The spread between short-term and long-term interest rates - better known as the yield curve - contains more information than meets the eye. In addition to today's rates, the yield curve reveals the market's expectation of future rates, known as the forward yield curve.

For example, every day The Bond Buyer publishes a tax-exempt yield curve supplied by Municipal Market Data. The curve stretches from 1995 to 2024.

According to the data published yesterday, an investor wanting to buy a one-year bond from a single-A rated issuer could expect a yield of 3.75%. The investor could also select a two-year bond yielding 4.50%.

If the investor wants to invest for two years, she could buy the two-year bond, locking in a 4.50% return, or buy the one-year bond and reinvest in another one-year bond when the first bond matures.

The investor may have a particular interest rate outlook. If she expects rates to decline, the two-year bond is probably the better option. If she expects rates to rise, the one year bond followed by another one-year bond next year is preferable.

But how does the investor's outlook compare to the market's expectations? If the market expects rates to rise, that is factored into the rate on the two-year bond. And if rates rise, as the investor expected, but don't rise as much as the market had expected, the investor could make less buying consecutive one-year bonds than if she had opted for a two-year bond at the outset.

How much would rates have to rise to make the purchase of two one-year bonds more profitable than the purchase of a single two-year bond?

The market's expectation of the one-year rate a year from now can be implied from the current one-year and two-year rates. The one-year rate next year should allow the holder of one-year bond to "catch up" to the two year bond holder.

Although there are several complications in calculating the forward curve from current rates, a simple example involves zero-coupon bonds.

If the one-year rate on a zero is 3.75% and the two-year rate is 4.50%, what is the market's expectation of the one-year rate a year from now?

After two years of compound interest, the buyer of the two-year zero will have \$109.20 on a \$100 principal amount.

If the buyer of the one-year zero ends up with \$103.75 after one year, what is the rate that will "catch up" to the two-year return of \$109.20?

Simple interpolation provides answer. The market view of the one-year rate on a zero coupon bond a year from now is about 5.26%. In other words, if the investor put the \$103.75 into a new one-year zero coupon bond with a rate of 5.26%, at the end of two years, the investor will also have \$109.20.

If the yield curve, including the spread between one-year and two-year bonds, is relatively wide, the market is expecting much higher future rates. And if the yield curve flattens, the market is lowering its expectations of future rates.

For example, if the one-year rate rose to 4% and the two-year rate stayed at 4.50%, flattening the yield curve, the one-year forward rate drops to 5%.

If the one-year rate rises to 4% but the two-year rate rises to 5%, widening the yield curve, then the one-year forward rate rises to 6%.

Issuers and investors can take advantage of implied forward rates using forward bond issues and other derivative transactions.

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