## Bond Math

As rates rise, investors struggle to understand why bond prices are falling, especially after last year’s rout in the bond market. Bonds are supposed to be stable and boring, not a volatile asset class, yet, they are complicated instruments, providing something for all investors.

The Federal Reserve raised interest rates from 0% to 4.5% last year, a significant increase and the steepest rise in history. As a result, the rate increase destroyed bonds, causing damage to numerous portfolios.

Bonds are fixed-income investments, meaning the coupon does not move, but the other yields can gyrate significantly. A bond is a contract with terms outlined in the prospectus, a legal document. Let’s explore some bond pricing to help you make better investment decisions.

Terms and Data

Coupon: The coupon is the fixed rate on your bond.

Current Yield: The current yield is a function of your coupon rate and today’s price.

Yield To Maturity: The yield to maturity rate is what you’ll earn on your bond at maturity, based on the coupon rate and the price of your bond.

Stable Rates

If interest rates are stable, flat, or not moving, then the coupon, current yield, and yield-to-maturity are equal. For example, if a bond trades at \$100 with a 4% coupon, the current yield and yield to maturity are also 4%. You will earn \$4,000 annually if you own a \$100,000 bond.

Falling Rates

If interest rates are falling, your bond’s price rises like a see-saw in the park. For example, if the coupon is 4% and the price of your bond increases to \$110, then the current yield is 3.64%, and the yield to maturity is 2.84%. When rates fall, the coupon is higher than the current yield, which is higher than the maturity yield. You will earn \$4,000 annually if you own a \$100,000 bond, regardless of the current yield or price.

Rising Rates

If interest rates are rising, then the price of your bond is falling. For example, if your bond has a 4% coupon and the price drops to \$90, the current yield is 4.44%, and the yield to maturity is 5.3%. When rates rise, the coupon is lower than the current yield, which is lower than the yield to maturity. You will earn \$4,000 annually if you own a \$100,000 bond, regardless of the current yield or price.

One Percent Decrease

If you own a ten-year bond, then a one percent decrease in interest rates will increase the price of your bond by 8.5 percent, rising from \$100 to \$108.50.

One Percent Increase

If you own a ten-year bond, then a one percent increase in interest rates will decrease the price of your bond by 7.7 percent, falling from \$100 to \$92.30.

Bond Funds

What about bond funds since they don’t have a fixed interest rate or maturity? Vanguard’s Intermediate-Term Bond fund owns 2,144 individual bonds with an average duration of 6.29 years. The yield to maturity is a function of the portfolio’s average coupon, duration, and the prices of their bonds.

Bonds can be simple and complicated. A US T-Bill is simple, but a junk bond issued by a cryptocurrency company is complex. Pay attention to the rating and yield to maturity if you buy individual bonds. If you don’t want to sift through thousands of bonds, purchase a bond fund.