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Tokyo R "Watching Macro Stress Test of Bank of Japan Using R"

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English version for Tokyo R presentation at 22/10/2012 …

English version for Tokyo R presentation at 22/10/2012

日本語バージョンは以下:
http://www.slideshare.net/ssuserb0db22/tokyorr


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  • 1. Watching Macro Stress Test of Bank of  Japan Using R Motoharu Dei 2012/10/20
  • 2. Source of Today’s TopicWebsite of Bank of Japan (BOJ) “Research & Study” corner http://www.boj.or.jp/research/index.htm/ “Financial System Report”
  • 3. Financial System Report• Published twice a year since 2005• Studying & evaluating the stability of  financial system in Japan• We focus on “Macro Stress Test” under  Chapter 5 “Risk resistance of the  Financial System” this time.
  • 4. What is Stress Test?• A test to simulate the level of damages and/or  mitigation plans under the assumed “exceptional but  plausible” stress scenarios – For example, “ Is the financial system OK, if a stock plunge  event at the level of Lehman shock happens again?” – Check a vague concern “If it is OK when a major shock  happens?” or “What to do?” by actually projecting it.• We recently saw the word on the newspaper: – Stress test for banks in EU countries at Greek economic  crisis – Stress test for nuclear power plant
  • 5. Macro Stress Test by BOJ• Calculate the impact of macro economy stress to each of the  following risks on the equity capital ratio (Tier1) of banks. – Credit risk of bank lending + Equity risk of cross‐shareholdings ←Simultaneous shock of real GDP and TOPIX with 5% probability (once a 20  periods event) on bank lending and bank’s portfolio stocks – Interest rising risk ←3 types of interest rising shocks on interest income decline and price decline of  securities held by banks – Market value loss risk of securities against shock in overseas market ←Shock of European equity price and German government bond interest rate  with 1% probability on securities price held by banks – Foreign currency liquidity risk ←Malfunction for the period of 1 month of foreign currency swap market, repo  market and CD&CP market – Loss enlargement risk due to interaction of financial capital market  and real economy in case of a shock in overseas market
  • 6. Flow of the Test • Calculate the impact of macro economy stress to each of the  following risks on the equity capital ratio (Tier1) of banks. – Credit risk of bank lending + Equity risk of cross‐shareholdings Credit cost model Real effective  Financial situation of foreign  borrower Transition probability of  Credit cost exchange rate (ICR, cash‐to‐current  debtor’s classification* liabilities ratio)5% probability Real GDP shock Negative impact in line with lower growth rate GDP deflator Nominal GDP Tier I  Ratio Equity valuation simulation5% probability TOPIX Equity price Market Beta Equity valuation gain & loss shock Income simulation Long‐term lending  interest rate Long‐term lending  Lending spread Core business net income interest rate VAR model Economic forecast of private think tank
  • 7. Flow of the Test • Calculate the impact of macro economy stress to each of the  following risks on the equity capital ratio (Tier1) of banks. – Credit risk of bank lending + Equity risk of cross‐shareholdings Real effective  foreign  exchange rate We focus on only this as all is too much.5% probability Real GDP shock GDP deflator Equity valuation simulation5% probability TOPIX Equity price Market Beta Equity valuation gain & loss shock Long‐term lending  interest rate VAR model
  • 8. Flow of the Test • Calculate the impact of macro economy stress to each of the  following risks on the equity capital ratio (Tier1) of banks. – Credit risk of bank lending + Equity risk of cross‐shareholdings Real effective  foreign  exchange rate5% probability Real GDP shock GDP deflator Equity valuation simulation5% probability TOPIX Equity price Market Beta Equity valuation gain & loss shock Long‐term lending  interest rate VAR model Analysis using a macro economic index Analysis by bank
  • 9. Stressing Macro Economy using a VAR Model• VAR (Vector AutoRegression) model? Equity  price GDP Interest  Equity  rate price Correlation FX t -3GDP Interest  rate t -1 FX Equity  price Interest  t -4 t GDP rate FX t-2 (when k=2 under the illustration)
  • 10. Stressing Macro Economy using a VAR Model• VAR (Vector AutoRegression) model? Equity  price GDP Interest  Equity  rate Occurrence of sock!! price Correlation FX t -3GDP Interest  rate t -1 FX Equity  price Interest  t -4 t GDP rate FX t-2 (when k=2 under the illustration)
  • 11. Stressing Macro Economy using a VAR Model• VAR (Vector AutoRegression) model? Equity  price GDP Interest  Equity  rate price Correlation FX t -3GDP Interest  rate t -1 FX Equity  price Interest  t -4 t GDP rate FX t-2 (when k=2 under the illustration)
  • 12. Stressing Macro Economy using a VAR Model• VAR (Vector AutoRegression) model? Equity  price GDP Interest  Equity  rate price Correlation FX t -3GDP Interest  rate t -1 FX Equity  price Interest  t -4 t GDP rate FX t-2 (when k=2 under the illustration)
  • 13. Stressing Macro Economy using a VAR Model• VAR (Vector AutoRegression) model? Equity Shock Propagation!! price GDP Interest  Equity  rate price Correlation FX t -3 GDP Interest  rate t -1 FX Equity  price Interest  t -4 t GDP rate FX t-2 (when k=2 under the illustration)
  • 14. Stressing Macro Economy using a VAR Model• VAR (Vector AutoRegression) model?Shock Propagation!!
