non Rate assets Examples of model to get NMD not used currently Non maturity deposits quarterly 1 Dependent Variable: LOG(NMD) Date: 8/6/1 Time: 17:8 Sample (adjusted): 7Q 1Q1 Included observations: 1 after adjustments LOG(NGDPA) C R-squared.8739 Mean dependent var Adjusted R-squared S.D. dependent var.7593 S.E. of regression.7965 Akaike info criterion Sum squared resid.781 Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic).8 9 P age

10 Sample 7Q 1Q1 Observations 1 Mean. Median.13 Maximum.86 Minimum Std. Dev..666 Skewness Kurtosis Q3 8Q1 8Q3 9Q1 9Q3 1Q Jarque-Bera.987 Probability.9383 Non maturity deposits quarterly Dependent Variable: LOG(NMD) Date: 8/6/1 Time: 17: Sample (adjusted): 7Q 1Q1 Included observations: 1 after adjustments LOG(TOTAL_PSCE) C R-squared Mean dependent var Adjusted R-squared S.D. dependent var.7593 S.E. of regression.5839 Akaike info criterion Sum squared resid.11 Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat 1.79 Prob(F-statistic) Q3 8Q1 8Q3 9Q1 9Q3 1Q1 3 1 Sample 7Q 1Q1 Observations 1 Mean 1.5e-15 Median -.66 Maximum.6577 Minimum -.66 Std. Dev..375 Skewness.598 Kurtosis Jarque-Bera Probability P age

11 Non maturity deposits monthly 1 Dependent Variable: LOG(NMD) Date: 8/6/1 Time: 9:33 Sample (adjusted): 7M6 1M3 Included observations: 3 after adjustments LOG(NGDPA) C R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression.38 Akaike info criterion Sum squared resid.8855 Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat.9355 Prob(F-statistic) Sample 7M6 1M3 Observations 3 Mean -1.3e-15 Median. Maximum.63 Minimum Std. Dev..957 Skewness Kurtosis M7 8M1 8M7 9M1 9M7 1M Jarque-Bera Probability P age

12 Non maturity deposits monthly Dependent Variable: LOG(NMD) Date: 8/6/1 Time: 19: Sample (adjusted): 7M6 1M Included observations: 35 after adjustments LOG(TOT_PSCE) C R-squared.6511 Mean dependent var Adjusted R-squared.6157 S.D. dependent var.7353 S.E. of regression.1 Akaike info criterion Sum squared resid.6395 Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat.95 Prob(F-statistic) Sample 7M6 1M Observations 35 Mean -6.1e-16 Median.3579 Maximum.799 Minimum Std. Dev Skewness.1776 Kurtosis M7 8M1 8M7 9M1 9M7 1M Jarque-Bera Probability P age

13 Examples of model to get equity not used currently Total equity quarterly Dependent Variable: LOG(TOT_EQ) Date: 8/6/1 Time: 19:9 Sample (adjusted): 7Q 1Q1 Included observations: 1 after adjustments LOG(NGDPA) C R-squared Mean dependent var Adjusted R-squared.875 S.D. dependent var S.E. of regression.961 Akaike info criterion Sum squared resid.67 Schwarz criterion Log likelihood.19 Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic) Sample 7Q 1Q1 Observations Q3 8Q1 8Q3 9Q1 9Q3 1Q Mean -1.78e-15 Median.9175 Maximum.657 Minimum Std. Dev Skewness Kurtosis Jarque-Bera Probability P age

14 Total equity monthly Dependent Variable: LOG(TOTEQ) Date: 8/6/1 Time: 19:13 Sample (adjusted): 7M6 1M3 Included observations: 3 after adjustments LOG(NGDPA) C R-squared.87 Mean dependent var Adjusted R-squared S.D. dependent var.1378 S.E. of regression.791 Akaike info criterion Sum squared resid.7356 Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat.813 Prob(F-statistic) Sample 7M6 1M3 Observations M7 8M1 8M7 9M1 9M7 1M Mean 7.89e-16 Median.578 Maximum Minimum Std. Dev..79 Skewness.115 Kurtosis Jarque-Bera Probability.8 1 P age

15 Net non rate assets quarterly 1 Dependent Variable: LOG(NNRA_ADJ) Date: 8/6/1 Time: 19:3 Sample (adjusted): 8Q1 1Q1 Included observations: 9 after adjustments LOG(TOTAL_PSCE) C DUM R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic) Sample 8Q1 1Q1 Observations 9 Mean -5.5e-15 Median.853 Maximum.513 Minimum Std. Dev Skewness Kurtosis Q1 8Q 8Q3 8Q 9Q1 9Q 9Q3 9Q 1Q1 1 Jarque-Bera 1.85 Probability P age

