# Zeroing in on the Bond Market

by: Eddy Elfenbein

Bloomberg wins the award for cheekiest headline: “Strippers Declare Inflation Dead as Dealers Revive Zero-Coupon Treasuries.” The article is, of course, about stripped zero-coupon bonds (though I’m sure exotic dancers are probably privy to much inside Wall Street info).

Strips are zero-coupon Treasury bonds. So instead of getting semi-annual dividend checks, you get all your money back once the bond matures. The hitch is that zeros can be very volatile—in fact, as volatile as stocks. The longer term the bond, the more volatile it can be.

Of course, if you insist on holding the zeros to maturity, there’s no risk at all. One method of investing that zero-buyers use is to ladder their purchases. They work their portfolio so bonds come due each year, so there’s a continuous stream of cash.

If you time zeros right, you can make a lot of money (that’s a big if though). The Bloomberg article notes that with inflation so low, investors are crowding into zeros. The 30-year zero is up close to 17% this year. What can I say? That’s pretty darn good. Think of zeros as like regular Treasuries but they have their own automatic dividend reinvestment program. Although they’ve done well this year, I would steer clear of all Treasuries or all maturities, TIP or not, coupon or not.

One more thing... and this is for all you math nerds. If you want to know what should be the difference between the coupon yield of a bond and its zero-coupon equivalent, then you get to be super geeky and whip out Euler’s Number (the mathematical constant e which I’m rounding off to 2.718).

For example, a 5% coupon bond is e^.05. Then subtract 1, which is about 5.127% for the zero.

All this comes from the compound-interest problem that was solved by mathematician Jacob Bernoulli. I’ll turn it over to Wikipedia:

The compound-interest problem

Jacob Bernoulli discovered this constant by studying a question about compound interest.

One example is an account that starts with \$1.00 and pays 100% interest per year. If the interest is credited once, at the end of the year, the value is \$2.00; but if the interest is computed and added twice in the year, the \$1 is multiplied by 1.5 twice, yielding \$1.00×1.5² = \$2.25. Compounding quarterly yields \$1.00×1.254 = \$2.4414…, and compounding monthly yields \$1.00×(1.0833…)12 = \$2.613035….

Bernoulli noticed that this sequence approaches a limit (the force of interest) for more and smaller compounding intervals. Compounding weekly yields \$2.692597…, while compounding daily yields \$2.714567…, just two cents more. Using n as the number of compounding intervals, with interest of 100%/n in each interval, the limit for large n is the number that came to be known as e; with continuous compounding, the account value will reach \$2.7182818…. More generally, an account that starts at \$1, and yields (1+R) dollars at simple interest, will yield eR dollars with continuous compounding.