Dear R helpers,
Yesterday I had raised following query which was addressed by Mr Ellison. The
query and the wonderful solution as provided by Mr. Ellison are as given below.
## PROBLEM
I am calculating the 'Yield to Maturity' for the Bond with following
characteristics.
Its a $1000 face value, 3 year bond with 10% annual coupon and is priced at
101. The yield to maturity can be calculated after solving the equation -
1010 = [100 / (1+ytm)] + [100 / (1+ytm)^2] + [ 1100 / (1 + ytm)^3]
This can be solved by trial and error method s.t. ytm = 9.601%. I wanted to
find out how to solve this equation in R.
## SOLUTION
Mr. Elisson had given me following wonderful solution
f.ytm<-function(ytm) 100 / (1+ytm) +100 / ((1+ytm)^2) + 1100 / ((1 +
ytm)^3) -1010
uniroot(f.ytm, interval=c(0,25))
#$root has the answer
And I got the answer as 9.601.
## _____________________________________________________________
I was just trying to generalize this solution to any equation and accordingly
written a code as given below.
The following input I will be reading using csv file and thus my equation will
change if tenure or no_comp etc. changes. So taking into account the variable
nature of the input, I am trying to write a generalized code.
## Input
price = 101 # Price of bond
tenure = 3
no_comp = 1 # no of times coupon paid in a year.
coupon_rate = 0.10 # i.e. 10%
face_value = 100
# Computations
coupon_payment = face_value * coupon_rate
cash_flow = c(rep(c(coupon_payemnt), (no_comp * tenure - 1)), face_value +
coupon_payment)
cash_flow
## I am trying to customize the code as given by Mr Ellison.
f.ytm = function(ytm)
{
for (i in 1 : (tenure * no_comp - 1))
E = NULL
F = NULL
{
E[i] = cash_flow[i]/(1+ytm)^i
F = (sum(E) + (face_value + coupon_payment)/((1+ytm)^(tenure * no_comp))) -
price
}
}
solution = uniroot(f.ytm, interval=c(0,25))
ytm = solution$root
However, when I execute this code I get following error.
> solution = uniroot(f.ytm, interval=c(0,25))
Error in uniroot(f.ytm, interval = c(0, 25)) : f.lower = f(lower) is NA
Please guide. ytm should be 0.09601 (i.e. 9.601%)
with regards
Madhavi Bhave
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