  • 15. Stressing Macro Economy using a VAR Model• VAR (Vector AutoRegression) model?Shock Propagation!!• It can simulate how a shock occurred in a certain macro  index at a certain timing is transmitted to other macro  indices toward the future.
  • 16. VAR Model on R Real effective  foreign  exchange rate5% probability Real GDP shock GDP deflator Equity valuation simulation5% probability TOPIX Equity price Market Beta Equity valuation gain & loss shock Long‐term lending  interest rate VAR model • In R, the package “vars” can solve major parts of technical difficulties in VAR model • Just one command in R script outputs such as coefficient matrix A1 and shock propagation function (impulse response function) Ij(n)
  • 17. VAR Model on R• Example of implementation• Data should be gathered in advance from a package of  RFinanceYJ, and website of the BOJ and the Cabinet Office. #Package vars library(vars) #Prepare the data in advance datafile <- read.csv("data.csv") #Calibrate factors using VAR function p2ct<-VAR(datafile,p=2,type="both") #Calculate function of shock propagation using irf function var.irf <- irf(p2ct, response=c("EFEXRIND","REGDP","GDPDEF","TOPIX","LPRIMR_LOG"), n.ahead=19, boot=F) #Shocks on each of the real GDP and TOPIX shock.ByrealGDP <- var.irf$irf$REGDP shock.ByTOPIX <- var.irf$irf$TOPIX shock <- shock.ByrealGDP + shock.ByTOPIX shockToTOPIX <- shock[,4]
  • 18. VAR Model on R#Project future macro indices using predict functionpp2ct <- predict(p2ct,n.ahead=20)TOPIXfcstn <- pp2ct$fcst$TOPIX[,1]#Calculate the one applying a 5% shock as an after-the-shock TOPIXTOPIXfcstnAfterShock <- TOPIXfcstn + shockToTOPIX * (-1.64)TOPIXfcst <- c(datafile[,4],TOPIXfcstn)TOPIXfcstAfterShock <- c(datafile[,4], TOPIXfcstnAfterShock)#Working on Excel hereafterexcel.w <- function(dat){ write.table(dat, "clipboard", sep="¥t", row.names = FALSE) }excel.w(TOPIXfcst)#Paste once on Excelexcel.w(TOPIXfcstAfterShock)#Paste again on Excel
  • 19. 500 600 700 800 900 1000 1100 1200Sep‐08Apr‐09Nov‐09Jun‐10Jan‐11Aug‐11Mar‐12Oct‐12 TOPIXMay‐13Dec‐13 Jul‐14Feb‐15Sep‐15 VAR Model on RApr‐16 w/ shock w/o shockNov‐16 ショック無 ショック有
  • 20. Equity Valuation Gain & Loss  Analysis by Bank Real effective  foreign  exchange rate5% probability Real GDP shock GDP deflator Equity valuation simulation5% probability TOPIX Equity price Market Beta Equity valuation gain & loss shock Long‐term lending  interest rate VAR model Analysis using a macro economic index Analysis by bank
  • 21. Equity Valuation Gain & Loss  Analysis by Bank• “Market Beta” is an index showing relative size of a  change in price of a share to the change of the  benchmark. – When the benchmark (TOPIX) increases 10% and the share  increases 15% on average, the market beta of the share is  1.5. Change in the objective share (%) 1.5 1 Change in TOPIX (%) (For illustration purpose, return on risk-free asset is assumed to be zero hereinafter)
  • 22. Equity Valuation Gain & Loss  Analysis by Bank• Calculation of valuation gain & loss of equity  portfolio by bank – Calculate the amount of change in valuation gain & loss of  equity by bank through the following calculation by bank. Equity portfolio of Bank A T Market beta of each share Value of share ① Share ①β Value of share ② Share ②β × × Change in Value of share ③ Share ③β TOPIX ・ ・ ・ ・ Result of the ・ ・ VAR model
