# 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.