Pricing Bond Futures Duration in Excel

Bond futures are contracts that allow traders to buy or sell a bond at a fixed price on a future date. The bond futures price depends on the expected value of the bond on the delivery date, as well as the interest rate and the supply and demand of the market.

One way to think of the bond futures price is to imagine that you are buying or selling the bond today, but you agree to settle the transaction on a later date. In this case, you would need to adjust the bond price for the time value of money and the interest rate risk. The time value of money means that a dollar today is worth more than a dollar tomorrow, because you can invest it and earn interest. The interest rate risk means that the bond price can change if the interest rate changes, because the bond pays a fixed coupon that becomes more or less attractive compared to the market rate.

To account for these factors, bond futures use a conversion factor, which is a number that adjusts the bond price to a standard yield of 6%. The conversion factor makes different bonds in the same basket comparable, because they have different coupon rates and maturities. The bond futures price is then calculated by multiplying the bond price by the conversion factor, and adding the accrued interest. The accrued interest is the interest that has accumulated since the last coupon payment, and it is paid by the buyer to the seller.

The bond futures price also reflects the option that the seller has to choose which bond to deliver from the basket. The seller will usually choose the cheapest bond to deliver, which is the one that has the lowest value in the market. The cheapest to deliver bond can change over time, depending on the interest rate movements and the bond characteristics. The seller’s option affects the bond futures price, because it gives the seller an advantage over the buyer. The buyer does not know which bond they will receive until the delivery date, and they may end up with a bond that has a lower value than the futures price.

To summarize, the bond futures price is determined by the expected value of the bond on the delivery date, the conversion factor, the accrued interest, and the seller’s option. The bond futures price can change over time, as the market conditions and the cheapest to deliver bond change. Bond futures are used by traders to speculate on the bond price movements, or to hedge their bond holdings against interest rate risk.

Basic Theory:

Bond futures represent an agreement to buy or sell a bond at a predetermined future date and price. Duration is a measure of a
bond’s interest rate sensitivity. When pricing bond futures duration, we focus on the underlying bond’s cash flows, interest
rates, and time to maturity.

The Macaulay duration of a bond measures the weighted average time until a bond’s cash flows are received. Modified duration
adjusts Macaulay duration for interest rate changes, providing a more accurate measure of interest rate risk.

Procedures:

1. Gather Information:
   • Obtain the bond’s coupon rate, face value, time to maturity, and yield to maturity (YTM).
   • Identify the bond futures contract specifications, including the conversion factor.
2. Calculate Macaulay Duration:
   • Use Excel formulas to calculate the present value of each bond cash flow, including coupons and face value, discounted
     at the YTM.
   • Multiply each present value by the time to receive the cash flow.
   • Sum these values to get the Macaulay duration.
3. Calculate Modified Duration:
   • Modified duration is calculated as Macaulay duration / (1 + YTM/n), where n is the number of compounding periods per
     year.
4. Calculate Bond Futures Price:
   • Bond futures price = (Conversion factor) * (Bond price) / (1 + YTM/n)

Comprehensive Explanation:

Let’s consider a scenario with a 5-year bond, $1,000 face value, 6% coupon rate, and a YTM of 4%. The bond pays semi-annual
coupons, so n = 2.

Excel Table:

Calculations:

1. Macaulay Duration = 121.57
2. Modified Duration = 121.57 / (1 + 0.04/2) ≈ 119.46
3. Bond Futures Price = (Conversion factor) * (Bond price) / (1 + 0.04/2)

Result:

The calculated bond futures price provides insight into the market’s expectation of future interest rates.

Other Approaches:

1. Excel Add-Ins:
   • Utilize specialized Excel add-ins designed for bond pricing and duration calculations.
2. Yield Sensitivity Analysis:
   • Conduct sensitivity analysis by varying the yield to observe its impact on bond futures prices.
3. Scenario Analysis:
   • Explore different scenarios by adjusting bond characteristics or market conditions to assess the potential impact on bond
     futures prices.