Benchmark data

Risk-free Rates

tbill <- vroom("https://fred.stlouisfed.org/graph/fredgraph.csv?bgcolor=%23e1e9f0&chart_type=line&drp=0&fo=open%20sans&graph_bgcolor=%23ffffff&height=450&mode=fred&recession_bars=on&txtcolor=%23444444&ts=12&tts=12&width=1168&nt=0&thu=0&trc=0&show_legend=yes&show_axis_titles=yes&show_tooltip=yes&id=DTB3&scale=left&cosd=2009-08-01&coed=2020-10-09&line_color=%234572a7&link_values=false&line_style=solid&mark_type=none&mw=3&lw=2&ost=-99999&oet=99999&mma=0&fml=a&fq=Daily&fam=avg&fgst=lin&fgsnd=2020-02-01&line_index=1&transformation=lin&vintage_date=2020-10-14&revision_date=2020-10-14&nd=1954-01-04") %>%
  mutate(DTB3 = DTB3/100) %>%
  rename("date" = "DATE",
         "T_bill" = "DTB3") %>% 
  mutate(T_bill_d = (1 + T_bill)^(1/252)-1,
         date = as.Date(date,"%Y-%m-%d"))

Indices

benchmark <- 
  data.frame(index = c("MNA", "^RUA", "^FTSE","^FTAS", "^IXIC","NYA", "^DJI", "^GSPC"),
             description = c("IQ Merger Arbitrage ETF", "Russell_3000", "FTSE 100", "FTSE All Share","NASDAQ_Composite", "NYSE Composite", "Dow Jones Industrial Average", "SP_500")) %>% 
  tq_get(get  = "stock.prices",
         from = "2009-01-01",
         to   = "2020-08-31") %>%
  select(index, description, date, close) %>%
  group_by(index) %>%
  mutate(index_return = close/lag(close) - 1)

Merger Data

Merger Deals

stocks2 <- read_excel("MA_vF.xlsx", sheet = "Sheet1") %>% 
  select(acquirer, target, DealStatus, announce_date, close_date) %>%
  mutate(DealStatus = case_when(
    DealStatus == "Completed" ~ DealStatus,
    TRUE ~ "Failed"),
    DealID = paste(acquirer,target))

Get Stock Data and build Dataframes

To create our data set we used the acquired deal data from Bloomberg and downloaded the respective companies’ opening stock prices from Yahoo Finance. Here a big part of the data got lost due to the nature of Yahoo Finance stopping to track stocks that are no longer traded. As companies that have been acquired do no longer trade their shares, we have poor data quality for the target data set.

acquirer_raw <- stocks2 %>%
  select(acquirer) %>% 
  tq_get(get  = "stock.prices",
         from = "2009-01-01",
         to   = "2020-08-31") %>%
  select(date, acquirer, open, close)

target_raw <- stocks2 %>% 
  select(target) %>% 
  tq_get(get  = "stock.prices",
         from = "2009-01-01",
         to   = "2020-08-31") %>%
  select(date, target, open, close)

# Reformat acquirer data
stock_data_acquirer <- acquirer_raw %>%
  group_by(acquirer) %>% 
  mutate(close_acquirer = sprintf("%.2f", open, na.rm = TRUE)) %>%
  select(acquirer, date, close_acquirer)

# Reformat target data
stock_data_target <- target_raw %>%
  group_by(target) %>% 
  mutate(close_target = sprintf("%.2f", open, na.rm = TRUE)) %>%
  select(target, date, close_target)

Daily Return and Acquirer - Target Spread

To investigate the stock return spread between targets and acquirers in M&A deals we then calculated the mean daily returns for all targets and acquirers per period from announcement day. We found that in the early days after an announcement the target’s stocks tends to outperform the acquirer and achieves a positive return. The acquirer’s stock on the other hand often suffers from negative returns. As can be seen in the chart below this spread quickly vanishes and is predominantly kept alive by some sporadic high returns of targets in our data set.

