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Illustrate how equity futures, forwards and swaps can change a portfolio's return and risk profile

CFA® Level III · Derivatives and Risk Management · Swaps, Forwards, and Futures Strategies · L3.DR.2.c

The idea

To move beta, futures needed = ((target beta − current beta) ÷ futures beta) × (portfolio value ÷ contract value), where contract value is price × multiplier. A 100 million portfolio with beta 1.10, target 0.80, using futures at 4,000 with multiplier 250 and beta 1.0, sells 30 contracts. Buying futures against cash equitises it. Equity forwards are the tailored OTC equivalent. In an equity swap, paying the equity return and receiving a fixed or floating rate sheds exposure while keeping the shares, preserving votes and possibly deferring tax. The other side gains exposure without buying. When shares fall, the equity-return payer receives the loss. Traps: forgetting the multiplier, unstable beta and swap counterparty risk.

Formulas

Equity futures needed to change a portfolio's beta

futures needed = ((target beta − current beta) ÷ futures beta) × (portfolio value ÷ contract value)

target beta
the beta wanted
current beta
the portfolio's beta now
futures beta
the beta of the futures contract, often taken as 1
portfolio value
the market value of the portfolio
contract value
the futures price × the contract multiplier

A target beta of zero hedges out market risk, which leaves a return near the risk-free rate, not zero. The hedge is only as good as the beta estimate, so the result carries basis risk.

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