Yield Curve Inversion

Yields on US rates by duration since 1960

#Plotting the graph with years on the x-axis and yields on the y-axis
ggplot(yield_curve, aes(x = date, y = price, color = maturity)) +
#Facet_wrapping by maturity and var since the levels of maturity are ordered
    facet_wrap(maturity ~ var, ncol = 2) + 
#Choosing the plot type to be a line graph
    geom_line() +
#Black and white theme
    theme_bw() +
#Setting the x-axis labels to be in date format in years
    scale_x_date(labels=date_format("%Y")) +
#Removing legend and bolding plot title
    theme(legend.position = "none", plot.title = element_text(face = "bold")) +
#Setting plot and axis titiles
    labs(y = '%', title = 'Yields on U.S. Treasury rates since 1960', caption = "Source: St. Louis Federal Reserve Economic Database (FRED)", x = "") 

Monthly yields on US rates by duration since 1999 on a year-by-year basis

#Creating new data frame with years >= 1999 and new year and month variables
yield_curve_with_years <- yield_curve %>% 
  filter(date>="1999-01-01") %>% 
   mutate(year = year(date), month = month(date))
    
#Plotting the graph with the different maturities on x-axis, yields on y-axis and grouping the yields by month
ggplot(yield_curve_with_years, aes(x = maturity, y = price, color = year, group = month)) +
#Facet wrap the plot by year
    facet_wrap(~year, ncol = 4) +
#Choosing the plot to be a line graph 
    geom_line() +
#Choosing a black and white theme
    theme_bw() +
#Removing plot legend
    theme(legend.position = "none") +
#Setting plot labels
    labs(y = 'Yield (%)', title = 'US Yield Curve', caption = "Source: St. Louis Federal Reserve Economic Database (FRED)", x = "Maturity") +
#Bolding plot title
    theme(plot.title = element_text(face = "bold"))

3-month and 10-year yields since 1999

#Creating new data frame with only 3m Treasury Bill and 10y Treasury Note, and years since 1999
yield_curve_3m_10m <- yield_curve %>% 
  filter(date>="1999-01-01", (maturity == "3m" | maturity == "10y"))

#Plotting graph with date on the x-axis and yields on the y-axis, colors grouped by var
ggplot(yield_curve_3m_10m, aes(x = date, y = price, color = var)) +
#Choosing plot to be a line graph   
    geom_line() +
#Choosing black and white theme   
    theme_bw() +
#Removing legend title and bolding plot title
    theme(legend.title = element_blank(), plot.title = element_text(face = "bold")) +
#Setting plot and axis titles
    labs(y = '%', title = 'Yields on 3-month and 10-year US Treasury rates since 1999', 
         caption = "Source: St. Louis Federal Reserve Economic Database (FRED)", x = "") +
#Setting x-axis labels to be in 5 year increments
    scale_x_date(date_breaks="5 years",labels=date_format("%Y"), limits = c(as.Date("1999-01-01"),NA))

According to Wikipedia’s list of recession in the United States, since 1999 there have been two recession in the US: between Mar 2001–Nov 2001 and between Dec 2007–June 2009. Does the yield curve seem to flatten before these recessions? Can a yield curve flattening really mean a recession is coming in the US? Since 1999, when did short-term (3 months) yield more than longer term (10 years) debt?

Besides calculating the spread (10year - 3months), there are a few things we need to do to produce our final plot

1. Setup data for US recessions
2. Superimpose recessions as the grey areas in our plot
3. Plot the spread between 30 years and 3 months as a blue/red ribbon, based on whether the spread is positive (blue) or negative(red)

• For the first, the code below creates a dataframe with all US recessions since 1946