acq_tar %>%
  group_by(period) %>%
  # Summarise means per period whilst removing all NAs. Bad data quality forces us to do this
  summarise(mean_acq = mean(ret_acq, na.rm = TRUE),
            mean_tar = mean(ret_tar, na.rm = TRUE),
            mean_strat = mean(ret_combined, na.rm = TRUE)) %>%
  filter(period <= 50) %>%
  ggplot() +
  theme_bw() +
  geom_line(aes(x = period, y = (mean_acq)), colour = "red") + # Acquirer return
  geom_line(aes(x = period, y = (mean_tar)), colour = "blue") + # Target return

  labs(title = "Return spread between Target and Acquirer narrows quickly",
       subtitle = "Mean Daily Returns of Targets and Acquirers per Day from Announcement",
       y = "Daily Returns",
       x = "Day from initial announcement") + 
  theme_economist_white()

ggsave("Return Spread Target an Acquirer.png",
       plot = last_plot(),
       scale = 1,
       width = 20,
       height = 15,
       units = "cm",
       dpi = 300,
       limitsize = TRUE)

knitr::include_graphics(here::here("Return Spread Target an Acquirer.png"), error = FALSE)

acq_tar %>%
  group_by(period) %>%
  # Summarise means per period whilst removing all NAs. Bad data quality forces us to do this
  summarise(mean_acq = mean(ret_acq, na.rm = TRUE),
            mean_tar = mean(ret_tar, na.rm = TRUE),
            mean_strat = mean(ret_combined, na.rm = TRUE)) %>%
  filter(period <= 50) %>%
  ggplot() +
  theme_bw() +
  geom_line(aes(x = period, y = (mean_strat)), colour = "green") + # Portfolio 
  labs(title = "Target and Acquirer Spread drives Strategy Return",
       subtitle = "Mean Daily Returns of Strategy per Day from Announcement",
       y = "Daily Returns",
       x = "Day from initial announcement") + 
  theme_economist_white()

ggsave("Strategy Return from Spread.png",
       plot = last_plot(),
       scale = 1,
       width = 20,
       height = 15,
       units = "cm",
       dpi = 300,
       limitsize = TRUE)

knitr::include_graphics(here::here("Strategy Return from Spread.png"), error = FALSE)

Cumulative Return

To put the previously discovered spread in daily returns into more context we calculated the average cumulative returns of both acquirers and targets over time. We then calculated the mean cumulative return of all targets and acquirers per period p.

# Cumulative return for acquirer
initial_acq <- acq_tar %>%
  filter(period == 0) %>%
  rename(initial_acq = close_acquirer) %>%
  select(acquirer, target, initial_acq) %>%
  distinct()

cum_acq <- left_join(acq_tar, initial_acq, by = c("acquirer", "target")) %>%
  mutate(cum_ret_acq = ifelse(period > -1, close_acquirer/initial_acq - 1, NA)) %>%
  group_by(period) %>%
  summarise(mean_cum_ret_acq = mean(cum_ret_acq, na.rm =TRUE)) %>%
  filter(period <= 50)

# Cumulative return for target
initial_tar <- acq_tar %>%
  filter(period == 0) %>%
  rename(initial_tar = close_target) %>%
  select(acquirer, target, initial_tar) %>% 
  distinct()

cum_tar <- left_join(acq_tar, initial_tar, by = c("acquirer", "target")) %>%
  mutate(cum_ret_tar = ifelse(period > -1, close_target/initial_tar - 1, NA)) %>%
  group_by(period) %>%
  summarise(mean_cum_ret_tar = mean(cum_ret_tar, na.rm =TRUE)) %>%
  filter(period <= 50)

# Combine all
cum_all <- left_join(cum_acq, cum_tar, by = "period") %>%
  filter(period <= 50)
  

ggplot(cum_all) +
  
  geom_line(aes(x = period, y = mean_cum_ret_tar), colour = "blue") +
  geom_line(aes(x = period, y = mean_cum_ret_acq), colour = "red") +
  theme_bw() +
  labs(subtitle = "Mean Cumulative Return - Investments start 1 day after announcement",
       title = "Target outperformance in cumulative return driven by early gains",
       y = "Cumulative Return",
       x = "Day from announcement") + 
  theme_economist_white()

ggsave("Cumulative Returns Target and Acquirer.png",
       plot = last_plot(),
       scale = 1,
       width = 20,
       height = 15,
       units = "cm",
       dpi = 300,
       limitsize = TRUE)

knitr::include_graphics(here::here("Cumulative Returns Target and Acquirer.png"), error = FALSE)

