Current Yield Versus Yield To Maturity

Why Two Bond Yield Measures?

A bond’s coupon rate describes its contractual coupon relative to face amount. But an investor who buys the bond in the market pays its current price, which may differ from face amount. Current yield measures annual coupon income relative to that price. Yield to maturity also accounts for the amount and timing of all remaining contractual payments, including redemption at maturity.

These measures answer different questions. Current yield is a simple income-to-price ratio; it does not measure the total return implied by the bond’s cash flows. Yield to maturity is the rate that equates the bond’s price to the present value of its remaining coupons and redemption payment, under the standard assumption that the bond is held to maturity and the promised payments are made.

Definition: For a bond with current price $P$ and annual coupon income $A$, the current yield is $A/P$. If the bond pays a coupon $C$ each of $m$ times per year, then $A=mC$. Current yield is usually expressed as a percentage per year; it does not include any gain or loss when the bond is redeemed.

Calculating Current Yield

The denominator is the bond’s current market price, not its face amount or redemption value. The numerator is the total coupon income for one year, not the coupon payment for one period unless coupons are annual. For example, if a bond pays $25 every six months, its annual coupon income is $2(25)=\$50$.

Current yield does not require knowing the bond’s maturity or redemption value. Those details matter for yield to maturity, which is found by discounting the full set of remaining cash flows. For annual coupons, a bond with annual coupon $A$, redemption value $R$, $n$ years to maturity, and annual yield $i$ satisfies

P=Aa_{\overline{n}|}+Rv^n,\qquad v=\frac{1}{1+i}.

The current-yield formula alone cannot replace this equation: it does not use $R$ or $n$, and therefore cannot measure the effect of receiving redemption value at maturity.

Worked Example: Current Yield and a One-Year Premium Bond

A hypothetical bond has a current price of $105, pays a coupon of $8 in one year, and redeems for $100 at the same time. Calculate its current yield and its yield to maturity. State how they compare.

Method. First calculate annual coupon income divided by price. Then use the one-year cash flow to find the yield to maturity. This avoids treating the redemption amount as coupon income.

The annual coupon income is $A=\$8$, so

\text{Current yield}=\frac{A}{P}=\frac{8}{105}=0.076190476\ldots=7.6190\%.

At the end of the year the investor receives the $8 coupon and $100 redemption payment, for a total of $108. The yield to maturity $i$ satisfies $105=108/(1+i)$. Thus

1+i=\frac{108}{105},\qquad i=\frac{108}{105}-1=\frac{3}{105}=0.028571428\ldots=2.8571\%.

The bond is bought for $105 and redeemed for $100, a $5 capital loss. That loss reduces the yield to maturity substantially, so the current yield of 7.6190% is above the yield to maturity of 2.8571%. The calculation is checked by $105(1.028571428\ldots)=108$, the total amount received after one year.

How Redemption Affects the Comparison

For a conventional bond with positive coupons and a single redemption payment, a premium bond generally has current yield above yield to maturity, while a discount bond generally has current yield below yield to maturity. At par, the two are equal. The difference arises because the bond’s price relative to its redemption value creates a gain or loss that yield to maturity includes and current yield omits.

Here is a direct justification for the comparison. Suppose coupons of $C$ are paid $m$ times per year, there are $n$ coupon periods remaining, and the yield per coupon period is $j$. Let $y=mj$ be the nominal annual yield convertible $m$ times per year, and let $A=mC$ be annual coupon income. The price equation is $P=Ca_{\overline{n}|}+Rv^n$, where $v=(1+j)^{-1}$. Since $a_{\overline{n}|}=(1-v^n)/j$, multiplying the price equation by $j$ and then by $m$ gives

$$ Py=A(1-v^n)+Ryv^n =A+v^n(Ry-A). $$

The current yield is $A/P$. Subtracting $A$ from both sides and dividing by $P$ yields the exact difference:

y-\frac{A}{P}=\frac{v^n}{P}(Ry-A).

This equation shows that the sign of the difference depends on $Ry-A$. The earlier material on yield inequalities establishes that, for a conventional premium bond, its nominal annual yield is below its coupon rate $A/R$. Therefore $Ry<A$, and the displayed difference is negative: yield to maturity is below current yield. For a discount bond, the yield is above the coupon rate, so $Ry>A$ and yield to maturity is above current yield. At par, the two rates are equal. For annual coupons, $m=1$, so $y$ is the effective annual yield; with more frequent coupons, $y$ here is a nominal annual yield, not an effective annual yield.

Worked Example: Discount Bond With a Redemption Gain

A hypothetical bond costs $93.05785124, pays $6 annually, and redeems for $100 in two years. Calculate its current yield and yield to maturity, then explain their ordering. Treat the stated price as the unrounded value $6/1.10+106/(1.10)^2$.

Method. Compute current yield directly from annual coupon income and price. For yield to maturity, verify the rate using the present value of both coupons and the redemption payment. This avoids omitting either coupon from the yield equation.

The annual coupon income is $A=\$6$, so the current yield is

\frac{6}{93.05785124\ldots} =0.064476\ldots =6.4476\%.

The yield to maturity is 10% if the price equals the present value of the contractual cash flows at that rate. At 10%, the first-year coupon has present value $6/1.10=\$5.454545\ldots$. The second-year coupon and redemption payment total $106, with present value $106/(1.10)^2=\$87.603306\ldots$. Therefore,

\frac{6}{1.10}+\frac{106}{(1.10)^2} =5.454545\ldots+87.603306\ldots =93.057851\ldots=P.

