--- title: "The Bond-Futures Basis Trade" book: "Strategies II: Volatility, Relative Value, Macro and the Bank Desks" subject: quant language: en chapter: 11 exercises: 8 source: https://one-course.com/books/quant/9/en/chapter/11-the-bond-futures-basis-trade --- # Chapter 11 — The Bond-Futures Basis Trade Buy a Treasury, sell the future on it, finance the bond in repo, and earn the few basis points by which the future’s implied repo rate exceeds the rate you pay. At its peak before March 2020, the Office of Financial Research estimated hedge funds’ basis-trade positions at $400 to $500 billion. That was more than 60% of their Treasury exposure and more than 70% of their repo borrowing. Between 18 February and 17 March 2020 they cut their short positions in the 2-, 5- and 10-year futures from $659 billion to $554 billion. The Federal Reserve then committed to buy Treasuries in whatever amounts were needed. On this chapter’s synthetic market a basis book at 50 times its capital earns 10.3% a year until a planted ten-day funding stress. Margin calls force it to sell at the worst basis, and it ends the stress’s aftermath 9.6% poorer than it began. At ten times, it earns 2.1% and ends only 0.2% down. The build is `firm.basistrade`. ## 11.1 Mechanics: cash, future, repo A Treasury future (Book 2, chapter 6) is delivered by the short, who chooses the cheapest-to-deliver bond from a basket. The gross basis is the bond’s price minus the futures price times its conversion factor. Net of the carry to delivery, it is the net basis. The implied repo rate is the financing rate at which buying the bond, delivering it into the future and repaying the loan breaks even. When the implied repo rate exceeds the repo rate, a long basis position earns the difference: long the bond financed in repo, short the future. The book below earns 20 basis points a year on the face it holds, the chapter’s own assumption. The trade has three legs of risk. The basis can move against the book before delivery. The repo loan must be rolled, often overnight. And the futures exchange and the repo lender each hold collateral: a margin on the futures and a haircut on the bond. **Definition 11.1 (Basis-trade leverage).** *Basis-trade leverage* is the face value of bonds held long (and futures short) per unit of the trader’s capital; it is capped by the collateral the trade needs, so at most one divided by the repo haircut plus the futures margin (per unit of face), and it falls when either rises. **Definition 11.2 (Repo rollover risk).** *Repo rollover risk* is the risk that a position financed in short-term repo cannot be refinanced on the same terms when the loan matures: at a higher rate, a higher haircut, a smaller amount, or not at all. ## 11.2 Leverage and who does it Barth and Kahn traced the trade in regulatory data. Asset managers wanted duration without using their balance sheets, and bought Treasury futures. That pushed futures above their no-arbitrage price, and hedge funds met the demand by going long the basis. From the end of 2017 to September 2019, hedge funds’ Treasury exposure grew from $1.06 trillion to $2.02 trillion and their short futures by $352 billion. The authors describe the funds as warehouses. They store Treasuries for the holders of long futures and fund them in repo, and in doing so link the Treasury, futures and repo markets. **As of September 2026 — Leveraged funds in Treasury futures.** The CFTC’s Traders in Financial Futures report places each large trader in a category; “leveraged funds” include hedge funds and other managed money, and hold positions of many kinds, not only basis trades. Summing their net positions in the six CBOT Treasury futures (2-, 5-, 10-year, Ultra 10-year, bond and Ultra bond) at face value, they were net long $34 billion on average from July 2010 to 2014 and net short $116 billion at the end of 2017. They were net short $475 billion on 18 February 2020 and $376 billion on 17 March 2020, reached a net short of $1 184 billion on 12 November 2024, and were net short $787 billion on 15 September 2026. The public series ([Figure 11.1](#fig-s2-the-bond-futures-basis-trade-tff)) shows the crowding the trade depends on, and the size of the flow that would come if it unwound. ![Leveraged funds’ weekly net position in the six CBOT Treasury futures, at face value, July 2010 to September 2026 (negative: net short). The category holds more than basis trades. Derived from the CFTC’s Traders in Financial Futures files. Data: s2_fetch_tff.](https://one-course.com/images/onecourse/chapters/quant-9/s2-the-bond-futures-basis-trade/fig-2048faebe79e.svg) ***Figure 11.1.