Derivatives and Alternative Investments

Introduction

Derivatives and alternative investments extend the investment universe beyond conventional holdings of shares, bonds and cash. A derivative derives its value from an underlying asset, rate, index or event. Alternative investments include assets and strategies that are less traditional, less liquid or less transparent than publicly traded securities. Together, they are important tools for institutional investors, banks, insurers, corporations and sophisticated individual investors.

Derivatives can transfer price, interest-rate, currency and credit risk. They can also create leverage, allowing a relatively small initial payment to control a large notional exposure. Alternative investments may improve diversification and provide access to inflation-sensitive or return-seeking opportunities, but they often involve valuation uncertainty, limited liquidity, complex governance and high fees.

The central investment principle is that derivatives and alternatives should be used to express a clearly defined economic exposure—not merely to pursue complexity or leverage.

Learning Objectives

By the end of this chapter, students should be able to:

• distinguish forwards, futures, options and swaps;
• calculate and interpret basic derivative payoffs and prices;
• explain hedging, speculation and arbitrage applications;
• evaluate counterparty, leverage, liquidity and model risks;
• compare real estate, commodities, private equity, hedge funds, infrastructure and digital assets;
• assess valuation, governance, regulatory and ethical issues in alternative investments.

1. Derivative Instruments

1.1 Forwards

A forward contract is a privately negotiated agreement to buy or sell an underlying asset at a specified future date for a price agreed today. The buyer takes a long position and the seller takes a short position. Forwards are usually over-the-counter (OTC), so their terms can be customized, but they expose each party to counterparty default risk.

For a non-income-producing asset, the theoretical forward price is:

where F₀,T is the fair forward price, S₀ is the current spot price, r is the annual risk-free interest rate and T is time to maturity in years. This version assumes annual compounding, no storage costs, no income and no credit or liquidity adjustments. With continuous compounding:

If the asset pays a known income with present value I, the price becomes:

For commodities, storage costs and convenience yield matter. A simplified continuous-compounding relationship is:

where u is the storage-cost rate and y is the convenience-yield rate. The relationship is an arbitrage benchmark, not a guarantee: funding costs, storage constraints, credit risk and market frictions can produce deviations.

At maturity, the payoff to a long forward is:

where S_T is the spot price at maturity and K is the contracted delivery price. The short position receives the opposite payoff, K − S_T.

1.2 Futures

A futures contract is a standardized, exchange-traded agreement to buy or sell an underlying asset at a future date. The exchange specifies contract size, maturity, quality and delivery terms. A clearing house stands between buyers and sellers, requiring initial margin and variation margin.

Futures are marked to market daily. If the contract price moves against a trader, the trader must provide additional funds through a margin call. This substantially reduces the accumulation of unpaid losses but creates liquidity risk.

The futures payoff at maturity is conceptually the same as the forward payoff. However, daily settlement means that the timing of cash flows differs. Consequently, futures and forward prices may differ when interest rates are volatile and correlated with futures prices.

A hedge ratio for a simple one-to-one hedge is:

where N is the number of contracts, Q_A is the exposure quantity and Q_F is the quantity represented by one futures contract. A more refined minimum-variance hedge ratio is:

where ρ_ΔS,ΔF is the correlation between changes in the spot and futures prices, σ_S is the standard deviation of spot-price changes and σ_F is the standard deviation of futures-price changes. The formula assumes that historical relationships are informative about the hedging period and that a linear hedge is suitable.

1.3 Options

An option gives its holder a right, but not an obligation, to buy or sell an underlying asset. A call gives the right to buy at the strike price; a put gives the right to sell. The buyer pays a premium. The seller, or writer, receives the premium but accepts a contingent obligation.

At expiration, the call payoff is:

The put payoff is:

These are payoffs before considering the premium. The profit to a long call is max(S_T − K,0) − c, where c is the premium. The profit to a long put is max(K − S_T,0) − p, where p is the put premium.

