# Derivatives and Risk Management Course Guide: [Your programme, term and section] > A course guide for the second-year MBA elective in derivatives and risk management: forwards, futures and swaps, > options and their Greeks, corporate hedging, value at risk and expected shortfall, backtesting and stress testing, > counterparty risk, and the governance that keeps a hedging programme from becoming a trading book. It builds on the > core corporate finance course and links to it instead of repeating it: read mba/mba-corporate-finance-guide, > mba/mba-options-real-options-card and mba/mba-fx-interest-parity-card first. It is for MBA students choosing or > taking the elective, candidates for treasury, risk, sales and trading or asset management roles, and study groups > that want a shared plan. It gives the competencies the course builds, the prerequisites, a 13-session roadmap linked > to the concept cards, a key concepts map, an original mini-case on a fictional company (Northfield Outdoor Co.) with > exhibits, discussion questions and a teaching note, a grading rubric, an exam preparation plan, common struggles, a > reading list and a self-test with an answer key. Source basis: the primary works of derivatives pricing and risk > management from Black and Scholes (1973) to Froot, Scharfstein and Stein (1993) and Artzner et al. (1999), with dated > regulatory facts checked on official pages in October 2026, all written up in original words. Session order and > grading are typical of leading international programmes; your syllabus decides. Replace every [bracketed] value and > every row marked *Example*. This is a learning aid, not investment, accounting, legal or regulatory advice. ## Document control | Field | Value | |---|---| | Programme, term and section | [Programme name, term, section] | | Learner | [Your name] | | Faculty and teaching assistants | [Names, office hours] | | Syllabus version used | [Date of syllabus] | | Learning team | [Team name and members] | | Software used in the course | [Excel / Python / a pricing library named in the syllabus] | | Exam date(s) | YYYY-MM-DD | | Reviewed by | [Learning team member, tutor or mentor] | | Version | [0.1] | | Last updated | YYYY-MM-DD | ## Contents - [What the course is for](#what-the-course-is-for) - [Prerequisites](#prerequisites) - [The course in one page](#the-course-in-one-page) - [Session roadmap](#session-roadmap) - [Key concepts map](#key-concepts-map) - [Mini-case: Northfield Outdoor Co. and the hedging programme](#mini-case-northfield-outdoor-co-and-the-hedging-programme) - [Teaching note](#teaching-note) - [Typical assignments and how they are graded](#typical-assignments-and-how-they-are-graded) - [Exam preparation plan](#exam-preparation-plan) - [Common struggles](#common-struggles) - [Reading list](#reading-list) - [Self-test questions](#self-test-questions) - [My notes and next steps](#my-notes-and-next-steps) - [Sources and further reading](#sources-and-further-reading) - [Answer key](#answer-key) - [Revision history](#revision-history) ## What the course is for Derivatives move risk from those who do not want it to those who will carry it for a price. The elective asks three questions. **How are derivatives priced?** By no-arbitrage: a forward, a swap or an option is worth what it costs to replicate it with traded assets and borrowing. **How should a company or an investor use them?** To reduce risks that are costly to bear, sized to the exposure, inside a policy the board has approved. **How is risk measured and governed?** With measures such as VaR and expected shortfall, stress tests, limits and backtesting, which are only as good as the people and processes around them. The core course gave you options and parity; this course gives you the full toolkit and the judgement to know when a hedge is a hedge and when it is a bet. The competencies the course builds, mapped to the competency list used across this library (see mba/mba-core-curriculum-map). AACSB's Global Standards for Business Education (ratified 20 April 2026) leave each school to define its own learning goals, so check your programme's list (as of October 2026, see aacsb.edu): | Competency area | What you should be able to do by the end of the course | |---|---| | Analytical and quantitative reasoning | Price