Yield Measures

Why this matters

Part 2 introduced bonds with one coupon and one yield. Real quotations are busier. A single bond can be shown with a coupon of 5%, a current yield of 5.4%, and a yield to maturity of 6.0%, and a bond fund reports yields of its own. These numbers answer different questions, and choosing a bond by the wrong one is an easy mistake. This lesson takes them in order, with one bond worked through all of them.

Coupon rate

The coupon rate is the yearly interest as a percentage of face value, set when the bond is issued, and it doesn't change over the bond's life.¹ A $1,000 bond with a 5% coupon pays $50 a year, usually as two payments of $25.² The coupon tells you the cash you'll receive. It tells you nothing about your return unless you paid exactly $1,000.

Current yield

Current yield = Yearly coupon payment ÷ Price

Current yield adjusts for the price you pay.² Buy that 5% bond for $925 and the current yield is $50 ÷ $925 = 5.41%. It's a quick measure of income, and it leaves something out. At maturity you'll be repaid $1,000 for a bond that cost $925. That $75 is part of your return too, and current yield ignores it.

Yield to maturity

Yield to maturity, or YTM, is the overall interest rate earned by an investor who buys at the market price and holds until maturity. Mathematically, it's the discount rate at which all the bond's future payments, coupons and principal, add up to its price.² It's the internal rate of return from Investing Math in a Spreadsheet, applied to a bond.

A $1,000 bond with a 5% coupon, paid twice a year, and 10 years to maturity.

Price	Coupon rate	Current yield	Yield to maturity
$925, a discount	5.00%	5.41%	6.01%
$1,000, par	5.00%	5.00%	5.00%
$1,080, a premium	5.00%	4.63%	4.02%

At par, all three agree. Below par, the yield to maturity is the highest of the three, because it counts the $75 gained at maturity. Above par it's the lowest, because it counts the $80 lost. A buyer who chose the premium bond for its 4.63% current yield would earn 4.02% if they held to the end.

There's no formula that gives the yield to maturity directly. It's found by trial: guess a rate, discount the payments, compare with the price, and adjust. A spreadsheet's RATE function does this. For the $925 bond, =RATE(20, 25, -925, 1000) * 2 returns 6.01%: 20 half-year periods, $25 each period, $925 paid, $1,000 received at the end.

The half-year convention

That formula finds a rate of 3.0045% per half year and doubles it. Doubling is the convention for quoting bond yields, and it slightly understates the true yearly rate, because it ignores interest on the first half's interest. A 6% yield quoted this way is 1.03 × 1.03 − 1 = 6.09% a year. It rarely matters when comparing one bond with another, since both use the same convention. It does matter when comparing a bond with a savings rate that's quoted as a true yearly figure.

Bonds that can be called

A callable bond lets the issuer redeem it before maturity at a set price.² Issuers do that when it suits them, which is when interest rates have fallen and they can borrow more cheaply. For the investor that's the worst time: the bond is taken away just when it's paying more than new bonds would.

For a callable bond, two more yields are needed. Yield to call is figured the same way as yield to maturity, using the first date on which the issuer could call the bond and the call price in place of the maturity date and face value. Yield to worst is whichever of the two is lower.¹

A $1,000 bond with a 6% coupon and 10 years to maturity. The issuer can call it in 3 years at $1,030.

Price	Yield to maturity	Yield to call	Yield to worst
$1,090	4.85%	3.75%	3.75%
$960	6.55%	8.44%	6.55%

At $1,090 the bond trades above its call price. If it's called in three years, the buyer gets back $1,030 for something that cost $1,090, and earns 3.75% a year, more than a point less than the yield to maturity suggests. That's the likely outcome, because a bond trading above its call price is one the issuer has reason to call. At $960 the reverse is true: a call would be a windfall, and it's unlikely, so the yield to maturity is the conservative figure.

The rule from the regulator's guidance is simple. For every callable bond, know the yield to worst.¹

Why the yield isn't the return

A yield to maturity looks like a promise of what you'll earn. Three things can make the result different, and FINRA's guidance makes the same point: yield to maturity and yield to call may not be the same as a bond's total return.¹

Reinvestment

Calculations of yield to maturity generally assume each coupon is reinvested at that same yield.¹ In practice, coupons are reinvested at whatever rates are available when they arrive.

A 10-year 5% bond bought at $1,000 and held to maturity. Every $25 coupon is reinvested until the end.

Coupons reinvested at	Total at maturity	Yield actually earned
3%	$1,578	4.62%
5%	$1,639	5.00%
7%	$1,707	5.42%

The bond paid exactly what it promised in all three rows. The investor's return ranged from 4.62% to 5.42%, depending on what happened to rates afterward. The longer the bond and the higher its coupon, the more of the final total comes from reinvested coupons, and the more this matters. A bond that pays no coupons at all, a zero-coupon bond, has no reinvestment to worry about: held to maturity, it earns exactly its quoted yield.

Selling early

The yield to maturity applies only if you hold to maturity. Sell before then and your return depends on the price you get, which depends on where interest rates are that day. Suppose you bought the $925 bond, collected $150 of coupons over three years, and sold at $960. Your total return is ($150 + $35) ÷ $925 = 20.0%, or about 6.3% a year, close to the yield you bought at. If rates had risen and the price had fallen to $880, it would have been ($150 − $45) ÷ $925 = 11.4%, or about 3.7% a year.

Default

Every yield in this lesson assumes the issuer pays in full and on time. A high yield to maturity on a risky bond is the return if nothing goes wrong, and the reason it's high is that something might. Credit Analysis takes that up.

Which yield to use

Key takeaways

• Coupon rate is interest as a percentage of face value. Current yield divides the coupon by the price.
• Yield to maturity counts the coupons and the gain or loss against face value. It equals the coupon rate only at par.
• For a callable bond, work out the yield to call as well, and rely on the lower of the two.
• Quoted bond yields double a half-year rate, which slightly understates the true yearly rate.
• What you earn also depends on reinvestment rates, on selling before maturity, and on the issuer paying.

Check your understanding

A $1,000 bond with a 4% coupon trades at $800. What's its current yield, and how does its yield to maturity compare?

1. 4%, and the yield to maturity is the same, since the coupon is fixed.
2. 5%, and the yield to maturity is higher, since $200 is gained at maturity.
3. 5%, and the yield to maturity is lower, since the bond's price has fallen.

A callable bond trades at $1,100. Its yield to maturity is 5.2% and its yield to call, in two years at $1,020, is 2.9%. Which figure should a careful buyer rely on?

1. 5.2%, since issuers almost never use their right to call a bond.
2. The average of the two, about 4%, since either outcome could happen.
3. 2.9%, the yield to worst, since a call is likely at this price.

What's next

Yield says what a bond pays. Duration and Convexity measures how much its price moves when yields change, which decides what happens if you don't hold to the end.