A call buyer benefits from a price increase while limiting the loss to the premium. A put buyer can protect an asset against a price decline. The option writer has an asymmetric payoff and may face very large losses, particularly when writing uncovered calls.

Important option terminology includes:

A basic no-arbitrage relationship for European options on a non-dividend-paying asset is put–call parity:

Here c and p are call and put prices, K is the strike, r is the continuously compounded risk-free rate and T is time to expiry. The relationship assumes identical strike and expiry, European exercise, no arbitrage costs and a non-dividend-paying underlying. With known dividends, the present value of dividends is subtracted from the spot component.

Option values are commonly discussed through the Greeks. Delta measures sensitivity to the underlying price; gamma measures the change in delta; theta measures sensitivity to the passage of time; vega measures sensitivity to volatility; and rho measures sensitivity to interest rates. Greeks are local approximations, not complete measures of risk.

1.4 Swaps

A swap is an agreement to exchange cash flows according to a specified formula. In an interest-rate swap, one party pays a fixed rate and receives a floating rate, while the other does the reverse. Principal is generally not exchanged; it is a notional amount used to calculate payments.

For a plain-vanilla fixed-for-floating swap, the fixed rate at inception is set so that the present value of expected fixed payments equals the present value of expected floating payments. A simplified valuation is:

If a party pays fixed and receives floating, its value rises when market interest rates rise, all else equal. Currency swaps exchange interest and sometimes principal payments in different currencies, while commodity swaps exchange fixed and floating commodity prices. Credit default swaps transfer credit exposure from a protection buyer to a protection seller in exchange for a periodic premium.

Swaps create counterparty, collateral, settlement and documentation risks. The International Swaps and Derivatives Association (ISDA) framework commonly governs OTC contracts, but legal enforceability depends on jurisdiction and documentation.

2. Derivative Pricing and Economic Uses

2.1 No-arbitrage and replication

Derivative pricing begins with the no-arbitrage principle: two portfolios with identical future cash flows should have the same price, after allowing for financing, income, costs and risk. If prices differ, traders may construct offsetting positions to earn a theoretically riskless profit. In practice, transaction costs, funding constraints, taxes, execution risk and model risk limit arbitrage.

A derivative can be used for:

• Hedging: reducing an unwanted exposure;
• Speculation: accepting risk in expectation of profit;
• Arbitrage: exploiting inconsistent prices;
• Portfolio construction: obtaining exposure efficiently;
• Income generation: such as writing covered calls, while accepting capped upside and downside risk.

2.2 A simple worked example: currency hedge

An importer must pay USD 1,000,000 in three months. The importer’s domestic currency cost rises if the dollar appreciates. Suppose the current three-month forward exchange rate is 0.92 domestic currency units per dollar. The importer enters a long-dollar forward.

The locked domestic-currency payment is:

If the spot rate at maturity is 0.96, an unhedged payment would cost 960,000, whereas the forward payment remains 920,000, ignoring collateral, credit and transaction costs. The hedge gain is 40,000 relative to the unhedged position. If the spot rate instead falls to 0.88, the importer still pays 920,000 and gives up the benefit of the lower market rate. This illustrates that a forward reduces uncertainty but also removes favorable currency movements.

2.3 A simple worked example: protective put

An investor owns a share currently worth 50 and buys a three-month put with strike 48 for a premium of 2. At expiry, if the share price is 35, the put payoff is:

The combined share-and-put position is worth 35 + 13 = 48 before accounting for the premium. The investor has effectively established a minimum expiry value of 48, but the net economic floor after the premium is 46 relative to the initial share cost, ignoring financing and dividends. If the share rises to 60, the put expires worthless and the investor retains the share upside, less the premium.

3. Risks and Controls in Derivatives

Derivative risk is multidimensional. Market risk arises from movements in the underlying, volatility, interest rates, exchange rates or correlations. Leverage risk occurs because losses can exceed the initial cash commitment. Basis risk arises when the hedging instrument does not move perfectly with the exposure. Rollover risk occurs when a hedge expires before the underlying exposure ends.

