A Practitioner’s Guide to What a Hedge Costs, What It Saves, and What It Does to Your Cash
Julian R. Sterling
These are the companion files of Derivatives by Julian R. Sterling.The book on Amazon →
The four Excel workbooks that go with the book, corrected where they were wrong. Every figure the book
prints is reproduced in them by a live formula rather than a typed constant, both yield curves are bootstrapped
from their ten par rates, and each workbook ends with a Checks sheet setting the printed figure
beside the computed one: 175 controls in all, every one green. Around them: the same four models
with the inputs emptied, thirteen working documents to print, forty questions that mark themselves, and three
cases the book names and never takes to a number. Nothing is locked, protected or watermarked.
Free to download. No sign-up, no email address, nothing to fill in.
Eleven workbooks, the printable documents and the read-me. Each group below can also be
downloaded on its own. Last revised 24 September 2026.
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These carry the book’s own figures, so that every number it prints can be traced to a live
formula, and each closes on its checks sheet.
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Chapters 1 to 3, 9 and 10
The number that is not a cost
The treasury report's 1,233,698 reproduced first, then dismantled by an
identity: selling dollars forward and selling them spot while funding the gap both produce
106,766,301.76 of sterling in a year, to eight decimal places. If they did
not, there would be a riskless arbitrage. The forward points are the interest differential.
Beside it the three real cost lines in present value over five years — the swap's
2.5 basis points, the currency bid/offer, and the credit charge — totalling
1,542,782 against the reported figure's 5,715,274 on the
same basis. The largest of the three is the credit charge, the only one that is never
invoiced. The swap is then run year by year at the declared path and at the curve's own
implied forwards, where it returns minus 132,801: the dealer's spread, and
nothing else. Revised: the bid and offer in level annual terms is 69,076, not the 69,083 chapter 2
prints, and the credit charge is 3.61 times the larger spread, not “nearly four times either”.
The sheet also shows the other reading of the 8 pips, four either side of the middle: 152,937.
Each of the five years with its struck rate, its forward and its settlement rate, so the sign
of every annual result can be traced to one comparison. Years one and two are negative and
years three to five positive on a path where sterling falls and recovers — and the sheet
shows this is a property of rolling, not of the path.
Then the three policies on the same path and the same company: do nothing, roll twelve months,
lock five years at the outset. A spread of 35,179,321 between best and worst,
more than anything a treasurer can do inside a policy. A tenor switch turns one policy into
another so the spread can be watched opening and closing. Revised: the year-by-year ranges of
chapter 5 are computed on unrounded forwards (6,541,644 for the lock, not 6,546,047), and the sheet no
longer says both hedges lost “because sterling ends lower than it began”: it ended higher, and
settled below the forward at every date.
Black-76 written out in spreadsheet formulas rather than carried, so the cap and floor can be
re-struck at will. The collar sold as costing nothing transferred 1,577,235 to the
company — the cliche runs the other way, and the point is not that the bank
wins or loses but that nobody priced the structure in either direction.
Then the programme reconducted, under both re-fixing conventions, with the premiums received
and the settlements paid on common dates. And the year-three mechanism: a floor sold at 2,300
re-fixes to 2,731.84 after the price has risen, so the fall back to 2,640
charges the company 2,387,755 on a reduction in its own input cost. Under the
zero-premium convention it is worse, and the sheet computes that too.
The mark-to-market of both hedges at each of the path's dates, with the tenors actually open
and the swap netted against the currency position. Peaks of 43,749,502 before
settlement and 31,000,344 after, against 36,000,000 of
available liquidity. On one convention the five-year policy breaches by 7,749,502; on the
other it has 13.9 per cent of headroom. Neither convention is wrong.
Then a netting switch — one collateral agreement or two — and the rate and currency
shock ladders with their break-evens in closed form: liquidity exhausted at a fall of
25.63 per cent rolling and 7.09 per cent locked. The ratio
between the two policies is printed as the range it actually is, 4.43 to 4.50, and not as the
constant it is convenient to call it. Revised: the unshocked swap sits 586 below the dealer spread
because the grid discounts at a flat 4.36 per cent, not because of a quarter of a year; the rolling call
of 11,696,910 is 11,564,696 of discounted currency loss plus the swap’s 132,215; and the locked
policy runs out of liquidity after 8.86 cents of fall, not before eight.
