Lesson 3 of 8
Yield to maturity
YTM is the rate that makes a bond's discounted cash flows equal its price. It assumes every coupon is reinvested at that same rate, and usually they are not.
By Javier Sanz
Founder of ValueScreener. Built Ninety Nine, a securities services provider, and sold it to a tier-one global bank; ran operations and internationalization at Alpaca, the brokerage API.
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In one minute
- Yield to maturity is an internal rate of return on a bond's own cash flows.
- It only equals the investor's realised return if every coupon is reinvested at that exact rate until maturity.
- The assumption is invisible in the number, and it fails hardest on long bonds with large coupons.
Yield to maturity is the most quoted number in fixed income and the least qualified. It is a genuine internal rate of return, which means it carries the same silent assumption every internal rate of return carries.
What a 5 percent bond actually returns, by the rate coupons earn
- Coupons reinvested at 7 percent5.19%
- Coupons reinvested at 5 percent5.00%
- Coupons reinvested at 2 percent4.73%
The definition
YTM is the single rate that sets the present value of all remaining coupons and the principal equal to the current price. It answers: what constant annual rate would this purchase earn, if everything happens as promised.
Nothing about that definition is dishonest. The problem is what "as promised" covers. It covers the issuer paying. It does not cover what the holder does with each coupon on the day it arrives.
The reinvestment assumption
Discounting each coupon back at the yield is arithmetically the same as growing each coupon forward at the yield. So a quoted YTM of 5 percent assumes every coupon received is put to work at 5 percent for the rest of the bond's life.
In practice coupons are reinvested at whatever the market offers on the day they arrive. If rates fall, the reinvested coupons earn less and the realised return falls below the quoted yield. If rates rise, it goes the other way, and the price of the bond falls at the same time.
When it matters and when it does not
The gap widens with two things: how long the bond runs, and how much of its return arrives as coupons rather than principal. A zero-coupon bond has no coupons to reinvest, so its YTM is its realised return if held to maturity, with no assumption at all. That is the clean case, and it is the exception.
A thirty-year bond with a large coupon is the other extreme. Most of its total cash arrives before maturity, so most of its outcome depends on rates nobody can see yet.
What to do with it anyway
Use YTM as what it is: a comparable quote across bonds, computed the same way for all of them, which is genuinely useful. Do not read it as a promised return. Two bonds with equal yields and very different coupon structures do not have equal exposure to the assumption behind the number.
Check yourself
Which bond's yield to maturity requires no reinvestment assumption?
- A long bond with a high coupon
- A zero-coupon bond held to maturity
- Any bond bought at face value
Show the answer
Answer: B.
With no coupons there is nothing to reinvest. The single payment at maturity makes the quoted yield the realised return, if the issuer pays.Rates fall sharply after you buy a coupon bond and you hold it to maturity. What happens to your realised return against the quoted YTM?
- It is higher
- It is lower
- It is unchanged, because you held to maturity
Show the answer
Answer: B.
Holding to maturity removes price risk, not reinvestment risk. Each coupon is put to work at the new lower rate, so the realised return falls below the yield quoted at purchase.Yield to maturity is most precisely described as which of these?
- The coupon divided by the price
- An internal rate of return on the bond's cash flows
- The return the investor is promised
Show the answer
Answer: B.
It is an IRR, which is why it inherits both the comparability and the reinvestment assumption that an IRR always carries.Sources
- Damodaran, Investment Valuation: yield to maturity as an internal rate of return and the reinvestment assumption inside it.
- Williams, The Theory of Investment Value, 1938: the present-value identity that a yield solves.
What this leaves out
- Every figure here is invented arithmetic, chosen so the three outcomes can be recomputed by hand.
- The lesson assumes the issuer pays in full and on time. A yield to maturity says nothing about whether that happens.
- Callable and putable bonds have a yield to call or to put that can matter more than the yield to maturity, and neither is covered here.
- Nothing here is advice about any security.