OTC derivatives introduce counterparty and legal risks. Collateral reduces credit exposure but can create liquidity demands and disputes over valuation. Model risk occurs when pricing models use inappropriate assumptions, stale data or incorrect implementation. Operational risk includes confirmation errors, failed settlements and inaccurate position records.

Best-practice controls include independent valuation, daily margin monitoring, stress testing, position limits, collateral agreements, legal review, segregation of duties, central clearing where appropriate and transparent reporting of notional and potential future exposure. Notional principal is not itself a measure of loss; fair value, sensitivity and stress loss are more informative.

4. Alternative Investments

Alternative investments are not defined solely by asset class. They often share several characteristics: limited secondary markets, complex valuation, high minimum commitments, specialist management, long holding periods or performance fees. Correlations with public markets may appear low, but reported correlations can be distorted by stale pricing, appraisal smoothing or infrequent dealing.

4.1 Real estate

Real estate includes direct property, private funds, real-estate investment trusts (REITs), mortgage investments and property-related securities. Returns arise from rental income, operating income and capital appreciation. A simplified property value based on a constant capitalization rate is:

where V is estimated value, NOI is normalized net operating income and R is the capitalization rate. The formula assumes a stable, capitalized income stream and is highly sensitive to assumptions about rents, vacancies, expenses, interest rates and risk.

Real estate may provide inflation-linked income and diversification, but it is exposed to vacancy, maintenance, location, environmental regulation, leverage and illiquidity. Direct property is usually valued through comparable sales, discounted cash flow and income capitalization. Appraisal values may adjust slowly when market prices move rapidly.

4.2 Commodities

Commodities include energy, metals, agriculture and livestock. Investors obtain exposure through physical holdings, futures, swaps, exchange-traded products or shares of commodity-producing firms. Commodity returns may reflect spot-price changes, collateral income and roll yield. A futures investor can lose money even when the expected long-term commodity story is favorable if contracts are repeatedly rolled at unfavorable prices.

Commodity prices are influenced by inventories, weather, geopolitics, production capacity, transportation, currency movements and demand cycles. Physical commodities also introduce storage, insurance, quality and delivery risks.

4.3 Private equity

Private equity involves investment in privately held companies, commonly through venture capital, growth capital, buyouts or restructuring funds. Returns depend on entry valuation, operating improvement, leverage, exit valuation and timing. The internal rate of return (IRR) is the discount rate that makes the net present value of cash flows equal to zero:

where CF_t is cash flow at time t. IRR can be misleading when cash flows are irregular, interim distributions are reinvested at unrealistic rates or managers control the timing of distributions. Multiple on invested capital (MOIC) is:

Private equity offers active ownership and potential illiquidity premia, but it involves commitment risk, capital calls, valuation discretion, concentration, high fees and uncertain exit markets. Investors should distinguish gross returns from net returns after management fees, carried interest and fund expenses.

4.4 Hedge funds

Hedge funds use strategies such as long–short equity, global macro, relative value, event-driven investing and managed futures. They may employ leverage, short selling and derivatives. Their performance should be assessed using risk-adjusted measures, drawdowns, liquidity terms, transparency and capacity—not simply historical returns.

The Sharpe ratio is:

where R_p is portfolio return, R_f is the risk-free return and σ_p is portfolio return volatility, measured over the same period. The ratio assumes that volatility is a useful representation of risk and can be unreliable for nonlinear, illiquid or serially correlated returns.

Hedge funds may impose lock-ups, notice periods, gates or side pockets. These terms mean that an investor’s ability to redeem may be much less than the apparent frequency of reported performance.

4.5 Infrastructure

Infrastructure assets include transport, utilities, telecommunications, renewable energy and social infrastructure. They may generate long-lived cash flows, sometimes linked to inflation or regulated tariffs. Risks include construction delays, political intervention, demand shortfalls, technological change, refinancing, environmental obligations and regulatory changes.

