Index Futures, Replication Costs, and ETF Fees
Summary
The discussion distinguishes the cost of trading an index portfolio from the price of a futures contract on the index. Because an index is a calculated measure rather than a directly traded asset, its forward price is generally derived from the index level, financing, and expected dividends. Costs incurred when buying or rebalancing the constituent stocks affect an investor’s replication strategy; they do not automatically become a cost adjustment to the index futures price.
The answer contrasts this with SPY, a tradable fund that tracks the index and charges a management fee. That fee reduces the fund’s returns, but the response does not derive a futures pricing formula for SPY or fully resolve the proposed fee-adjusted expression. Its practical point is that index futures and ETF shares have different underlying exposures and costs. The note also characterizes futures rolling costs as very small, without providing supporting figures, and should not be treated as a quantitative comparison of total trading costs.
Key ideas
- An index is calculated from constituent securities and is not itself directly traded.
- Replication and rebalancing can incur costs even when the index level has no direct trading cost.
- An index forward price reflects financing and expected dividends under no-arbitrage reasoning.
- An ETF management fee reduces fund returns and is distinct from costs of trading the index constituents.
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Full text
# No-arbitrage arguments: how do additional fees affect futures on an index?
# No-arbitrage arguments: how do additional fees affect futures on an index?
I am considering a fund that replicates the returns of an index minus a fee, using the following case-study my lecturer used regarding SPY:
> In practice, futures and forwards can be written on assets which are not directly tradeable. Consider the E-mini futures contract example on the S&P 500 index, where due to transaction costs it is not possible to invest directly in the index. Now, SPY is a managed fund which replicates the returns on the index minus an $k\approx1\%$ per annum management fee. So, if you denote $X_t$ as the value of the S&P 500, and $Y_t$ as the value of one unit in SPY, then you have $Y_t=X_t\mathrm{e}^{-kt}$. You can then derive the E-mini futures price in terms of the price of a unit of SPY.
Is the no-arbitrage futures price on $Y_t$ just naively $$F_{t,T}=Y_t\mathrm{e}^{r(T-t)}=X_t\mathrm{e}^{(r-k)(T-t)}?$$
If so, what is the justification behind it? Furthemore, I'm thinking that just as how dividend payouts cause a fall in stock price, transaction costs should cause a rise in this index price, which really doesn't make sense.
It feels like I am missing something painfully obvious, but can’t figure it out. I know this is a silly question, so if it has been asked before/it’s common sense please let me know.
## Answer by demully (score 3)
https://quant.stackexchange.com/a/60376
I might have misunderstood the question; but the index is just a weighted-average of its constituent stocks. As such, it does not trade, and thus does not incur any transaction costs. The forward price on said index is just the spot, adjusted for interest-rate versus (expected) dividend basis. Lest there be arbitrage.
Trading all of the stocks to replicate the index might well generate transactions costs (given inflows and outflows), assuming full physical replication. But the transaction costs of rolling quarterly futures are de-minimus. Hence the attraction of futures.
The futures themselves don't need any adjustment for transaction costs, because the index itself doesn't trade, and thus generate costs. The problem is with anyone wishing to replicate the index. So SPX futures have no transaction costs; but SPY (the ETF) does. But nobody trades futures on SPY...
Hopefully, this makes sense. Shout if it doesn't. DEMShown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.