** Leveraged funds’ weekly net position in the six CBOT Treasury futures, at face value, July 2010 to September 2026 (negative: net short). The category holds more than basis trades. Derived from the CFTC’s Traders in Financial Futures files. Data: `s2_fetch_tff`.* ## 11.3 March 2020 Barth and Kahn describe the stress. In the first week of March 2020, bid–ask spreads on longer Treasuries widened, repo rates on Treasury collateral jumped, and arbitrage spreads diverged. Sales by real-money investors raised futures margins and made repo volatile. Hedge funds partly unwound their basis positions: their short 2-, 5- and 10-year futures fell from $659 billion to $554 billion between 18 February and 17 March. The authors estimate that large basis traders sold $91 to $105 billion of Treasuries between the end of February and the end of March. They also argue that the basis trade was unlikely to be the primary cause of the stress before 17 March, since the Treasuries it held kept trading at a premium. On 15 March the Federal Open Market Committee said it would increase its holdings of Treasuries by at least $500 billion. On 23 March it said it would buy them in the amounts needed to support smooth market functioning. The synthetic stress has the same ingredients. For ten days from year 2.5 the basis moves 60 cents per 100 of face against the book. The repo haircut and the futures margin rise from 1% to 3% each, and the repo rate rises by one percentage point. Afterwards the basis comes back over two months, while the haircut and margin stay high. A book whose capital no longer covers its collateral must sell down to what its capital funds, paying 10 cents per 100 on what it sells, and cannot re-lever until the stress has passed ([Listing 11.1](#lst-s2-the-bond-futures-basis-trade-book)). | five years, capital 1 | 10$\times$ | 20$\times$ | 30$\times$ | 50$\times$ | | --- | --- | --- | --- | --- | | annual return before the stress (%) | 2.1 | 4.1 | 6.2 | 10.3 | | trough in the stress (%) | $-6.1$ | $-10.8$ | $-13.2$ | $-17.8$ | | after the basis recovered (%) | $-0.2$ | $-1.9$ | $-4.5$ | $-9.6$ | | days with forced sales | 0 | 10 | 10 | 66 | | face held after the stress | 10.4 | 16.5 | 16.8 | 17.5 | | five-year annual return (%) | 1.9 | 3.5 | 4.8 | 7.1 | At ten times, the book never falls short of its collateral. It rides out the move and recovers almost all of it. At fifty times, the book already sits at its collateral cap, one over 2%, so even ordinary days force small sales: 25 before the stress. In the stress the higher haircut and margin cap its leverage at 16.7, and its face falls from 60.7 to 17.5, sold into the stressed basis. Over the stress and recovery its P&L as a share of capital was $-6.6\%$ from marks, $-3.3\%$ from forced-sale costs, $-0.6\%$ from dearer repo, and $+0.8\%$ from the spread still earned. The marks came back for the positions it kept, not for the ones it sold ([Figure 11.2](#fig-s2-the-bond-futures-basis-trade-capital)). ![Capital of the synthetic basis book at three leverages over five years, with a funding stress at year 2.5. The fifty-times book’s losses are locked in by forced sales; the ten-times book rides the basis back. Data: s2_basis.paths.](https://one-course.com/images/onecourse/chapters/quant-9/s2-the-bond-futures-basis-trade/fig-3c12963771d9.svg) ***Figure 11.2.** Capital of the synthetic basis book at three leverages over five years, with a funding stress at year 2.5. The fifty-times book’s losses are locked in by forced sales; the ten-times book rides the basis back. Data: `s2_basis.paths`.* ## 11.4 Measuring the crowding The trade’s risk is not in any one book: it is the sum of everyone’s. Public measures include leveraged funds’ short futures in the CFTC report, dealers’ repo lending, and the gap between futures-implied and cash yields. None of them separates basis trades from other positions. Barth and Kahn used regulatory filings that are not public. A trader running the book should measure what the market would have to absorb if every holder’s collateral rose at once. The synthetic stress shows how quickly that collateral cap binds when it does. ## 11.5 Strategy files **Strategy file 11.1 — Cash-futures basis long.** **Who pays you, and why.** Asset managers who want duration through futures without using their balance sheets, and push futures above fair value. **Instruments and venues.** Treasury notes bought and financed in repo; Treasury futures sold on CBOT. **Signal.** Implied repo rate against the repo rate for the cheapest-to-deliver. **Sizing and execution.** Leverage well inside one over (haircut plus margin) under stressed terms; repo term matched to the trade. **Costs.** Repo spread, futures fees, roll costs. **How it dies.