Treasury Futures Delivery Options: CTD, Wildcards, and Hidden Optionality

Key Takeaways

• Conversion factors normalize different bonds in a deliverable basket, but they do not fully neutralize coupon and maturity differences, creating embedded optionality.
• The cheapest to deliver, or CTD, is the bond that minimizes the short deliverer's net cost after accounting for conversion factors, accrued interest, and financing carry.
• Shorts in futures hold two delivery options: the substitution option to pick which bond to deliver and the timing option to choose the exact delivery day within the delivery window. These options can dominate P&L.
• Implied repo and break-even repo calculations reveal when a bond becomes the CTD and quantify the embedded value of delivery choices.
• Small moves in yield or financing costs can flip the CTD and produce nonlinear, gamma-like P&L. Trade design and hedging must account for wildcard risk and delivery timing optionality.

Introduction

Treasury futures are cash-settled through physical delivery of eligible Treasury bonds, but the delivery process is far from mechanical. Conversion factors, a deliverable basket, and the short's right to choose both which bond to deliver and when to deliver embed real option value into futures positions. That optionality can drive P&L more than directional rate moves.

Why does this matter to you as a rates trader or portfolio manager? If you hedge or speculate using Treasury futures without quantifying CTD selection risk and the delivery timing option, you may be exposed to large, nonlinear outcomes. This article explains the mechanics, shows how to compute implied repo and CTD thresholds, and gives practical hedging and trading guidance.

You'll learn how conversion factors work, how to compute the cheapest to deliver with concrete numbers, why small yield moves flip CTD status, and how to measure and hedge wildcard and timing optionality. Ready to dive in?

How Conversion Factors Work and Why They Matter

Conversion factors are published numbers that adjust the futures settlement price so the short can deliver bonds with different coupons and maturities. The invoice price the short receives equals the futures settlement price times the conversion factor plus accrued interest. That formula makes the delivery process workable across heterogeneous bonds, but it leaves residuals.

Conversion factors are calculated assuming a reference coupon, historically six percent for U.S. Treasury futures, and discounting scheduled cash flows at a yield that equates to the bond's maturity. The result is a number less than, equal to, or greater than one that scales the futures price to an effective cash price for each deliverable bond.

Invoice price and cash market comparison

Invoice price = Futures settlement price * Conversion factor + Accrued interest. The short compares that invoice price to the market clean price they would have to pay to buy the bond outright. The bond that minimizes the short's net cost is the CTD.

This comparison ignores financing carry and repo for a first pass, but you can add those to calculate implied repo and a more precise ranking. Conversion factors equalize gross amounts, but the short can still exploit differences in coupon, maturity, convexity, and repo financing. That is where optionality comes from.

Cheapest to Deliver and Implied Repo: Step-by-Step

CTD selection is often analyzed with implied repo. Implied repo tells you the annualized financing rate that arbitrageurs earn by buying the cash bond and selling the futures, then delivering the bond at expiry. Higher implied repo makes a bond more attractive to deliver because it implies greater carry benefit.

Formula and worked example

Implied repo, simplified, can be calculated as the annualized return from buying the bond today and delivering it into the futures contract on the chosen delivery date. One common approximation is:

Implied repo = ((Invoice price + Coupon carry - Cash bond price) / Cash bond price) * (365 / Days to delivery)

Example, simple numbers to make the mechanics clear. Suppose the futures settles at 100.00, and Bond A has conversion factor 0.95, clean market price 96.00, and accrued interest 1.00. Invoice if delivered = 100.00 * 0.95 + 1.00 = 96.00. At first glance invoice equals market clean plus accrued, implying zero immediate arbitrage. But now include financing costs and coupon carry. If Bond B has conversion factor 0.90, clean price 89.50, and accrued 0.90, invoice would be 90.90. The implied repo for each bond will differ and that difference determines which bond is cheapest after financing.

In practice traders compute implied repo precisely using clean prices, exact coupon dates, and repo financing assumptions. The bond with the highest implied repo is typically the CTD because it gives the short the best financing-adjusted outcome.

Hidden Optionality: Substitution and Timing Options

When you sell a Treasury futures contract you are short the underlying with two valuable options in your pocket. The first is the substitution option, the right to choose any bond from the deliverable set. The second is the timing option, the right to choose the delivery day within the delivery month after notice is given. Both options have value and they can dominate P&L.

Substitution option and wildcard risk

Imagine two deliverable bonds, one with higher coupon but lower conversion factor and one with lower coupon but higher conversion factor. As yields move, relative prices shift and the CTD can switch. That switch may occur with a small yield movement, causing a discrete jump in the futures basis and in the P&L of hedges tied to a specific bond. Traders call this wildcard risk, where an unexpected CTD change blows up a hedge.

Quantify the substitution option by computing the value of being able to pick the cheaper bond ex ante. This can be approximated by the expected positive payoff of the difference in invoice minus cash price across scenarios, discounted by probabilities. For market makers and hedge funds this equals the basis between futures-implied financing and actual repo plus an option premium that depends on volatility.