The four workbooks with the 47 inputs of their shared Inputs sheet emptied. The checks sheets count what is still missing and test what holds for any inputs.
All chapters · the appendix
Your curves, your hedges, your paths
The cost of the hedge, the rolling programme, the collar and the collateral ledger, with the same formulas and every input emptied: the company, the two par curves, the hedging programme, the collar and the three declared paths. The rate and currency shock ladders and the tenor switch stay, because they are the axes of their tables, not data.
The book’s 47 inputs are listed in a text file inside the archive. Type them back in and the book’s figures come back with them: 1,542,782 of real cost, 35,179,321 between the policies, 43,749,502 at the peak.
Thirteen pages to print and use. A4, with margins wide enough for US Letter.
Chapters 1 to 18 · the appendix
Thirteen working documents
The seven questions for somebody else’s hedging proposal, with Kilmartin’s answers beside a blank column. The cost line relabelled, from forward points to three real lines. The swap report with the combined interest bill and the forwards. The rolling programme, one row a year. Three policies on one page. The collar term sheet interrogated, down to the rollover formula. The accounting memo and the derivative note. The valuation note and the collateral annex. The cash table every proposal should carry. The settlement convention and the facility. The counterparty list read as a liquidity document. The symmetric stress pack. The fact pattern, with the running order of chapter 17.
A workbook that marks itself. Answer in the yellow cells; the marking fills in as you go.
All parts of the book
Forty questions on the book
Eight on cost and carry, seven on rolling and policy, six on the collar, six on accounting and valuation, eight on cash and collateral, and six on the three cases below. Numbers are marked to a tolerance, multiple choice to the letter, and the score sheet counts your errors part by part: that is your revision list.
Nothing is hidden. The marking sheet holds every answer, every tolerance, and the reason for each answer.
New material, not a restatement. Three situations the chapters name and never take to a number. Each case is one workbook: the note is the first sheet, the model is the rest, and a checks sheet closes it. Type your own figures in and every finding recomputes.
Chapters 4, 5 and 17 · Case one
The path the reservation needed
The book’s reservation says that if sterling fell to 1.14 and stayed there, locking would have protected and rolling would have been the mistake. Run, it says the opposite: for a seller of dollars a weaker pound is the good news, and the lock ends 63,351,943 behind doing nothing against 17,008,870 for the roll. The path on which locking protects is sterling rising and staying up (1.31, then 1.36: ADDED), where the lock ends 23,665,387 ahead and the roll 2,922,661. The reservation stands; its direction turns round.
Chapters 16 and 17 · Case two
The tenor limit the policy never states
Chapter 16 says policies set a hedge ratio and almost never a tenor sized against the facility. Sized: at the chapter’s own 10 per cent instantaneous fall, one year locked calls 11,696,910, three 33,133,195, four 43,022,964. Three years fit inside 36,000,000; two if a fifth is held back for other calls (ADDED); none if the facility cannot be drawn overnight. Five years fit only at 51.5 per cent of sales, not 75.
Chapters 7, 8 and 17 · Case three
The collar, locked
The currency programme is priced locked for five years; the collar never is. Struck on day one along the forward curve, it transfers 10,082,012 of option value at once. On the book’s path it settles at -7,791,781 against -1,347,755 rolled; on a price that rises and stays (ADDED) re-fixing costs the company, on one that falls and stays it saves 55,175,793. Chapter 17 has that sentence the wrong way round.
an input cell; everything else on the sheet is a formula
Black text
a formula — do not overtype these
Checks sheet
the printed figure beside the computed one, with a PASS or a FAIL; in the blank set and the cases, each control states its own verdict and the file ends ALL OK
ADDED
a figure the book does not give, used in the cases and marked wherever it appears
Why the checks matter more than the models
A workbook that agrees with a book proves nothing on its own — the author wrote both. What
the Checks sheets do is different: they force the model to reproduce, from a formula, a number
that was printed before the model existed.
