treasury.R

library(tidyquant)

ty10 <- tq_get("DGS10", get = "economic.data", from = as.Date("1950-01-01"))


mod_dur <- function(yield) {
  # out <- (1-(1/(1+0.5*yield/100)^(2*10)))/(yield/100)
  out <- (1-(1/(1+0.5*yield)^(2*10)))/(yield)
  
  return(out)
}

convexity <- function(yield) {
  # out <- (2/(yield/100)^2)*(1-(1/(1+yield/200)^(20)))-20/((yield/100)*(1+yield/200)^(21))
  out <- (2/(yield)^2)*(1-(1/(1+yield/2)^(20)))-20/((yield)*(1+yield/2)^(21))
  
  return(out)
}

return_m <- function(yield, yield_lag, mdur = mod_dur(yield), convex = convexity(yield), scale = 252) {
  if (is.na(yield_lag)) {
    return(NA_real_)
  }
  
  # out <- -mdur*(yield/100-yield_lag/100) + 0.5*convex*(yield/100-yield_lag/100)^2 + ((1+yield_lag/100)^(1/12)-1)
  out <- -mdur*(yield-yield_lag) + 0.5*convex*(yield-yield_lag)^2 + ((1+yield_lag)^(1/scale)-1)
  
  return(out)
}


convexity_m_V <- Vectorize(convexity)
return_m_V <- Vectorize(return_m)



mod_dur(4)
convexity(4)

ty10 %>%
  group_by(m = floor_date(date, "months")) %>% 
  filter(date == max(date)) %>% 
  ungroup() %>% 
  select(-m) %>% 
  mutate(r = return_m_V(yield = price/100, yield_lag = lag(price)/100), scale = 12) %>% 
  filter(!is.na(r)) %>% 
  mutate(p = cumprod(1+r)*100) %>% 
  group_by(m = floor_date(date, "months")) %>% 
  filter(date == max(date))

ty10 %>% 
  mutate(r = return_m_V(yield = price/100, yield_lag = lag(price)/100))

return_m(yield = 3.86, yield_lag = 3.86)