Changing Portfolio Beta with Futures

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

Buy (long) index futures. N^* = (1.4 - 0.6) × V_P / V_F = 0.8 × V_P / V_F > 0. A positive contract count means going long index futures, which raises the portfolio's market sensitivity. Options A and C would lower beta. Option D would add downside protection but not lift beta in the linear CAPM sense.

Q: A fund holds A8 million in ASX equities with\beta = 1.0and wants to raise beta to\beta^* = 1.4. SPI 200 is at 8,000 with a A25 multiplier. The required futures position is closest to:

Long 16 contracts. V_F = 8,000 × 25 = A200,000.N^* = (1.4 - 1.0) \times (8{,}000{,}000 / 200{,}000) = 0.4 \times 40 = 16$. The positive sign means long 16 SPI 200 contracts. Shorting would cut, not raise, beta.

Stock index futures let a manager dial portfolio beta up or down without trading any of the underlying stocks. The required position is $N^* = (\beta^* - \beta) \times V_P / V_F$ , where $\beta^*$ is the target beta, $\beta$ is the current beta, $V_P$ is the portfolio value, and $V_F$ 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.

Try it yourself

Minimum-variance hedge ratio

You hold an asset and short futures to offset its price moves. The hedge ratio h is how many units of futures you short per unit of exposure. The variance of the hedged position is a parabola in h, minimised at h* = ρ · σ_spot / σ_futures. The deeper the correlation, the more variance the hedge removes — exactly ρ² of it.

Hedge effectiveness 64%. At h* the hedge removes 64% of the unhedged variance, leaving 0.52 of residual (basis) risk you cannot diversify away.

Hedge ratio h*0.96

Optimal contracts N* (exact)19.2

N* rounded to whole contracts19

Hedge effectiveness ρ²64%

Unhedged variance σ_spot²1.44

Minimum variance at h*0.52

Correlation ρ0.8

σ_spot (spot change std dev)1.2

σ_futures (futures change std dev)1

Exposure Q_A (units to hedge)10,000

Contract size Q_F (units per contract)500

h* = ρ · σ_spot / σ_futures · N* = h* · Q_A / Q_F · Var(h) = σ_spot² + h²·σ_futures² − 2·h·ρ·σ_spot·σ_futuresσ_spot and σ_futures are standard deviations of price changes over the hedge horizon. Effectiveness ρ² is the share of spot variance the hedge removes; the rest is basis risk. Contracts are discrete, so N* is rounded to whole contracts in practice.

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.

Before you read on — recall

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

Formulas

Contracts to move beta from $\beta$ to $\beta^*$

N^* = (\beta^* - \beta) \times \frac{V_P}{V_F}

Positive

N^*

means buy futures (raising beta). Negative

N^*

means sell futures (lowering beta). Source: Hull (2022) §3.5.

Futures contract value on ASX SPI 200

V_F = F \times m

F

is the futures price in index points and

m =

A$25 per point for the SPI 200. For the E-mini S&P 500,

m =

US$50.

Worked examples

Scenario

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

Solution

$V_F = 8{,}000 \times 25 =$ A$200,000. $N^* = (1.5 - 0.8) \times (5{,}000{,}000 / 200{,}000) = 0.7 \times 25 = 17.5$ , 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 $\beta = 1.0$ and wants to cut beta to $\beta^* = 0.6$ during a period of geopolitical tension. SPI 200 future is at 8,500.

Solution

$V_F = 8{,}500 \times 25 =$ A$212,500. $N^* = (0.6 - 1.0) \times (100{,}000{,}000 / 212{,}500) = -0.4 \times 470.6 = -188.2$ , 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 $V_F = F \times m$ . 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
• $N^* = (\beta^* - \beta) \times V_P / V_F$
•No need to trade underlying stocks
•Cheap and fast tactical rebalancing
•Re-size as $V_F$ 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 $\beta = 1.0$ and wants to raise beta to $\beta^* = 1.4$ . SPI 200 is at 8,000 with a A$25 multiplier. The required futures position is closest to:

Connected topics

Beta Hedge

More in Hedging & Basis Risk

Hedge vs Spec Short Hedge Long Hedge Basis Basis Risk Cross Hedge Min Var. HR Tailing

In learning paths

Hedging & Risk Path

Sources

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.
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.
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.
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