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Equities

Equities · E5 · 9 min

Equity forwards and futures

Work out what an index future should cost, say what to do when it costs something else, and size a futures hedge for a portfolio.

In the news: “FTSE futures point to a lower open”: what an index future is worth, and why it can trade below the index.

The essentials

Index future
An agreement to buy or sell an index on a set date at a price fixed today, settled in cash. The FTSE 100 future is worth £10 a point (the E-mini S&P 500, $50), and gains and losses are paid daily as .
Fair value
The index plus the interest saved by not buying the shares, minus the dividends missed. An index at 10,000 with interest at 4% and dividends at 3% gives a one-year of 10,100.
Basis
The gap between the future and the index. When dividends outweigh interest the future sits below the index: at 2% interest and 3% dividends, a one-year future on 10,000 is worth 9,900. The shrinks to zero at expiry.
Index arbitrage
If the future trades above fair value, traders buy the shares and sell the future to lock in the gap; below it, they do the reverse. This keeps futures within a band set by trading costs.
Hedging with futures
Selling futures removes a portfolio’s market risk: £9m with a of 1.2 needs 120 FTSE 100 contracts at 9,000. Stocks that do worse than the index are left unhedged: that is .

Index future fair value

F = S × (1 + (r − d) × t)

S
the index level now
r
the interest rate, % a year
d
the index’s dividend yield, % a year
t
time to expiry in years (days ÷ 365)
All Equities essentials on one page →

How it works

1. A price fixed today for later

A is an agreement to buy something on a set date at a price fixed today. An index future lets you agree now to buy the FTSE 100 in three months at, say, 9,000. If the index is at 9,300 when the future expires, you gain 300 points; at 8,800, you lose 200. No shares change hands: the gain or loss is paid in cash.

2. Two ways to own the index

To own the index in three months, you could buy the shares today with borrowed money: you pay interest, but you collect the dividends. Or you could buy the future and leave your cash in the bank: you earn interest, but you get no dividends. Both end with the same index, so they must cost the same.

3. Fair value: index plus interest minus dividends

So the future should cost the index plus the interest you save, minus the dividends you miss. With the index at 10,000, interest at 4% a year and dividends at 3% a year, a one-year future is worth 10,000 × (1 + 4% − 3%) = 10,100. For three months, take a quarter of the gap: 10,025. This is the future’s .

4. When the future sits below the index

If dividends are bigger than the interest saved, fair value is below the index. With interest at 2% and dividends at 3%, a one-year future on an index at 10,000 is worth 9,900. The gap between the future and the index is the , and it shrinks to zero as the future expires.

5. Arbitrage keeps it close

If the future trades above fair value, a trader can buy the shares, sell the future and lock in the gap at expiry. If it trades below, the trade runs the other way: sell the shares and buy the future. This keeps futures within a small band around fair value, set by the cost of trading all those shares.

6. Contract size and daily margin

Each FTSE 100 future is worth £10 per index point, so at 9,000 one contract is £90,000. (The US E-mini S&P 500 is $50 a point.) You don’t pay that up front. You post a deposit, and every day gains and losses are paid in cash: that is . Ten contracts that fall 50 points cost 10 × 50 × £10 = £5,000 that day.

7. Hedging a portfolio

Selling futures protects a portfolio: if the market falls, the futures gain what the shares lose. Say you hold £9m of shares that move exactly with the FTSE 100, and the future is at 9,000. One contract covers 9,000 × £10 = £90,000, so you sell £9m ÷ £90,000 = 100 contracts.

8. Adjusting for beta

Most portfolios don’t move exactly with the index. measures how much they do: a beta of 1.2 means the portfolio tends to move 1.2% when the index moves 1%. So multiply by beta: £9m with a beta of 1.2 needs 120 contracts. What the futures can’t cover is your stocks doing worse than the index: .

Worked example

Suppose the FTSE 100 is at 9,000, the interest rate is 4.0% and the index’s dividend yield 3.5%. The next future expires in 73 days. You run a £40m UK portfolio with a beta of 1.2 and want to hedge it.

  1. t = 73 ÷ 365 = 0.2 years.
  2. Fair value = 9,000 × (1 + (4.0% − 3.5%) × 0.2) = 9,000 × 1.001 = 9,009.
  3. One contract = 9,009 × £10 = £90,090.
  4. Beta-weighted value = £40m × 1.2 = £48m.
  5. Contracts = £48m ÷ £90,090 = 532.8: sell 533.

Fair value is about 9,009, 9 points over the index; sell about 533 futures to hedge.

Check yourself

8 quick questions on the explanation above.

Practice

New numbers every set. Misses and guesses go into your review deck.

In the interview

Answer out loud in under a minute, then compare.

Remember

F = S × (1 + (r − d) × t)

A future is the index plus interest minus dividends; when dividends outweigh interest, it trades below the index.

Next · E6Delta one: swaps, CFDs and ETFs

Sources

Definitions and maths are standard textbook material; dated facts link to the sources above. Worked numbers are illustrative.