Short-term spot rates can be derived directly from various short-term securities, such as zero-coupon bonds, T-bills, notes, and Eurodollar deposits. However, longer-term spot rates are typically derived from the prices of long-term bonds through a bootstrapping process, taking into account the spot rates of maturities corresponding to the coupon payment date. After obtaining short-term and long-term spot rates, the yield curve can then be constructed.
Let's illustrate the bootstrapping of the yield curve with an example. The following table shows a list of bonds with different maturities and prices:
|
Bond face value in Dollars |
Time to maturity in years |
Annual coupon in Dollars |
Bond cash price in Dollars |
|---|---|---|---|
|
100 |
0.25 |
0 |
97.50 |
|
100 |
0.50 |
0 |
94.90 |
|
100 |
1.00 |
0 |
90.00 |
|
100 |
1.50 |
8 |
96.00 |
|
100 |
2.00 |
12 |
101.60 |
An investor of a 3-month zero-coupon bond today at $97.50 would earn an interest of $2.50. The 3-month spot rate can be calculated as follows:
