In Martin-Summer-1090/syslosseval: Provide data and functions to support the analysis in Systemic Loss Evaluation

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

library(syslosseval)
library(tidyverse)
library(xtable)

The EBA stress test results

One year, two year and three year ahead stress scenario. We read the stress data and use the make_state_variables() function to compute the state variables:

stress_data_2016 <- make_stress_data(eba_exposures_2016, eba_impairments_2016, 1, 2015)
data_2016 <- make_state_variables(stress_data_2016)

stress_data_2017 <- make_stress_data(eba_exposures_2016, eba_impairments_2016, 2, 2015)
data_2017 <- make_state_variables(stress_data_2017)

stress_data_2018 <- make_stress_data(eba_exposures_2016, eba_impairments_2016, 3, 2015)
data_2018 <- make_state_variables(stress_data_2018)

We can now use the make_table_initial_state() and the make_table_stress_state() function to generate dataframes with the relevant data. We can then make a comparison with the EBA figures on leverage ratio from the EBA Results report (https://www.eba.europa.eu/sites/default/documents/files/documents/10180/1532819/e5fe6caf-8a52-4879-a694-d17a45f24c8c/2016-EU-wide-stress-test-Results.pdf?retry=1)

initial_state <- make_table_initial_state(data_2016) %>% 
  add_column(State = "initial_2015") %>%
  add_column(Case = "No_Del") %>% 
  rename(Total_Assets = a_0) %>% 
  rename(CET1 = e_0) %>% 
  rename(Leverage = lambda_0)

stress_state_2016 <- make_table_stress_state(data_2016) %>% 
  add_column(State = "adverse_2016")%>% 
  add_column(Case="No_Del") %>% 
  rename(Total_Assets = a_1) %>% 
  rename(CET1 = e_1) %>% 
  rename(Leverage = lambda_1)

stress_state_2017 <- make_table_stress_state(data_2017) %>% 
  add_column(State = "adverse_2017")%>%
  add_column(Case="No_Del") %>% 
  rename(Total_Assets = a_1) %>% 
  rename(CET1 = e_1) %>% 
  rename(Leverage = lambda_1)

stress_state_2018 <- make_table_stress_state(data_2018) %>% 
  add_column(State = "adverse_2018")%>%
  add_column(Case ="No_Del") %>% 
  rename(Total_Assets = a_1) %>% 
  rename(CET1 = e_1) %>% 
  rename(Leverage = lambda_1)

Combine all data in a common long dataframe

leverage_data_no_del <- bind_rows(initial_state, stress_state_2016, stress_state_2017, stress_state_2018) %>% 
  mutate(State = factor(State, levels = c("initial_2015", "adverse_2016", "adverse_2017", "adverse_2018")))

Now we make the comparable figure to Figure 13 in EBA 2016 Results using our data.

pb_2016 <- ggplot(data = leverage_data_no_del, mapping = aes(x = State, y = Leverage, fill = State)) 


box_plots_2016 <- pb_2016 + geom_boxplot(alpha = 0.5) +
  labs(x="Year") +
  scale_x_discrete(labels=c("initial_2015" = "2015", "adverse_2016" = "2016",
                              "adverse_2017" = "2017", "adverse_2018" = "2018")) +
  scale_fill_discrete(name = "State", labels = c("Initial state year end 2015", 
                                                 "Adverse scenario 2016", "Adverse scenario 2017",
                                                 "Adverse scenario 2018"))

#box_plots_2016
ggsave(filename = "../paper/Figures/leverage_box_plots_2016.png", plot = box_plots_2016)

Make a plot of the exceeding banks

exceeders_no_del <- leverage_data_no_del %>% 
  filter(Leverage >= 33)