16 Net non rate assets monthly 1 Dependent Variable: LOG(NNRA_ADJ) Date: 8/6/1 Time: 19:5 Sample (adjusted): 8M1 1M Included observations: 8 after adjustments LOG(TOT_PSCE) C DUM R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression.516 Akaike info criterion.1837 Sum squared resid Schwarz criterion.353 Log likelihood.7698 Hannan-Quinn criter..593 F-statistic.81 Durbin-Watson stat.6191 Prob(F-statistic) Sample 8M1 1M Observations M1 8M7 9M1 9M7 1M Mean -3.16e-15 Median.575 Maximum Minimum Std. Dev..5 Skewness Kurtosis.356 Jarque-Bera Probability P age

17 Net non rate assets quarterly Dependent Variable: LOG(NNRA_ADJ) Date: 8/7/1 Time: 13:51 Sample (adjusted): 8Q1 1Q1 Included observations: 9 after adjustments LOG(NGDPA) C DUM R-squared.7689 Mean dependent var Adjusted R-squared.6919 S.D. dependent var S.E. of regression.3778 Akaike info criterion Sum squared resid.8885 Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic) Q1 8Q 8Q3 8Q 9Q1 9Q 9Q3 9Q 1Q1 17 P age

18 Net non rate assets monthly Dependent Variable: LOG(NNRA_ADJ) Date: 8/7/1 Time: 13:53 Sample (adjusted): 8M1 1M3 Included observations: 7 after adjustments LOG(NGDPA) C DUM R-squared.6938 Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression.6576 Akaike info criterion Sum squared resid Schwarz criterion.3557 Log likelihood Hannan-Quinn criter..33 F-statistic.3783 Durbin-Watson stat Prob(F-statistic) M1 8M7 9M1 9M7 1M Sample 8M1 1M3 Observations 7 Mean 7.79e-17 Median.85 Maximum.313 Minimum Std. Dev..558 Skewness Kurtosis Jarque-Bera Probability P age

19 . Non interest revenue Note: Currently only the fee and commissions income portion of Non interest revenue is assumed to be macro driven i.e. Fee and commission income is modeled with the function below and assume to impact the income statement while the residual change income from other non interest revenue is assumed to be constant or macro insensitive..1. Fee and commission income Current balance 16 = R million Current balance 11 = R million Level in fee and comm. income is modelled through the following function; Dependent Variable: LOG(FEE_COMM_INC) Date: /8/11 Time: 13:9 Sample (adjusted): 199Q 1Q Included observations: 19 after adjustments LOG(NGDP(-)) DUM C R-squared Mean dependent var Adjusted R-squared.9971 S.D. dependent var.9313 S.E. of regression.795 Akaike info criterion Sum squared resid.1997 Schwarz criterion Log likelihood.7967 Hannan-Quinn criter F-statistic 18.8 Prob(F-statistic). 19 P age

20 Q 9Q 9Q 96Q 98Q Q Q Q 6Q 1Q Sample 199Q 1Q Observations 19 Mean.e-15 Median.87 Maximum Minimum Std. Dev..796 Skewness.331 Kurtosis Jarque-Bera Probability.336 P age

21 18, 16, 1, 1, 1, 8, 6,,, 199Q 1991Q 199Q 1993Q 199Q 1995Q 1996Q 1997Q 1999Q Q 1Q Q 3Q Q 5Q 6Q 7Q 8Q 9Q 1Q Actual Fitted.. Total Non interest income not used currently pls see note above Current balance 16 = R 6 1 million Dependent Variable: LOG(NIR) Date: 8/1/1 Time: 1:9 Sample (adjusted): 1983Q 9Q Included observations: 6 after adjustments LOG(RGDPA) LOG(ECPI) DUM C R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression.957 Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Prob(F-statistic). 1 P age

22 Sample 1983Q 9Q Observations 6 Mean -.3e-15 Median.1395 Maximum.1799 Minimum Std. Dev Skewness Kurtosis Jarque-Bera Probability Q 198Q 1985Q 1986Q 1987Q 1988Q 1989Q 199Q 1991Q 199Q 1993Q 199Q 1995Q 1996Q 1997Q 1999Q Q 1Q Q 3Q Q 5Q 6Q 7Q 8Q 9Q Non interest income Model P age

23 5. Margin income Assumed to be.1% of balance sheet as per the Dec 1 results presentation Current BS size as per Dec 1 results = R61 53 bill BS growth = private sector credit extension growth 6. Operating expenditure Opex growth =inflation+% this is already low with respect to historical real growth rates (see graph below out of 1 yr review data) Current opex = R6 88 as per Dec 1 result presentation Advances Advances are modeled as a function of private sector credit extension growth. Current balance = P age