Bond language: When does 4 percent beat 6?

Bonds confuse people. The language of bonds is mathematics. I spent the first dozen years of my career working on nothing but municipal bonds. Despite my fluency in math, I will confess that it took the better part of my first working year before the basics of bond math were second-nature to me.

I guess it’s like making the leap from being able to read and speak a foreign language to being able to actually think in that language.

While there are many subtleties to understanding bonds, perhaps the most prevalent is the confusion between yield and coupon. When you are buying or selling a bond, or even analyzing whether to buy or sell, what matters is the current yield to maturity. Yet most investors look only to the coupon rate and miss opportunities to earn more on their bond portfolios.

The coupon rate is the interest rate printed on the bond. It is the figure that is used to calculate the periodic interest payments. The yield, however, is set by the marketplace for bonds and changes daily.

If you buy a $10,000 bond with a coupon of 5 percent, what is your yield? If you paid exactly $10,000 for the bond, or par, then the yield equals the coupon. But, if you paid more than $10,000 for the bond, then your yield is less than 5 percent. Yes, you still get interest payments calculated at 5 percent, but the 5 percent number is multiplied by the face amount of the bond, not the higher price you paid. Further, at maturity, you get back a little less than you paid. These two factors serve to reduce the actual yield on your money.

Conversely, if you pay less than par for the bond, your yield will be higher than 5 percent. The coupon rate on a bond is merely the contractual method for calculating your payments. Your yield depends entirely on what you paid for the bond.

The confusion between yield and coupon often prevents bond investors from making changes to their portfolios that can be profitable. Let’s say you own a $50,000 bond that is due in five years, with a coupon rate of 6 percent. I might suggest to you that you sell that bond and buy a different five-year bond with a coupon of only 4 percent.

Hearing this, you might be inclined to think I was nuts. That’s because many perfectly rational investors see only the coupon rate, and they are not fools. Six percent is more than 4 percent, so why make the trade?

Now let’s say that the bond I recommend can be purchased at its face value, or par. That means that it has a yield to maturity of 4 percent. Your bond, on the other hand, can be sold in the open market for a yield of 3 percent. Your bond would sell for a price of $56,916. That money can be re-invested in my bond and earn 4 percent.

Let’s walk through the math for a moment. If you keep your existing bond, your total cash flow over the five-year holding period is $15,000 in interest plus the $50,000 face amount at maturity. Keeping your bond, you receive a total of $65,000.

If instead you sell your bond and buy my bond, things work a little differently. Of the $56,916 you received for selling your bond, you reinvest $55,000 in the new 4 percent bond. Over the next five years, you will receive $11,000 in interest, plus your $55,000 at maturity, for a total of $66,000. Add in the leftover $1,916 from the initial trade, and you receive $2,916 more by swapping to my bond.

Despite the fact that the new bond had a substantially lower coupon rate, you made more money.