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Now that you have a deeper understanding of the U.S. Treasury basis, we need to delve a little deeper into what is known as the cheapest-to-deliver (CTD) security. While each U.S. Treasury futures contract has its own basket of eligible securities for delivery generally one, or sometimes two, price out to be most efficient for the short position to deliver to the long position. This security is most efficient because it is considered cheaper or cheapest to deliver versus the other alternative securities.

Knowing which security is the CTD is important because the futures contract tends to trade like the CTD security. It is also important when calculating hedge ratios because the futures contract’s theoretical basis point value is derived from the CTD security.

## What Determines the CTD?

Before we dive deeper into how to ascertain which issue is the CTD some additional background on the market forces that go into the calculation might be useful. If we take a snapshot of a typical U.S. Treasury futures contract settlement prices of quarterly contracts currently listed for trading, we will see a discernable pricing pattern.

### Example

On February 10, 2017 the following were the settlement prices for the listing quarterly futures for the 10-Year Note (ZN) futures:

March 2017 = 124-250

June 2017 = 124-075

September 2017 = 123-280.

Notice that as the futures contract goes out further in time, the price goes lower in value. There is a very good reason for this. Remember that the underlying product of a U.S. Treasury futures contract is a U.S. Government security that pays interest twice per year based on its coupon value established when it was originally auctioned. This means the cash Treasury is an asset. Futures contracts are not assets. They represent a price point for future delivery. Because of this opportunity cost, or time value of money, the futures prices trade at a discount or premium to cash.

## The Yield Curve

On February 10 when these prices were posted, the yield curve for U.S. Treasuries was positively sloped, that is, rates at the short end of the yield curve were lower than yields further out. Generally speaking, when the yield curve is positively sloped it results in what we call positive carry. If I borrow overnight funds (short-end) and buy a long dated (long-end) U.S. Treasury security with a higher paying rate I enjoy positive carry. To account for this revenue in the underlying physical note or bond the futures contract must price at a discount and gradually converge to cash by time of delivery.

Carry can be either positive or negative depending on the level of rates and the slope of the yield curve.

### Example

It might be useful to walk through the financial calculation for carry to see why this works and why it is important regarding the CTD.

Assume we buy the 1-3/4% of November 30, 2021. This issue is eligible for delivery into the March 2017 5-Year Note (ZFH7) contract. We borrow funds through the repo market to purchase this security and will be charged an interest rate known as the repo rate every day we keep this borrowed position open. Carry is defined as the difference between the coupon income and the financing cost.

Carry = Coupon Income (CI) – Financing Cost (FC)

Assume the CI = \$599.45 per million face value from original trade settlement date to futures contract last delivery date. Additionally, assume the FC = \$206.54 for the same terms. Therefore, Carry = 599.45 – 206.54 = \$392.91. Notice the carry number is positive.

If we were to calculate the carry for all the ZFH7 futures contracts eligible securities, we could then use that number along with each security’s basis to determine each eligible security’s net basis.

Net basis = Basis – Carry

This is important because the issue with the lowest net basis tends to be the CTD issue.

## Implied Repo Rate (IRR)

There is another widely accepted method for determining the CTD issue. It is called the implied repo rate (IRR). It is a theoretical yield produced by buying the cash security, selling the futures contract, lending the cash security in the repo market and finally, delivering the security into the futures contract on last delivery day. The issue with the highest IRR is generally considered CTD. What you will find if you follow these methods is they arrive at the same result. Bloomberg, for example, has a function that calculates the CTD for U.S. Treasury futures using both methods.

The point of knowing the CTD is to understand how the futures contract will behave. U.S. Treasury futures contracts trade like their CTD securities. Knowing what goes into determining the CTD issue is useful to understanding U.S. Treasury futures valuation. It can also help understand how the CTD can shift or change.

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