Introduction

One of the key innovations introduced by the new accounting standards refer to lifetime losses. Though this concept is not new in risk management, its implementation in the financial industry is extremely contemporary.

Account-level data is usually required to develop a lifetime PD. Based on data availability, one may consider the lifetime PD based on porfolio-level data when account-level data is not available.

IFRS 9 requires banks to compute ECL, based on point-in-time (PIT or Oneyear PD), unbiased, forwardlooking, and lifetime estimates. The previous post focused on one-year PIT PD, the aim of this post is to embed a forward-looking perspective, and extend over a lifetime PD modelling for portfolio-level data. Few alternative approaches can be as follows:

Lifetime PD Modelling for Portfolio-level

When data are not available at account-level, or micro-granularity is not needed, one may conduct the study at portfolio-level. The idea is to fit a creditworthiness index against MVs (Bellini, 2017). A PD shift, based on macroeconomic projections, is applied on top of one-year PIT PDs to derive forward-looking PDs. Finally, a lifetime term structure is computed for each account, based on Equation 3.5 (page 99).

Lifetime PD modelling based on portfolio-level data can be implemented by a four-step procedure described as follows:

Step 1: Modelling Oneyear PD as presented in previous post.
Step 2: Develop a link function rely on default rates (DRs).
Step 3: Calculate PD shift based on macroeconomic projections feeding the link function investigated above.
Step 4: Calculate lifetime PD.

This post presents process of modelling lifetime PD for portfolio-level data by using R language.

Step 2

# Import some R packages: 

rm(list = ls())
library(tidyverse)
library(lubridate)
library(hrbrthemes)
library(tseries)
library(knitr)

# Import data: 
df_macro <- readxl::read_excel("C:\\Users\\Zbook\\Desktop\\ifrs9_Bellini\\chap3\\chap3drts.xlsx")
names(df_macro) <- str_to_upper(names(df_macro))
df_macro <- df_macro %>% mutate(DATE = ymd(DATE))


# Macroeconomic Indicators and PD from 2004 to 3013 (as presented in page 101): 
df_macro %>% 
  gather(a, b, -DATE) %>% 
  mutate(b = b / 100) %>% 
  ggplot(aes(DATE, b)) + 
  geom_line(color = "orange") + 
  scale_y_continuous(labels = scales::percent) + 
  facet_wrap(~ a, scales = "free") + 
  theme_ft_rc() + 
  labs(x = "Report Date", y = NULL, 
       title = "Fluctuation of Some Macroeconomic Indicators, 2004 - 2013")

#===================================
#  Perform Stage 2: link function
#===================================

# Funtion for conduct KPSS test for time series: 

kpssTest_Trend <- function(x) {
  m <- kpss.test(x, null = "Trend", lshort = TRUE)
  return(data.frame(KPSS_Level = m$statistic, P_Value = m$p.value, Hypothesis = "Trend"))
  
}


lapply(df_macro %>% select_if(is.numeric), kpssTest_Trend) -> m1

# Show results: 
do.call("bind_rows", m1) %>% 
  mutate(Variable = names(m1)) %>% 
  mutate_if(is.numeric, function(x) {round(x, 3)}) %>% 
  select(Variable, everything()) %>% 
  kable()

Variable	KPSS_Level	P_Value	Hypothesis
DR	0.112	0.100	Trend
GDP	0.112	0.100	Trend
UER	0.132	0.076	Trend
CPI	0.068	0.100	Trend
HPI	0.141	0.060	Trend
IR	0.228	0.010	Trend

kpssTest_Level <- function(x) {
  m <- kpss.test(x, null = "Level", lshort = TRUE)
  return(data.frame(KPSS_Level = m$statistic, P_Value = m$p.value, Hypothesis = "Level"))
  
}


lapply(df_macro %>% select_if(is.numeric), kpssTest_Level) -> m2

# Show results: 
do.call("bind_rows", m2) %>% 
  mutate(Variable = names(m2)) %>% 
  mutate_if(is.numeric, function(x) {round(x, 3)}) %>% 
  select(Variable, everything()) %>% 
  kable()

Variable	KPSS_Level	P_Value	Hypothesis
DR	0.930	0.010	Level
GDP	0.302	0.100	Level
UER	0.991	0.010	Level
CPI	0.739	0.010	Level
HPI	0.666	0.017	Level
IR	0.810	0.010	Level

# Conduct regression for Default Rate (DR) by means of Lag 4 for GDP and UER as 
# described in page 102: 

df_macro %>% 
  mutate(GDP_lag = lag(GDP, n = 4)) %>% 
  na.omit() -> df_lag4


df_lag4 %>% 
  lm(DR ~ GDP_lag + UER, data = .) -> ols_lag4

# Results: 
ols_lag4 %>% summary()

## 
## Call:
## lm(formula = DR ~ GDP_lag + UER, data = .)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.3011 -0.4325 -0.1886  0.4557  1.6665 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -5.20442    0.78398  -6.638 1.29e-07 ***
## GDP_lag     -0.21198    0.06081  -3.486  0.00137 ** 
## UER          1.40331    0.11205  12.524 2.73e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7805 on 34 degrees of freedom
## Multiple R-squared:  0.9046, Adjusted R-squared:  0.899 
## F-statistic: 161.2 on 2 and 34 DF,  p-value: < 2.2e-16

