Estimating the yield of a bond
Bond Valuation and Analysis in R
Clifford Ang
Senior Vice President, Compass Lexecon
Finding the yield by trial-and-error
- For traded bonds, we can imply the yield
- If you know the price and the bond's cash flows, you can make "guesses" as to the yield
- The "correct" yield equates the price of the bond with the PV of the bond's cash flows
Iterating through different guesses
- Consider bond with $100 par value, 5% coupon rate, 10 years to maturity, and a price of $92.64
- 1st Guess: 5% → Price is $100 (too high)
- 2nd Guess: 7% → Price is $85.95 (too low)
- 3rd Guess: 6% → Price is $92.64 (correct)
Automating the process
- Trial-and-error is inefficient
- Fortunately, we can use the
uniroot()function in R to help us automate the process
Create function using uniroot()
ytm <- function(cf) {
uniroot(bval, c(0, 1), cf = cf)$root
}
- Create the
ytm()function usinguniroot() - Function takes a modified cash flow vector (
cf) and uses a modified bond valuation function (bval) c(0,1)limits the interval for the search to a yield between 0% and 100%
Modified cash flow vector
cf <- c(-92.64, 5, 5, 5, 5, 5, 5, 5, 5, 5, 105)
- First element is bond's price entered as a negative number
- Second element onwards are the bond's cash flows - coupons plus par value
- Same bond: Price is -$\$92.64$, par value is $\$100$, 5% coupon rate, and 10 years to maturity
Modified bond valuation function
bval <- function(i, cf, t = seq(along = cf)) sum(cf / (1 + i)^t)
- Need to create bond valuation function
bval()that uses the modified cash flow vector (cf) - Same logic as our
bondprc()function - Create time indicator (
t) - Discount cash flow using interest rate (
i)
Let's practice!
Bond Valuation and Analysis in R