Correlation between return and deal completion

end_acq <- acq_tar %>%
  mutate(diff = close_date - date) %>%
  filter(diff == 0) %>%
  rename(end_acq = close_acquirer) %>%
  select(acquirer, period, target, end_acq, DealStatus) %>%
  distinct()


deal_ret_acq <- left_join(end_acq, initial_acq, by = c("acquirer", "target")) %>% 
  distinct() %>%
  mutate(annualised_ret = (end_acq/initial_acq)^(252/period) - 1) %>%
  group_by(DealStatus) %>%
  summarise(mean_annualised_acq_ret = median(annualised_ret, na.rm = TRUE))

deal_ret_acq

end_tar <- acq_tar %>%
  mutate(diff = close_date - date) %>%
  filter(diff == 0) %>%
  rename(end_tar = close_target) %>%
  select(acquirer, period, target, end_tar, DealStatus) %>%
  distinct()


deal_ret_tar <- left_join(end_tar, initial_tar, by = c("acquirer", "target")) %>%
  filter(!is.na(end_tar)) %>%
  mutate(annualised_ret = (end_tar/initial_tar)^(252/period) - 1) %>%
  group_by(DealStatus) %>%
  summarise(mean_annualised_tar_ret = sprintf("%.2f",median(annualised_ret, na.rm = TRUE)))

deal_ret_tar

Returns of strategy over timeline

From our analysis above we can find an arbitrage strategy that should yield risk-free returns by going long on target stocks and going short on acquirer stocks. Whereas we could protect ourselves from more risk by following a strategy closer to the one described in the economic rational chapter, longing and shorting the respective companies in a ratio as per the announced deal proposal, we follow a more simplified strategy for this project.

For every deal announced we will execute a long transaction for the target and a short transaction for the acquirer. In periods where deals overlap, we will assume an equal weighting in our investments, i.e. the strategy return will be the average of all targets’ and acquirers’ returns. For every time period without an active deal being in place, we will move our portfolio into the market, proxied by the S&P500 index.

Due to our difficulties of attaining target companies’ stock price data from Yahoo Finance for older deals we decided to use 01-01-2015 as our inception date for strategy. The majority of deals with good quality data are post this date which means we have less data-quality driven random fluctuations in our calculations.

As seen in the earlier section our performance spread between targets and acquirers narrows very quickly and hovers around 0% after 50 days. Due to our simplified nature of our strategy we want to avoid low spreads in later periods (post day 50) to neutralize high spreads of other deals in early periods if their dates happen to overlap. We therefore excluded all spready post day 50 from announcement.

acq_tar2 <- acq_tar %>%
  filter(period <= 50) %>% 
  group_by(date) %>%
  summarise(ret_strat = mean(ret_combined)) %>% 
  filter(!is.na(ret_strat))




SP_initial <- benchmark %>%
  filter(description == "SP_500") %>%
  filter(date >= "2015-01-01") %>%
  arrange(date) %>%
  head(n = 1) %>%
  rename(initial_index = close) %>%
  select(- date, - index_return)

  ggplot(acq_tar2) +
  geom_line(aes(x = date, y = ret_strat), colour = "red") 

benchmark %>%
  filter(description == "SP_500") %>%
  arrange(date) %>%
  left_join(SP_initial, by = c("description", "index")) %>%
  left_join(acq_tar2, by = "date") %>%
  select(date, close, initial_index, ret_strat) %>%
  mutate(index_ret = close/lag(close) - 1,
         cum_index_ret = close/initial_index,
         ret_strat_adjusted = ifelse(is.na(ret_strat), index_ret, ret_strat)) %>%
  filter(date >= "2015-01-01") %>%
  mutate(retplus1 = ret_strat_adjusted + 1,
    cum_ret_strat = cumprod(retplus1)) %>%
  ggplot() +
  geom_line(aes(x = date, y = cum_index_ret), colour = "red") +
  geom_line(aes(x = date, y = cum_ret_strat), colour = "green") +
  labs(subtitle = "Cumulative Return Strategy vs Index",
       title = "Perfect Foresight Generates Above Market Returns",
       y = "Cumulative Return",
       x = "Day from initial investment") + 
  theme_economist_white()

ggsave("Cumulative Return Strategy vs Index.png",
       plot = last_plot(),
       scale = 1,
       width = 20,
       height = 15,
       units = "cm",
       dpi = 300,
       limitsize = TRUE)

knitr::include_graphics(here::here("Cumulative Return Strategy vs Index.png"), error = FALSE)