** A rise in haircut and margin that forces sales into a moving basis; repo that cannot be rolled. **Horizon, capacity, infrastructure.** Quarterly rolls; repo and futures clearing lines. **Backtest honestly.** Stress collateral terms, not only prices. **Sources.** Barth and Kahn (2021): $400–500 billion at the peak; this chapter: 10.3% a year at 50 times and $-9.6\%$ after a funding stress. **Strategy file 11.2 — Delivery option trade.** **Who pays you, and why.** Futures longs who give the short the choice of bond and timing. **Instruments and venues.** Deliverable bonds; the future. **Signal.** The net basis against the value of the switch option as rates and the curve move. **Sizing and execution.** Long the net basis of bonds likely to become cheapest. **Costs.** Bid-ask on off-the-run bonds. **How it dies.** Rates stay where the cheapest bond does not change. **Horizon, capacity, infrastructure.** A delivery cycle; a delivery-option model. **Backtest honestly.** Actual delivery baskets and conversion factors. **Sources.** No performance figure verified. **Strategy file 11.3 — Basis-trade crowding signal.** **Who pays you, and why.** Forced sellers in an unwind: a trader with dry capital buys the basis they sell. **Instruments and venues.** As for the basis long. **Signal.** Leveraged funds’ short futures at extremes, collateral terms rising, the basis widening fast. **Sizing and execution.** Small, added as forced selling peaks; funded with term repo. **Costs.** Wide markets in stress. **How it dies.** Buying too early into a longer unwind. **Horizon, capacity, infrastructure.** Weeks; committed funding. **Backtest honestly.** Few episodes; the CFTC category mixes strategies. **Sources.** CFTC Traders in Financial Futures (this chapter’s derived series); no performance figure verified. ## 11.6 Tutorial: fifty times **Goal.** Run the basis book at several leverages through a funding stress, and read leveraged funds’ positions in the CFTC data. **End state:** the table and the two figures. 1. **The book**. `def run_book (sim: dict , cfg: BasisConfig | None = None , leverage: float = 20.0 ) -> dict : """Capital starts at 1; face held is leverage x capital, reset at each roll, cut when funding falls short.""" cfg = cfg or BasisConfig() T = cfg.days mark = sim[" dev " ] + sim[" shock " ] # a rise is a loss to the long basis cap, face = np.ones(T + 1 ), np.zeros(T + 1 ) face[0 ] = leverage carry, marks, funding, costs = np.zeros(T), np.zeros(T), np.zeros(T), np.zeros(T) forced, (a, b) = 0 , sim[" stress " ] stressed = range (a, b + cfg.recover_days) for t in range (T): n = face[t] carry[t] = n * cfg.spread / YEAR marks[t] = -n * (mark[t + 1 ] - mark[t]) funding[t] = -n * (1 - sim[" haircut " ][t]) * sim[" repo " ][t] / YEAR cap[t + 1 ] = cap[t] + carry[t] + marks[t] + funding[t] need = sim[" haircut " ][t + 1 ] + sim[" margin " ][t + 1 ] n_next = n if cap[t + 1 ] <= 0 : n_next, cap[t + 1 ] = 0.0 , 0.0 elif cap[t + 1 ] < n * need: # margin call: sell down to what capital funds n_next = cap[t + 1 ] / need costs[t] = -(n - n_next) * cfg.sale_cost cap[t + 1 ] += costs[t] n_next = max (cap[t + 1 ], 0.0 ) / need forced += 1 if (t + 1 ) % cfg.roll_every == 0 and t + 1 not in stressed and cap[t + 1 ] > 0 : n_next = leverage * cap[t + 1 ] if leverage * need <= 1 else cap[t + 1 ] / need face[t + 1 ] = n_next return {" capital " : cap, " face " : face, " forced " : forced, " carry " : carry, " marks " : marks, " funding " : funding, " costs " : costs}` **Listing 11.1.** Carry, marks, funding and forced sales, with re-levering at the rolls. code/firm/basistrade/firm_basistrade.py 2. **By leverage**. `def table (): """By leverage: annual return before the stress, the trough in the stress and the loss left after the recovery (both against the capital the day before), the forced-sale days, and five-year annual return.""" cfg, sim, b = books() a, e = sim[" stress " ] out = {} for L, r in b.items(): c = r[" capital " ] pre = c[a - 1 ] out[L] = {" before " : float (pre ** (YEAR / (a - 1 )) - 1 ), " trough " : float (c[a:e + cfg.recover_days].min() / pre - 1 ), " after " : float (c[e + cfg.recover_days] / pre - 1 ), " forced " : r[" forced " ], " five_years " : float (c[-1 ] ** (YEAR / cfg.days) - 1 ), " face_after " : float (r[" face " ][e])} return out` **Listing 11.2.** Return before, trough and loss after the stress, by leverage. code/strategies-2/11-the-bond-futures-basis-trade/python/s2_basis.py 3. **Run** `s2_fetch_tff.py` once, then `table()` , `parts()` and `fig_basis.py` . **What to change next.** Finance with term repo that cannot be withdrawn during the stress and find the leverage it allows; hold a cash buffer of 2% and compare; let the stress come twice in a year. ## 11.7 Build: basis trade **Purpose.