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Suppose that the Treasury bond futures price is \(101-12\). Which of the following four bonds is cheapest to deliver? $$\begin{array}{ccc} \hline \text {Bond} & \text {Price} & \text {Conversion factor} \\ \hline 1 & 125-05 & 1.2131 \\ 2 & 142-15 & 1.3792 \\ 3 & 115-31 & 1.1149 \\ 4 & 144-02 & 1.4026 \\ \hline \end{array}$$

Short Answer

Expert verified
Bond 4 is the cheapest to deliver.

Step by step solution

01

Understand the Problem

We are given the Treasury bond futures price of \(101-12\), which means 101 and 12/32. We also have a list of bonds with their prices and conversion factors. The goal is to find out which bond is the cheapest to deliver.
02

Convert Prices

Convert each bond price from a fraction to a decimal format for ease of calculation. - Bond 1: \(125 + \frac{5}{32} = 125.15625\)- Bond 2: \(142 + \frac{15}{32} = 142.46875\)- Bond 3: \(115 + \frac{31}{32} = 115.96875\)- Bond 4: \(144 + \frac{2}{32} = 144.0625\)
03

Calculate the Adjusted Futures Price

The adjusted futures price is calculated by multiplying the futures price by the conversion factor. Convert the futures price first: \( 101 + \frac{12}{32} = 101.375 \)
04

Calculate Delivery Cost

For each bond, calculate the cost to deliver using the formula:\[ \text{Delivery Cost} = \text{Bond Price} - (\text{Futures Price} \times \text{Conversion Factor}) \] - Bond 1: \( 125.15625 - (101.375 \times 1.2131) \)- Bond 2: \( 142.46875 - (101.375 \times 1.3792) \)- Bond 3: \( 115.96875 - (101.375 \times 1.1149) \)- Bond 4: \( 144.0625 - (101.375 \times 1.4026) \)
05

Compute Delivery Costs

Calculate the actual delivery costs:- Bond 1: \( 125.15625 - 123.001 \approx 2.155\)- Bond 2: \( 142.46875 - 139.781 \approx 2.688\)- Bond 3: \( 115.96875 - 112.981 \approx 2.988\)- Bond 4: \( 144.0625 - 142.114 \approx 1.948\)
06

Identify the Cheapest Bond to Deliver

Compare the delivery costs calculated in the previous step. Bond 4 has the lowest delivery cost of approximately \(1.948\). Thus, Bond 4 is the cheapest to deliver.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Cheapest to Deliver
In the world of Treasury bond futures, the term "cheapest to deliver" refers to the bond that a seller can deliver, at the least cost, to fulfill a futures contract obligation. When you are working with multiple bonds, each with different prices and conversion factors, identifying which bond is the most economical to deliver is a strategic decision. The cheapest to deliver bond is the one that minimizes the cost difference between the agreed futures price and the bond's market value.
This choice is crucial for optimizing profits or minimizing losses. Hence, investors calculate and analyze to select the bond that offers these least expenses, when factors like the current market price and conversion factor are taken into account. It ensures that the delivery process of fulfilling a futures contract is cost-effective.
Conversion Factor
A conversion factor in Treasury bond futures is a crucial number that helps in standardizing bonds with different coupon rates and maturities. It provides a mechanism to compare bonds with different characteristics on an equal basis. Specifically, it's used to adjust the quoted futures price, making it applicable to deliver any bond in a basket of eligible securities.
The conversion factor considers elements such as the bond's coupon, maturity, and yield environment. Simply put, it establishes how much a bond's price must be adjusted to reflect its true value in the context of a standardized futures contract. This is critical to correct any mismatches caused by differing cash flows and timings associated with each bond.
Futures Price Adjustment
When working with Treasury bond futures, the futures price often needs adjustment using the conversion factor to find the real cost implications of delivering a particular bond. This adjustment bridges the gap between a bond's quoted market price and the futures contract price. By multiplying the futures price by the corresponding conversion factor of the bond, we derive the adjusted future price.
This adjusted figure represents the value used in calculating the delivery cost for each bond option within a futures contract. Essentially, it provides an unbiased platform to compare and establish which bond is more affordable or lucrative to deliver under the prevailing market conditions.
Bond Price Calculation
Calculating the bond price accurately is fundamental in determining the delivery cost. The bond price needs to be expressed in decimal form because this format simplifies various financial calculations, including determining the cheapest to deliver bond. For example, a bond price quoted as 125-05 translates to 125.15635 in decimal after converting the fractional part \( \frac{5}{32} \).
Such conversions allow investors to systematically compute the exact delivery cost by subtracting the adjusted futures price, established earlier, from the bond's current market price. Thus, this conversion is pivotal to getting precise and actionable insights regarding bond deliverability in futures contracts.

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