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

Watching Macro Stress Test of Bank of Japan Using R

Motoharu Dei2012/10/20

Source of Today’s Topic

http://www.boj.or.jp/research/index.htm/

Website of Bank of Japan (BOJ)

“Research & Study” corner

“Financial System Report”

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.

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

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

• 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

Flow of the Test

Financial situation ofborrower

(ICR, cash‐to‐current liabilities ratio)

Nominal GDP

Equity price

Long‐term lending interest rate

Negative impact in line with lower growth rate

Transition probability of debtor’s classification* Credit cost

Market Beta Equity valuation gain & loss

Tier I RatioGDP deflator

TOPIX


Real effective foreign

exchange rate

Real GDP

VAR model

Economic forecast ofprivate think tank

Credit cost model

Equity valuation simulation

Income simulation

Lending spread Core business net income

5% probabilityshock

5% probabilityshock


Flow of the Test

Equity price Market Beta Equity valuation gain & loss

GDP deflator

TOPIX



exchange rate

Real GDP

VAR model


5% probabilityshock

5% probabilityshock

We focus on only this as all is too much.


Flow of the Test


GDP deflator

TOPIX



exchange rate

Real GDP

VAR model


5% probabilityshock

5% probabilityshock

Analysis using a macro economic index Analysis by bank

• VAR (Vector AutoRegression) model?

Stressing Macro Economyusing a VAR Model

Equity price

GDP

FX

Interest rate

Correlation

t

Equity price

GDP

FX

Interest rate

t -1

Equity price

GDP

FX

Interest rate

t - 2

t -3

t -4

(when k=2 under the illustration)



Equity price

GDP

FX

Interest rate

Correlation

t

Equity price

GDP

FX

Interest rate

t -1

Equity price

GDP

FX

Interest rate

t - 2

t -3

t -4


Occurrence of sock!!



Equity price

GDP

FX

Interest rate

Correlation

t

Equity price

GDP

FX

Interest rate

t -1

Equity price

GDP

FX

Interest rate

t - 2

t -3

t -4




Equity price

GDP

FX

Interest rate

Correlation

t

Equity price

GDP

FX

Interest rate

t -1

Equity price

GDP

FX

Interest rate

t - 2

t -3

t -4




Equity price

GDP

FX

Interest rate

Correlation

t

Equity price

GDP

FX

Interest rate

t -1

Equity price

GDP

FX

Interest rate

t - 2

t -3

t -4


Shock Propagation!!



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.

Shock Propagation!!

VAR Model on R


GDP deflator

TOPIX



exchange rate

Real GDP

VAR model


5% probabilityshock

5% probabilityshock

• 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)

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 varslibrary(vars)

#Prepare the data in advancedatafile <- read.csv("data.csv")

#Calibrate factors using VAR functionp2ct<-VAR(datafile,p=2,type="both")

#Calculate function of shock propagation using irf functionvar.irf <- irf(p2ct, response=c("EFEXRIND","REGDP","GDPDEF","TOPIX","LPRIMR_LOG"), n.ahead=19, boot=F)

#Shocks on each of the real GDP and TOPIXshock.ByrealGDP <- var.irf$irf$REGDPshock.ByTOPIX <- var.irf$irf$TOPIX

shock <- shock.ByrealGDP + shock.ByTOPIXshockToTOPIX <- shock[,4]

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

VAR Model on R

500

600

700

800

900

1000

1100

1200Sep‐08

Apr‐09

Nov‐09

Jun‐10

Jan‐11

Aug‐11

Mar‐12

Oct‐12

May‐13

Dec‐13

Jul‐1

4

Feb‐15

Sep‐15

Apr‐16

Nov‐16

TOPIX

ショック有

ショック無

w/ shock

w/o shock

Equity Valuation Gain & Loss Analysis by Bank


GDP deflator

TOPIX



exchange rate

Real GDP

VAR model


5% probabilityshock

5% probabilityshock

Analysis by bankAnalysis using a macro economic index

• “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 TOPIX (%)

Change in the objective share (%)

1

1.5

(For illustration purpose, return on risk-free asset is assumed to be zero hereinafter)


• 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

Value of share ①

Value of share ②

Value of share ③

・・・

×

Market beta of each share

Share ①β

Share ②β

Share ③β

・・・

T

× Change in TOPIX

Result of the VAR model


• 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 sharefor 2.5 billion yen each.

library(RFinanceYJ)

#Index (TOPIX) 998405ST0 <- quoteStockTsData("998405",since="2007-01-01", time.interval="monthly")#IT share: Yahoo Japan 4689ST1 <- quoteStockTsData("4689",since="2007-01-01", time.interval="monthly")#Infrastructure share: JR East 9020ST2 <- quoteStockTsData("9020",since="2007-01-01", time.interval="monthly")#Manufacturing share: Toyota 7203ST3 <- quoteStockTsData("7203",since="2007-01-01", time.interval="monthly")#Retailing share: Lawson 2651ST4 <- 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 changeIncST <- ST[2:70,]/ST[1:69,]-1


#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 each with 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


Beta: TOPIX vs. Yahoo Japan Beta: TOPIX vs. JR East

Beta: TOPIX vs. Toyota Beta: TOPIX vs. Lawson

0.59 0.43

1.03 0.14


ＩＴ share: ¥2.5 billion

Infrastructure: ¥2.5b

Manufacturing: ¥2.5b ×

ＩＴ share β

Infrastructure share β

Manufacturing share β

T

×

Retailing share: ¥2.5b Retailing share β

500

600

700

800

900

1000

1100

1200

Sep‐08

Apr‐09

Nov‐09

Jun‐10

Jan‐11

Aug‐11

Mar‐12

Oct‐12

May‐13

Dec‐13

Jul‐1

4

Feb‐15

Sep‐15

Apr‐16

Nov‐16

TOPIX

ショック有

ショック無

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!

0.59

0.43

1.03

0.14


w/ shock

w/o shock

Summary of Conclusion


GDP deflator

TOPIX



exchange rate

Real GDP

VAR model


5%probability

shock

5%probability

shock

500

600

700

800

900

1000

1100

1200

Sep‐08

Apr‐09

Nov‐09

Jun‐10

Jan‐11

Aug‐11

Mar‐12

Oct‐12

May‐13

Dec‐13

Jul‐1

4

Feb‐15

Sep‐15

Apr‐16

Nov‐16

TOPIX

ショック有

ショック無

Valuation loss of 1.13 billion yen after 1 year of the shock on the hypothetic bank with equity of 10.0 billion yen

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

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