** A leveraged cash-futures basis book with haircuts, futures margin, repo cost and forced deleveraging. **Interface.** `BasisConfig(…)`, `simulate_basis(cfg)`, `run_book(sim, cfg, leverage)`. **Rules.** Capital covers haircut plus margin on the face held or the book sells; no re-levering in the stress; quarterly re-levering after. **Acceptance tests.** `code/firm/basistrade/tests/`: a calm book earns the spread times leverage; forced sales only when capital falls short, and capital covers collateral afterwards; the stress scenario’s shape. **Stretch.** Term repo; the delivery option; several contracts. Sources and further reading - D. Barth and R. J. Kahn, “Hedge funds and the Treasury cash-futures disconnect”, Office of Financial Research Working Paper 21-01, 2021. - Board of Governors of the Federal Reserve System, press releases of 15 and 23 March 2020. - CFTC, Traders in Financial Futures, 2010–2026. ## 11.8 Exercises **Exercise 11.1 ★.** The haircut and the futures margin are 1% each. What is the highest leverage? And at 3% each? **Solution of Exercise 11.1.** $1/(0.01 + 0.01) = 50$ times; at 3% each, $1/0.06 = 16.7$ times. **Exercise 11.2 ★.** A book earns 20 basis points a year on its face at 50 times its capital. What does it earn on capital, before costs? **Solution of Exercise 11.2.** $0.002 \times 50 = 10\%$ a year on capital, before costs and compounding. **Exercise 11.3 ★.** The basis moves 60 cents per 100 against a book at 50 times. What does it lose on capital, before any sale? **Solution of Exercise 11.3.** $50 \times 0.006 = 30\%$ of capital. **Exercise 11.4 ★★.** Why does the ten-times book recover and the fifty-times book not? **Solution of Exercise 11.4.** At ten times, capital covers the stressed collateral (6% of face needs 0.6 of capital), so the book keeps its whole position and gets the basis back. At fifty times it must sell down to 16.7 times at the stressed basis; the positions it sold never recover, and the sales cost 10 cents per 100. **Exercise 11.5 ★★.** By how much did hedge funds cut their short 2-, 5- and 10-year futures between 18 February and 17 March 2020, in percent? **Solution of Exercise 11.5.** $(659 - 554)/659 = 15.9\%$. **Exercise 11.6 ★★.** Why is the CFTC’s leveraged-funds series only a rough measure of the basis trade? **Solution of Exercise 11.6.** Leveraged funds hold Treasury futures for many reasons (duration views, curve trades, trend following), and the report shows futures only, not the cash bonds or repo on the other side; a net short can be a basis trade or an outright bet. **Exercise 11.7 ★★★.** *Coding.* Rerun the fifty-times book with `BasisConfig(haircut_stress=0.01, margin_stress=0.01)`, so that collateral terms do not change. What happens, and what does it show? **Solution of Exercise 11.7.** The fifty-times book still sells on 66 days, since it sits at its collateral cap; its trough is deeper ($-27.7\%$) because it cuts less early, and it keeps more of the recovery ($-6.2\%$ after instead of $-9.6\%$). Part of the locked-in loss comes from the higher collateral terms, part from running at the cap. **Exercise 11.8 ★★★.** *Find the flaw.* “The basis always converges at delivery, so the trade cannot lose if we hold to delivery.” **Solution of Exercise 11.8.** Convergence at delivery helps only a book that is still holding at delivery. Margin calls and repo that cannot be rolled can force a sale before then, at the basis of the day, and the loss is then real. ## 11.9 Problem: Fifty Times **Problem 11.1.** Weekend problem — a leveraged basis book The chapter’s synthetic book, the CFTC data and the public record. **Part I — Mechanics.** 1. Define the gross basis, net basis and implied repo rate. 2. When does a long basis position earn? 3. Define [basis-trade leverage](#def-s2-the-bond-futures-basis-trade-leverage) and [repo rollover risk](#def-s2-the-bond-futures-basis-trade-rollover) . 4. What caps the leverage? **Part II — Who does it.** 5. Why do asset managers push futures above fair value? 6. What did Barth and Kahn estimate about size? 7. What does the CFTC series show? 8. Why do the authors call hedge funds warehouses? **Part III — March 2020.** 9. What happened in the Treasury and repo markets? 10. What did hedge funds do? 11. What did the Federal Reserve announce? 12. Were basis trades the primary cause, according to Barth and Kahn? **Part IV — The verdict.** 13. State the *named result* : the trade’s return on capital by leverage and the loss in the planted funding stress. 14. Decompose the fifty-times book’s loss. 15. What would term funding change? 