The Derivatives-on-Line Pages

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Stock index futures

The stock index follows the value of a hypothetical portfolio. Such indices are the S&P500, the NASDAQ, the FTSE100 or the NIKKEI225. Most of these indices are portfolios weighted according to the market capitalization of their companies. An exception is the

NIKKEI225, where the weighting is done according to the prices. Dividend payments and other incomes are not included in the normal indices, the total return index includes dividend payments and assumes that they are reinvested in the market portfolio. Futures contracts on indices are settled in cash, not by delivering all stocks underlying the index.

Since the stock index consists of just a hypothetical portfolio, in theory all investors are able to replicate it. Therefore the underlying asset of the futures is indeed a marketable asset.

3.1 In most countries --in particular in the U.S.-- the stock index is viewed as an asset that pays a continuous dividend yield. In other countries companies tend to pay dividends at around the same time in the year, then the index can be treated as an asset that provides a known income. Note here that future dividends are announced in advance hence the known income assumption.

The above, together with the assumption that forwards and futures have the same price, imply the following pricing relationship

$\displaystyle F\left( t,\tau \right) =S\left( t\right) e^{\left( r-q\right) \left( \tau -t\right) }\text{.} $

If the above relationship does not hold, arbitrageurs can engage into the index arbitrage. For instance, if $ F\left( t,\tau \right) >S\left( t\right) e^{\left( r-q\right) \left( \tau -t\right) }$ they can replicate the index portfolio by buying all the index stocks in the index proportions and short a futures contract.

next up previous contents
Next: Hedging using index futures Up: Futures and Forwards Previous: Forwards vs futures   Contents
Kyriakos 2003-03-17