Basis Trades (Cash vs Futures)
Trading the basis between JGB cash bonds and futures contracts
Basis Trades (Cash vs Futures)
Basis trading is a fundamental strategy in JGB markets that exploits the relationship between cash JGBs and JGB futures contracts. The “basis” represents the difference between the actual price of a cash bond and its implied price derived from the futures contract. Understanding basis trades requires knowledge of futures mechanics, conversion factors, and the cheapest-to-deliver (CTD) concept.
What is the Basis?
The basis is defined as:
\[\text{Gross Basis} = P_{cash} - (F \times CF)\]Where:
- $P_{cash}$ = Clean price of the cash JGB
- $F$ = Futures price
- $CF$ = Conversion factor for that specific bond (see Chapter 2.7)
The conversion factor adjusts for differences in coupon rates between deliverable bonds, normalizing them to a 6% coupon standard (historically; Japan uses different conventions).
Interpretation:
- Positive basis: Cash bond is expensive relative to futures
- Negative basis: Cash bond is cheap relative to futures
However, the gross basis doesn’t tell the whole story. We need to account for carry to delivery.
Net Basis
The net basis adjusts for the cost/benefit of holding the cash bond until futures delivery:
\[\text{Net Basis} = \text{Gross Basis} - \text{Carry to Delivery}\]Where Carry to Delivery includes:
- Coupon income earned while holding the bond
- Repo financing cost to fund the cash bond position
The net basis represents the pure delivery option value embedded in the futures contract.
Cheapest-to-Deliver (CTD) Bond
JGB futures contracts allow delivery of any bond from a basket of eligible bonds (typically those with remaining maturity within a specified range). The seller chooses which bond to deliver, naturally selecting the cheapest-to-deliver (CTD) bond.
The CTD is the bond with the lowest net basis (or most negative net basis).
Why this matters:
- Futures prices are driven primarily by the CTD bond’s price
- Basis trades typically involve the CTD bond
- CTD can switch as market conditions change, creating risk and opportunity
For detailed CTD mechanics, see Chapter 2.6.
Worked Example: Basis Trade Calculation
Let’s calculate the basis for a potential CTD bond.
Market Data (90 days before delivery):
- Bond: JGB #362 (10Y), Coupon 0.8%, Maturity 10 years
- Cash price: ¥100.25 (clean)
- 10Y JGB futures price: 150.50
- Conversion factor: 0.9850
- Repo rate (GC): 0.10%
Step 1: Calculate Gross Basis
\[\text{Gross Basis} = P_{cash} - (F \times CF)\] \[\text{Gross Basis} = 100.25 - (150.50 \times 0.9850) = 100.25 - 148.24 = -47.99\]Wait—this seems odd. The issue is JGB futures quote differently. Let me recalculate with realistic pricing:
Corrected Market Data:
- Cash price: ¥101.50
- Futures price: 101.80
- Conversion factor: 0.9850
The gross basis is ¥1.23 per ¥100 face value.
Step 2: Calculate Carry to Delivery (90 days)
Coupon income over 90 days: \(\text{Coupon Income} = 0.8\% \times \frac{90}{365} = 0.197\%\)
Repo financing cost over 90 days: \(\text{Repo Cost} = 101.50 \times 0.10\% \times \frac{90}{365} = 0.025\%\)
Net carry: \(\text{Carry} = 0.197\% - 0.025\% = 0.172\%\)
Step 3: Calculate Net Basis
\[\text{Net Basis} = \text{Gross Basis} - \text{Carry}\] \[\text{Net Basis} = 1.23 - 0.172 = 1.058\]The net basis is ¥1.058 per ¥100 face value, or approximately 106 ticks.
The Classic Basis Trade
A basis trade involves:
- Buy the cash CTD bond (e.g., ¥10 billion)
- Sell equivalent futures contracts
- Finance via repo market
- Hold to delivery (or unwind when basis converges)
Number of futures contracts needed:
\[\text{Contracts} = \frac{\text{Cash Notional} \times \text{Conversion Factor}}{100 \text{ million}}\]For ¥10 billion cash position: \(\text{Contracts} = \frac{10,000,000,000 \times 0.9850}{100,000,000} = 98.5 \approx 99 \text{ contracts}\)
Expected P&L (held to delivery):
At delivery, the basis converges to zero (cash and futures prices align). The profit from a positive net basis trade:
\[\text{Profit} = \text{Initial Net Basis} \times \text{Notional}\] \[\text{Profit} = 1.058\% \times ¥10,000,000,000 = ¥105,800,000\]This ¥105.8 million profit accrues over 90 days with minimal directional risk (since we’re long cash and short futures in equivalent amounts).
