Bond futures are contracts that allow investors to buy or sell bonds at a fixed price and date in the future. They are used to hedge against interest rate risk, speculate on bond price movements, or take advantage of price differences between different markets. Bond futures trade on futures exchanges, such as the CME Group, and are standardized by the exchange in terms of contract size, delivery date, and eligible bonds for delivery.
When a bond futures contract expires, the seller must deliver a bond to the buyer. However, the seller can choose which bond to deliver from a range of bonds that meet the contract specifications. The bond that is most profitable for the seller to deliver is called the cheapest-to-deliver (CTD) bond. The CTD bond is usually the one with the lowest interest rate and the longest maturity among the eligible bonds.
Bond futures are indirectly used to trade or hedge interest rate moves, because bond prices and interest rates have an inverse relationship. When interest rates rise, bond prices fall, and vice versa. Therefore, buying a bond futures contract means betting that interest rates will fall, and selling a bond futures contract means betting that interest rates will rise.
Bond futures are different from bond options, which give the buyer the right, but not the obligation, to buy or sell a bond at a specified price and date. Bond options are also traded on futures exchanges, but they have different contract specifications and pricing models than bond futures.
Bond Futures Duration Basics:
Bond futures duration is a crucial concept in finance that helps investors and traders assess the interest rate risk associated with bond investments. Duration is a measure of the sensitivity of a bond’s price to changes in interest rates. It helps investors gauge how much the price of a bond is likely to change in response to a change in interest rates.
The formula for Macaulay duration (D) is given by:
D = ∑ [t * CFt / (1 + YTM)^t + n * M / (1 + YTM)^n] / ∑ [CFt / (1 + YTM)^t]
where:
- CFt is the cash flow at time t,
- YTM is the yield to maturity, and
- M is the final maturity of the bond.
Procedures for Calculating Bond Futures Duration in Excel:
- Gather Bond Information: Collect details about the bond, including cash flows, yield to maturity, and maturity.
- Set Up Excel Table: Create an Excel table with columns for time (t), cash flow (CFt), and discount factor (1 / (1 + YTM)^t).
- Calculate Cash Flows: Enter the cash flows for each period.
- Calculate Discount Factors: Use the formula 1 / (1 + YTM)^t to calculate discount factors for each period.
- Calculate Weighted Cash Flows: Multiply each cash flow by the corresponding discount factor.
- Sum Weighted Cash Flows: Sum up the weighted cash flows to get the numerator of the duration formula.
- Sum Cash Flows: Sum up the cash flows to get the denominator of the duration formula.
- Apply Duration Formula: Use the Macaulay duration formula in Excel to calculate the duration.
Explanation with Real Numbers:
Let’s consider a bond with the following details:
- Face value (FV): $1,000
- Annual coupon rate: 5%
- Years to maturity: 5
- Yield to maturity (YTM): 4%
Excel Table:
| Time (�) | Cash Flow (���) | Discount Factor |
|---|---|---|
| 1 | $50 | 1(1+0.04)1 |
| 2 | $50 | 1(1+0.04)2 |
| 3 | $50 | 1(1+0.04)3 |
| 4 | $50 | 1(1+0.04)4 |
| 5 | $1,050 | 1(1+0.04)5 |
Calculation:
D = [(1 * 50 * 0.9615) + (2 * 50 * 0.9246) + (3 * 50 * 0.8890) + (4 * 50 * 0.8548) + (5 * 1,050 * 0.8227)] /
[(50 * 0.9615) + (50 * 0.9246) + (50 * 0.8890) + (50 * 0.8548) + (1,050 * 0.8227)]
Result: The Macaulay duration of the bond is approximately 4.34 years.
Other Approaches:
- Excel Functions: Excel has built-in functions such as PV, FV, and RATE that can be used to calculate present value, future value, and yield, making the process more automated.
- Sensitivity Analysis: Conduct sensitivity analysis by changing the YTM to observe how duration reacts to different interest rate scenarios.
- Modified Duration: Modified duration is another measure often used. It is calculated as Macaulay duration divided by (1 + YTM). This approximation is particularly useful when interest rates change.
