The Ins and Outs of Bond Yield

Step 3: How Is Yield to Maturity Calculated?

Yield to maturity (YTM) calculations are not easily made using paper and pencil, but they can easily be determined using either a financial calculator, or by using the various calculators available on the Internet.

YTM is the measure most widely quoted by brokers when selling individual bonds. However, it is not a prediction of what you will actually earn on a bond. Your actual return is likely to differ from the YTM, perhaps considerably, because the YTM will only be realized under certain conditions, which are:

• That you hold the bond to maturity;
• That the coupons are reinvested (rather than spent); and that
• Coupons are reinvested at an interest rate equal to the yield-to-maturity.

Let's look briefly at each assumption:

• Holding to Maturity
  The YTM quote is based on the redemption price of par (that is, $1,000). If you sell a bond before it matures at a price other than par, then the capital gain or loss will alter what you actually earn.
• Reinvesting Coupons
  YTM calculations are based on the assumption that coupons are never spent; they are always reinvested. If you spend coupons, then you do not earn the interest-on-interest, and your return would be less than the anticipated YTM. How much less depends both on how many coupons you spend, the reinvestment rate and on the maturity of the bonds.
• Coupons are Reinvested at an Interest Rate Equal to the YTM
  This may sound like double talk, but it means that if a bond has a YTM of 7%, it is assumed that each and every coupon is reinvested at a rate of 7%. However, if in reality you reinvest coupons at a higher rate than 7%, you will earn more than the bond's stated YTM, while if you reinvest coupons at lower rates than 7%, you will earn less.

  You may think that the interest-on-interest earned from reinvesting the coupons represents only an insignificant source of potential return and that, therefore, this is a minor point. But you would be wrong. Over long periods of time, reinvestment matters enormously. To understand why, you have to understand how compounding works.

  Let's assume that you have $10,000 worth of four-year bonds with 8% coupons paid semiannually. Let's also assume you are reinvesting the $400 in semiannual coupons received at 8%. At the end of the first year, interest-on-interest totals will be unexciting and represent only 2% of the total amount of interest earned that year. By the end of the fourth year, interest-on-interest will comprise about 13% of total interest income. If the bonds are allowed to continue to compound semiannually for 30 years at 8%, interest-on-interest will comprise 75% of total interest earned. Compound interest has been called the 8th wonder of the world, and it works for all investments.

• Reinvestment Risk
  Interest-on-interest from reinvested coupons plays a big role in the earnings of a bond. Yet in the examples above, the reinvestment rate was both known in advance and constant.

  In real life, of course, you cannot know at the time you buy an interest bearing bond what the reinvestment rate is going to be, since you don't know where interest rates will be in the future. Moreover, the uncertainty is greater for longer maturities and higher coupon rates, since the amount represented by the interest-on-interest becomes greater on a percentage basis.

  This uncertainty is known as "reinvestment risk"—the risk that coupons may have to be reinvested at a lower interest rate, in which case an investor's actual return would then be lower than the YTM quoted at the time of purchase. On the other hand, the reinvestment risk may work in your favor if coupons are reinvested at a higher rate, and that would increase the actual return above the YTM quoted at the time of purchase.

  If YTM does not predict your actual return, what does it tell you? The chief usefulness of YTM quotes is that they allow you to compare different kinds of bonds—those with dissimilar coupons, different market prices relative to par (for instance, bonds selling at premiums or discounts), and different maturities.

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