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?

  • $\begingroup$ search for index arbitrage. That will explain the difference $\endgroup$
    – LazyCat
    Oct 24, 2018 at 18:43
  • $\begingroup$ You have to put (all or most of) the cash in T-bills, otherwise you will undeperform the theoretical (or arbitrage free) return. The risk free rate is an essential part of the index arbitrage calculations. If your cash does not earn interest you are losing out. $\endgroup$
    – Alex C
    Oct 24, 2018 at 20:00
  • $\begingroup$ Is there any impact due to the fact that the future is bought on margin? If I get 100% exposure via future I will still have say 90% of cash in the fund (say I have to give 10% margin to the counterparty). Is this going to generate tracking error? If I invest all the cash I will be levered a lot and then the returns of the portfolio will be magnified when compared to the benchmark? $\endgroup$
    – tweedi
    Oct 25, 2018 at 14:24

1 Answer 1


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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