forwards, futures, swaps and European options; compute hedge ratios, Greeks, VaR and ES; run a backtest | | Ethical decision making | Recognise when a "hedge" is speculation, when incentives reward hidden tail risk, and when a product is mis-sold to a client | | Communication | Explain a hedging recommendation to a board in one page: exposure, instrument, cost, residual risk | | Leadership and teamwork | Divide a pricing model in a team, check each other's formulas, defend a risk limit | | Global perspective | Handle currency exposures, cross-currency funding and different regulatory regimes | | Technology, data and AI | Build transparent pricing and risk models, test them against hand calculations, document data and model limits | ## Prerequisites | Skill | Check yourself | Where to fix it | |---|---|---| | Discounting with annual, money market and continuous rates | Convert 4 percent annual to continuous | mba/pre-mba-finance-primer, mba/pre-mba-quant-refresher | | Bond prices, zero rates and discount factors | Price a three-year 5 percent bond from zero rates | mba/mba-fixed-income-card | | Portfolio variance and correlation | Compute the volatility of a two-asset portfolio | mba/mba-capm-wacc-card | | The normal distribution and quantiles | Find the 99 percent quantile with `NORM.S.INV` | academic/stats-distributions-sheet | | Option payoffs and put-call parity | Draw a long put and state parity | mba/mba-options-real-options-card | | Covered interest parity | Compute a 180-day forward from spot and two rates | mba/mba-fx-interest-parity-card | | Spreadsheet fluency | Build a binomial tree with absolute and relative references | mba/pre-mba-excel-modeling-drills | ## The course in one page **Forwards and futures.** No-arbitrage sets the forward price at spot plus the cost of carry, $F_0 = S_0 e^{(r + u - q - y)T}$. Futures are standardised forwards settled daily through margin; forward and futures prices coincide when interest rates are deterministic (Cox, Ingersoll and Ross 1981). Commodity forwards below full carry reveal a convenience yield (mba/mba-forwards-futures-swaps-card). **Hedging.** The minimum-variance hedge ratio is $h^* = \rho\,\sigma_S/\sigma_F$ (Johnson 1960; Ederington 1979); the part of the variance left is basis risk. Index futures move a portfolio's beta. Hedging adds value to a firm when cash flow volatility is costly: convex taxes and distress costs (Smith and Stulz 1985) and, most of all, when costly external finance would force a firm to cut good investments in bad years (Froot, Scharfstein and Stein 1993). **Swaps.** A plain interest rate swap is a long position in one bond and a short position in another; the par swap rate is $(1 - D_n)/\sum D_i$. Since the end of LIBOR, floating legs reference overnight risk-free rates such as SOFR, SONIA and €STR, compounded in arrears. **Options.** Payoffs, put-call parity, binomial trees and Black-Scholes-Merton (Black and Scholes 1973; Merton 1973) are in mba/mba-options-real-options-card. The elective extends the Greeks the core card introduces (delta, gamma, vega) with theta and dynamic hedging of an option book, implied volatility and the smile, option strategies (spreads, collars), currency options (Garman and Kohlhagen 1983) and options on futures (Black 1976). **Risk measurement.** VaR is a loss quantile; expected shortfall is the average loss beyond it and is coherent (Artzner et al. 1999; Acerbi and Tasche 2002). Parametric VaR is $z_{\alpha}\sigma_P$; historical simulation reads the quantile from past moves; Monte Carlo simulates. Backtesting counts exceptions and tests them (Kupiec 1995; Christoffersen 1998). The Basel market risk standard uses ES at 97.5 percent with liquidity horizons (mba/mba-value-at-risk-card). **Governance.