Thus the yield to maturity is 10%, above the 6.4476% current yield. The bond is bought below its $100 redemption value, so the investor receives a $6 gain at maturity in addition to the coupons. The price equation checks the yield: discounting the two promised cash flows at 10% reproduces the stated price.

Coupons Paid More Than Once Per Year

When coupons are paid $m$ times per year, use $mC$ for annual coupon income in the current-yield calculation. Do not divide the annual coupon income by the number of payments, and do not use just one coupon as the annual numerator. For yield to maturity, use the coupon-period rate $j$ in the present-value equation and keep the number of periods and annualization convention consistent.

Worked Example: Semiannual Coupons on a Premium Bond

A hypothetical bond with face amount $1,000 pays coupons semiannually at a nominal annual coupon rate of 8%. It has six half-year periods remaining and sells for $1,054.171915. Calculate its current yield. If its nominal annual yield to maturity convertible semiannually is 6%, verify the price and compare the two measures.

Method. Convert the coupon rate to a payment per half-year, use two payments to get annual coupon income, and then check the price using the six-period yield equation. This avoids comparing annual coupon income with a half-year yield.

Each half-year coupon is $0.08(1000)/2=\$40$. Annual coupon income is $A=2(40)=\$80$. Therefore,

\text{Current yield} =\frac{80}{1054.171915} =0.0758889\ldots =7.5889\%.

A nominal annual yield of 6% convertible semiannually gives a period rate $j=0.06/2=0.03$. The price at this rate is

40a_{\overline{6}|}+1000(1.03)^{-6} =40\left(\frac{1-(1.03)^{-6}}{0.03}\right)+1000(1.03)^{-6}.

Since $(1.03)^{-6}=0.837484256\ldots$, the annuity factor is $(1-0.837484256\ldots)/0.03=5.41719147\ldots$. The coupon present value is $40(5.41719147\ldots)=\$216.687659\ldots$, and the redemption present value is $1000(0.837484256\ldots)=\$837.484256\ldots$. Their sum is $\$1,054.171915\ldots$, agreeing with the stated price. The nominal annual yield to maturity is 6%, below the 7.5889% current yield, as expected for a premium bond.

Common Mistakes and Practical Interpretation

A common mistake is to divide coupon income by face amount when calculating current yield. Face amount belongs in the coupon-rate calculation; current yield uses the price paid by the investor. Another is to calculate a correct current yield and then treat it as the bond’s total yield, ignoring the difference between the purchase price and redemption value.

Wrong denominator: For annual coupons of $8 and a market price of $105, the incorrect calculation $8/100=8\%$ uses a $100 face amount. The correction is $8/105=0.076190\ldots=7.6190\%$.
Wrong coupon period: If a bond pays $25 twice per year, $25/P$ is not its current yield. Annual coupon income is $50, so current yield is $50/P$.
Ignoring redemption: Current yield does not include the gain or loss from receiving $R$ after paying $P$. Yield to maturity does include the redemption cash flow through its price equation.
Mixing yield conventions: With frequent coupons, identify whether the rate is per coupon period, nominal annual, or effective annual. The nominal annual yield $mj$ is not generally the same as an effective annual yield.

Current yield can be useful as a quick measure of coupon income relative to market price, but it is incomplete as a measure of total return. Yield to maturity is the more comprehensive cash-flow measure when the bond is held to maturity under its stated payment terms. Neither measure guarantees an investor’s realized return if the bond is sold early, payments differ from those promised, or the assumptions used for yield to maturity are not met.

Key takeaway: Current yield is annual coupon income divided by current price. Yield to maturity also reflects redemption value and timing. For conventional bonds, a premium redemption loss generally puts yield to maturity below current yield; a discount redemption gain generally puts it above current yield.

Check Your Understanding

For each problem, distinguish the annual coupon income from the coupon rate, and account for redemption when comparing current yield with yield to maturity.

A hypothetical bond pays $18 annually and has a current price of $300. Calculate its current yield. (Answer: $18/300=0.0600$, or 6.00%.)
A bond has face amount $300, pays $24 annually, costs $320, and will redeem for $300. Calculate current yield and state how it compares with yield to maturity. (Answer: Current yield is $24/320=7.50\%$; as a premium bond, its yield to maturity is below current yield.)
A one-year bond costs $950, pays a $50 coupon at year-end, and redeems for $1,000 then. Calculate current yield and yield to maturity. (Answer: Current yield is $50/950=5.2632\%$; yield to maturity is $1050/950-1=10.5263\%$.)
A hypothetical bond with face amount $1,000 pays a 4% nominal annual coupon rate semiannually, costs $1,040, and has three years remaining. Calculate current yield and state how it compares with yield to maturity. (Answer: Annual coupon income is $2(0.04(1000)/2)=\$40$; current yield is $40/1040=3.8462\%$, above yield to maturity because the bond is a premium bond.)
A bond with face amount $1,000 pays a 12% nominal annual coupon rate quarterly, costs $900, and redeems for $1,000 in two years. Calculate current yield and write the equation for the nominal annual yield to maturity $4j$, where $j$ is the quarterly yield. (Answer: Annual coupon income is $4(0.12(1000)/4)=\$120$, so current yield is $120/900=13.3333\%$; the yield equation is $900=30a_{\overline{8}|}+1000(1+j)^{-8}$, and yield to maturity exceeds current yield because the bond is a discount bond.)

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