16. How would you measure crowding? 17. How would you size the book? 18. How would you backtest it honestly? 19. Which strategy file profits from others’ forced sales? 20. In one sentence: what does a basis trader provide to the market? **Solution of Problem 11.1.** 1. Gross basis: bond price minus futures price times conversion factor; net basis: gross basis less carry; implied repo: the financing rate at which buying, delivering and repaying breaks even. 2. When the implied repo rate exceeds the repo rate paid. 3. Face per unit of capital, capped by one over haircut plus margin; the risk that repo cannot be refinanced on the same terms. 4. The collateral: haircut plus futures margin. 5. They want duration without using their balance sheets and buy futures. 6. $400 to $500 billion at the peak, over 60% of hedge funds’ Treasury exposure and 70% of their repo borrowing. 7. Leveraged funds net short $475 billion on 18 February 2020, a record $1 184 billion on 12 November 2024. 8. They hold Treasuries for futures longs and fund them in repo. 9. Wider bid–ask spreads, repo rates jumping, arbitrage spreads diverging, higher futures margins. 10. Cut short futures from $659 to $554 billion and sold $91 to $105 billion of Treasuries. 11. At least $500 billion of Treasury purchases on 15 March, then purchases in the amounts needed on 23 March. 12. No: the Treasuries the trade held kept trading at a premium before 17 March. 13. **Named result.** The book earns 2.1% a year at ten times and 10.3% at fifty; in the planted funding stress the fifty-times book is forced to sell and ends 9.6% below its pre-stress capital after the basis recovers, the ten-times book 0.2%. 14. Marks $-6.6\%$ , forced-sale costs $-3.3\%$ , dearer repo $-0.6\%$ , carry $+0.8\%$ . 15. Term repo keeps the funding in place through the stress, so only the futures margin can force sales. 16. Futures positions of leveraged funds, repo volumes, the futures-implied versus cash yield gap, collateral terms. 17. So that stressed collateral terms and a basis move leave capital above the requirement. 18. Stress collateral terms, include forced-sale costs, use the repo actually available. 19. The basis-trade crowding signal. 20. Balance sheet: it holds Treasuries for those who want futures. ## 11.10 Interview questions **Interview question 11.1 ★ trader.** Explain the Treasury cash-futures basis trade. **Solution of Interview question 11.1.** Futures trade rich to cash when demand for them is high; a trader buys the cheapest-to-deliver bond, finances it in repo, sells the future and earns the implied repo rate less the repo rate, at high leverage because both legs are collateralised. **Interview question 11.2 ★★ risk.** A basis book is levered 50 times. What stress would you run, and what limit would you set? **Solution of Interview question 11.2.** A joint rise in haircut and margin, a basis move against the book and a repo spike, applied to the whole position at once; set leverage so that capital still covers collateral under the stressed terms, and hold term funding. **Interview question 11.3 ★★ researcher.** How would you compute the implied repo rate, and what does its gap to repo tell you? **Solution of Interview question 11.3.** From the bond’s full price today, the invoice price at delivery (futures times conversion factor plus accrued) and the coupons in between; a gap above repo means the futures are rich, below means they are cheap. **Interview question 11.4 ★★ trader.** Your repo lender raises the haircut from 1% to 3% overnight. What do you do? **Solution of Interview question 11.4.** Post more capital if available; otherwise reduce the position, ideally in the less liquid legs first, and seek term repo; never let the margin call go unmet. **Interview question 11.5 ★★ developer.** Design the daily process for a basis book: data, collateral, margin calls, rolls. **Solution of Interview question 11.5.** Prices and repo rates each morning; collateral requirements from each lender and the exchange; variation margin; the capital check against stressed terms; roll schedules; with alerts when capital approaches the requirement. **Interview question 11.6 ★★★ researcher.** Show that, with capital $C$, face $N$ and collateral rate $k$ per unit of face, a loss of $x$ per unit of face forces sales when $C - Nx < Nk$, and find the largest move a book at leverage $L$ can take without selling. **Solution of Interview question 11.6.** After a move $x$ capital is $C - Nx$ and the requirement $Nk$, so sales start when $C - Nx < Nk$. With $N = LC$ the largest move without selling is $x < 1/L - k$: at $L = 50$ and $k = 0.02$ it is zero, which is why a book at its cap sells on ordinary days.