** A hedging programme needs a board-approved policy (instruments, limits, tenors, hedge ratios), separation of dealing, confirmation and accounting, and reporting of effectiveness and liquidity. Large derivative losses at non-financial firms have mostly come from positions that exceeded the exposure or from margin calls that were not planned for, not from pricing errors. ## Session roadmap | Session | Topic | Card to read | Case or exercise | Deliverable | |---|---|---|---|---| | 1 *(Example)* | Why firms and investors use derivatives; forwards and cost of carry | mba/mba-forwards-futures-swaps-card (A1, A2) | Index and commodity carry problems | Problem set 1 | | 2 *(Example)* | Futures markets, margin and basis | mba/mba-forwards-futures-swaps-card (A4) | Margin account simulation in Excel | Spreadsheet drill | | 3 *(Example)* | Hedging with futures: minimum-variance ratio, index futures and beta | mba/mba-forwards-futures-swaps-card (A3, B), mba/mba-capm-wacc-card | Hedge ratio estimation on price data | Problem set 2 | | 4 *(Example)* | Interest rate swaps; the benchmark transition from LIBOR | mba/mba-forwards-futures-swaps-card (A5), mba/mba-fixed-income-card | Swap valuation from a zero curve | Swap worksheet | | 5 *(Example)* | Currency forwards, cross-currency swaps and exposure | mba/mba-fx-interest-parity-card | Currency exposure exercise | Problem set 3 | | 6 *(Example)* | Options I: payoffs, parity, binomial trees, early exercise | mba/mba-options-real-options-card | Binomial tree build | Problem set 4 | | 7 *(Example)* | Options II: Black-Scholes-Merton, Greeks, implied volatility and the smile | mba/mba-options-real-options-card (A1) | Delta hedging simulation | Spreadsheet drill | | 8 *(Example)* | Option strategies and corporate hedging: caps, collars, currency options | mba/mba-options-real-options-card, mba/mba-fx-interest-parity-card | Collar design exercise | Team memo | | 9 *(Example)* | Integrative corporate hedging case | This guide: mini-case | Northfield Outdoor Co. and the hedging programme | Individual case write-up | | 10 *(Example)* | Value at risk and expected shortfall | mba/mba-value-at-risk-card (A1, A2) | Parametric and historical VaR on a portfolio | Problem set 5 | | 11 *(Example)* | Backtesting, stress testing and the regulatory framework | mba/mba-value-at-risk-card (A3, A4), finance/var-backtesting-report | Backtest of a VaR series | Backtest memo | | 12 *(Example)* | Credit derivatives and counterparty risk: credit default swaps, collateral, central clearing | mba/mba-fixed-income-card, finance/bond-credit-analysis | Counterparty exposure exercise | Problem set 6 | | 13 *(Example)* | Risk governance and lessons from derivative losses; review | This guide, finance/market-risk-limit-framework | Integrative review problems | Exam | ## Key concepts map | Concept | One-line meaning | Card | |---|---|---| | Cost of carry, convenience yield | Forward price = spot plus the cost of holding minus the benefit of holding | mba/mba-forwards-futures-swaps-card | | Daily settlement, margin, basis | Futures move cash daily; the hedge is imperfect when spot and futures differ | mba/mba-forwards-futures-swaps-card | | Minimum-variance hedge ratio | $h^* = \rho\,\sigma_S/\sigma_F$, effectiveness $\rho^2$ | mba/mba-forwards-futures-swaps-card | | Par swap rate, swap value | Fixed rate that makes a swap worth zero; value moves like a bond | mba/mba-forwards-futures-swaps-card, mba/mba-fixed-income-card | | SOFR, SONIA, €STR | Overnight risk-free benchmarks that replaced LIBOR | mba/mba-forwards-futures-swaps-card | | Covered interest parity | The currency forward from spot and two interest rates | mba/mba-fx-interest-parity-card | | Put-call parity, binomial, BSM | Option prices by replication | mba/mba-options-real-options-card | | Greeks, implied volatility | Sensitivities used to hedge an option book; the market's volatility input | mba/mba-options-real-options-card | | Why hedge | Value from avoiding costly external finance, distress and tax convexity | mba/mba-forwards-futures-swaps-card, mba/mba-capital-structure-card | | VaR, ES, component VaR | Loss quantile, tail average, and who contributes to risk | mba/mba-value-at-risk-card | | Backtesting, Kupiec test, traffic light | Checking the model against realised losses | mba/mba-value-at-risk-card, finance/var-backtesting-report | | Stress testing | Losses in named scenarios outside the data window | finance/stress-testing-programme | | Hedge accounting | Matching the timing of hedge and exposure in earnings | finance/hedge-designation-documentation | ## Mini-case: Northfield Outdoor Co. and the hedging programme **Situation.