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We've been using this formula to price Bonds. c/y + (100-(c/y))/(1+y)^m where c=coupon y=yield to maturity m=time to maturity

Let's take a 10 year U.S treasury for example. Price of existing bonds change according to new bonds issued on the market at par. So to price an existing 10-year US Treasury, do we look at the y-t-m of a
newly issued 10-year US- treasury, to insert into the formula above?

If that is the case, does that mean that all bonds of the same maturity have the same yield to maturity?

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In practice, bonds of the same maturity will have yields that vary slightly from each other. Several possible reasons (a) a bond with a higher coupon is effectively shorter maturity than a bond with lower coupon, because a higher percentage of the cash flows are returned earlier. So if the yield curve is upward sloping, high coupon bonds will yield a bit less than low coupon bonds. (B) liquidity. Usually the most recently issued bond is more heavily traded so commands a higher price/lower yield than its neighbors. (C) financing. If a bond is difficult to borrow in the repo market, which may happen if that specific bond is scarce for some reason , then it can trade at a lower yield than its neighbors. Reason (a) above is purely mathematical. Whereas (b) and (c) are more technical in nature.

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  • $\begingroup$ Why investors are more attracted to recent series ? The bonds with the same seniority bear the same risk. So Why pay more for the same risk. I know you actually pay for liquidity but yet why equivalent bonds in risk &return aren't equally liquid) $\endgroup$
    – Jiem
    Commented Jul 31, 2018 at 17:20
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Yield to maturity is a very misleading measure of return for bonds with coupons. With a zero coupon bond, there is only one payment from the bond, so the maturity and the yield to maturity are well defined. But with coupon bonds there are multiple payments and then one final payment at maturity. So two 10 year bonds with different coupon sizes have different cash flows over time, they cannot be compared by using Yield to Maturity (even if they have the same maturity).

Quant Finance downplays the role of Maturity and Yield to Maturity, replacing them with Duration and Spread over a yield curve as the proper way to compare bonds. (Of course people still speak of maturity and YTM, but they are no longer considered fundamental concepts).

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