Check the rank of exceeders with respect to total assets:

ranks <- leverage_data_no_del %>% 
  arrange(desc(Total_Assets)) %>% 
  filter(State == "initial_2015")

exceed_no_del <- ggplot(data=exceeders_no_del, mapping = aes(x=State, fill = State))

exceed_plot <- exceed_no_del + geom_bar()+
  scale_x_discrete(labels=c("initial_2015" = "2015", "adverse_2016" = "2016",
                              "adverse_2017" = "2017", "adverse_2018" = "2018"))+
  scale_fill_discrete(name = "State", labels = c("Initial state year end 2015", 
                                                 "Adverse scenario 2016", "Adverse scenario 2017",
                                                 "Adverse scenario 2018"))+
  labs(x="Year")+
  labs(y="Number of Banks")+
  coord_flip() +
  annotate("text", x=1, y=2.7, size=2, label="N.V. Bank Nederlandse Gemeenten, rank: 40")+
  annotate("text", x=2.3, y=2.5, size=2, label="N.V. Bank Nederlandse Gemeenten, rank:40")+
  annotate("text", x=2.2, y=2.5, size=2, label="Lloyds Banking Group Plc, rank:10")+
  annotate("text", x=2.1, y=2.5, size=2, label="Deutsche Bank AG, rank:3")+
  annotate("text", x=2.0, y=2.5, size=2, label="La Banque Postale, rank:30")+
  annotate("text", x=1.9, y=2.5, size=2, label="Barclays Plc, rank 5")+
  annotate("text", x=1.8, y=2.5, size=2, label="Banca Monte dei Paschi di Siena S.p.A., rank: 35")+
  annotate("text", x=1.7, y=2.5, size=2, label="Société Générale S.A., rank 7")+
  annotate("text", x=3.3, y=2.5, size=2, label="N.V. Bank Nederlandse Gemeenten, rank: 40")+
  annotate("text", x=3.2, y=2.5, size=2, label="Lloyds Banking Group Plc, rank:10")+
  annotate("text", x=3.1, y=2.5, size=2, label="Deutsche Bank AG, rank: 3")+
  annotate("text", x=3.0, y=2.5, size=2, label="La Banque Postale, rank: 30")+
  annotate("text", x=2.9, y=2.5, size=2, label="Barclays Plc, rank: 5")+
  annotate("text", x=2.8, y=2.5, size=2, label="Banca Monte dei Paschi di Siena S.p.A., rank: 35")+
  annotate("text", x=2.7, y=2.5, size=2, label="Société Générale S.A., rank: 7")+
  annotate("text", x=2.6, y=2.5, size=2, label="BNP Paribas, rank: 2")+
  annotate("text", x=4.3, y=2.5, size=2, label="N.V. Bank Nederlandse Gemeenten, rank: 40")+
  annotate("text", x=4.2, y=2.5, size=2, label="Lloyds Banking Group Plc, rank:10")+
  annotate("text", x=4.1, y=2.5, size=2, label="Deutsche Bank AG, rank:3")+
  annotate("text", x=4.0, y=2.5, size=2, label="La Banque Postale, rank 30")+
  annotate("text", x=3.9, y=2.5, size=2, label="Barclays Plc, rank: 5")+
  annotate("text", x=3.8, y=2.5, size=2, label="Banca Monte dei Paschi di Siena S.p.A., rank: 35")+
  annotate("text", x=3.7, y=2.5, size=2, label="Société Générale S.A., rank: 7")



ggsave(filename = "../paper/Figures/exceed_plot_2016.png", plot = exceed_plot)
exceed_plot

What's the relative size of these banks in relation to the entrire total assets?

relative_size_no_del <- leverage_data_no_del %>% 
  mutate(Agg_Total_Assets = sum(Total_Assets)) %>% 
  filter(Leverage > 33) %>% 
  group_by(State) %>% 
  summarize(Share = sum(Total_Assets))

Loss in CET1

relative_cet1_no_del <- leverage_data_no_del %>% 
  group_by(State) %>% 
  summarize(Tot = sum(CET1)) 

near_threshold_no_del <- leverage_data_no_del %>% 
  filter(Leverage >= 31 & Leverage < 33)

