Interest Rates and Rates of Return
When you make an investment, you are most concerned with what you earn during a given period of time, often called a holding period. If you buy a bond and hold it for one year, the return on your investment in the bond for that year consists of (1) the coupon payment received and (2) the change in the price of the bond, which will result in a capital gain or loss. Usually, you are most interested in measuring your return as a percentage of your investment, which gives us your rate of return, R. For example, consider again your purchase for $1,000 of a GE bond with a face value of $1,000 and a coupon rate of 8%. If at the end of the year following your purchase, the price of the bond increases to $1,271.81, then during that year you will have received a coupon payment of $80 and had a capital gain of $271.81. So, your rate of return for the year was:
When you make an investment, you are most concerned with what you earn during a given period of time, often called a holding period. If you buy a bond and hold it for one year, the return on your investment in the bond for that year consists of (1) the coupon payment received and (2) the change in the price of the bond, which will result in a capital gain or loss. Usually, you are most interested in measuring your return as a percentage of your investment, which gives us your rate of return, R. For example, consider again your purchase for $1,000 of a GE bond with a face value of $1,000 and a coupon rate of 8%. If at the end of the year following your purchase, the price of the bond increases to $1,271.81, then during that year you will have received a coupon payment of $80 and had a capital gain of $271.81. So, your rate of return for the year was:
If the price of your bond had declined to $812.61, then you would have received the $80 coupon payment but suffered a capital loss of $187.39. So, your rate of return for the year would have been negative:
A General Equation for the Rate of Return
We can extend these examples for coupon bonds to write a general equation for the rate of return during a holding period of one year. First, recall that the current yield on a coupon bond is the coupon divided by the current price of the bond. The rate of capital gain or loss on a bond is the dollar amount of the capital gain or loss divided by the initial price.We can then write the following general equation for the rate of return for a holding period of one year
We can extend these examples for coupon bonds to write a general equation for the rate of return during a holding period of one year. First, recall that the current yield on a coupon bond is the coupon divided by the current price of the bond. The rate of capital gain or loss on a bond is the dollar amount of the capital gain or loss divided by the initial price.We can then write the following general equation for the rate of return for a holding period of one year
Here are three important points to note about rates of return:
- In calculating the rate of return, we will use the price at the beginning of the year to calculate the current yield.
- . You incur a capital gain or loss on a bond even if you do not sell the bond at the end of the year. If you sell the bond, you have a realized capital gain or loss. If you do not sell the bond, your gain or loss is unrealized. In either case, the price of your bond has increased or decreased and needs to be included when calculating the rate of return on your investment.
- . If you buy a coupon bond, neither the current yield nor the yield to maturity may be a good indicator of the rate of return you will receive as a result of holding the bond during a particular time period because they do not take into account your capital gain or capital loss.
Interest-Rate Risk and Maturity
We have seen that holders of existing bonds suffer a capital loss when market interest rates rise. Economists refer to the risk that the price of a financial asset will fluctuate in response to changes in market interest rates as interest-rate risk. But are all bonds equally subject to interest-rate risk? We might expect that bonds with fewer years to maturity will be less affected by a change in market interest rates than would bonds with more years to maturity. The economic reasoning is that the more years until a bond matures, the more years the buyer of the bond will potentially be receiving abelow-market coupon rate, and, therefore, the lower the price a buyer would be willing to pay.
Table 3.2 shows that the arithmetic of bond prices bears out this reasoning. Assume that at the beginning of the year, you pay $1,000 for a $1,000 face value bond with a coupon rate of 6%. Assume that at the end of the year, the yield to maturity on similar bonds has risen to 10%. The table shows your rate of return, assuming that the bond you purchased has different maturities. For instance, the top row shows that if you purchased a one-year bond, your rate of return is equal to the current yield of 6%; you held the one-year bond for one year and received the $1,000 face value at maturity, so the change in market interest rates did not affect you. The second row shows that
if your bond has a maturity of two years, you will take a capital loss that is greater than the current yield, so your rate of return will be negative. The remaining rows show that the longer the maturity of your bond, the lower (more negative) your return. With a maturity of 50 years, your rate of return for the first year of owning your bond will be -33.7%.
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