Alternative methods of weighting

It is generally considered that capitalization weighted indices give the most accurat indication of the collective movement in corporate asset or liability prices. However two alternative methods of weighting the constituents of equity indices are fowl^,‘equally weighted‘ and ‘price weighted‘. In the case of equally weighted indices, a’ equal amount of money is assumed to be invested in each security in the index Changes in the index thus represent changes in the value of the portfolio. Pri weighted indices reflect the average price of the securities in the index and Chang: in the index represent the average price change of the securities in the index. The Dow—Jones and the Major Market Index of the American Stock Exchange (MMI) a. both of the price weighted form. The FT 30 is a geometric average equally weight index. Only the Major Market Index has a futures contract based upon it.

Equally weighted and price weighted indices give greater relative weight to small company constituents than do capitalization weighted indices. However, in t Dow—Jones, the FT30 and the MMI this influence is negligible because only a f• stocks — all relatively large — are included.

Typically the indices upon which futures and options are based are market capitalization weighted arithmetic means of prices. The two notable exceptions are t Major Market Index, mentioned above, and the Value Line Composite Index in USA. This latter index is calculated as an unweighted geometric mean of constitute share prices. This has a major drawback in terms of derivative valuation, in that it not possible to derive an arbitrage strategy that replicates the returns to this type I index. We will therefore limit our discussion to derivatives on indices that are calculated using market capitalization weighted arithmetic means.

Price indices and total rate of return

It should be noted that the published indices are price indices only. The moveme in the index only reflect movement in the share prices; they take no account of dividends received by shareholders and therefore do not calculate the total rate return.

The exclusion of dividend payments results in the return as measured by movements in the index understating the actual returns to holding a portfolio t replicates that index. To see how this occurs, imagine that company C paid a dividend of 5. On the ex-dividen date the share price will fall by 5 (assuming no tax effects) to 95. The index will to 99.16. Yet the investor gets the 5 in dividend and the overall value of the portfolio has not changed. Thus, when comparing the returns to an index with the returns a portfolio, the influence of dividends upon the index must be taken into account.

Unlike futures contracts which require physical delivery of the underlying financial instrument, equity index futures require cash settlement of the difference between the current and future levels of the index. In practice, because the futures contract is marked to market daily, there is one final marking to market based upon the level of the index when the future expires.

Thus a futures contract based upon an equity index may be defined as: an agreement to make or receive a cash payment based upon the difference between the current and future values of a specified index.

The process of cash settlement avoids the difficulties of delivering the many individual securities that constitute the particular index. It also avoids the risk of the securities being cornered or squeezed. However, it also requires that the index calculation is transparent, reliably accurate and free from manipulation. Moreover, it does introduce difficulties in hedging futures positions with the underlying equities, and thus difficulties in the arbitrage process that is the theoretical basis of valuing such futures.

In order to avoid manipulation of the index for the purposes of calculating the futures expiry price, the procedure adopted by LIFFE is typical. The settlement price, the Exchange Delivery Settlement Price (EDSP), is calculated as the arithmetic mean, after the exclusion of the highest and the lowest levels, of the index levels between 10.10 and 10.30 a.m. on the expiry day. The index itself is recalculated by the Stock Exchange each minute, giving timely adjustments to reflect the movements of the stock market.

Conceptually, the various equity index futures contracts traded around the world are all very similar; therefore, we shall here only describe in detail the LIFFE futures contract on the FTSE 100 index.

The futures contract represents a future claim on a notional index fund with a market value of £25 per index point. Thus with the future standing at, say, 2500 the notional index fund is valued at 2500 x £25 = £62 500. The market quotations have a minimum price movement or tick size of 0.5 of an index point. This tick size represents £12.50 in terms of the monetary value of the FTSE 100 index.

The futures trade on a March, June, September and December cycle, with the expiry dates being the last business day of each delivery month; although as from the June 1992 delivery month, the delivery day will be the third Friday in the delivery month. The contracts are cash settled, with settlement being the first business day after expiry.

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