On this book the reference model went through four adversarial audit passes before a word
was written, and two of them reversed a conclusion that had already been drafted. A
forward ratio was upside down, so the rolling programme's five-year result changed sign; and a
consumer's option positions had been coded as a producer's, so the collar's direction inverted.
Twelve guards were then added because a mutation test showed the model would print a false
sentence without them — including one that refuses to print any sentence claiming a movement
the model does not compute.
The last pass found no wrong figure at all. What it found were sentences that were true when they
were written and false when they were read.
Go beyond the companion files
Derivatives develops the complete framework behind these models, with the assumptions, trade-offs and worked examples tied together.
The workbooks open in Microsoft Excel, LibreOffice Calc, Google Sheets and Numbers; the PDF
prints on A4 or US Letter. They use no macros and no add-ins, so nothing needs to be enabled or trusted. If your spreadsheet asks
to update links on opening, decline — there are none.
What changed, and when
24 Sep 2026
The four workbooks corrected, 175 checks. Chapter 2’s level bid and offer is 69,076, not 69,083; chapter 5’s locked range is 6,541,644, not 6,546,047; chapter 15’s gap of 586 is the discounting basis, not a quarter of a year; the locked break-even is 8.86 cents of fall, not “before eight”. The book’s reservation names a falling pound as the path that favours locking; for a seller of dollars it is a rising one (case one). Added: a blank set, thirteen working documents, forty questions that mark themselves, and three cases.
Is a zero-cost collar really zero cost?Zero premium is not zero value. Priced with Black-76, a cap at 2,680 is worth 182.84 a tonne and the floor sold at 2,300 only 122.18: 1,577,235 changes hands.
How do you calculate an FX forward rate?Forward = spot x (1 + quote-currency rate) / (1 + base-currency rate). At 1.2700 spot, 4.5% USD and 4.0% GBP, one-year GBP/USD is 1.2761.
How do you price a swaption with Black's model?Notional x annuity x Black on the forward swap rate: a 1y into 4y payer at 4.50 per cent on 50,000,000, 20% vol, costs 428,065, 85.6 bp upfront.
How do you calculate a forward-starting swap rate?Take DF at start minus DF at end over the annuity: on an illustrative curve a 2y into 5y swap fixes at 3.72%, 33 bp above the 3.39% spot five-year rate.
Closing the DealTwo defensible bridges 20.70 million apart, a peg worth 7.00 million, and the six choices that remove 6.60 of a 12.00 earn-out.
CMBS and CRE CLOsWhere the loss actually lands, from appraisal reduction to realised severity, and what the B-piece is really being paid for.
How to Read a Commercial LeaseThe three refinements chapter 19 names and never performs, and the renewal rate below which the mark-to-market is worth nothing.
How to Read a Credit AgreementWhere the default actually comes from, the cure that costs 5.5 times the other, and the capacity nobody adds up.
How to Read a Real Estate Loan AgreementThe cure ratio in closed form, the four-point window in which the cheap cure works, and the cure sized to the wrong threshold.
Office Real EstateA six per cent yield that returns 3.2 per cent once the re-letting cycle is paid for, and the headline-to-net-effective rent arithmetic.
Private Equity Real EstateBoth worked waterfalls to the dollar, the two capital stacks, and the arithmetic of the promote made changeable.
Private Markets PerformanceThirty-one of the thirty-three figures chapter 19 publishes reproduce exactly — and the two that do not are named rather than quietly adopted.
Raising a Real Estate FundThe chapter 17 funnel run on a calendar — when the first close actually lands, and why more travel does not help.
Real Estate FinanceFour people look at one building and reach four numbers; the lender is whole only above 105,109,489, twelve per cent below today’s value rather than forty.
Real Estate Financial ModelingProperty, development and fund models built line by line, and the modelling test worked end to end.
Real Estate Fund ManagementThe waterfall of 6.11, the build-to-core of 8.7 and the proceeds gap, reproduced as live formulas rather than asserted.
REIT Analysis and ValuationFFO of 532.0, AFFO of 381.0, net asset value and dividend safety — every figure a formula you can change.
Retail Real EstateThe occupancy cost of every unit in a centre, the sixteen per cent of the rent roll no tenant can sustain, and the right-size-convert-or-hold decision priced.
