Calculating Bond Yields

Summary: Few bond investors (if any) trade in order to lose money. For those seeking to make a profit, comparing the potential returns over different time spans of different instruments is essential. In that effort, calculating bond yield is central. This article summarizes how a bond yield is calculated

Related Articles: i bond interest rates, florida municipal bond, california municipal bond


The most general meaning of yield is the amount of money returned (usually annually), expressed as a percentage of the initial investment.

CURRENT YIELD

Estimating current yield on a bond is simple. Divide the annual interest amount paid by the current market price. CY = IA/P*100. (The 100 turns the fraction into a percentage.) For example, a $1000 face-value (par) bond with a coupon (interest rate) of 7% that matures in 10 years may sell currently at a discount for $950.

The current yield is then,

$1000 x 0.07   = $70 per year in interest
$70/$950 x 100 = 7.37%

Notice how the yield is a little higher than the nominal interest rate, obviously owing to the discounted price of the bond.

This simple calculation allows comparisons between bonds of similar credit risk and maturity.

But, the example assumes the holder bought at par and held to maturity. Taking into account potential capital gains, to arrive at the Adjusted Current Yield is also easy:

ACY = [(IA/P) x 100] + [(Par Value – P)/10]/Years Until Maturity

(Be sure to perform the subtraction first, before dividing, in the last term.)

So, [($70/$950) x 100] + [($1000 -$950)/10]/10 = 7.87%, where the capital gains added half a percent to the overall yield. (Remember the yields are annualized, so this is the percentage one would gain each year.)

YIELD TO MATURITY

The sample calculation above shows the return on the bond today, but ignores the time value of money. Would you rather have $1000 today or $1000 a year from now, even assuming you're assured of getting paid in a year? Having $1000 sooner rather than later means earning interest on that for an additional year.

Accounting for that fact is straight-forward, by using a value called Yield To Maturity. The formula looks daunting but fortunately calculators for estimating it are readily available on the Internet.

Suppose again that a bond is selling for $950, and has a coupon rate of 7%. It has 4 years left until it matures, and the par value is $1000. What's the YTM, Yield To Maturity? Plugging the values into the calculator produces YTM = 8.53%, substantially higher than the previous estimates.

For those interested in the mathematics the formula is:
c(1 + YTM)-1 + c(1 + YTM)-2 + . . . + c(1 + YTM)-YUM + B(1 + YTM)-YUM = P
where
c  = annual coupon payment (in dollars, not a percentage)
YUM = number of years until maturity
B   = par value (original issue price)
P   = purchase price

So, for our example:

70(1 + YTM)-1 + 70(1 + YTM)-2 + 70(1 + YTM)-3 + 70(1 + YTM)-4 + 1000(1 + YTM)-4 = 950.

Solving for YTM gives 8.53%.

YTM is the best number to use when comparing bonds with different rates and maturity dates. With a little practice, the process becomes familiar and loses the aura of numerology. Profits go to the fearless.