  • 23. Equity Valuation Gain & Loss  Analysis by Bank• Example of implementation• As it is too cumbersome to check the actual portfolio of banks,  the shock is applied to a hypothetic bank holding IT share,  infrastructure share, manufacturing share and retailing share for 2.5 billion yen each. library(RFinanceYJ) #Index (TOPIX) 998405 ST0 <- quoteStockTsData("998405",since="2007-01-01", time.interval="monthly") #IT share: Yahoo Japan 4689 ST1 <- quoteStockTsData("4689",since="2007-01-01", time.interval="monthly") #Infrastructure share: JR East 9020 ST2 <- quoteStockTsData("9020",since="2007-01-01", time.interval="monthly") #Manufacturing share: Toyota 7203 ST3 <- quoteStockTsData("7203",since="2007-01-01", time.interval="monthly") #Retailing share: Lawson 2651 ST4 <- quoteStockTsData("2651",since="2007-01-01", time.interval="monthly") ST <-data.frame(ST0=ST0[,5],ST1=ST1[,7],ST2=ST2[,7],ST3=ST3[,7],ST4=ST4[,7]) #Calculation of rate of change IncST <- ST[2:70,]/ST[1:69,]-1
  • 24. Equity Valuation Gain & Loss  Analysis by Bank#Calculate each βST1.lm <- lm(ST1~ST0, data=IncST)ST1.beta <- ST1.lm$coefficients[2]ST2.lm <- lm(ST2~ST0, data=IncST)ST2.beta <- ST2.lm$coefficients[2]ST3.lm <- lm(ST3~ST0, data=IncST)ST3.beta <- ST3.lm$coefficients[2]ST4.lm <- lm(ST4~ST0, data=IncST)ST4.beta <- ST4.lm$coefficients[2]ST.beta <- rbind(ST1.beta, ST2.beta, ST3.beta, ST4.beta)#Calculate the amount of change in the asset of a hypothetic bank (holding shares of ST1-ST4 for 2.5 billion eachwith total of 10.0 billion) to the shock 1 on TOPIXSTVariance <- as.numeric( 10^10 * t(as.matrix(rep(0.25,4)))%*%as.matrix(ST.beta))#Drop rate of TOPIX after 1 year (after 4 quarters) since the shock under the VAR modelTOPIXvar.1yrAfterShock <- TOPIXfcstAfterShock[nrow(datafile)+4]/datafile$TOPIX[nrow(datafile)]-1#Valuation loss of equity portfolio of the objective banksSTLoss <- STVariance * TOPIXvar.1yrAfterShock
  • 25. Equity Valuation Gain & Loss  Analysis by Bank 0.59 0.43Beta: TOPIX vs. Yahoo Japan Beta: TOPIX vs. JR East 1.03 0.14 Beta: TOPIX vs. Toyota Beta: TOPIX vs. Lawson
  • 26. Equity Valuation Gain & Loss  Analysis by Bank T TOPIX 1200IT share: ¥2.5 billion IT share β 1100 ショック有 w/ shock 0.59 ショック無 w/o shock 1000 Infrastructure Infrastructure: ¥2.5b share β 0.43 900 800Manufacturing: ¥2.5b × Manufacturing  share β 1.03 × 700 600 500 Retailing  Apr‐09 Apr‐16 Sep‐08 Feb‐15 Sep‐15 Jun‐10 Jul‐14 Mar‐12 Dec‐13 Aug‐11 Oct‐12 Nov‐09 Jan‐11 Nov‐16 May‐13Retailing share: ¥2.5b share β 0.14 Drop of 20.6% after 1 year Result of calculation: Valuation loss of 1.13 billion yen is generated after 1 year of the shock on the equity portfolio of 10.0 billion yen of the hypothetic bank!
  • 27. Summary of Conclusion TOPIX 1200 1100 ショック有 ショック無 1000 900 800 700 600 Real effective  500 Apr‐09 Apr‐16 Sep‐08 Feb‐15 Sep‐15 Jun‐10 Jul‐14 Mar‐12 Dec‐13 Aug‐11 Oct‐12 Nov‐09 Jan‐11 Nov‐16 foreign  May‐13 exchange rate 5% Real GDPprobability shock GDP deflator Equity valuation simulation 5% TOPIX Equity price Market Beta Equity valuation gain & lossprobability shock Long‐term lending  interest rate VAR model Valuation loss of 1.13 billion yen after 1 year of the shock on the hypothetic bank with equity of 10.0 billion yen