Derivatives and Risk Management Course Guide Template

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

Contents

• What the course is for
• Prerequisites
• The course in one page
• Session roadmap
• Key concepts map
• Mini-case: Northfield Outdoor Co. and the hedging programme
• Teaching note
• Typical assignments and how they are graded
• Exam preparation plan
• Common struggles
• Reading list
• Self-test questions
• My notes and next steps
• Sources and further reading
• Answer key
• 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):

Prerequisites

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

Key concepts map

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).

Exhibit 2. Market data (fictional teaching values).

Exhibit 3. Bank quotes (fictional).

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).

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].

Use mba/mba-case-write-up for structure and mba/mba-case-prep-sheet before each case discussion.

Exam preparation plan

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

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

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. The template is independent and not affiliated with or endorsed by any business school, accreditation body, regulator or publisher. Check your own syllabus and the current official versions of any standard before you rely on it. Template licence: MIT.