** It is autumn at Northfield Outdoor Co., a mid-size retailer and brand of outdoor gear with stores and an e-commerce business. Northfield reports in US dollars. Its EBITDA for the current year is forecast at USD 60m and its net debt stands at USD 168m, so leverage is 2.8 times EBITDA against a bank covenant of 3.0 times. Next spring the board plans to fund twelve new stores from internal cash; the CEO calls them "the growth plan we cannot afford to pause". Hana Lindqvist-Obi, the chief financial officer, has been asked by the audit and risk committee to propose a hedging programme. Until now Northfield has hedged nothing systematically. Three exposures dominate (Exhibit 1). First, a European supplier of technical fabrics invoices in euros; EUR 6.0m is due in 180 days for the spring range. Second, Northfield's own-brand cookware and tent poles use aluminium; under a new supply contract, Northfield pays the market price for 1,200 tonnes next month. Third, the company has a USD 80m five-year term loan at SOFR plus 1.75 percent, reset annually in this simplified version. The treasurer, Diego Ferraz, has collected market data and bank quotes (Exhibits 2 and 3). The bank offers a 180-day EUR/USD forward, a 180-day euro call option, and a five-year pay-fixed swap. For aluminium, no futures contract matches Northfield's grade and delivery terms; Diego proposes to use the exchange contract for primary aluminium, with 25 tonnes per contract, and has estimated the statistics of monthly price changes from three years of data. The committee is divided. One director, a former private equity partner, argues that "shareholders can diversify these risks themselves; every dollar of premium and bank spread is a dollar wasted". Another, who sat on the board of a manufacturer that lost heavily on rolling commodity futures in the past, insists that "if we do this, the board needs to know the worst month for margin calls before we sign anything". The chair has asked Hana for a recommendation that the board can understand in ten minutes: what to hedge, with what, how much it costs, what risk remains, and how the programme will be governed. Hana has also asked Diego to show what would happen in a bad but plausible scenario (Exhibit 4): the euro rises 10 percent against the dollar, aluminium rises 25 percent, and SOFR rises 2 percentage points, all before Northfield's payments are fixed. She wants to know whether, in that scenario, the covenant and the store plan would be at risk, with and without hedges. **Exhibit 1. Exposures (fictional).** | *Example* exposure | Amount | Timing | Direction of loss | |---|---|---|---| | EUR supplier payment | EUR 6.0m | 180 days | Euro strengthens | | Aluminium purchase | 1,200 tonnes | Next month | Aluminium price rises | | Term loan interest | USD 80m at SOFR + 1.75% | Five years, annual reset | SOFR rises | **Exhibit 2. Market data (fictional teaching values).** | *Example* item | Value | |---|---| | EUR/USD spot | 1.0900 (USD per EUR) | | 180-day USD and EUR money market rates (ACT/360) | 4.00% and 2.20% | | EUR/USD implied volatility, 180 days | 7.5% | | Aluminium spot (Northfield's contract price) | USD 2,450 per tonne | | Aluminium three-month futures | USD 2,475 per tonne, 25 tonnes per contract | | Monthly price changes: std dev of spot, std dev of futures, correlation | 3.0%, 2.8%, 0.90 | | SOFR today | 3.70% | | Zero rates from the SOFR swap curve, years 1 to 5 (annual compounding) | 3.70%, 3.60%, 3.55%, 3.58%, 3.62% | **Exhibit 3. Bank quotes (fictional).** | *Example* instrument | Quote | |---|---| | 180-day EUR/USD forward | 1.0997 | | 180-day European EUR call, strike 1.1000 | USD 0.0227 per EUR, paid today | | Five-year pay-fixed swap against SOFR, notional USD 80m | 3.66% fixed | **Exhibit 4. Stress scenario (fictional).** The euro rises 10 percent from spot by the payment date (to 1.1990); Northfield's aluminium price rises 25 percent to USD 3,062.50 and the three-month futures price to USD 3,080 by the purchase date; SOFR rises to 5.70 percent at the next reset. **Discussion questions.** 1. What does each exposure cost at today's forward or current rates, and what would a forward, an option and a swap do to it? Is the bank's forward quote fair? 2. How many aluminium futures contracts should Northfield buy, how much risk would they remove, and what risk would remain? What is the one-month 95 percent VaR of the aluminium exposure with and without the hedge? 3. Is the bank's 3.66 percent swap quote fair? What does the gap cost Northfield, and how would you negotiate? 