YTM for a zero coupon bond?

[sudeepdoon]

Hi David,

While solving one of the questions i came to a section where I was to calculate the YTM of a zero coupon bond. i had the term and the price of the bond. Thinking that zero coupon bond has just one payment, i calculated the discount rate using term, par value and the price. To my surprise the value that I got was different to what my calc gave me.. I tried the calc using continous discounting, annual and even semi annual. but the results did not match.

What can be the explanation to this difference?

Thanks,
Sudeep

 

[David Harper CFA FRM]

Hi Sudeep,

Maybe the Q&A is wrong? I too think only compound frequency can explain differences. Under continuous, as you know,

P*exp(rT) = F, where p=price & F = face
so, yeild (YTM) = r = LN(F/P)*1/T; i.e., given the three unknowns, there is only one yield
...and similar logic for discrete frequencies
...Re: "zero coupon bond has just one payment," totally agree

so, I'd trust your approach here...(the ex post "realized" yield can vary from the ex ante "yield to maturity," but the question would need to give additional info)

Thanks, David