Bond Yields Explained: Current Yield, YTM and Yield to Call

Treasury bills are still quoted on a basis that assumes a year of 360 days, a convention inherited from an era when the person working out the yield had a pencil and a table of reciprocals and wanted a number divisible by twelve. Nobody has needed that shortcut for decades. The convention survived anyway, because quote conventions outlive their reasons, and the result is that the same bill carries two different yields on the same auction result sheet, roughly a tenth of a point apart, neither of them wrong.

That is the shape of the whole subject. Ask what a bond yields. A quote screen can hand you four answers, every one of them arithmetically defensible, each measuring a different thing. The gap between them is where money goes quietly missing.

Start from the one number that does not move. The coupon rate is a property of the bond as it was drafted: a $1,000 bond with a 4% coupon pays $40 a year, usually in two instalments of $20, until the day it matures, and no market event changes that. It tells you what the issuer promised. It tells you almost nothing about what a buyer earns today, because every other measure on this page divides by a price, and the price moves. How bonds work walks a 5% bond down to $926.40 when yields reach 6%.

Current yield measures the cash, and only the cash

Current yield = annual coupon / current price

Take a $1,000 face bond with a 4% coupon and six years to run. It changes hands at $950. The current yield is $40 / $950 = 4.21%.

That is a true statement about the cash arriving against the cash paid, and it is silent about the $50 the issuer will hand over at maturity on top of the coupons. For a bond bought at a discount, current yield understates what the holder earns, and for a bond bought above par it overstates it, because the premium erodes to nothing on a schedule the measure does not look at.

Yield to maturity, computed twice

Yield to maturity is the discount rate that sets the present value of every remaining payment equal to today’s price, and it folds the coupon income and the pull to par into a single annualised compound rate, which is what makes bonds with different coupons and different maturities comparable at all.

There is no closed-form solution for it. Solvers find it by iteration, which is unremarkable now and was a genuine obstacle when yield books were printed volumes and a trader looked the answer up. The approximation below is the one that survived from those books, and it is close enough to sanity-check a broker:

Approximate YTM = [C + (F - P) / n] / [(F + P) / 2]

For the same bond, with a $40 coupon, $1,000 face, $950 price and six years left:

1. The discount to be earned back is $1,000 - $950 = $50, or $50 / 6 = $8.33 a year.
2. The numerator is $40 + $8.33 = $48.33.
3. The denominator is ($1,000 + $950) / 2 = $975.
4. $48.33 / $975 = 4.96%.

An iterative solver puts the exact figure at about 4.98%. The approximation lands a couple of basis points low because it spreads the discount evenly across the six years and never discounts it, which is close enough for a first look and wrong enough that the bond yield calculator should see the trade before your money does.

Measure	This bond at $950	What it counts
Coupon rate	4.00%	Cash against face value
Current yield	4.21%	Cash against price paid
Yield to maturity	4.98%	Cash plus the pull to par, compounded

The two assumptions buried in it

Yield to maturity carries two conditions. Neither appears anywhere near the number on a screen, and both are worth saying out loud.

The first is that you hold the bond until it matures. Sell before then and you take whatever price the market offers that day, which depends on where yields have travelled in the meantime and on nothing else.

The second is that every coupon is reinvested at the same yield to maturity for the remaining life of the bond. Collect $40 a year and spend it. Reinvest it at 2% because rates fell. Either way the realised return departs from the quoted one. This is reinvestment risk. It bites hardest on high-coupon, long-dated bonds, where the coupon stream is supposed to do the bulk of the promised compounding, and where there are thirty years of coupons to find a home for. The holders of 1980s long corporates learned this from the other side: the coupons were generous, and every one of them had to be put back to work at rates that kept falling.

Neither assumption makes the measure useless. A yield to maturity is the return on a specific plan. Depart from the plan and the answer changes.

Yield to call, and yield to worst

A great many corporate and municipal bonds allow the issuer to redeem early, at a stated price, on stated dates, and the issuer exercises that right when it suits the issuer, which is when rates have fallen far enough that the debt can be refinanced more cheaply. You are the one who sold the option, and you were paid for it in the coupon, whether or not anybody described the transaction that way.

Yield to call runs the same present value arithmetic with the call date standing in for maturity and the call price standing in for face value. Take a 5% coupon bond, ten years from maturity, trading at $1,060, callable in three years at $1,020:

1. Over three years you collect 3 x $50 = $150 in coupons.
2. You paid $1,060 and are handed $1,020, a capital loss of $40.
3. Solving for the rate that equates $1,060 today with those cash flows gives 3.50%.

Scenario	Ends in	You receive	Annual yield
Held to maturity	10 years	$50 a year, then $1,000	4.25%
Called at first date	3 years	$50 a year, then $1,020	3.50%

Yield to worst is the lower of those, 3.50%. That is the number to plan on. A bond trading well above its call price is telling you plainly that the market expects the call to be exercised.

Bills, and the 360-day year

Treasury bills pay no coupon and are sold below face value, so the discount basis described at the top of this page has nowhere to hide, and a 26-week bill bought at $97.50 per $100 of face value has a bank discount rate of ($2.50 / $100) x (360 / 182) = 4.95%.

The investment yield measures the gain against what was actually paid. It uses a 365-day year, and comes to ($2.50 / $97.50) x (365 / 182) = 5.14%. One bill, nineteen basis points apart, depending only on which convention the quote follows. Both figures print on the auction result. The mechanics of those auctions are in the Treasury securities guide.

Two adjustments before any comparison

Two adjustments come first. Yields from different corners of the market cannot be laid beside each other until both have been made.

Tax comes first. Municipal bond interest is generally exempt from federal income tax, so a 3.40% muni is worth 3.40% / (1 - 0.32) = 5.00% to an investor in a 32% federal bracket, and considerably less to someone in a low one, with the full arithmetic, including state tax and the alternative minimum tax, set out in municipal bonds explained.

Inflation comes second and is the one more often skipped. A 5% yield with inflation at 3% leaves a real return of 1.05 / 1.03 - 1 = 1.94%. The real return calculator does this for any pair of figures, and inflation and CPI explained covers what the inflation figure itself contains, which is a longer argument than most yield discussions allow for.

Which number belongs in which decision

Use current yield when the question is how much cash arrives over the next twelve months, which is a real question if you are living on the income. Use yield to worst when the bond is callable. Any other figure there is marketing. Use yield to maturity everywhere else, and compare it across bonds only after adjusting for tax treatment and for how much price risk each one is carrying, which is the subject of duration and interest rate risk.

Line those yields up across maturities and you have the yield curve, whose slope carries information about what the market expects from the Federal Reserve, and rather less information than its more enthusiastic readers claim. Read the yield curve explained next, plot the shape for yourself on the yield curve tool, and check what stuck with the bonds and yields quiz.