| | | | | | | Curiosity 10.1: How Is Yield to Maturity Calculated? | | | | | | | | | | For the case of exactly one year to maturity, calculation of the interest rate i is straightforward because one simply calculates the return and divides by the cost: | | | | | | | | | | | | This equation produces a fraction which must be multiplied by 100 to get the percentage, so that, for example, i = 0.06 corresponds to 6 percent. For a discount bond with one year to maturity the same formula applies, with the coupon equal to zero. Discount bonds such as T-bills frequently are for periods less than a year, though, requiring a modification of this formula. If a discount bond has N days to maturity, its annualized yield is calculated as | | | | | | | | | | | | The logic of this modification is straightforward: the percentage return over six months, say, needs to be doubled to find the annual interest rate. | | | | | | | | | | For maturities longer than one year the calculations are much more complicated, and for this reason are not required for any questions found in this book. For those interested, however, the nature of the calculation is spelled out in appendix 10.1, which provides a variety of additional information on bonds. | | | | | |
| | | | | substantial capital gains or losses for those holding bonds, particularly for those holding long-term bonds. It is for this reason that the financial pages of newspapers provide so much commentary on the future course of the interest rate. | | | | | | | | | Why are the capital gains and losses greater for longer-maturity bonds? Let's look at the earlier example of a $1,000 face-value coupon bond with coupon $100 and time to maturity five years. A rise in the interest rate to 12 percent dropped the bond price to $927.90. Suppose there had only been one year to maturity; then the price would have fallen to $982.14. Someone buying this bond would, during the remaining year of its life, receive the $100 coupon plus that year's capital gain, $17.86, generating a 12 percent return on outlay. If there had been five years to maturity, however, there would have to be five such annual capital gains as the bond price crawls up to its face value over the five years. Consequently, the price must fall further for a longer maturity bond. Capital losses and gains are much larger on long-term bonds than on short-term bonds. | | | | | | | | | 10.3
Monetary Policy and Interest Rates | | | | | | | | | The central bank controls the money supply through open-market operations buying and selling government bonds. If it wishes to increase the money supply, it buys government | | | | |
