Now let’s change the example shown on the table – interest rates rise and the yield paid on newly issued treasury notes rises towards 7% as shown in the second column of the table. Further, the coupon income is reinvested in six-month T-bills which pay 1.25% less than treasury notes. The table works out this example: every six months a coupon payment is received and it is added to the past coupon income and the total is invested at the T-bill rate. These coupon payments – the interest paid on the bond – earn “interest on interest.” At the end of ten years the accumulated coupons total $31.10 ($25 of payments plus $6.10 interests earned on the coupons). The total investment is worth $131.10. The green line on the chart plots the investment value. In the early years the rising rates depress the bond price and send the investment into negative territory. As the accumulated coupon interest increases and as the bond approaches maturity, the investment moves into positive territory and surpasses the theoretical case of no change in interest rates (the dotted line).
If it is possible to make money with bonds when interest rates rise, why are so many people worried that rates will rise? The blue line at the bottom of the chart plots the price of the bond for the same time pattern of rising interest rates. Just as the math requires, rising rates mean lower bond prices. At maturity approaches the price approaches the par value of the bond – the principal to be repaid at maturity. If an investor didn’t reinvest the coupons, if instead he spent the coupon income, all he would have at maturity is the par value. Likewise, if the investor had sold out at the low point on the green line (July 15, 2016) the proceeds for the $100 invested would have been $96.50, a loss of $3.50.
There are no magic formulas for bond investing in any interest rate environment, but working the math sometimes helps.