# Futures and ETF trading cost

#### Tombata

Hello everybody,
I am making a research on Futures and ETF costs. I have found two formulas, which describe the cost but I do not quite understand them. So I would appreciate your help. Here are the formulas and their description.
"The cost of a futures transaction is the cost of crossing the futures market spread (bid offer of futures=BOf, which is smaller than the bid offer of the cash market for major indexes), plus the roll cost=R multiplied by the number of times you have to roll the position. If you own the position for “T” years and roll over “n” months, then “12T/n” is the number of futures contracts you own and one less than this value is the number of times you have to suffer the roll cost “R”. There is also the carry or running cost of the position which is equal to the funding cost of the margin (percentage of position to be margined=m, and normally you receive a lower rate of interest on the margin rm than implied interest rate of futures price rf), less the borrow cost received=b (as you receive all the borrow cost in the futures market).

Futures cost = BOf + (12T/n - 1) R + m (rf - rm) T - bT

We define the bid offer and roll cost to include all trading and exchange fees, and these two terms are the only terms that do not have to be multiplied by the length of time the position is kept=T (all other costs are a yield, hence have to be multiplied by time to get the cost). We note that rf -rm should be equal to the LIBOR-OIS spread if rf is the LIBOR and rm is an OIS (e.g. EONIA).
The cost of an ETF transaction is the cost of crossing the spread (due to creation/redemption process this is the same as bid offer in cash market=BOc), less the proportion of the borrow cost “b” received (proportion of borrow returned to investor=e, where “e” is usually 60-70 percent or less) plus the ETF fees or expense ratio (E) plus the funding cost of the fully funded position (F). To simplify the calculation the funding spread of the client “F” is defined versus the implied interest rate in the futures market (rf, which is normally close to LIBOR).
ETF cost = BOc - ebT + (E + F) T"
When it comes to the futures formula as I understand it:
BOf - the spread of the future
T - years the position is open
n - futures roll frequency
R - Roll cost, e.i. the spread between the current future and the next future
m - margin in %
rf - interest rate received on the margin (usually Libor, Euribor, etc.)
rm - implied interest rate of the futures price
b - borrow cost received (as you receive all the borrow cost in the futures market)
When it come to the ETF costs:
BOc - spread
ebT - the tracking difference
E - expense ratio of the ETF
F - funding cost of the fully funded position (usually Libor, Euribor, etc.)
Now I have the following question:
1. Are my considerations correct?
2. What exacly is the rm by the futures cost and which value/interest rate should I take?
3. What is b by the futures cost and which value/interest rate should I take?
4. Is ebT by the ETF cost really the tracking difference (TD)? And ist ebT = TD or ebT = TD*T?
Thank you very much for the help and sorry for the long post.

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