A forward bond price is the price that you agree to pay today for a bond that you will buy or sell at a future date. For example, suppose you want to buy a 10-year bond that pays 5% interest every year, but you don’t have the money right now. You can enter into a forward contract with another party, who agrees to sell you the bond at a certain price on a certain date in the future, say one year from now. This price is the forward bond price.
The forward bond price depends on several factors, such as the current market price of the bond, the interest rates in the market, the time to maturity of the bond, and the coupon payments of the bond. Generally speaking, the forward bond price is equal to the current market price of the bond, plus the interest that you would earn if you invested the money at the market rate, minus the coupon payments that you would miss out on if you waited to buy the bond.
For example, suppose the current market price of the 10-year bond is $1000, and the market interest rate is 4%. If you invested $1000 at 4% for one year, you would have $1040 at the end of the year. However, if you waited to buy the bond, you would miss out on the $50 coupon payment that the bond pays every year. Therefore, the forward bond price is approximately $1040 – $50 = $990. This means that you agree to pay $990 one year from now for the bond that is worth $1000 today.
Basic Theory
Bond Duration
Bond duration is a measure of the weighted average time it takes for the bond’s cash flows (coupon payments and principal repayment) to be repaid. It quantifies the interest rate risk associated with a bond. The duration of a bond is influenced by factors such as coupon rate, time to maturity, and prevailing interest rates.
Forward Bond Prices Duration
Forward bond prices duration extends the concept of bond duration to assess the interest rate risk in the context of forward bond prices. It provides insights into how sensitive the forward bond prices are to changes in interest rates.
Procedures for Calculating Forward Bond Prices Duration in Excel
Step 1: Gather Necessary Information
Before diving into Excel, you need the following bond-related information:
- Coupon Rate (C): The annual interest rate on the bond.
- Yield to Maturity (YTM): The rate of return anticipated on the bond.
- Time to Maturity (T): The number of years until the bond matures.
Step 2: Calculate Present Value of Cash Flows
In Excel, use the formula for present value (PV) to calculate the present value of each cash flow (coupon and principal repayment) considering the given YTM.
=PV(YTM, period, C, FV, type)Step 3: Calculate Weights
Determine the weights for each present value by dividing the present value of each cash flow by the bond’s current price.
=PV of Cash Flow / Current Bond PriceStep 4: Calculate Duration
Multiply the time to maturity for each cash flow by its corresponding weight and sum the results.
=SUM(T * Weight)Practical Example
Let’s consider a scenario:
- Coupon Rate (C): 5%
- Yield to Maturity (YTM): 4%
- Time to Maturity (T): 5 years
- Current Bond Price: $950
Excel Table
| Period | Cash Flow | PV of Cash Flow | Weight |
|---|---|---|---|
| 1 | $50 | $47.62 | $0.05 |
| 2 | $50 | $45.66 | $0.048 |
| 3 | $50 | $43.77 | $0.046 |
| 4 | $50 | $41.94 | $0.044 |
| 5 | $1,050 | $888.50 | $0.936 |
Excel Formulas
Use the PV function to calculate the present value of each cash flow. Calculate the weights. Multiply the time to maturity by the corresponding weight for each period and sum the results to find the forward bond prices duration.
Result
After performing the calculations, the forward bond prices duration is approximately 4.43 years.
Other Approaches
While the above approach is a common and straightforward method, there are alternative approaches such as Macaulay Duration and Modified Duration. These methods provide similar insights into interest rate risk but may be preferred in different contexts.
