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Hedging & Basis Riskadvanced

Portfolio Beta Hedging

Portfolio beta hedging uses stock index futures to neutralise the systematic risk of an equity portfolio without selling any underlying stocks. The Capital Asset Pricing Model implies that a portfolio with beta β\beta moves on average by β\beta for every one unit move in the market. To remove that exposure, the manager shorts N∗=β×VP/VFN^* = \beta \times V_P / V_F index futures, where VPV_P is the portfolio value and VFV_F is the dollar value of one futures contract. In Australia, ASX SPI 200 futures at A$25 per index point are the standard instrument.

Why it matters

An equity portfolio carries two layers of risk. Systematic risk moves with the broad market, and idiosyncratic risk is specific to the individual stocks. Selling index futures removes the systematic layer because the futures pay off in proportion to the market index. The idiosyncratic layer is unchanged. A manager who anticipates a market wobble can short SPI 200 futures to park the systematic risk for days or weeks, then unwind without disturbing the underlying portfolio.

Formulas

Contracts to fully hedge market risk
N∗=β×VPVFN^* = \beta \times \frac{V_P}{V_F}
VPV_P is portfolio value and VF=F×mV_F = F \times m is the dollar value of one futures contract, where FF is the futures price and mm is the multiplier. For ASX SPI 200, m=m = A$25 per point. Source: Hull (2022) §3.5.
Contracts to reach target beta $\beta^*$
N∗=(β∗−β)×VPVFN^* = (\beta^* - \beta) \times \frac{V_P}{V_F}
Setting β∗=0\beta^* = 0 recovers the full-hedge case. Negative N∗N^* means short futures; positive N∗N^* means long futures.

Worked examples

Scenario

An Australian super fund holds an A$10 million ASX 200 portfolio with β=1.2\beta = 1.2 relative to the ASX 200. The SPI 200 future trades at 8,000 with multiplier A$25 per point, giving VF=8,000×25=V_F = 8{,}000 \times 25 = A$200,000 per contract. The fund wants to fully neutralise market risk for one month.

Solution

N∗=1.2×(10,000,000/200,000)=1.2×50=60N^* = 1.2 \times (10{,}000{,}000 / 200{,}000) = 1.2 \times 50 = 60. The fund shorts 60 SPI 200 futures. If the ASX 200 falls 5%, the portfolio loses about $1.2 \times 5\% = 6\%$ or A$600,000, and the short futures position gains roughly $60 \times 8{,}000 \times 0.05 \times 25 = $ A$600,000. The two offset and only stock-specific risk remains.

Scenario

A pension fund holds A$50 million in Australian equities with β=0.9\beta = 0.9. It wants to dial beta down to β∗=0.5\beta^* = 0.5 ahead of an RBA meeting. The SPI 200 is at 8,500.

Solution

VF=8,500×25=V_F = 8{,}500 \times 25 = A$212,500. N∗=(0.5−0.9)×(50,000,000/212,500)=−0.4×235.3=−94.1N^* = (0.5 - 0.9) \times (50{,}000{,}000 / 212{,}500) = -0.4 \times 235.3 = -94.1. The fund shorts 94 SPI 200 futures, cutting the market-driven part of its portfolio variance in half without selling any stocks. After the meeting, the futures can be lifted to restore the original beta.

Common mistakes

  • ✗Beta hedging eliminates all portfolio risk. It only removes systematic risk. Stock-specific or idiosyncratic risk remains, which is why a fully beta-hedged portfolio still moves day to day. A perfectly hedged S&P 500 ETF position would have near-zero residual risk, but a concentrated 20-stock portfolio could move several percent on stock-specific news.
  • ✗Beta is constant. Stock betas drift over time and across market conditions. A 5-year monthly beta may misrepresent the next month's sensitivity, so practitioners often shorten the estimation window when hedge horizons are short.
  • ✗Selling futures means selling the portfolio. The point of futures hedging is precisely the opposite. The underlying portfolio stays intact, so transaction costs and capital gains tax on the stocks are avoided. Only the index future trades.

Revision bullets

  • •Use index futures to hedge market exposure
  • •**N∗=β×VP/VFN^* = \beta \times V_P / V_F** to neutralise beta
  • •ASX SPI 200 multiplier is A$25 per point
  • •Removes systematic risk only
  • •Stock-specific risk remains
  • •Avoids transaction costs of selling underlying stocks

Quick check

To reduce portfolio beta from 1.5 to 0.5 using index futures, a manager should:

An A$20 million Australian equity portfolio has β=1.0\beta = 1.0. The SPI 200 future trades at 8,000 with a A$25 per point multiplier. To fully hedge market risk, the manager should:

Connected topics

Short HedgeChange Beta

In learning paths

Hedging & Risk Path

Sources

  1. Hull (2022), §3.5
    Hull, John C. Options, Futures, and Other Derivatives. 11th ed. Pearson, 2022. ISBN 978-0-13-693997-9.
    Derives the index-futures hedge formula using CAPM and provides worked examples with US S&P 500 futures that translate directly to ASX SPI 200 futures.
  2. ASX, ASX SPI 200 Futures
    Australian Securities Exchange. ASX SPI 200 Futures product brochure. ASX.
    Confirms the A$25 per point multiplier and outlines the contract specifications used in Australian portfolio hedging.
  3. Sharpe (1964)
    Sharpe, William F. Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk. Journal of Finance, Vol. 19, No. 3, 1964, pp. 425-442.
    Original derivation of the CAPM, the source of the beta concept that underpins index-futures hedging.
  4. CME Group, Hedging with E-mini S&P 500
    CME Group. Hedging with E-mini S&P 500 Future. CME Education Whitepaper, accessed 2026.
    Practitioner explanation of beta-based equity hedging that mirrors the Australian SPI 200 mechanics.
How to cite this page
Dr. Phil's Quant Lab. (2026). Portfolio Beta Hedging. Derivatives Atlas. https://phucnguyenvan.com/concept/portfolio-beta-hedging
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