Infrastructure valuation requires analysis of concession terms, projected demand, operating costs, financing structure and residual value. Its apparent stability should not be confused with absence of risk, particularly when leverage is high.

4.6 Digital assets

Digital assets include cryptocurrencies, stablecoins, tokenized securities and other blockchain-based instruments. Potential benefits include programmable ownership, continuous trading and new settlement arrangements. Risks include extreme price volatility, cyberattack, custody failure, smart-contract defects, governance disputes, fraud, market manipulation, uncertain legal status and energy or environmental concerns.

A stablecoin may seek to maintain a reference value but can face reserve, redemption, banking, governance and run risks. Tokenization can improve transferability, but a token does not automatically create legal ownership of an underlying asset. Investors must verify the legal claim, custody arrangement, governing jurisdiction and recovery process.

5. Valuation, Liquidity and Portfolio Construction

Valuation risk is the possibility that an estimated value differs materially from realizable value. It is particularly important when assets do not trade frequently. A private fund may report a smooth quarterly net asset value, while the price obtainable in a stressed secondary market is substantially lower.

Liquidity has at least three dimensions:

1. Market liquidity: ability to sell without materially moving the price;
2. Funding liquidity: ability to meet cash obligations and margin calls;
3. Institutional liquidity: ability to redeem or transfer an investment under its legal terms.

A portfolio should be evaluated under normal and stressed conditions. Investors should map capital calls, derivative margin, redemptions, debt maturities and operating expenses against liquid resources. Diversification across managers does not necessarily diversify the underlying risk if all managers own similar companies, sectors or financing structures.

Alternative investments can improve portfolio efficiency when their risk exposures are genuinely distinct. However, correlations may increase during crises, leverage can amplify losses and illiquid assets can prevent timely rebalancing. Strategic allocation should therefore consider liquidity budgets, loss capacity, governance resources, tax effects, fees and the investor’s time horizon.

6. Governance, Regulation and Ethics

Derivative and alternative-investment governance requires clear mandates, independent oversight and accurate disclosures. A board or investment committee should understand permitted instruments, leverage limits, collateral rules, valuation policies, conflicts of interest and escalation procedures.

Regulatory requirements vary by jurisdiction but commonly address suitability, disclosure, market abuse, clearing, margin, capital, custody, anti-money-laundering controls and investor protection. Banks and insurers must also consider how derivatives and alternatives affect regulatory capital, solvency and liquidity ratios.

Ethical issues include mis-selling complex products, presenting gross rather than net performance, hiding liquidity restrictions, overstating diversification and using valuation models to smooth losses. Fiduciary practice requires that risk, fees, conflicts and uncertainty be communicated in a manner that a reasonable investor can understand.

Technology can improve trade capture, collateral management, portfolio monitoring and anomaly detection. Artificial intelligence may assist in analysing documents, forecasting cash flows or identifying unusual transactions, but it should not replace human accountability. Models require validated data, explainability, cybersecurity controls and monitoring for bias or error.

7. Illustrative Case: Hedging an Energy-Importing Utility

Background

A fictional electricity utility expects to purchase 500,000 barrels of fuel over the next six months. Its revenues are regulated and cannot be adjusted immediately when fuel prices rise. The utility is therefore exposed to a margin squeeze.

Problem

Management must decide whether to use futures, a swap or options. A full fixed-price hedge would reduce price uncertainty but could be costly if prices fall. An unhedged strategy preserves potential savings but leaves the utility vulnerable to a sharp price increase.

Analysis

The treasury team estimates fuel requirements by month, assesses available liquidity for futures margin and reviews the utility’s risk limit. It also considers basis risk because the fuel used locally may not exactly match the futures contract. Stress scenarios include a 40% price increase, a 30% decline, exchange-rate depreciation and a temporary inability to post collateral.

Approach and solution

The committee selects a layered programme: part of expected consumption is hedged with futures, another part with fixed-for-floating swaps and the remaining exposure with call options. The options preserve benefit from falling prices, while futures and swaps provide greater certainty for essential consumption. The programme includes counterparty limits, daily independent valuation, collateral forecasting and a prohibition on hedging speculative volumes.

