Fixed-Income Features: Coupon Rate and Frequency

Many bonds offer periodic payments to investors right up through the maturity date. These are called __coupon payments__. The __coupon rate__ is a certain percentage of the denomination of the bond. Suppose you had a $1,000 bond that offers annual coupon payments of 2.6%. The coupon payments each year would then be: $$\displaystyle 2.6 \% \times \$ 1,000 = \$ 26 $$

A lot of bonds pay annual coupons, and a lot of them pay semi-annual coupons. Others pay quarterly or even monthly. There are a lot of bonds out there. For different coupon frequencies, the coupon rate just provides an annual coupon payment total, and this is then divided among whatever the frequency of the payments is during the year.

Suppose a $5,000 bond paid a quarterly coupon with a 3.1% coupon rate. If you bought this bond, how much would you expect to be paid every three months?

Correct! The annual coupon is just the bond's 3.1% coupon rate multiplied by the $5,000 of principal, and then the quarterly payments are this product divided by the four quarters in a year: $$\displaystyle Payment = \frac{3.1 \% \times \$ 5,000}{4} = \$ 38.75 $$

No, this is incorrect. Consider what the annual payment would be for the bond, and then consider that this sum is divided among four quarters each year. It's possible to obtain this value by dividing the annual coupon payment by just three instead of four.

No, this is the annual coupon payment, but this bond doesn't have an annual coupon, it has a quarterly coupon. So this value needs to be adjusted to reflect the division among the four quarters in each year.

A bond which has this simple, fixed coupon size and schedule is often called a "conventional bond." This is quite popular, since an investor knows what all future cash flows will be when making the purchase, which is nice. But on the other hand, there is some risk in signing on to a set interest rate for a number of years. If interest rates rise, investors will wish they could reinvest their money at the higher rate. So some prefer __floating-rate notes (FRNs)__ which are also referred to as "floaters," that have payments based on some __market reference rate (MRR)__. This can be beneficial to those just wanting the market rate of interest, since the coupon rate of a floater adjusts with each payment to some reference interest rate.

Suppose you purchased a bond a couple of years ago, but forgot if it was a conventional bond or a floater. Interest rates have fallen to close to zero since then. Which type would you hope you have?

Absolutely! A conventional bond would have a fixed coupon rate, and those payments would start looking pretty good now that interest rates are lower. In hindsight, this would be a better choice.

No, a floating-rate note would have decreased its coupon payments over time as interest rates fell, providing you with less money.

No, it would certainly matter. Recall that a conventional bond would pay a fixed coupon rate while a floating-rate note would have a coupon rate that changes with some reference rate.

For example, 3-month MRR might be 1.21%. An FRN is issued with a coupon rate which is 3-month MRR plus 0.8 percentage point. What coupon rate would you expect to be paid?

Some bonds don't pay coupons at all. Buy a bond, and you get a single principal payment when the bond matures. That's it. These are called __zero-coupon bonds__, or __zeros__. Sometimes they are referred to as __pure discount bonds__.

Suppose you purchased a zero-coupon bond that was set to mature 10 years later and make its single payment, but you sold the bond eight years after you purchased it. What do you think your return would be on the bond?

No, this shouldn't be the case. The single cash flow of the bond is more attractive to investors when it is just two years away rather than when it is 10 years away, so it wouldn't make much sense that the bond would have less value as the cash flow gets closer.

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No, the return wouldn't be zero. It's true that you wouldn't have received any coupon payments over this time, but the value of the bond will certainly be different eight years later.

That's right! As the payment draws near, it becomes more valuable. No one likes to wait longer for a fixed payment. So a zero coupon bond is priced much lower than this payment, and that value grows over time at the rate of interest investors demand, until it matures and makes its single payment (called the __par value__ or __face value__). So zero-coupon bonds provide a return, but the return is in the form of implied interest. The implied interest of a zero-coupon bond is the difference between its par value and the price at which it is purchased.

Perfect!

No, it's actually 2.01%.

The FRN's spread is measured in __basis points__ over the reference rate, since issuers don't typically get this rock-bottom interest rate. A basis point is just 1% of 1%, or 0.0001. So here, the spread is 0.8 percentage points, or 80 basis points. Since the 3-month MRR is currently 1.21%, then the FRN should pay a coupon rate of 1.21% + 0.80% = 2.01%.

$38.75

$51.67

$155.00

Conventional bond

Floating-rate note

It wouldn't matter

0%; holding a zero-coupon bond for this period was worthless

Something positive; the bond would be worth more when I sold it than when I bought it

Something negative; the bond will be worth less eight years later than it was when I bought it

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2.01

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