4. In the Exhibit 4 scenario, what happens to costs, EBITDA and the covenant with and without hedges? 5. Answer the first director: under what conditions does corporate hedging create value for shareholders, and do they hold for Northfield? 6. Answer the second director: what governance, limits and liquidity plan should the programme have? ## Teaching note **Q1. Costs and instruments.** Covered interest parity gives $F = 1.0900 \times (1 + 0.04 \times 180/360)/(1 + 0.022 \times 180/360) = 1.099703$, about 97 pips above spot; the bank's 1.0997 is fair (`=1.09*(1+4%*180/360)/(1+2.2%*180/360)`). A forward fixes the payment at USD 6,598,220 against USD 6,540,000 at today's spot: the difference is the interest differential, not a cost of hedging. The euro call, priced with Garman and Kohlhagen (1983) at a forward of 1.099703, strike 1.10, volatility 7.5 percent and half a year, is worth USD 0.022666 per euro ($d_1$ = 0.0214, $d_2$ = -0.0316, discount factor 0.980392), so the bank's quote of 0.0227 is fair. Its premium is USD 135,993 today, or USD 138,713 carried to the payment date. With the option, Northfield's worst case is USD 6,738,713, and it keeps the benefit if the euro falls: the call hedge beats the forward when the euro ends below about 1.0766. At a final rate of 1.0300 the costs are USD 6,180,000 unhedged, USD 6,598,220 with the forward and USD 6,318,713 with the option. **Q2. Aluminium.** $h^* = 0.90 \times 3.0/2.8 = 0.9643$, so $N^* = 0.9643 \times 1{,}200/25 = 46.29$; buy 46 contracts (`=ROUND(0.9*0.03/0.028*1200/25,0)`). Effectiveness is $\rho^2$ = 0.81: 81 percent of the variance is removed and basis risk remains. The one-month standard deviation of the purchase cost falls from USD 88,200 (`=3%*2450*1200`) to USD 38,445, and the one-month 95 percent VaR from USD 145,076 to USD 63,237 (`=NORM.S.INV(0.95)*38445`). Margin is the liquidity cost: Diego should estimate how much the futures could lose in a month if aluminium falls and hold that cash or credit line (mba/mba-forwards-futures-swaps-card, A4). **Q3. Swap.** Discount factors 0.964320, 0.931709, 0.900637, 0.868753 and 0.837109 give a five-year par rate of 3.6178 percent (`=(1-D5)/SUM(D1:D5)`). The quote of 3.66 percent is 4.22 basis points above mid, worth about USD 33,788 a year or USD 152,131 in present value (the PV01 of the swap's fixed leg is about USD 36,020 per basis point). That spread pays the bank for credit risk, capital and profit; it is not wrong, but it is negotiable. Ask two or three banks for quotes at the same time, agree the reference curve and time of pricing, and consider a shorter tenor or hedging a share of the loan (for example 60 to 75 percent, as a policy might set). With the swap the all-in fixed cost is 5.3678 percent at mid, USD 4,294,212 a year. **Q4. Stress.** The base cost at today's forward and current rates is USD 13,898,220 (the forward cost of the euros, 1,200 tonnes at spot, and one year of interest at 3.70 + 1.75 percent). | *Example* item (USD) | Unhedged in stress | Hedged in stress | |---|---|---| | Euro payment | 7,194,000 | 6,598,220 (forward) | | Aluminium, net of futures gain of 695,750 | 3,675,000 | 2,979,250 | | One year of loan interest | 5,960,000 | 4,294,212 (swap at mid 3.6178%) | | Total | 16,829,000 | 13,871,682 | | Change against base | +2,930,780 | -26,538 | Unhedged, the scenario costs USD 2.93m of cash. Only the euro and aluminium part, USD 1.33m, reduces EBITDA (2.2 percent of the forecast USD 60m); the extra USD 1.60m of interest sits below EBITDA but still drains cash, so net debt rises. Assuming the shortfall is funded with debt, leverage rises from 2.80 to 2.91 times (`=(168+2.930780)/(60-1.330780)`), close to the 3.0 covenant, and the store plan would compete with covenant headroom for cash. Hedged, the cost is almost unchanged (slightly below base, because the swap's 3.62 percent mid rate is below today's 3.70 percent SOFR, while the aluminium hedge leaves a small USD 39,250 shortfall from basis and rounding), and leverage stays at 2.80 times. At the bank's quoted 3.66 percent instead of mid, the hedged interest is USD 4,328,000 and the hedged total USD 13,905,470, USD 7,250 above base. The aluminium hedge leaves an effective price of about USD 2,483 per tonne, not exactly USD 2,450, which is basis risk at work. **Q5. Does hedging create value here?