How to calculate leverage when trading futures

[Martinghoul]

Suppose you are offered to play the following game. We flip a coin. If it's heads, you lose your bet. If it's tails, you win twice the amount of the bet. You can play as many times as you want.

The house sets the rule: you may not bet more than 95% of your account. Let's call it the margin rule. Now, the question is, how much should you bet on each flip of the coin? Your answer would determine your leverage.

Yes, sure...

I think maybe there's a misunderstanding here somewhere. When I talk about "margin", I am really referring to "margin requirement". To use your terminology, the house has a rule that, in order for you to participate in the game you've described, where you bet $1 for every flip of the coin, you need to put, say, $20 into an escrow account held at the exchange. This $20 is an absolute amount that has nothing to do with your account size, a priori.

 

[Martinghoul]

Could be but without actually running the numbers I can't tell. You see, if your account is let's say 10K, and ES margin is $4600, you are already maxed out on ES. Now if the Eurodollar margin is $5100, you can only trade 1 contract, but your leverage is still far less than using 2 ES.

Hold on a moment...

My question wasn't about margin. I was asking about what happens if I apply your formula.

Case A: 2 ES contracts: leverage = 2 x 2473 x $50 / Acct Size
Case B: 1 GEU7 contract: leverage = 1 x 98.655 x $2500 / Acct Size

These quantities are very similar, if my arithmetic is correct. Does that mean that my account would be as leveraged in case A as in case B, according to your definition of leverage?

 

[Pekelo]

Does that mean that my account would be as leveraged in case A as in case B, according to your definition of leverage?

Yes...

Also, since NQ's 1 point is $20 and the value is almost 6000, that makes its notional value almost the same as ES's. So if you trade 2 ES, you have to trade 5 NQs to have the same leverage.

Basically you can hedge ES with NQ if you use the 2:5 ratio...

 

[Martinghoul]

Yes...

Also, since NQ's 1 point is $20 and the value is almost 6000, that makes its notional value almost the same as ES's. So if you trade 2 ES, you have to trade 5 NQs to have the same leverage.

Basically you can hedge ES with NQ if you use the 2:5 ratio...

Ah, that's fine, then...

If this is the case, then your notion of "leverage" isn't really all that useful, at least not to me. I know, just from simple common sense, that leverage characteristics of the two cases I've given are extremely different. This is further corroborated by the different margin requirements that CME computes for them. Using your formula produces estimates of "leverage" which make no relative sense.

I will not be nominating you for a Nobel. Sorry, mate.

 

[lindq]

Because your position sizing should not be determined by the margin, but rather by the quality of your trading system.

The famous last words of an over-leveraged and busted trader:

"BUT IT WAS SUCH A GREAT SYSTEM."

 

[HobbyTrading]

I have seen quite a few times people calculating the leverage using notional value of the index, when it is rather irrelevant to the correct calculation. It is your account size and the number of contract that affects the leverage mostly. Bigly, if I might say so. Leverage tells you how much your account moves compared to 1 unit movement of the index. In plain, if the index drops 1% and your account loss is 12%, then your leverage was 1:12...

Since I won the Nobel prize last year in Math, I feel authorized without further much ado, to reveal the formula, free of charge:

Lev=(Ctr # x Index value x Point value)/Account size

Ctr#: number of contracts used
Index value: the current value of the index (ES would be 2473)
Point value: the value of 1 point (ES is $50)
Acc Size: Your account in dollars

Let's see an example. A trader with a 10K account using 2 ES contracts has a leverage of:

(2 x 2473 x $50)/ $10000= 24.7

Extra credit: Just because you are trading futures, you still can under leverage your account, meaning that your account movement can be LESS than the movement of the traded future.

I'm not sure whether I understand both the text and the formula. The text mentions as example a 1% drop in index, resulting in a 12% account value drop. Thus it talks about a relative change. The formula only applies to a 100% drop in index (ES in this case).
I thought that the formula should be something like:
Lev = (Ctr# x (current price - buy price) x Point value)/Account size
Ctr#: number of contracts used
current price: the current value of the index (ES would be 2473)
buy price: the buy value of the index (e.g. ES bought at 2465)
Point value: the value of 1 point (ES is $50)
Acc Size: Your account in dollars

What is it that I'm not understanding correctly?

 

[Pekelo]

I'm not sure whether I understand both the text and the formula. The text mentions as example a 1% drop in index, resulting in a 12% account value drop. Thus it talks about a relative change. The formula only applies to a 100% drop in index (ES in this case).

Well, since apparently I don't have a Nobel prize in math, I am not sure I can explain it but I will try.

The text was just an example, I could have used 2% index drop with a 25% account loss. The idea was with the text to show how leverage works. The formula is for general usage, no matter what the index drop. You are trying to make it for just one particular move, but the leverage is the same as long as you use the same number of contracts with the same account size.

As others pointed out, the formula can be made simpler:

Lev=(Ctr# x Notional Value)/Acct Size

Where the Notional Value = Current Future Price x Point Value

Now the Point Value doesn't change, and the Current Future Price usually changes just a few %, thus we can look at the Notional value as an almost constant component.

So out of the 3 components of the Leverage formula, most of the time only the Contracts used and the Account Size changes, the Notional Value is fairly constant.

 

[Overnight]

...

So out of the 3 components of the Leverage formula, most of the time only the Contracts used and the Account Size changes, the Notional Value is fairly constant.

I do not see how trading futures contracts has anything to so with notional value of the underlying. Please explain.

 

[nonlinear5]

I do not see how trading futures contracts has anything to so with notional value of the underlying. Please explain.

In the formula given by the OP,
Notional Value = Current Future Price x Point Value

The notional value is based on the current price of the futures contract, not the price of the underlying index. The formula is correct.

 

[Overnight]

In the formula given by the OP,
Notional Value = Current Future Price x Point Value

The notional value is based on the current price of the futures contract, not the price of the underlying index. The formula is correct.

I understand notional value. But why in trading a futures contract should it have any bearing on a futures contract trade, assuming we are not holding to expiration of said contract?