benchmark %>%
  filter(description == "SP_500") %>%
  arrange(date) %>%
  left_join(SP_initial, by = c("description", "index")) %>%
  left_join(acq_tar2, by = "date") %>%
  left_join(tbill, by = "date") %>%
  select(date, close, initial_index, ret_strat, T_bill_d) %>%
  mutate(index_ret = close/lag(close) - 1,
         cum_index_ret = close/initial_index,
         ret_strat_adjusted = ifelse(is.na(ret_strat), T_bill_d, ret_strat)) %>%
  filter(date >= "2014-05-01") %>%
  mutate(retplus1 = ret_strat_adjusted + 1,
    cum_ret_strat = cumprod(retplus1)) %>%
  ggplot() +
  geom_line(aes(x = date, y = cum_index_ret), colour = "red") +
  geom_line(aes(x = date, y = cum_ret_strat), colour = "green") +
  labs(subtitle = "Cumulative Return Strategy vs Index",
       title = "Perfect Foresight Generates Above Market Returns",
       y = "Cumulative Return",
       x = "Day from initial investment") + 
  theme_economist_white()

CAPM

To test the performance of our strategy in more detail we regressed our strategy’s excess returns to our benchmark’s (S&P500) excess return, where excess return means any return above the risk-free rate as per the respective 3-month US T-Bill

benchmarkSP <- benchmark %>%
  filter(description == "SP_500") %>%
  pivot_wider(values_from = index_return, names_from = description) %>%
  select(date, SP_500)


CAPM <- acq_tar %>%
  filter(period <= 20) %>% 
  left_join(tbill, by = "date") %>%
  left_join(benchmarkSP, by = "date") %>% 
  filter(!is.na(ret_combined)) %>% 
  mutate(Rm_Rf = SP_500 - T_bill_d,
         Rs_Rf = ret_combined - T_bill_d) %>%  # CAN MUTATE RET_Strat = S&P/TBill if return = NA, then use that to replace ret_combined here
  drop_na(Rm_Rf, Rs_Rf) %>%
  filter(!is.infinite(Rs_Rf))

ggplot(CAPM, aes(x = Rm_Rf, y = Rs_Rf, na.rm = TRUE)) +
  geom_point() +
  geom_smooth(method = lm)  +
  ylim(-1,1) +
  labs(subtitle = "Excess Returns of Startegy vs Market Benchmark (scale ignoring 2 outliers)",
       title = "Regression shows minimal positive Alpha and Beta for daily returns",
       y = "Excess Return Strategy",
       x = "Excess Return Benchmark") + 
  theme_economist_white()

ggsave("Excess Returns of Startegy vs Market Benchmark.png",
       plot = last_plot(),
       scale = 1,
       width = 25,
       height = 15,
       units = "cm",
       dpi = 300,
       limitsize = TRUE)

knitr::include_graphics(here::here("Excess Returns of Startegy vs Market Benchmark.png"), error = FALSE)

CAPM_regression <- lm(Rs_Rf ~ Rm_Rf, data = CAPM, na.rm =TRUE)

CAPM_regression

## 
## Call:
## lm(formula = Rs_Rf ~ Rm_Rf, data = CAPM, na.rm = TRUE)
## 
## Coefficients:
## (Intercept)        Rm_Rf  
##    0.005822     0.000526

huxreg(CAPM_regression,
       statistics = c('#observations' = 'nobs', 
                      'R squared' = 'r.squared', 
                      'Adj. R Squared' = 'adj.r.squared', 
                      'Residual SE' = 'sigma'), 
       bold_signif = 0.05, 
       stars = NULL
)

msummary(CAPM_regression)

##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept) 0.005822   0.002950    1.97    0.049 *
## Rm_Rf       0.000526   0.311403    0.00    0.999  
## 
## Residual standard error: 0.139 on 2211 degrees of freedom
## Multiple R-squared:  1.29e-09,   Adjusted R-squared:  -0.000452 
## F-statistic: 2.85e-06 on 1 and 2211 DF,  p-value: 0.999

Our slope β not being statistically different from zero for our strategy is intuitive: for every deal we long and short one stock – every market related movement should be cancelled out. That being said, we still find a statistically significant alpha that is positive. On average our strategy, assuming perfect foresight, returns 0.87% daily unrelated to the market