** In perfect markets, no: shareholders can hedge or diversify these risks themselves (the Modigliani and Miller logic). The director is right that premiums and spreads are a real cost. But Northfield has the frictions that make hedging valuable: a covenant close to binding (expected distress costs, Smith and Stulz 1985) and an investment plan funded from internal cash that would be cut or financed expensively in a bad year (Froot, Scharfstein and Stein 1993). The case for hedging is strongest for the exposures that threaten that plan and the covenant, and weakest for small, diversifiable ones. A good answer quantifies it: the hedges cost roughly USD 0.15m in swap spread (PV) and USD 0.14m of option premium if chosen, against USD 2.9m of stress cost removed. **Q6. Governance.** Recommend a written hedging policy approved by the board: hedge only committed or highly probable exposures; hedge ratios by horizon (for example 75 to 100 percent of committed payments, a declining share of forecasts); approved instruments (forwards, futures, plain swaps, bought options and collars; no sold options except inside collars); counterparty limits and ISDA documentation; separation of dealing, confirmation and accounting; monthly reporting of mark to market, effectiveness and margin; a liquidity buffer sized from the worst plausible month of margin calls; hedge accounting documentation at inception (finance/hedge-designation-documentation). See finance/fx-interest-rate-hedging-policy for a full policy. **Recommendation in one paragraph.** Hedge the committed euro payment with the forward (or with the call option if the board values keeping the upside at a premium of about USD 0.14m), buy 46 aluminium futures for next month's purchase and hold a margin buffer, and swap 60 to 75 percent of the term loan to fixed after negotiating the swap spread with several banks. In the stress scenario this removes about USD 2.9m of cost, keeps leverage at 2.8 times and protects the store plan. Govern the programme with a board-approved policy, limits that tie every hedge to an exposure, and monthly reporting. ## Typical assignments and how they are graded Common assessment forms in leading programmes: problem sets (often 20% to 30% of the grade), a team case or hedging project (20% to 30%), class participation (10% to 20%), and a final exam (30% to 50%), sometimes open book with a spreadsheet. Your syllabus decides the weights; record them here: [weights]. | Criterion | Excellent (4) | Adequate (2 to 3) | Weak (0 to 1) | |---|---|---|---| | Pricing | Correct no-arbitrage prices with conventions stated (compounding, day count) | Minor convention errors | Wrong method or sign errors | | Exposure analysis | Exposure, timing and direction mapped before choosing instruments | Exposure described but not quantified | Instrument chosen first | | Hedge design | Hedge ratio, contract count, residual risk and liquidity needs shown | Hedge sized one for one without justification | No sizing | | Risk measurement | VaR or ES and a stress scenario with assumptions and limits | One measure without interpretation | None | | Rationale | Why hedging creates value here, with the theory applied | Theory named but not applied | "Hedging reduces risk, so it is good" | | Governance and ethics | Policy, limits, controls and incentives addressed | Mentioned in passing | Ignored | | Exhibits and model | Clear, labelled, checkable, formulas visible | Readable but hard to audit | Hard-coded numbers | Use mba/mba-case-write-up for structure and mba/mba-case-prep-sheet before each case discussion. ## Exam preparation plan | Week before exam | Focus | Method | |---|---|---| | 4 | Forwards, futures, carry, hedge ratios | Redo problem sets 1 and 2 without notes; log misses in mba/mba-error-log | | 3 | Swaps and currency instruments | Rebuild the A5 swap and the mini-case Q3 from a blank sheet in 30 minutes | | 2 | Options, Greeks, strategies | Price one option by binomial and BSM, compute delta and gamma, design a collar | | 1 | VaR, ES, backtesting, mixed practice | Interleave problems from every topic; take one past exam under time | | Final 2 days | Formula sheet, error log | Review mba/mba-formula-sheet and your error log; sleep | Retrieval practice and spacing beat re-reading (Dunlosky et al. 2013); interleaving trains the skill exams test most, choosing the right method. Turn the key concepts map into flashcards with mba/mba-concept-flashcards. ## Common struggles 1. **Rate conventions.