Portfolio Beta Hedge Calculator
How many index futures hedge your portfolio, and what is left unhedged.
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- Free preview: the number of futures contracts in full, with the first rows of each table (up to 3) and a watermarked chart; every other figure is hidden.
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Hedged and unhedged, for index moves
What the hedge does
β × index move for the portfolio; basis, dividends and the portfolio’s own moves away from its beta are left out.
How this was calculated
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For education only, not investment advice: no tool here tells you what to buy, sell or hold. Results use only the figures you enter, the files you load (read in your browser, never uploaded) and the published rules each page names. Check them against your broker's or exchange's own figures, and consider a licensed or registered adviser for advice on your situation.
About the Portfolio Beta Hedge Calculator
A share portfolio with a beta of 1.2 tends to move 1.2% for every 1% the index moves. Selling index futures takes some of that exposure away: the number of contracts is the beta you want to remove, times the portfolio’s value, divided by what one futures contract is worth. This calculator works it out exactly and rounded to whole contracts, the beta left after rounding, the hedge notional, and what the portfolio, the futures and the two together do for index moves from −20% to +20%.
Choose an index future from the presets — the E-mini S&P 500 and Nasdaq-100, the DAX, EURO STOXX 50, FTSE 100, CAC 40, Nikkei 225, TOPIX, SPI 200, S&P/TSX 60 and Nifty contracts, each with its exchange’s multiplier — or type any other. Set a target beta of 0 to hedge the whole beta, or a figure in between to reduce it; a target above the current beta buys futures. As an alternative, it works out how many index puts would cover the same exposure and what they cost.
You type the beta (the Sharpe ratio calculator works one out from your returns) and the prices: no market data is used.
How to use it
- Choose the portfolio’s currency and enter its value and its beta against the index of the futures.
- Enter the target beta: 0 for a full hedge, or the beta you want to keep.
- Choose the index future and enter its price; check the multiplier and the currency, and the exchange rate if the currencies differ.
- Optionally open “Index puts instead” and enter the index level, the strike, the premium and the option’s multiplier.
- Read the contracts to sell, the beta after rounding and the scenario table; then copy the summary or download the table as CSV — with a pass, or after unlocking this result.
Examples
Portfolio $5,050,000, beta 1.5; futures price 1,010, multiplier $250; target beta 0
30 contracts to sell (1.5 × 5,050,000 ÷ 252,500)
Portfolio $1,000,000, beta 1.2; futures 5,000 × $50
4.8 contracts exactly → sell 5; beta after rounding −0.05
The same portfolio, target beta 0.5
2.8 contracts exactly → sell 3; beta after rounding 0.45
Common uses
- Work out how many index futures cover a share portfolio before a period of risk.
- Lower a portfolio’s beta to a target without selling the shares.
- Compare a futures hedge with buying index puts.
- See how much a hedge over- or under-covers after rounding to whole contracts.
The formulas
- Contracts N* = (β − β) × V ÷ (F × m), where β is the portfolio’s beta, β the target, V the portfolio’s value, F the futures price and m its multiplier. A positive N* is sold, a negative one bought.
- Beta after rounding = β − N × F × m ÷ V with N rounded to whole contracts.
- Hedged change ≈ (β − N × F × m ÷ V) × index move × V.
- Puts instead ≈ β × V ÷ (index level × option multiplier).
These are the hedge-ratio and changing-beta results in Hull, Options, Futures, and Other Derivatives (equation 3.5 and section 3.5) and its portfolio-insurance chapter.
Reading the results
- Contracts to sell are rounded to the nearest whole contract; the exact figure shows how much rounding changes.
- Beta after rounding is the exposure left: −0.05 means the hedge slightly over-covers the portfolio.
- The scenario table shows the portfolio’s change (β × the index move), the futures’ profit or loss and the sum. It is a beta model: a real portfolio also moves for its own reasons.
- Puts limit the fall below their strike while keeping the gains above it, for the premium you pay now.
What it leaves out
The basis between futures and spot and the dividends of the index, which change what the hedge earns; the margin the futures need; the portfolio’s own risk (beta only measures the part that moves with the index, and it is estimated from the past); changes in beta over time; the exchange rate when the futures are in another currency; rolling the futures before expiry; and the strike a put needs for a given floor on a portfolio whose beta is not 1.
Limitations
- Beta is typed by you; it comes from past returns and can change.
- The scenarios use beta alone and leave the basis, dividends and the portfolio’s own moves out.
- One futures contract type at a time.
- It calculates from your numbers and uses no market data: it says nothing about where any price is going.
Privacy
Everything happens in your browser. What you enter or open here is not uploaded or stored by MySmartCoPilot. Downloads the ECB’s daily reference exchange rates when you ask for them; the amounts you enter are never sent.
Frequently asked questions
What do I get without a pass?
Without a pass, Portfolio Beta Hedge Calculator shows the number of futures contracts in full, with the first rows of each table (up to 3) and a watermarked chart; every other figure is hidden. Until you unlock it, the result can’t be downloaded or copied. A Pro, Premium or Ultimate pass, a one-time payment that never renews, unlocks the full result. The pricing page lists the passes and their prices.
How many futures contracts do I need to hedge a portfolio?
Beta × portfolio value ÷ (futures price × multiplier). Hull’s example: 1.5 × $5,050,000 ÷ (1,010 × $250) = 30 contracts.
What if the hedge is not a whole number of contracts?
Round it to whole contracts and check the beta that is left. 4.8 contracts rounded to 5 leaves a beta of −0.05: the hedge is a little larger than the exposure. A smaller contract, such as a micro, gets closer.
Can I hedge only part of the beta?
Yes: set a target beta. To bring a beta of 1.2 down to 0.5 on $1,000,000 with 5,000 × $50 futures, sell 2.8 contracts, which rounds to 3 and leaves a beta of 0.45.
Where do I find my portfolio’s beta?
From the regression of your portfolio’s returns on the index’s. The Sharpe ratio calculator works it out from returns or prices you paste, or your broker may show it.
Is buying index puts better than selling futures?
They do different jobs. Selling futures removes both the losses and the gains of the beta part; puts remove losses below the strike and keep gains, for a premium paid now. The calculator shows how many puts match the exposure and what they cost; it does not say which to use.