A $150 million cash inflow arrives in 18 days. For those 18 days, the cash earns the risk-free rate while equities rally 3.2%. The opportunity cost: $4.8 million, more than the portfolio's annual management fee. A single equity futures trade on day one would have captured the return.
Number of contracts = (Target beta - Current beta) / Futures beta x (Portfolio value / (Futures price x Multiplier))
HIGH-FREQUENCY: This formula appears in nearly every L3 derivatives item set. The sign convention matters. Target beta > Current beta = buy futures (positive). Target beta < Current beta = sell futures (negative). Target beta = 0 = full equity hedge.
Futures beta is not always 1.0. If the portfolio tracks the Russell 2000 but the futures contract is on the S&P 500, the futures beta reflects that cross-exposure.
When a portfolio expects a cash inflow, buy equity index futures to gain immediate market exposure:
Number of contracts = Target beta x (Cash amount / (Futures price x Multiplier))
Common mistakes
- Forgetting the sign convention. Buying futures increases exposure (beta or duration). Selling decreases it. Target above current = buy. Target below current = sell. Getting the sign wrong produces the opposite of the intended position.
- Ignoring basis risk. If the portfolio holds corporate bonds and the futures reference Treasuries, credit spread changes create tracking error. The hedge works for interest rate risk but not credit risk.
- Using portfolio value instead of the specific asset pool. When adjusting equity beta, use the equity portfolio value, not the total fund value. When adjusting bond duration, use the bond portfolio value. Mixing pools produces wrong contract counts.
Bottom line
- Number of equity futures = (Target beta - Current beta) / Futures beta x (Portfolio value / Contract value); if target beta is 0 it removes all equity exposure, and futures beta is not always 1.0.
- Equitizing (pre-investing) cash creates synthetic equity exposure while cash sits in the money market; the futures must be unwound once the cash is actually invested.
- Duration management with bond futures: Number of contracts = (Target DD - Current DD) / DD per futures contract, using dollar duration (not modified duration) per contract.
- Interest rate swaps add or remove duration: receive fixed adds duration, pay fixed removes it.
Exam shortcut
For beta/duration adjustment calculations, write the formula first and pay attention to the sign. Target - Current in the numerator tells you buy (positive) or sell (negative). For swaps, "receive fixed = long duration" and "pay fixed = short duration." For equitizing cash, the formula is just the beta adjustment formula with current beta = 0. Contract count = target beta x (cash / contract value).
The full lesson (about 4,919 words, 33 min read) adds 2 worked examples, all 12 common mistakes, a self-check, free in the app.
Learning objectives
- swaps forwards futures
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