Fire Sales

Compute the fixed points first:

fix_2016 <- fixed_point_computation_function(
                                       mat = data_2016, lb = 33,
                                       data_idx = sovereign_bond_indices,
                                       data_adv = average_daily_volume_sovereign,
                                       base_year = 2015,
                                       constant = 5 )

fix_2017 <- fixed_point_computation_function(
                                       mat = data_2017, lb = 33,
                                       data_idx = sovereign_bond_indices,
                                       data_adv = average_daily_volume_sovereign,
                                       base_year = 2015,
                                       constant = 5 )

fix_2018 <- fixed_point_computation_function(
                                       mat = data_2018, lb = 33,
                                       data_idx = sovereign_bond_indices,
                                       data_adv = average_daily_volume_sovereign,
                                       base_year = 2015,
                                       constant = 5 )

Make a table with the values of the fixed points

c1 <- fix_2016 %>% select(sec_class, delta_lower) %>% 
  rename(delta_2016 = delta_lower)
c2 <- fix_2017 %>% select(delta_lower) %>% 
  rename(delta_2017 = delta_lower)
c3 <- fix_2018 %>% select(delta_lower) %>% 
  rename(delta_2018 = delta_lower)

fixed_points <- bind_cols(c1,c2,c3)

Write a Latex-table

latex_fixed_points <- xtable(fixed_points)
print(latex_fixed_points, file = "../paper/Tables/fixed_points_2016.txt")

Make a table of the results:

stress_state_2016_del <- make_table_final_state(data_2016, fix_2016, 33) %>% 
  add_column(State = "adverse_2016")%>% 
  add_column(Case="Del") %>% 
  rename(Total_Assets = a_1_tau) %>% 
  rename(CET1 = e_1_tau) %>% 
  rename(Leverage = lambda_1_tau)

stress_state_2017_del <- make_table_final_state(data_2017, fix_2017, 33) %>% 
  add_column(State = "adverse_2017")%>%
  add_column(Case="Del") %>% 
  rename(Total_Assets = a_1_tau) %>% 
  rename(CET1 = e_1_tau) %>% 
  rename(Leverage = lambda_1_tau)

stress_state_2018_del <- make_table_final_state(data_2018, fix_2018, 33) %>% 
  add_column(State = "adverse_2018")%>%
  add_column(Case ="Del") %>% 
  rename(Total_Assets = a_1_tau) %>% 
  rename(CET1 = e_1_tau) %>% 
  rename(Leverage = lambda_1_tau)

Bind all data into one frame

leverage_data_del <- bind_rows(stress_state_2016_del, stress_state_2017_del, stress_state_2018_del) %>% 
  mutate(State = factor(State, levels = c("adverse_2016", "adverse_2017", "adverse_2018")))

Compare to the maximum impact:

max_delta_2016 <- fix_2016 %>% 
  mutate(rel_2016 = delta_upper/delta_max)

max_delta_2017 <- fix_2017 %>% 
  mutate(rel_2017 = delta_upper/delta_max)

max_delta_2018 <- fix_2018 %>% 
  mutate(rel_2018 = delta_upper/delta_max)

Make a table

aux1 <- max_delta_2016 %>% 
  select(sec_class, delta_max, rel_2016)
aux2 <- max_delta_2017 %>% 
  select(rel_2017)
aux3 <- max_delta_2018 %>% 
  select(rel_2018)

rel_table <- bind_cols(aux1, aux2, aux3)

Make a latex table

latex_rel_table <- xtable(rel_table)
print(latex_rel_table, file = "../paper/Tables/rel_table.txt")

exceeders_del <- leverage_data_del %>% 
  filter(Leverage >= 33)