** Continuous, annual and money market rates mixed in one formula. Write the convention next to every rate. 2. **Long and short, buyer and seller.** Many errors are sign errors. Write "we pay" or "we receive" for every leg. 3. **Margin calls to initial margin.** Students top up to maintenance. 4. **Hedging the wrong quantity.** One-for-one hedges without the hedge ratio, or hedging forecasts as if they were committed. 5. **Swap valuation from the fixed rate alone.** Always build discount factors first. 6. **Greeks as numbers without meaning.** Translate each into "if X moves by 1, the position changes by Y". 7. **VaR as a worst case.** It is a quantile; the tail beyond it is the point of ES and stress tests. 8. **Judging a hedge by its own profit.** Judge the hedge and the exposure together. ## Reading list - Classic works: Keynes (1923); Johnson (1960); Black and Scholes (1973); Merton (1973); Black (1976); Ederington (1979); Cox, Ross and Rubinstein (1979); Cox, Ingersoll and Ross (1981); Garman and Kohlhagen (1983); Stulz (1984); Smith and Stulz (1985); Froot, Scharfstein and Stein (1993); Kupiec (1995); Artzner et al. (1999); Acerbi and Tasche (2002). Full references are under Sources. - Textbooks (by name only): Hull, J. C., *Options, Futures, and Other Derivatives*; McDonald, R. L., *Derivatives Markets*; Hull, J. C., *Risk Management and Financial Institutions*; Jorion, P., *Value at Risk*; Christoffersen, P. F., *Elements of Financial Risk Management*. - Open resource: OpenStax, *Principles of Finance* (check the licence on the book page). ## Self-test questions 1. A non-dividend asset trades at 100; the one-year rate is 5 percent continuous. What is the one-year forward price? 2. Why does a forward price below full carry not create an arbitrage for a consumption commodity? 3. A hedge ratio of 0.8 applies to an exposure of 1,000 tonnes and a contract of 25 tonnes. How many contracts? 4. Discount factors for years 1 and 2 are 0.97 and 0.94. What is the two-year par swap rate? 5. A USD 10m position has a daily volatility of 2 percent. What is its one-day 99 percent parametric VaR? 6. A one-year European call on a non-dividend share costs 6.00; the share is at 100, the strike 100 and the rate 4 percent continuous. What must the put cost? 7. Give the two strongest reasons from the literature for a non-financial company to hedge, with authors. 8. Why did the Basel Committee move from VaR to expected shortfall? 9. Name three controls that keep a corporate hedging programme from becoming speculation. 10. In the mini-case, why does the aluminium hedge not fix the price at exactly USD 2,450 per tonne? ## My notes and next steps | Item | My entry | |---|---| | Weakest topic after week 4 | [ ] | | Questions for office hours | [ ] | | Cases completed and grades | [ ] | | Mistakes logged in mba/mba-error-log | [Date and short description] | | Next review date | YYYY-MM-DD | | Roles or electives this course prepares me for | [Treasury, risk, sales and trading, asset management; mba/mba-investments-guide] | ## Sources and further reading - Keynes, J. M. (1923). *A Tract on Monetary Reform*. Macmillan. - Johnson, L. L. (1960). The theory of hedging and speculation in commodity futures. *The Review of Economic Studies*, 27(3), 139-151. - Black, F., and Scholes, M. (1973). The pricing of options and corporate liabilities. *Journal of Political Economy*, 81(3), 637-654. - Merton, R. C. (1973). Theory of rational option pricing. *The Bell Journal of Economics and Management Science*, 4(1), 141-183. - Black, F. (1976). The pricing of commodity contracts. *Journal of Financial Economics*, 3(1-2), 167-179. - Ederington, L. H. (1979). The hedging performance of the new futures markets. *The Journal of Finance*, 34(1), 157-170. - Cox, J. C., Ross, S. A., and Rubinstein, M. (1979). Option pricing: a simplified approach. *Journal of Financial Economics*, 7(3), 229-263. - Cox, J. C., Ingersoll, J. E., and Ross, S. A. (1981). The relation between forward prices and futures prices. *Journal of Financial Economics*, 9(4), 321-346. - Garman, M. B., and