Annualized return: \(\text{Annual Return} = 1.058\% \times \frac{365}{90} = 4.28\%\)
This is a healthy return for a low-risk, market-neutral strategy.
Implied Repo Rate (IRR)
The basis contains information about the implied repo rate (IRR)—the financing rate implied by the futures price. This provides an alternative method for identifying the CTD bond and spotting arbitrage opportunities.
The IRR Concept
The IRR answers the question: “What return would I earn if I bought this bond today, sold futures against it, and delivered at expiration?”
A rational trader maximizes return. The bond offering the highest IRR is the most profitable to buy-and-deliver, making it the cheapest-to-deliver option.
Cash-and-Carry Strategy
The IRR is calculated based on the cash-and-carry trade:
- Buy a bond from the delivery basket in the cash market
- Finance the purchase through the repo market (borrow cash, pledge the bond as collateral)
- Sell JGB futures (locking in the delivery price)
- Hold the bond, collect coupon payments, and deliver it at futures expiration
IRR Calculation Formula
\[\text{IRR} = \frac{(F \times CF) + \text{Accrued Interest at Delivery} - P_{cash} - \text{Accrued Interest at Purchase}}{P_{cash} + \text{Accrued Interest at Purchase}} \times \frac{365}{\text{Days to Delivery}}\]Where:
- $F$ = Futures price
- $CF$ = Conversion factor
- $P_{cash}$ = Clean price of the cash bond
Simplified version for quick analysis:
\[\text{IRR} \approx \frac{\text{Gross Basis} + \text{Coupon Income}}{\text{Dirty Price}} \times \frac{365}{\text{Days to Delivery}}\]Comparing IRR to Market Repo Rates
Traders compare each bond’s IRR to the market GC (General Collateral) repo rate:
- If IRR > GC Repo Rate: Arbitrage opportunity! You can profit by executing the cash-and-carry.
- If IRR ≈ GC Repo Rate: Fair pricing, no arbitrage (market is in equilibrium)
- If IRR < GC Repo Rate: The bond is “rich” relative to futures; reverse cash-and-carry may be profitable
Since all market participants run this calculation simultaneously, arbitrage activity drives IRRs toward the repo rate. The bond with the highest remaining IRR becomes the CTD.
Worked Example: IRR Calculation
Market Data:
- Bond: JGB #362, 0.8% coupon, 10 years to maturity
- Cash price (clean): ¥101.50
- Accrued interest: ¥0.20
- Dirty price: ¥101.70
- Futures price: 101.80
- Conversion factor: 0.9850
- Days to delivery: 90 days
- GC repo rate: 0.10%
Step 1: Calculate invoice amount at delivery
Assume accrued interest at delivery = ¥0.40
\[\text{Invoice} = (F \times CF) + \text{Accrued} = (101.80 \times 0.9850) + 0.40 = 100.27 + 0.40 = 100.67\]Step 2: Calculate return
\[\text{Return} = \frac{100.67 - 101.70}{101.70} = \frac{-1.03}{101.70} = -1.01\%\]Step 3: Annualize
\[\text{IRR} = -1.01\% \times \frac{365}{90} = -4.10\%\]This negative IRR indicates the bond is rich relative to futures—not attractive for cash-and-carry.
Step 4: Compare to repo rate
GC repo rate = 0.10%, but IRR = -4.10%. This bond is clearly not the CTD. A true CTD would have an IRR close to or slightly above the GC rate.
Using IRR for CTD Identification
Professional traders calculate IRR for all bonds in the delivery basket:
| Bond | Coupon | Price | CF | IRR | CTD? |
|---|---|---|---|---|---|
| #360 | 0.5% | ¥99.80 | 0.9720 | 0.12% | ✅ CTD |
| #361 | 0.7% | ¥100.50 | 0.9800 | 0.08% | — |
| #362 | 0.8% | ¥101.50 | 0.9850 | -4.10% | ❌ Rich |
| #363 | 1.0% | ¥102.80 | 0.9950 | -2.50% | ❌ Rich |
Bond #360 has the highest IRR (0.12%), making it the CTD. Its IRR is also close to the GC rate (0.10%), indicating fair pricing with minimal arbitrage opportunity.
