Current yield and where it sits

The third yield

A bond has three rates worth naming. The coupon rate is the annual coupon over par — fixed. The yield to maturity is the rate that discounts every cash flow to the price — the full return, including the price's journey to par. Between them sits the current yield:

$$\text{Current yield}=\frac{\text{annual coupon}}{\text{market price}}$$

It is the income yield a buyer at today's price collects this year — nothing more. It ignores the capital gain a discount bond will deliver as it is pulled to par, and the capital loss a premium bond will suffer. That omission is exactly what places it.

Worked example — Prairie Grid, a discount bond

Prairie Grid 5.2 % at 940.49 (a 6 % market yield): annual coupon 52, so =52/940.49 = 5.529 %. Line the three up:

$$\text{coupon }5.2\%;<;\text{CY }5.53\%;<;\text{YTM }6\%$$

The current yield beats the coupon rate because the same 52 is earned on a price below par; it falls short of the YTM because it leaves out the 59.51 the bond will gain on its way to 1,000.

Tamarack, a premium bond

Tamarack 7 % at 1,096.03 (a 5.5 % yield): =70/1096.03 = 6.387 %. The order reverses:

$$\text{YTM }5.5\%;<;\text{CY }6.39\%;<;\text{coupon }7\%$$

The current yield is below the coupon rate because 70 is earned on a price above par; it is above the YTM because it ignores the 96.03 the bond will lose by maturity. Either way the current yield is the middle number — the coupon rate at one end, the YTM at the other, and the pull to par the distance between them. At par all three are equal, because there is no pull.

Why the paper likes it

The current yield is the one that dealers and newspapers quote alongside price, and it is quick: one division. The MCQ tests whether you know what it leaves out; the calculation part gives you a coupon and a price and wants the division to four places. Two traps: coupon ÷ par is the coupon rate, not the current yield; and YTM ÷ 2 is a half-year rate, not a yield of any kind.

Recompute

The 4.5 % bond at 925.60 (Lesson 10.4, YTM 5.81 %): =45/925.60 = 4.862 % — between 4.5 % and 5.81 %, as a discount bond must be. Cold, the ordering for any discount bond: coupon rate < current yield < YTM.