Timing option and delivery notice mechanics

The short can time delivery inside the delivery window to exploit intra-month moves in yields and accrued interest. For instance, delivering right after a coupon payment or just before a Treasury auction may change the economics. Shorts often exercise the timing option to maximize profit given anticipated repo and carry. That makes the basis path-dependent, since the short's optimal delivery date depends on rate and financing path inside the month.

Real-World Examples and Numbers

Let's walk through a concrete scenario using a 10-year Treasury futures contract. These are representative rather than prescriptive, but they show the magnitudes involved. Suppose futures trade at 103.00. The deliverable basket includes Bond X with CF 0.9200 and Bond Y with CF 0.9700.

1. Bond X: Clean price 95.00, accrued 0.50. Invoice = 103.00 * 0.9200 + 0.50 = 95.96. Net cost to short equals cash purchase price 95.00 plus financing carry until delivery. If implied repo after carry is 0.8% annualized, that may make Bond X attractive.
2. Bond Y: Clean price 99.50, accrued 0.70. Invoice = 103.00 * 0.9700 + 0.70 = 100.01. Net cost looks worse on invoice alone, but Bond Y might have superior repo availability or a coupon schedule that creates favorable carry, making its implied repo higher under some scenarios.

Now suppose yields fall 10 basis points. Bond prices rise, but the conversion-factor scaled invoice moves differently for each bond. The CTD can switch from X to Y if the change in implied repo crosses the breakeven threshold. That switch can cause rapid marking adjustments for hedges constructed using the prior CTD, producing large P&L swings even though the underlying yield move was modest.

Practical Measurement and Hedging Techniques

To manage optionality you need to quantify it, not just acknowledge it. Start with a break-even implied repo grid across the deliverable basket. Compute implied repo for each bond across plausible yield and repo shocks and identify CTD switching surfaces. That gives you a map of where embedded optionality will bite.

Hedging strategies

• Basis hedge with the CTD and keep contingency hedges for wildcard candidates. A primary hedge matched to the CTD plus smaller hedges in other deliverables reduces the jump risk if CTD flips.
• Use cash-and-carry arbitrage to lock in implied repo when it is favorable, but account for financing and operational constraints like repo haircuts and collateral shortages.
• Synthetic hedges via Treasury strips or interest rate swaps can neutralize interest rate exposure while leaving delivery options isolated, but they may not fully remove substitution optionality.
• Model the timing option using scenario analysis. Trade sized to survive worst-case CTD flips during the delivery month, not just expected-case, preserves capital in stress events.

Common Mistakes to Avoid

• Ignoring the timing option. Many traders hedge as if delivery happens at a single fixed date. The short will choose the most profitable day to deliver, so your hedge should reflect that path dependency.
• Assuming conversion factors fully neutralize coupon risk. Conversion factors normalize but do not eliminate coupon, convexity, and repo differentials. Always model residuals.
• Hedging only with the current CTD. A hedge tied exclusively to the present CTD leaves you exposed to wildcard flips. Maintain contingency or cross-CTD hedges.
• Using naive implied repo estimates. Small errors in accrued interest calculation or day count can materially change implied repo. Use exact cash flows and correct settlement day counts.

FAQ

Q: What exactly is a conversion factor?

A: A conversion factor is a published scalar that converts the futures settlement price into an invoice price for a specific deliverable bond. It is calculated from a reference coupon assumption and standard discounting rules but does not fully remove differences in coupon, maturity, or convexity.

Q: How do I compute which bond is the CTD?

A: Compute invoice price for each deliverable bond as futures price times conversion factor plus accrued interest. Then calculate implied repo for buying the bond and delivering it on the settlement date including coupon carry and financing. The bond with the highest implied repo is typically the CTD.

Q: Can options traders hedge CTD optionality directly?

A: You can partially hedge substitution optionality using options on short-term rates or straddles on the CTD basis, but there is no single off-the-shelf option that removes wildcard value. Hedgers often use a mix of cash bonds, futures across adjacent maturities, and repo trades.

Q: How big is the delivery option's value relative to directional risk?

A: It varies with volatility, repo availability, and the dispersion of conversion factors in the deliverable basket. In low-volatility, deep-repo markets it may be small. During stressed repo or high-volatility regimes it can dominate P&L, sometimes accounting for a majority of basis movement relative to directional rate P&L.

Bottom Line

Treasury futures embed real, tradable optionality through conversion factors, substitution across a deliverable basket, and timing within the delivery window. Those options can create nonlinear P&L outcomes that overwhelm simple directional exposure to interest rates.

If you trade or hedge with Treasury futures, quantify implied repo and CTD switching thresholds, model the timing option, and build contingency hedges for wildcard candidates. At the end of the day, a robust risk framework that treats delivery mechanics as first-order drivers will reduce surprise and improve trade design.

Next steps: run an implied repo grid across your deliverable set, stress repo rates and yields, and size contingency hedges to withstand CTD flips. That disciplined approach turns hidden optionality from a trap into a managed exposure.