Calculating Bond Yield to Maturity Between Coupon Dates

Summary

The document explains how to calculate the yield to maturity of a semiannual coupon bond when the valuation date falls between coupon dates. It converts the quoted price from fractional bond notation into a decimal price, then identifies the timing issue in a proposed present-value equation: the bond’s remaining cash flows occur at fractional-period offsets rather than at standard half-year intervals from today.

The answer places the next coupon a quarter year ahead and discounts the value on that coupon date back by a quarter year. It then discounts later coupons and principal in half-year steps from that date. This provides a way to account for the stub period without treating maturity as an integer number of coupon periods from today. The explanation assumes the stated coupon schedule and yield convention; it does not discuss accrued interest, alternative market conventions, or numerical solution of the resulting yield equation.

Key ideas

• A bond priced between coupon dates has a first remaining cash flow at a fractional coupon-period offset.
• The standard half-year discounting formula needs adjustment when the valuation date is not a coupon date.
• The cash flows can be valued at the next coupon date and then discounted for the stub period.
• The quoted price is converted from fractional notation before solving for yield.

Tags

# Bond is maturing in 10.25 years, YTM calculation


# Bond is maturing in 10.25 years, YTM calculation












Bond is maturing in 10.25 years and has an annual coupon rate 4.15% paid semiannually and price 92-12+

I need to calculate yield to maturity

Ok so I know that 92-12+ is basically 92 + 12/32 + 1/64 = 92.390625.

Now here comes the yield to maturity confusion. Normally I'd expect to have the maturity time to be divisible by the compounding rate, but 10.25 is not divisible by 0.5 which confuses me.

The formula for YTM (let $y$ be the YTM) if my memory serves me well is this:

$\sum_{n=1}^{20} \frac{2.075}{(1+0.5y)^n} + \frac{100}{(1+0.5y)^{20.5}} = 92.390625$

But the last summand confuses me abit. Is this actually correct?

## Answer by Alex C (score 2, accepted)

https://quant.stackexchange.com/a/43093

The first coupon occurs 0.25 years from now, the next 0.75 years from now, the twentieth and last 10.25 years from now. So no, the equation is not correct. You can only use your formula on a coupon date and today is not a coupon date. You could calculate PV at time 0.25 and then discount to the present (i.e. half a period):

$$\frac{1}{1+0.25y}\left(\sum_{n=1}^{20} \frac{2.075}{(1+0.5y)^{n-1}} + \frac{100}{(1+0.5y)^{19}}\right) = 92.390625.$$

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.