Estimated study time: 45 minutes
Content:
Futures and forward contracts are linear derivatives used extensively in portfolio risk management for their capital efficiency, liquidity, and precision in adjusting exposures. Unlike options, futures and forwards have symmetric payoffs — gains on one side equal losses on the other. They are used to modify duration, equity beta, currency exposure, and commodity exposure without buying or selling the underlying assets.
Equity futures are used to adjust portfolio beta. The number of futures contracts needed to change portfolio beta from β_P to β_T (target) is: N = (β_T − β_P) × (V_P / V_F), where V_P is portfolio value and V_F is the value of one futures contract (futures price × multiplier). To increase beta, buy futures (long); to decrease beta (including hedging to zero), sell futures (short). Portable alpha strategies use futures to separate alpha from beta: invest the portfolio in an alpha-generating strategy (e.g., long-short equity) and use equity index futures to overlay the desired market beta separately.
Fixed income futures are used to adjust portfolio duration. The number of contracts needed: N = [(D_T − D_P) × V_P] / (D_F × V_F), where D_T is target duration, D_P is portfolio duration, D_F is the futures contract duration (typically the cheapest-to-deliver bond's duration), and V_F is futures contract value. Sell futures to shorten duration (rates rising view); buy futures to extend duration (rates falling view).
Forward contracts are OTC (over-the-counter) instruments with no standardized specifications and no daily mark-to-market settlement (unlike futures, which are settled daily through variation margin). Forwards are used when customization is required — specific settlement date, custom notional amount, or currency pair not available in futures markets. The credit risk (counterparty risk) of forwards is higher than futures (which are cleared through a central counterparty).
Stock index futures can also be used to synthetically replicate equity exposure — "equitizing" cash. A manager who receives a large cash inflow can immediately buy equity index futures to gain the equity market exposure while investing the cash in Treasury bills. Total return = T-bill return + equity futures return ≈ equity index return. This "equitize cash" strategy is used while the manager gradually deploys cash into the actual equity portfolio, avoiding cash drag.
Futures pricing and basis: Futures price = Spot price × e^(r−d)T (continuous compounding) or (1+r)^T / (1+d)^T using discrete compounding, where r is the risk-free rate and d is the dividend yield (or convenience yield for commodities). Basis = Spot − Futures. Basis risk arises when the asset being hedged is not the same as the futures contract underlying — for example, hedging a corporate bond portfolio with Treasury bond futures.
Key Terms:
Quiz Questions:
Q1. A portfolio manager has a $50 million equity portfolio with beta 1.2. She wants to reduce the beta to 0.8 using S&P 500 futures contracts. Each contract has a notional value of $250,000. How many contracts should she sell?
A) 80 B) 160 C) 200 D) 240
Answer: A — N = (β_T − β_P) × (V_P / V_F) = (0.8 − 1.2) × ($50M / $250,000) = −0.4 × 200 = −80. The negative sign means sell. She should sell 80 contracts to reduce beta from 1.2 to 0.8.
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Q2. A fixed income manager wants to extend her portfolio's modified duration from 4.5 years to 7.0 years. The portfolio has a market value of $100 million. The T-bond futures contract has a modified duration of 8.5 years and a contract value of $100,000. How many contracts should she buy?
A) 29 B) 294 C) 53 D) 250
Answer: B — N = [(D_T − D_P) × V_P] / (D_F × V_F) = [(7.0 − 4.5) × $100M] / (8.5 × $100,000) = $250M / $850,000 ≈ 294 contracts. Buy 294 futures contracts.
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Q3. A "portable alpha" strategy using equity futures is best described as:
A) A long-only equity strategy that uses index futures to reduce transaction costs B) Investing portfolio capital in an alpha source (e.g., market-neutral fund) while separately buying equity index futures to maintain desired market beta exposure C) A futures overlay that removes all active management from the portfolio D) Selling equity futures to harvest alpha from short positions
Answer: B — Portable alpha separates the two return sources. The "alpha engine" (e.g., a long-short equity fund, a fixed income active strategy, or a hedge fund) generates excess returns. Equity index futures are layered on top as a "beta overlay" to deliver the total equity market return. The result: total return = alpha source return + equity beta. The alpha is "portable" because it's independent of the beta exposure.
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Q4. A portfolio manager receives $20 million in cash that will be invested in equities over the next three months. To avoid cash drag in a rising market, she uses equity futures to "equitize" the cash. After buying the futures, the portfolio's effective exposure is:
A) $20 million in equities and $20 million in T-bills (total $40 million, which is wrong) B) $20 million in equity market exposure, with cash invested in T-bills providing approximately the equity index return C) $20 million in T-bills only, with the futures providing downside protection D) Zero net exposure, because futures are offset by the cash position
Answer: B — By buying futures, the manager gains equity market exposure ($20M notional) immediately. The $20M cash is invested in T-bills. Total return ≈ T-bill yield + equity futures return = equity index total return (approximately, because futures prices already reflect the T-bill rate through cost-of-carry). This eliminates the cash drag during the deployment period.
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Q5. The key difference between a forward contract and a futures contract with the same underlying and settlement date is:
A) Forward contracts have higher counterparty risk because they are not marked to market daily and are not cleared through a central counterparty B) Futures contracts are more customizable in terms of notional amount and settlement date C) Forward contracts are exchange-traded; futures are OTC instruments D) Futures contracts do not require collateral, while forward contracts require full collateral
Answer: A — Futures are standardized, exchange-traded, and cleared through a central counterparty with daily mark-to-market. This eliminates counterparty risk. Forwards are customizable OTC contracts with no centralized clearing and no daily settlement — they accumulate gain/loss until settlement, creating counterparty credit risk. Futures are less flexible but lower counterparty risk; forwards are more flexible but carry counterparty risk.
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