Yield curve inversion

Every so often, we hear warnings from commentators on the “inverted yield curve” and its predictive power with respect to recessions. An explainer what a inverted yield curve is can be found here. If you’d rather listen to something, here is a great podcast from NPR on yield curve indicators

In addition, many articles and commentators think that, e.g., Yield curve inversion is viewed as a harbinger of recession. One can always doubt whether inversions are truly a harbinger of recessions, and use the attached parable on yield curve inversions.

In our case we will look at US data and use the FRED database to download historical yield curve rates, and plot the yield curves since 1999 to see when the yield curves flatten. If you want to know more, a very nice article that explains the yield curve is and its inversion can be found here.

First, we will use the tidyquant package to download monthly rates for different durations.

# Get a list of FRED codes for US rates and US yield curve; choose monthly frequency
# to see, eg., the 3-month T-bill https://fred.stlouisfed.org/series/TB3MS
tickers <- c('TB3MS', # 3-month Treasury bill (or T-bill)
             'TB6MS', # 6-month
             'GS1',   # 1-year
             'GS2',   # 2-year, etc....
             'GS3',
             'GS5',
             'GS7',
             'GS10',
             'GS20',
             'GS30')  #.... all the way to the 30-year rate

# Turn  FRED codes to human readable variables
myvars <- c('3-Month Treasury Bill',
            '6-Month Treasury Bill',
            '1-Year Treasury Rate',
            '2-Year Treasury Rate',
            '3-Year Treasury Rate',
            '5-Year Treasury Rate',
            '7-Year Treasury Rate',
            '10-Year Treasury Rate',
            '20-Year Treasury Rate',
            '30-Year Treasury Rate')

maturity <- c('3m', '6m', '1y', '2y','3y','5y','7y','10y','20y','30y')

# by default R will sort these maturities alphabetically; but since we want
# to keep them in that exact order, we recast maturity as a factor 
# or categorical variable, with the levels defined as we want
maturity <- factor(maturity, levels = maturity)

# Create a lookup dataset
mylookup<-data.frame(symbol=tickers,var=myvars, maturity=maturity)
# Take a look:
mylookup %>% 
  knitr::kable()

symbol	var	maturity
TB3MS	3-Month Treasury Bill	3m
TB6MS	6-Month Treasury Bill	6m
GS1	1-Year Treasury Rate	1y
GS2	2-Year Treasury Rate	2y
GS3	3-Year Treasury Rate	3y
GS5	5-Year Treasury Rate	5y
GS7	7-Year Treasury Rate	7y
GS10	10-Year Treasury Rate	10y
GS20	20-Year Treasury Rate	20y
GS30	30-Year Treasury Rate	30y

df <- tickers %>% tidyquant::tq_get(get="economic.data", 
                   from="1960-01-01")   # start from January 1960

glimpse(df)

## Rows: 6,774
## Columns: 3
## $ symbol <chr> "TB3MS", "TB3MS", "TB3MS", "TB3MS", "TB3MS", "TB3MS", "TB3MS",…
## $ date   <date> 1960-01-01, 1960-02-01, 1960-03-01, 1960-04-01, 1960-05-01, 1…
## $ price  <dbl> 4.35, 3.96, 3.31, 3.23, 3.29, 2.46, 2.30, 2.30, 2.48, 2.30, 2.…

Our dataframe df has three columns (variables):

symbol: the FRED database ticker symbol
date: already a date object
price: the actual yield on that date

The first thing would be to join this dataframe df with the dataframe mylookup so we have a more readable version of maturities, durations, etc.

yield_curve <-left_join(df,mylookup,by="symbol")

Plotting the yield curve

This may seem long but it should be easy to produce the following three plots

Yields on US rates by duration since 1960

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

3-month and 10-year yields since 1999

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

Setup data for US recessions
Superimpose recessions as the grey areas in our plot
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 gray shaded areas corresponding to recessions, we use geom_rect() and to color the ribbons blue/red we must see whether the spread is positive or negative and then use geom_ribbon().

# Pivot data
final_yield_curve <- yield_curve %>% 
  filter(symbol %in% c("GS10","TB3MS")) %>% 
  select(- symbol,- maturity) %>% 
  group_by(date) %>% 
  pivot_wider(names_from = var, 
              values_from=price) %>% 
  filter(date >= as.Date("1959-01-01"))
final_yield_curve$difference = final_yield_curve$`10-Year Treasury Rate` - final_yield_curve$`3-Month Treasury Bill`

# Filter data recessions
recessions1 <- recessions %>% 
  filter(From >= as.Date("1959-01-01")) %>% 
  filter(To >= as.Date("1959-01-01"))

# Plot graph
ggplot(final_yield_curve, aes(x = date, y = difference)) +
  geom_line() +
  
# Adding gray recession lines
geom_rect(data = recessions1, aes(NULL, NULL, xmin = From, xmax = To),
            ymin = -5, ymax = 5, colour = "grey", size = 0.5, alpha = 0.2) +
 
# Changing fill in color of graph  
geom_ribbon(aes(ymin = 0,
                  ymax = ifelse(difference > 0, difference, 0)), fill = "blue", alpha = 0.15) +
geom_ribbon(aes(ymin = ifelse(difference < 0,difference, 0), 
                  ymax = 0), 
              fill = "red", alpha = 0.15) +

# Adding rug 
geom_rug(sides = "b", alpha = 0.5, position = "jitter", aes(color = ifelse(difference < 0, "dark blue", "red"))) +
  guides(color = FALSE) +
  
# Adding titles
labs(title = "Yield Curve Inversion: 10 year minus 3 months U.S Treasury rates",
     subtitle = "Differences in % points, monthly averages. Shaded areas correspoind to recessions",
     x = "",
     y = "Difference (10 years - 3 months) yield in %",
     caption = "Source: TfL, London Data Store") + 
  theme_bw()

Yield curve inversion

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Yield curve inversion

2020-10-05T12:14:34+06:00

Plotting the yield curve

Yields on US rates by duration since 1960

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

3-month and 10-year yields since 1999

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