IB.3 Futures and Forwards

Discuss some uses of stock index futures

Stock index futures can be used to eliminate the market risk of a portfolio of stocks. Speculation on a bear or bull market is easier to achieve with index futures rather than

incurring the cost of buying or selling a large number of stocks if the quoted futures price is not equal to the synthetic futures price then you can make a (near) riskless arbitrage profit by simultaneously trading in the spot and futures markets on the index.

Define index point and value of an index point

Cash settlement is based on the value of an index point $z (or the contract multiple), which is set by the exchange (e.g. for the S&P 500, z = $250). For the S&P 500 futures the smallest price change, a tick, is 0.1 index points, representing $25 in value, while a one-point change in the S&P 500 futures index implies a change in the face value of the futures contract of $250. If the futures index on the S&P 500 is F0 = 1,500, then the face value of one futures contract is $375,000 (i.e. FVF = z F0).

Describe index arbitrage and program trading

If the equalities above do not hold, then index arbitrage can result in (almost) riskless profits.

In large financial institutions real-time data on r, , T, S and F are fed into computers and when a violation is detected the arbitrage strategy is applied.

Because the arbitrage opportunities are calculated with real-time data using a computer, it is also known as program trading.

There is some basis risk in the arbitrage strategy because the traders only buy (or sell) a proportion of the stocks in the S&P 500, say, so their ‘cash market position’ might not exactly mirror that in the futures index. There are transaction costs and the timing of

dividend payments may be uncertain. Also, it might not be possible to do the trades in the futures and the stock market at exactly the same time and in the meantime the prices of some of the underlying stocks might change.

Calculate a minimum variance hedge ratio for a portfolio of stocks, using futures, given beta

IB.3 Futures and Forwards

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