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Hedging & Basis Riskadvanced

Changing Portfolio Beta with Futures

Stock index futures let a manager dial portfolio beta up or down without trading any of the underlying stocks. The required position is N∗=(β∗−β)×VP/VFN^* = (\beta^* - \beta) \times V_P / V_F, where β∗\beta^* is the target beta, β\beta is the current beta, VPV_P is the portfolio value, and VFV_F is the value of one futures contract. Long futures raise beta, short futures cut it. On ASX SPI 200 futures the contract value is the index level times A$25.

Why it matters

Think of index futures as a beta volume knob bolted onto the portfolio. The cash equity book remains untouched. Buy futures and the portfolio behaves as if it owned more stocks. Short futures and it behaves as if it owned fewer. Managers use the knob to add equity exposure when new cash arrives, to defensively reduce risk before a known event such as a central-bank meeting, or to tilt tactically toward or away from the market.

Formulas

Contracts to move beta from $\beta$ to $\beta^*$
N∗=(β∗−β)×VPVFN^* = (\beta^* - \beta) \times \frac{V_P}{V_F}
Positive N∗N^* means buy futures (raising beta). Negative N∗N^* means sell futures (lowering beta). Source: Hull (2022) §3.5.
Futures contract value on ASX SPI 200
VF=F×mV_F = F \times m
FF is the futures price in index points and m=m = A$25 per point for the SPI 200. For the E-mini S&P 500, m=m = US$50.

Worked examples

Scenario

An Australian growth fund holds A$5 million with β=0.8\beta = 0.8 and wants to lift beta to β∗=1.5\beta^* = 1.5 ahead of an expected post-RBA rally. The SPI 200 future trades at 8,000 with a A$25 multiplier.

Solution

VF=8,000×25=V_F = 8{,}000 \times 25 = A$200,000. N∗=(1.5−0.8)×(5,000,000/200,000)=0.7×25=17.5N^* = (1.5 - 0.8) \times (5{,}000{,}000 / 200{,}000) = 0.7 \times 25 = 17.5, rounded to 18 contracts. The fund buys 18 SPI 200 futures. The portfolio still owns the same A$5 million of stocks, but its sensitivity to ASX 200 moves rises from 0.8 to 1.5.

Scenario

A super fund holds A$100 million in Australian equities at β=1.0\beta = 1.0 and wants to cut beta to β∗=0.6\beta^* = 0.6 during a period of geopolitical tension. SPI 200 future is at 8,500.

Solution

VF=8,500×25=V_F = 8{,}500 \times 25 = A$212,500. N∗=(0.6−1.0)×(100,000,000/212,500)=−0.4×470.6=−188.2N^* = (0.6 - 1.0) \times (100{,}000{,}000 / 212{,}500) = -0.4 \times 470.6 = -188.2, rounded to 188 contracts. The fund shorts 188 SPI 200 futures, reducing market exposure by 40% without selling a single Australian stock and avoiding brokerage and CGT crystallisation.

Common mistakes

  • ✗You must sell stocks to reduce beta. Index futures deliver synthetic beta adjustments at a fraction of the transaction cost. Underlying holdings stay in place, capital-gains realisations are deferred, and the manager retains discretion over individual stock weights.
  • ✗Buying futures only makes sense if you believe the market will rise. Long index futures raise beta, which is sensible when new cash needs to be deployed, when a benchmark needs to be tracked while a stock selection process completes, or when a manager wants tactical risk-on tilts.
  • ✗The same number of contracts works at any price level. Contract count depends on the current futures price through VF=F×mV_F = F \times m. As the SPI 200 rises, fewer contracts are needed to express the same dollar exposure, so positions should be resized periodically.

Revision bullets

  • •Long futures raise beta
  • •Short futures lower beta
  • •N∗=(β∗−β)×VP/VFN^* = (\beta^* - \beta) \times V_P / V_F
  • •No need to trade underlying stocks
  • •Cheap and fast tactical rebalancing
  • •Re-size as VFV_F changes with index level

Quick check

To increase portfolio beta from 0.6 to 1.4, a manager should:

A fund holds A$8 million in ASX equities with β=1.0\beta = 1.0 and wants to raise beta to β∗=1.4\beta^* = 1.4. SPI 200 is at 8,000 with a A$25 multiplier. The required futures position is closest to:

Connected topics

Beta Hedge

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.
    Develops the $(\beta^* - \beta) \times V_P / V_F$ formula for changing portfolio beta with index futures.
  2. ASX, ASX SPI 200 Futures
    Australian Securities Exchange. ASX SPI 200 Futures product brochure. ASX.
    Confirms the A$25 multiplier used in the Australian worked examples.
  3. CME Group, Hedging with E-mini S&P 500
    CME Group. Hedging with E-mini S&P 500 Future. CME Education Whitepaper, accessed 2026.
    US-market analogue showing how funds dial beta up and down with index futures, identical mechanics to ASX SPI 200.
  4. 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 beta, the theoretical foundation for adjusting portfolio market exposure with index futures.
How to cite this page
Dr. Phil's Quant Lab. (2026). Changing Portfolio Beta with Futures. Derivatives Atlas. https://phucnguyenvan.com/concept/changing-beta
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