Sale and LeasebackA €179.5 million transaction end to end, with rent cover measured on the entity that actually signs the lease.
Self-Storage Real EstateThe cohort engine behind a 590-unit store, and the rate increase on existing customers priced against the move-outs it causes.
The Fund Finance ProfessionalChapter 8 builds the reported-to-eligible NAV bridge; chapter 9 computes every ratio without it. Two points at every state — and what a subscription line does to the IRR.
The Growth Equity InvestorWhat a pro rata cheque really costs, and the band where defending your ownership loses money.
The Private Credit InvestorThe two coverage ratios are not measured on the same thing: the erosion is 47.7 per cent, not the 28.7 the headline implies.
The Private Equity Fund Controller PlaybookThe book defines IRR, DPI, RVPI and TVPI, tells you to update them at the exit, and prints not one value. Computed: a 1.833× deal inside a fund at 0.892 TVPI.
The Venture Capital AssociateWhat defending a position costs, and how many companies a reserve pool actually defends.
Financial Risk ManagementA fund inside every limit that cannot meet a redemption — and the number that decides it is the one with no currency attached.
Business ValuationThree advisers land 26.8 per cent apart on one company, and the whole gap turns out to be 1.96 points of perpetual growth.
Quantitative FinanceThree models agree to a quarter of one per cent about a number that one unobservable input moves a hundred and three times as much.
Asset ManagementFour people quote four returns for one mandate, all correct and 2.7017 points apart — forty-eight times the manager’s net skill.
Alternative InvestmentsA manager reports 13.29 per cent and the endowment earns 6.26 — both correct, and only a third of the advertised advantage arrives.
Credit AnalysisFour defensible EBITDAs on one borrower give leverage from 3.19x to 6.47x — and the add-back argument is fifty times the covenant headroom.
Venture CapitalOne company out of twenty-eight returns 56.7 per cent of the fund, and half the capital goes in after the decision — at half the return.
Machine Learning for FinanceFive people quote the accuracy of one credit model, all five are right, and the number that decides how much money it makes is none of them.
Commercial Real Estate InvestingThe equity earned 8.6647 per cent and the investor received exactly 8.0000 — the preferred return, and nothing above it.
Mergers and AcquisitionsThe board paper says the deal creates 13,436,667 of value. The arithmetic says it destroys 17,530,855. Nobody is lying.
Treasury ManagementFive cash balances for one company, all correct and 145,600,000 apart — and the revolver that is two-thirds of the liquidity leaves at a revenue fall of 8.4127 per cent.
Financial Planning and AnalysisRevenue 3.0190 per cent above budget and operating profit 16.3209 per cent below it, in the same quarter, with every figure correctly stated.
Energy TradingA position report that is 91.7031 per cent hedged and correctly computed, on a book that is short 2,542,000 MWh — and a margin call of 198,400,000 the next morning.
Construction Cost ControlA contract sum of 26,301,102 became a final account of 29,153,363 on the building that was drawn — and 85.8 per cent of what was lost was knowable on the day it was signed.
Trade FinanceSix routes to payment on one 4,200,000 export order cost between 178,040 and 223,268, a spread worth 14.8 per cent of the margin, and a day of buyer credit costs 1,031.76.
Cost AccountingOne factory costed twice on the same 13,440,000 of overhead, and 4,053,091 moves between four product families.
Pricing StrategyA list price of 148.00, a pocket price of 112.51, and the nine deductions in between — with what one point of price is actually worth.
Contract ManagementA bid 5.50 a unit cheaper, signed on paper worth 9.81 a unit more — and 94.68 per cent of it was knowable on the day of signature.
Capital MarketsFour defensible readings of one bond, the cost of an issue under each convention, and the placement discount computed at a constant discount.
Financial RegulationThree ratios pass and the fourth is in breach by 1,956.0 million: the output floor, the liquidity buffer after encumbrance, and the loan split.
Bank ManagementFour defensible readings of one balance sheet, the deposit beta measured two ways, and the liquidity that lasts 3.9 days.
The Real Estate WorkoutFour ways out of one broken loan, discounted to today, and the 58.7 cents at which a payoff beats enforcement.
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