Share of the two additional banks in total assets of the banking system:

additional <- exceeders_del %>% 
  filter(Bank_name %in% c("Banco Popolare - Società Cooperativa", "BNP Paribas"))
additional

relative_size_del <- leverage_data_del %>% 
  mutate(Agg_Total_Assets = sum(Total_Assets)) %>% 
  group_by(State) %>% 
  summarize(total = sum(Total_Assets))
relative_size_del

Some of the exceeders sell their entire portfolio.

delta <- select(fix_2016, delta_upper) %>% unlist() %>% unname()
shares <- bank_behavior_function(delta, data_2016, 33)
Bank_names <- rownames(shares) %>% unname()

dat <- bind_cols(Bank_names, shares) %>% 
  rename(Bank_names = ...1) %>% 
  rename(Shares = ...2)

sel <- dat %>% 
  filter(Bank_names %in% c("N.V. Bank Nederlandse Gemeenten", "Banco Popolare - Società Cooperativa", 
                           "Lloyds Banking Group Plc", "Deutsche Bank AG", "La Banque Postale", 
                           "Barclays Plc", "Banca Monte dei Paschi di Siena S.p.A.", "Société Générale S.A.", 
                           "BNP Paribas"))

Losses in equity:

relative_cet1_del <- leverage_data_del %>% 
  group_by(State) %>% 
  summarize(Tot = sum(CET1))

total_cet1 <- leverage_data_no_del %>% 
  filter(State == "initial_2015") %>% 
  summarize(Total = sum(CET1))

comp_data_no_del <- leverage_data_no_del %>%
  select(Bank_name, CET1, State, Case) 

aux <- filter(comp_data_no_del, State == "initial_2015") %>% 
  mutate(Case = "Del")

comp_data_del <- bind_rows(aux, leverage_data_del) %>%  
  select(Bank_name, CET1, State, Case) 

We need to transofrm the data for our computations:

comp_data_no_del_trans <- comp_data_no_del %>% 
  pivot_wider(names_from = "State", values_from= "CET1") %>% 
  mutate("Loss 2016" = 1 - adverse_2016/initial_2015) %>% 
  mutate("Loss 2017" = 1 - adverse_2017/initial_2015) %>% 
  mutate("Loss 2018" = 1 - adverse_2018/initial_2015) %>% 
  select(Bank_name, "Loss 2016", "Loss 2017", "Loss 2018", Case) %>% 
  pivot_longer(!c("Bank_name", "Case"), names_to = "Losses", values_to = "Percent")

comp_data_del_trans <- comp_data_del %>% 
  pivot_wider(names_from = "State", values_from= "CET1") %>% 
  mutate("Loss 2016" = 1 - adverse_2016/initial_2015) %>% 
  mutate("Loss 2017" = 1 - adverse_2017/initial_2015) %>% 
  mutate("Loss 2018" = 1 - adverse_2018/initial_2015) %>% 
  select(Bank_name, "Loss 2016", "Loss 2017", "Loss 2018", Case) %>% 
  pivot_longer(!c("Bank_name", "Case"), names_to = "Losses", values_to = "Percent")

compare_data_cet1 <- bind_rows(comp_data_no_del_trans, comp_data_del_trans)

aux_plot <- ggplot(data = compare_data_cet1, mapping = aes(x = Case, y = Percent, fill = Case))

compare_plot <- aux_plot + geom_boxplot(alpha = 0.5) +
  scale_x_discrete(labels=c("Del" = "Del.", "No_Del" = "No Del.")) +
  scale_fill_discrete(name = "Case", labels = c("Deleveraging", "No Deleveraging"))+
  scale_y_continuous(labels = scales::percent_format(accuracy = 1))+
  facet_wrap(~Losses)

compare_plot
ggsave(filename = "../paper/Figures/cet1_losses_2016.png", plot = compare_plot)

Martin-Summer-1090/syslosseval documentation built on Dec. 17, 2021, 3:14 a.m.