Outcome

The strategy does not produce the lowest possible fuel cost in every market outcome. Instead, it reduces the probability that fuel costs will threaten financial stability while retaining some participation in favorable price declines. The utility documents hedge effectiveness, reviews forecast volumes and closes or adjusts positions when operating assumptions change.

Learning points

The case demonstrates that hedging is a risk-management decision rather than a prediction of prices. Instrument choice depends on the shape of the exposure, basis risk, liquidity, accounting and governance. A hedge can fail if the underlying volume is overestimated, the contract is poorly matched or collateral needs are ignored.

Challenges and Limitations

Derivative models depend on assumptions about volatility, interest rates, correlations, liquidity and default. Historical data may not represent future crises. Alternative-investment performance may suffer from survivorship bias, selection bias, backfill bias and stale pricing. Reported returns can omit fees, leverage costs, taxes and delayed losses.

Investors should avoid treating complexity as sophistication. A transparent, liquid instrument may be superior to a theoretically higher-return strategy that cannot be valued or exited when needed. Due diligence should cover strategy, people, process, risk systems, service providers, valuation, liquidity, legal terms, cybersecurity and conflicts.

Best-Practice Checklist

• Define the economic exposure before selecting an instrument.
• Match derivative maturity, quantity and underlying as closely as possible.
• Measure gross and net exposure, sensitivity, leverage and stress loss.
• Maintain cash buffers for margin calls and capital commitments.
• Use independent pricing and challenge model assumptions.
• Read redemption, lock-up, gate, side-pocket and capital-call provisions.
• Evaluate total fees and performance after tax and expenses.
• Diversify managers, strategies, counterparties and sources of risk.
• Document authority, limits, reporting and escalation procedures.
• Treat digital custody, legal ownership and cybersecurity as investment risks.

Chapter Summary

Forwards, futures, options and swaps transfer or reshape financial risk. Forwards are customized OTC contracts; futures are standardized and marked to market; options provide asymmetric rights for a premium; and swaps exchange specified cash flows. Pricing is grounded in no-arbitrage, replication, financing and income assumptions. Hedging can stabilize cash flows but introduces basis, liquidity, rollover, counterparty and model risks.

Alternative investments include real estate, commodities, private equity, hedge funds, infrastructure and digital assets. They may broaden opportunity sets and diversify portfolios, but their benefits must be weighed against illiquidity, leverage, valuation uncertainty, fees, governance and regulatory risk. Effective portfolio construction considers liquidity budgets, stress scenarios, net returns, legal terms and the investor’s capacity to monitor complexity. Ethical and professional practice requires transparent disclosure, independent valuation and disciplined control of conflicts and leverage.

Key Terms

Derivative: A contract whose value depends on an underlying asset, rate, index or event.

Forward: A privately negotiated agreement to transact at a future date for a price fixed today.

Futures: A standardized exchange-traded derivative subject to daily marking to market.

Option: A contract giving the buyer a right, but not an obligation, to buy or sell.

Call option: An option giving the right to buy.

Put option: An option giving the right to sell.

Swap: An agreement to exchange cash flows according to specified terms.

Notional principal: Reference amount used to calculate derivative cash flows.

Margin: Collateral posted to support a derivative position.

Basis risk: Risk that the hedge and the exposure do not move together.

Leverage: Use of borrowed funds or derivatives to increase exposure relative to capital.

Counterparty risk: Risk that the other party fails to perform.

Real estate: Land and structures or securities representing property exposure.

Private equity: Investment in privately held companies.

Hedge fund: Pooled investment vehicle using flexible strategies, often including short selling and leverage.

Infrastructure: Long-lived assets providing essential economic or social services.

Digital asset: An electronically represented asset or claim, often using distributed-ledger technology.

Liquidity risk: Risk that an investment cannot be sold or obligations cannot be met promptly at a reasonable price.