# get US recession dates after 1946 from Wikipedia 
# https://en.wikipedia.org/wiki/List_of_recessions_in_the_United_States

recessions <- tibble(
  from = c("1948-11-01", "1953-07-01", "1957-08-01", "1960-04-01", "1969-12-01", "1973-11-01", "1980-01-01","1981-07-01", "1990-07-01", "2001-03-01", "2007-12-01"),  
  to = c("1949-10-01", "1954-05-01", "1958-04-01", "1961-02-01", "1970-11-01", "1975-03-01", "1980-07-01", "1982-11-01", "1991-03-01", "2001-11-01", "2009-06-01") 
  )  %>% 
  mutate(From = ymd(from), 
         To=ymd(to),
         duration_days = To-From)

recessions

## # A tibble: 11 x 5
##    from       to         From       To         duration_days
##    <chr>      <chr>      <date>     <date>     <drtn>       
##  1 1948-11-01 1949-10-01 1948-11-01 1949-10-01 334 days     
##  2 1953-07-01 1954-05-01 1953-07-01 1954-05-01 304 days     
##  3 1957-08-01 1958-04-01 1957-08-01 1958-04-01 243 days     
##  4 1960-04-01 1961-02-01 1960-04-01 1961-02-01 306 days     
##  5 1969-12-01 1970-11-01 1969-12-01 1970-11-01 335 days     
##  6 1973-11-01 1975-03-01 1973-11-01 1975-03-01 485 days     
##  7 1980-01-01 1980-07-01 1980-01-01 1980-07-01 182 days     
##  8 1981-07-01 1982-11-01 1981-07-01 1982-11-01 488 days     
##  9 1990-07-01 1991-03-01 1990-07-01 1991-03-01 243 days     
## 10 2001-03-01 2001-11-01 2001-03-01 2001-11-01 245 days     
## 11 2007-12-01 2009-06-01 2007-12-01 2009-06-01 548 days

• To add the grey shaded areas corresponding to recessions, we use geom_rect()
• to colour the ribbons blue/red we must see whether the spread is positive or negative and then use geom_ribbon(). You should be familiar with this from last week’s homework on the excess weekly/monthly rentals of Santander Bikes in London.

#Creating new data frame with only 3m and 10y maturities, pivoting wider and creating a new variable difference
yield_curve_final <- yield_curve %>% 
  filter((maturity == "3m" | maturity == "10y")) %>% 
  select(c("date","price","var")) %>%
  pivot_wider(names_from = "var", values_from = "price") %>% 
  mutate(difference=`10-Year Treasury Rate` - `3-Month Treasury Bill`)

#Plotting graph with date on the x-axis and the difference on the y-axis
ggplot(yield_curve_final, aes(x=date, y=difference)) +
#Choosing plot to be a line graph  
  geom_line() +
#Creating title and labels for graph
    labs(y = 'Difference (10 year-3 month) yield in %', title = 'Yield Curve Inversion: 10-year minus 3-month U.S. Treasury Rates', 
      caption = "Source: St. Louis Federal Reserve Economic Database (FRED)", 
      subtitle = "Difference in % points, monthly averages. \nShaded areas correspond to recessions", x="") +
#Selecting black and white theme
  theme_bw() +
#Fixing x-axis labels and limits
  scale_x_date(date_breaks="2 years",labels=date_format("%Y"), limits = c(as.Date("1959-01-01"),as.Date("2023-01-01"))) +
#Bolding plot title and removing legend
  theme(plot.title = element_text(face = "bold"), legend.position = "none") +
#Creating y-intercept line at 0
  geom_hline(yintercept=0,color="black") +
#Creating rugs at bottom of plot
  geom_rug(aes(colour=ifelse(difference >= 0,"steelblue2","red")), sides="b",alpha=0.5, position = "jitter") +
#Plotting the recession grey areas on plot
  geom_rect(data=filter(recessions), inherit.aes=F, aes(xmin=From, xmax=To, ymin=-Inf, ymax=+Inf), fill='grey', alpha=0.7) +
#Plotting graph ribbons
  geom_ribbon(aes(ymin = difference, ymax = pmin(difference, 0)), fill= "steelblue2", alpha=0.5) +
  geom_ribbon(aes(ymin = 0, ymax = pmin(difference, 0)),fill = "red", alpha=0.5)