Kohlhagen, S. W. (1983). Foreign currency option values. *Journal of International Money and Finance*, 2(3), 231-237. - Stulz, R. M. (1984). Optimal hedging policies. *Journal of Financial and Quantitative Analysis*, 19(2), 127-140. - Smith, C. W., and Stulz, R. M. (1985). The determinants of firms' hedging policies. *Journal of Financial and Quantitative Analysis*, 20(4), 391-405. - Froot, K. A., Scharfstein, D. S., and Stein, J. C. (1993). Risk management: coordinating corporate investment and financing policies. *The Journal of Finance*, 48(5), 1629-1658. - Kupiec, P. H. (1995). Techniques for verifying the accuracy of risk measurement models. *The Journal of Derivatives*, 3(2), 73-84. - Christoffersen, P. F. (1998). Evaluating interval forecasts. *International Economic Review*, 39(4), 841-862. - Artzner, P., Delbaen, F., Eber, J.-M., and Heath, D. (1999). Coherent measures of risk. *Mathematical Finance*, 9(3), 203-228. - Acerbi, C., and Tasche, D. (2002). On the coherence of expected shortfall. *Journal of Banking and Finance*, 26(7), 1487-1503. - Dunlosky, J., Rawson, K. A., Marsh, E. J., Nathan, M. J., and Willingham, D. T. (2013). Improving students' learning with effective learning techniques. *Psychological Science in the Public Interest*, 14(1), 4-58. - Bank of England. Transition to sterling risk-free rates from LIBOR; Federal Reserve Bank of New York, SOFR; European Central Bank, €STR (all checked 2026-10-28). - Basel Committee on Banking Supervision (2019). Minimum capital requirements for market risk; Basel Framework chapters MAR32 and MAR33, bis.org (checked 2026-10-28). - AACSB International (2026). Global Standards for Business Education, ratified 20 April 2026, aacsb.edu (checked 2026-10-28); context for the competency map; check the current text. ## Answer key 1. $100\,e^{0.05}$ = 105.13 (`=100*EXP(5%)`). 2. Arbitrage would require selling the commodity spot and buying it forward, but those who hold it need it for production and will not lend or sell it; the convenience yield measures the value of holding it. 3. $0.8 \times 1{,}000/25$ = 32 contracts. 4. $(1 - 0.94)/(0.97 + 0.94)$ = 3.1414 percent (`=(1-0.94)/(0.97+0.94)`). 5. $2.3263 \times 10 \times 2\%$ = USD 0.4653m (`=NORM.S.INV(0.99)*10*2%`). 6. Parity: $P = C - S + Ke^{-rT} = 6.00 - 100 + 100e^{-0.04}$ = 2.08 (`=6-100+100*EXP(-4%)`). 7. Costly external finance that would force underinvestment in bad years (Froot, Scharfstein and Stein 1993); expected distress costs and convex taxes (Smith and Stulz 1985). Managers' undiversified exposure (Stulz 1984) explains hedging but not necessarily value for shareholders. 8. VaR ignores the size of losses beyond the quantile and can fail subadditivity; ES at 97.5 percent captures the tail, is coherent, and under normality gives capital similar to 99 percent VaR. 9. Hedges tied to identified exposures with maximum hedge ratios; approved instruments and counterparty limits; separation of dealing, confirmation and accounting; independent monthly reporting of positions, mark to market and effectiveness. 10. Northfield's contract price and the exchange futures price differ (grade, delivery, timing): the futures rose USD 605 per tonne while Northfield's price rose USD 612.50, and 46 contracts cover 1,150 tonnes rather than 1,200, so the effective price is about USD 2,483. That residual is basis risk and rounding. ## Revision history | Version | Date | Author | Change summary | |---|---|---|---| | 0.1 | YYYY-MM-DD | [Your name] | Guide set up from the template, syllabus loaded | | 0.2 | YYYY-MM-DD | [Your name] | *Example:* Mini-case worked, teaching note compared, exam plan started | ## Standard and licence note Structure aligned with the derivatives and risk management electives common to leading international MBA programmes, with the competency areas mapped to learning goals of the kind accredited schools set under the AACSB Global Standards for Business Education (2026), summarised in original words; benchmark-rate and Basel facts as checked on official pages in October 2026. The text, the Northfield Outdoor Co. mini-case, its exhibits, its teaching note and all questions are original; no published case or textbook text is copied or paraphrased, and all companies and people are fictional. 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