# Compare actuals and predictions: 

df_lag4 %>%
  mutate(Predicted = ols_lag4$fitted.values) %>% 
  select(DATE, DR, Predicted) %>% 
  gather(a, b, -DATE) %>% 
  mutate(b = b / 100) %>% 
  ggplot(aes(DATE, b, color = a)) + 
  geom_line() + 
  theme_ft_rc() + 
  scale_y_continuous(labels = scales::percent) + 
  scale_colour_manual(values = c("orange", "purple"), name = "", labels = c("DR Actual", "DR Predicted")) + 
  labs(x = "Report Date", y = NULL, 
       title = "DR Actuals and Predictions, 2004 - 2013")

Step 3

#=======================================
#  Perform Stage 3: calculate PD shift
#=======================================

# A portfolio made by 5 accounts: 

my_port <- data.frame(ID = 1:5, 
                      Segment = c(rep("Corporate", 3), rep("SME", 2)), 
                      PD_0 = c(0.5, 2, 3, 3.5, 4))

# Data about macroeconomic scenario for next 5 quarters: 
macro_scenario <- data.frame(DATE = df_lag4 %>% slice(which.max(DATE)) %>% pull(DATE) + (1:5)*90, 
                             GDP_lag = c(-2.94, 1.05, 1.50, 1.75, 2), 
                             UER = c(8.5, 9, 7.5, 7, 6.8))

# The last value: 
last_value <- df_lag4 %>% slice(which.max(DATE)) %>% pull(DR)


#----------------------
#  Propotional shift
#----------------------

# Calculate proportional variation by proportional shift (page 148): 
prop_variation <- predict(ols_lag4, macro_scenario %>% slice(1)) / last_value

# Lifetime PD at t1 as presented in table 3.24, page 149: 
my_port %>% 
  mutate(LifetimePD_t1 = round(PD_0*prop_variation, 2)) -> df_pd1

kable(df_pd1)

ID	Segment	PD_0	LifetimePD_t1
1	Corporate	0.5	0.63
2	Corporate	2.0	2.52
3	Corporate	3.0	3.78
4	SME	3.5	4.41
5	SME	4.0	5.04

#-----------------
#  Logit shift
#-----------------

---
title: "IFRS 9 and CECL Credit Risk Modelling (Chapter 3, Part 1)"
author: "Nguyen Chi Dung"
date: "`r format(Sys.time(), '%d %B, %Y')`"
subtitle: "Training Course"
output:
  html_document:
    code_download: yes
    # code_folding: hide
    highlight: zenburn
    theme: flatly
    toc: yes
    toc_float: yes
  word_document:
    toc: yes
---

```{r setup,include=FALSE}
knitr::opts_chunk$set(echo = TRUE, warning = FALSE, message = FALSE, fig.retina=2)
```

![](C:\\Users\\Zbook\\Desktop\\ifrs9_Bellini\\chap2_p1.JPG)

# Introduction

One of the key innovations introduced by the new accounting standards refer to lifetime losses. Though this concept is not new in risk management, its implementation in the financial industry is extremely contemporary.

Account-level data is usually required to develop a lifetime PD. Based on data availability, one may consider the lifetime PD based on porfolio-level data when account-level data is not available. 


IFRS 9 requires banks to compute ECL, based on point-in-time (PIT or Oneyear PD), unbiased, forwardlooking, and lifetime estimates. [The previous post](http://rpubs.com/chidungkt/496068) focused on one-year PIT PD, the aim of this post is to embed a forward-looking perspective, and extend over a lifetime PD modelling for portfolio-level data. Few alternative approaches can be as follows: 


![](C:\\Users\\Zbook\\Desktop\\ifrs9_Bellini\\chap3_p2.png)

# Lifetime PD Modelling for Portfolio-level

When data are not available at account-level, or micro-granularity is not needed, one may conduct the study at portfolio-level. The idea is to fit a creditworthiness index against MVs (Bellini, 2017). A PD shift, based on macroeconomic projections, is applied on top of one-year PIT PDs to derive forward-looking PDs. Finally, a lifetime term structure is computed for each account, based on Equation 3.5 (page 99). 

Lifetime PD modelling based on portfolio-level data can be implemented by a four-step procedure described as follows: 

- **Step 1**: Modelling Oneyear PD as presented in [previous post]((http://rpubs.com/chidungkt/496068)). 
- **Step 2**: Develop a **link function** rely on default rates (DRs). 
- **Step 3**: Calculate **PD shift** based on macroeconomic projections feeding the link function investigated above.
- **Step 4**: Calculate **lifetime PD**. 

This post presents process of modelling lifetime PD for portfolio-level data by using R language. 