IRR and Arbitrage Opportunities
When IRR significantly exceeds the GC repo rate, cash-and-carry arbitrage becomes profitable:
Example Arbitrage Setup:
- IRR = 0.25% (annualized)
- GC repo rate = 0.10%
- Spread = 15bp (0.15%)
For a ¥10 billion position over 90 days:
\[\text{Profit} = ¥10bn \times 0.15\% \times \frac{90}{365} = ¥3,698,630\]This ¥3.7 million profit comes from the IRR-repo spread with minimal risk (assuming stable CTD status).
Reverse Cash-and-Carry
When a bond’s IRR is below the repo rate, the reverse strategy may be profitable:
- Sell (short) the cash bond
- Buy futures
- Lend cash in repo market at GC rate
- Accept delivery at expiration
This profits when the bond is “rich” relative to futures.
When Basis Trades Work
Basis trades are attractive when:
- Positive net basis exists: The delivery option has value
- Stable CTD: The cheapest-to-deliver bond is unlikely to switch
- Predictable repo rates: Financing costs remain stable
- Low interest rate volatility: Reduces delivery option value uncertainty
Best market conditions:
- Normal, stable yield curve environment
- Tight repo spreads between GC and special repo
- Clear CTD identification (one bond significantly cheaper than others)
Risks in Basis Trading
1. CTD Switch Risk
The most significant risk is that a different bond becomes CTD before delivery. This can happen when:
- Interest rates move significantly
- Yield curve shape changes
- Supply/demand shifts for specific bonds
If the CTD switches, your basis position may incur losses as you’re holding the wrong bond.
Example: You buy Bond A (CTD at time of entry) and short futures. Yields rise sharply, making Bond B the new CTD. Bond A underperforms, and your position loses value.
2. Repo Rate Volatility
Basis trade profitability depends on stable financing costs. If repo rates spike:
- GC repo (general collateral) rates rise
- Special repo rates for specific bonds become expensive
- Carry erodes, reducing or eliminating profit
This was particularly relevant during periods of BOJ policy uncertainty.
3. Delivery Squeeze
In rare cases, a delivery squeeze can occur:
- High demand for the CTD bond in the cash market
- Scarcity drives the bond “special” in repo (very low or negative repo rates)
- Cash bond price rises relative to futures (basis widens instead of converging)
Traders who are short the basis (short cash, long futures) can suffer significant losses.
4. Futures Roll Risk
If holding a basis position across futures contract expiry, you must:
- Close the old futures position
- Open a new position in the next contract
- Incur transaction costs and potential slippage
Hedging with Basis Trades
Institutional investors often use basis trades to hedge portfolio exposure while maintaining yield:
Example Use Case: A life insurance company holds ¥50 billion in 10Y JGBs for asset-liability matching. They want to reduce duration temporarily without selling the bonds (to avoid transaction costs and tax consequences).
Solution:
- Sell JGB futures against the cash position
- Effectively convert long-duration bonds into short-duration exposure
- Unwind futures when duration exposure is desired again
This creates a synthetic short position while maintaining the physical bonds.
Practical Considerations
When implementing basis trades:
- Monitor CTD daily: Track which bond is CTD and how close others are
- Use CTD analysis tools: Calculate net basis for all deliverable bonds
- Understand delivery options: The short futures holder chooses timing and bond
- Factor in transaction costs: Bid-offer spreads, futures commissions, repo costs
- Scale appropriately: Large positions can move the basis itself
- Track repo markets: Understand GC vs. special repo dynamics (Chapter 2.9)
Relationship to Portfolio DV01 Hedging
Basis trades are closely related to portfolio DV01 management (see Section 5.3).
When hedging a ¥10 billion cash JGB portfolio with futures:
\[\text{Hedge Ratio} = \frac{\text{Portfolio DV01}}{\text{Futures DV01}} \times \frac{1}{\text{Conversion Factor}}\]This calculation determines how many futures contracts to sell to neutralize interest rate risk while maintaining the basis relationship.
Example:
- Portfolio DV01: ¥92 million
- Futures DV01: ¥9,200 per contract
- Conversion factor: 0.985
Round to 10,150 contracts for practical execution.
Key Takeaways
- Basis = Cash Price - (Futures Price × CF): Fundamental relationship between cash and derivatives
- Net basis includes carry: Must account for financing costs and coupon income
- CTD drives futures pricing: Understanding which bond is cheapest-to-deliver is critical
- Low-risk, steady returns: Basis trades offer carry-like returns with convergence at delivery
- Monitor CTD switches: The primary risk is holding the wrong bond when CTD changes
Basis trading is essential knowledge for anyone managing large JGB portfolios or operating in the futures market.