Valuation risk: Risk that an estimated value differs materially from realizable value.

Review Questions

Short Answer Questions

1. How does a forward differ from a futures contract?
2. What is the difference between an option payoff and an option profit?
3. Explain basis risk using a commodity hedge as an example.
4. Why can a reported private-equity IRR be misleading?
5. Identify three risks associated with digital assets.

Long Answer Questions

1. Explain the economic uses, pricing foundations and principal risks of forwards, futures, options and swaps.
2. Discuss how derivatives can reduce risk while simultaneously creating leverage and liquidity risk.
3. Compare real estate, commodities and infrastructure as alternative investments.
4. Evaluate the benefits and limitations of hedge funds and private equity in a diversified portfolio.
5. Explain how governance, valuation and regulation should shape an institutional derivatives programme.

Analytical / Application Questions

1. An importer must pay USD 2 million in six months. Explain how a forward, a currency future and a call option would produce different risk and cash-flow outcomes.
2. A pension fund invests in an illiquid private fund while also writing derivative contracts requiring margin. Analyse the interaction between valuation risk, redemption risk and funding liquidity.
3. Design a risk-control framework for a utility using futures, swaps and options to hedge fuel costs. State the information, limits and stress tests required.

Multiple Choice Questions with Answers

Question 1

Which feature most clearly distinguishes a futures contract from a forward contract?

A. A futures contract always has an option-like payoff.

B. A futures contract is standardized and generally marked to market daily.

C. A futures contract has no underlying asset.

D. A futures contract can only be used for currencies.

Correct Answer: B. A futures contract is standardized and generally marked to market daily.

Question 2

A long call option with strike price K has an expiry payoff of:

A. max(K − S_T, 0)

B. S_T + K

C. max(S_T − K, 0)

D. K − S_T in all cases

Correct Answer: C. max(S_T − K, 0)

Question 3

An importer expecting to pay USD in three months is most directly protected against a dollar appreciation by:

A. Buying dollars forward

B. Selling dollars forward

C. Buying a put on domestic currency only

D. Shorting a domestic equity index

Correct Answer: A. Buying dollars forward

Question 4

In a plain-vanilla interest-rate swap, the notional principal is normally:

A. Exchanged at every payment date

B. Used to calculate payments but generally not exchanged

C. Equal to the swap’s market value

D. Always zero at inception

Correct Answer: B. Used to calculate payments but generally not exchanged

Question 5

If a property has normalized NOI of 600,000 and a capitalization rate of 6%, the simplified value is:

A. 10,000,000

B. 3,600,000

C. 100,000

D. 36,000,000

Correct Answer: A. 10,000,000

Question 6

Which risk arises when a futures contract does not move perfectly with the asset being hedged?

A. Basis risk

B. Settlement-free risk

C. Dividend certainty risk

D. Principal repayment risk

Correct Answer: A. Basis risk

Question 7

A major liquidity risk in private equity is that:

A. Investors can always redeem daily at market price

B. Capital may be committed for years and exits may be difficult

C. The investment has no valuation uncertainty

D. All returns are paid as fixed interest

Correct Answer: B. Capital may be committed for years and exits may be difficult

Question 8

For a long protective put, the principal benefit is that it:

A. Eliminates the option premium

B. Provides downside protection while retaining upside in the asset

C. Guarantees a profit regardless of the asset price

D. Requires the investor to sell immediately

Correct Answer: B. Provides downside protection while retaining upside in the asset

Question 9

Which measure is most directly concerned with the ability to meet a derivative margin call?

A. Funding liquidity

B. Accounting depreciation

C. Market capitalization

D. Dividend payout ratio

Correct Answer: A. Funding liquidity

Question 10

A stablecoin should not automatically be assumed to be risk-free because it may face:

A. Guaranteed redemption at all times

B. Reserve, custody and run risks

C. No legal or operational exposure

D. Only equity-market risk

Correct Answer: B. Reserve, custody and run risks