How Cash Returns Affect Index Tracking with Futures
Summary
The document explains why holding futures with notional exposure equal to an index mandate may still fail to track the index. A futures position reflects financing and expected dividends through its cost of carry, while the investor also holds cash. Tracking therefore depends on how the cash earns interest relative to the financing rate embedded in futures prices, as well as changes in dividend expectations and implied repo rates.
The cited discussion identifies further sources of slippage: initial margin, bid-offer spreads, and commissions when rolling contracts. It also reports a period in which a futures roll index lagged a gross total return index, attributing the gap to a futures implied repo rate that moved below zero. The example is a conceptual explanation rather than a full tracking-error calculation; actual results depend on financing terms, cash management, margin requirements, and trading costs.
Key ideas
- A futures position embeds exposure to financing costs and expected dividends.
- Cash yield can differ from the rate assumed in futures pricing, creating return slippage.
- Margin requirements and contract-roll trading costs can further reduce tracking performance.
- Changes in implied repo rates can cause futures returns to diverge from a total return index.
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# Track an index with futures only: what to do with the cash? # Track an index with futures only: what to do with the cash? Suppose your mandate is to track S&P500. Suppose the mandate size is $ 1,352,500. The contract size of the future is 50, today's index price is 2705. If I buy 10 contracts my exposure will be exactly similar as the fund's size. (to simplify imagine you don't have to post margins for counterparty risk). Apparently doing this would still result in a high tracking error because of the cash position, I don't understand this, can someone explain? ## Answer by 0xFEE1DEAD (score 2) https://quant.stackexchange.com/a/42363 This should help: > [A] long position in a futures contract implies a short position in dividends and repo rates, as reflected by the minus signs in the futures pricing equation for the dividend and repo rate terms. This means that any decline in dividend expectations and/or repo rates increases the value of futures contracts, all other things being equal. In the same way, any rise in dividend expectations and/ or repo rates reduces the value of futures contracts. [...] The futures roll index ignores some real-life costs faced by investors. First, a futures buyer may not be able to earn interest at a rate that matches the rate used in the futures cost of carry calculation. Any shortfall in interest earned, by comparison with the interest expense assumed in the futures calculation, will result in return slippage, vis-à-vis the index, for the futures buyer. Second, the futures roll index assumes that no initial margin is payable on a futures position. Third, the roll index ignores the effects of bid-offer spreads and commissions payable when futures are rolled each quarter. [...] In the last two years, however, the return on the futures roll index has lagged that of the Euro STOXX 50 gross total return index by 94 basis points a year. Why? The reason is a fall in the futures implied repo rate (the third component of the futures cost of carry calculation) into negative territory. Source: http://www.lyxor.com/uploads/tx_bilyxornews/140120-BRO-ETF-Swap-Future-HD-internet_02.pdf
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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.