# Step 2


```{r}
# Import some R packages: 

rm(list = ls())
library(tidyverse)
library(lubridate)
library(hrbrthemes)
library(tseries)
library(knitr)

# Import data: 
df_macro <- readxl::read_excel("C:\\Users\\Zbook\\Desktop\\ifrs9_Bellini\\chap3\\chap3drts.xlsx")
names(df_macro) <- str_to_upper(names(df_macro))
df_macro <- df_macro %>% mutate(DATE = ymd(DATE))


# Macroeconomic Indicators and PD from 2004 to 3013 (as presented in page 101): 
df_macro %>% 
  gather(a, b, -DATE) %>% 
  mutate(b = b / 100) %>% 
  ggplot(aes(DATE, b)) + 
  geom_line(color = "orange") + 
  scale_y_continuous(labels = scales::percent) + 
  facet_wrap(~ a, scales = "free") + 
  theme_ft_rc() + 
  labs(x = "Report Date", y = NULL, 
       title = "Fluctuation of Some Macroeconomic Indicators, 2004 - 2013") 

#===================================
#  Perform Stage 2: link function
#===================================

# Funtion for conduct KPSS test for time series: 

kpssTest_Trend <- function(x) {
  m <- kpss.test(x, null = "Trend", lshort = TRUE)
  return(data.frame(KPSS_Level = m$statistic, P_Value = m$p.value, Hypothesis = "Trend"))
  
}


lapply(df_macro %>% select_if(is.numeric), kpssTest_Trend) -> m1

# Show results: 
do.call("bind_rows", m1) %>% 
  mutate(Variable = names(m1)) %>% 
  mutate_if(is.numeric, function(x) {round(x, 3)}) %>% 
  select(Variable, everything()) %>% 
  kable()



kpssTest_Level <- function(x) {
  m <- kpss.test(x, null = "Level", lshort = TRUE)
  return(data.frame(KPSS_Level = m$statistic, P_Value = m$p.value, Hypothesis = "Level"))
  
}


lapply(df_macro %>% select_if(is.numeric), kpssTest_Level) -> m2

# Show results: 
do.call("bind_rows", m2) %>% 
  mutate(Variable = names(m2)) %>% 
  mutate_if(is.numeric, function(x) {round(x, 3)}) %>% 
  select(Variable, everything()) %>% 
  kable()


# Conduct regression for Default Rate (DR) by means of Lag 4 for GDP and UER as 
# described in page 102: 

df_macro %>% 
  mutate(GDP_lag = lag(GDP, n = 4)) %>% 
  na.omit() -> df_lag4


df_lag4 %>% 
  lm(DR ~ GDP_lag + UER, data = .) -> ols_lag4

# Results: 
ols_lag4 %>% summary()

# Compare actuals and predictions: 

df_lag4 %>%
  mutate(Predicted = ols_lag4$fitted.values) %>% 
  select(DATE, DR, Predicted) %>% 
  gather(a, b, -DATE) %>% 
  mutate(b = b / 100) %>% 
  ggplot(aes(DATE, b, color = a)) + 
  geom_line() + 
  theme_ft_rc() + 
  scale_y_continuous(labels = scales::percent) + 
  scale_colour_manual(values = c("orange", "purple"), name = "", labels = c("DR Actual", "DR Predicted")) + 
  labs(x = "Report Date", y = NULL, 
       title = "DR Actuals and Predictions, 2004 - 2013") 

```


# Step 3

```{r}
#=======================================
#  Perform Stage 3: calculate PD shift
#=======================================

# A portfolio made by 5 accounts: 

my_port <- data.frame(ID = 1:5, 
                      Segment = c(rep("Corporate", 3), rep("SME", 2)), 
                      PD_0 = c(0.5, 2, 3, 3.5, 4))

# Data about macroeconomic scenario for next 5 quarters: 
macro_scenario <- data.frame(DATE = df_lag4 %>% slice(which.max(DATE)) %>% pull(DATE) + (1:5)*90, 
                             GDP_lag = c(-2.94, 1.05, 1.50, 1.75, 2), 
                             UER = c(8.5, 9, 7.5, 7, 6.8))

# The last value: 
last_value <- df_lag4 %>% slice(which.max(DATE)) %>% pull(DR)


#----------------------
#  Propotional shift
#----------------------

# Calculate proportional variation by proportional shift (page 148): 
prop_variation <- predict(ols_lag4, macro_scenario %>% slice(1)) / last_value

# Lifetime PD at t1 as presented in table 3.24, page 149: 
my_port %>% 
  mutate(LifetimePD_t1 = round(PD_0*prop_variation, 2)) -> df_pd1

kable(df_pd1)

#-----------------
#  Logit shift
#-----------------



```












IFRS 9 and CECL Credit Risk Modelling (Chapter 3, Part 1)

Training Course

Nguyen Chi Dung

07 June, 2019

Introduction

Lifetime PD Modelling for Portfolio-level

Step 2

Step 3