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

1. Watching Macro Stress Test of Bank of
Japan Using R
Motoharu Dei
2012/10/20

2. Source of Today’s Topic
Website 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 simulation
5% 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 simulation
5% 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 rate
5% probability Real GDP
shock
GDP deflator
Equity valuation simulation
5% 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 -3
GDP 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 -3
GDP 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 -3
GDP 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 -3
GDP 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 rate
5% probability Real GDP
shock
GDP deflator
Equity valuation simulation
5% 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 function
pp2ct <- predict(p2ct,n.ahead=20)
TOPIXfcstn <- pp2ct$fcst$TOPIX[,1]
#Calculate the one applying a 5% shock as an after-the-shock TOPIX
TOPIXfcstnAfterShock <- TOPIXfcstn + shockToTOPIX * (-1.64)
TOPIXfcst <- c(datafile[,4],TOPIXfcstn)
TOPIXfcstAfterShock <- c(datafile[,4], TOPIXfcstnAfterShock)
#Working on Excel hereafter
excel.w <- function(dat){
write.table(dat, "clipboard", sep="¥t", row.names = FALSE)
}
excel.w(TOPIXfcst)
#Paste once on Excel
excel.w(TOPIXfcstAfterShock)
#Paste again on Excel

19. 500
600
700
800
900
1000
1100
1200
Sep‐08
Apr‐09
Nov‐09
Jun‐10
Jan‐11
Aug‐11
Mar‐12
Oct‐12
TOPIX
May‐13
Dec‐13
Jul‐14
Feb‐15
Sep‐15
VAR Model on R
Apr‐16
w/ shock
w/o shock
Nov‐16
ショック無
ショック有

20. Equity Valuation Gain & Loss
Analysis by Bank
Real effective
foreign
exchange rate
5% probability Real GDP
shock
GDP deflator
Equity valuation simulation
5% 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 β
ST1.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 each
with total of 10.0 billion) to the shock 1 on TOPIX
STVariance <- 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 model
TOPIXvar.1yrAfterShock <- TOPIXfcstAfterShock[nrow(datafile)+4]/datafile$TOPIX[nrow(datafile)]-1
#Valuation loss of equity portfolio of the objective banks
STLoss <- STVariance * TOPIXvar.1yrAfterShock

25. Equity Valuation Gain & Loss
Analysis by Bank
0.59 0.43
Beta: 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
1200
ＩＴ 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
800
Manufacturing: ¥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‐13
Retailing 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 GDP
probability
shock
GDP deflator
Equity valuation simulation
5% TOPIX Equity price Market Beta Equity valuation gain & loss
probability
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