# Futures Pricing

#### El Popino

##### Newbie
3 0
Hi All,

I have now some experience in trading in general and in trading futures.
But there is one thing I do not understand.
I will describe my problem in a simple manner in case there is an easy/known answer and I will give some more details/calculation later if necessary.

When you price a future on a stock, and we assume there is no dividend paid during the period to maturity and we only consider the financing cost in the futures price, you get:
F = P * (1+r)^T
where r is the risk free rate and T is the time to maturity.
I think everybody will agree on that.

So let's say you buy this future. If you wait until maturity, I have no problem. But if you offset your position one period later by selling this same contract, the profit or loss will already be credited on your account. But the financing costs are based on the time to maturity, therefore you should receive this PNL at the maturity of the contract, not when you offset it. Or it should be discounted, no?

So, where am I wrong?

El Popino

#### Shakone

##### Senior member
2,458 665
Hi All,

I have now some experience in trading in general and in trading futures.
But there is one thing I do not understand.
I will describe my problem in a simple manner in case there is an easy/known answer and I will give some more details/calculation later if necessary.

When you price a future on a stock, and we assume there is no dividend paid during the period to maturity and we only consider the financing cost in the futures price, you get:
F = P * (1+r)^T
where r is the risk free rate and T is the time to maturity.
I think everybody will agree on that.

So let's say you buy this future. If you wait until maturity, I have no problem. But if you offset your position one period later by selling this same contract, the profit or loss will already be credited on your account. But the financing costs are based on the time to maturity, therefore you should receive this PNL at the maturity of the contract, not when you offset it. Or it should be discounted, no?

So, where am I wrong?

El Popino

I believe - and there's always a good chance I'm wrong when interpeting posts - that you are considering this 'financing' as something that happens at maturity, when in fact it is not. It's a consequence of the time-value of money.

#### Shakone

##### Senior member
2,458 665
In short, learn where that formula comes from and that will resolve the diffiulty.

#### El Popino

##### Newbie
3 0
In short, learn where that formula comes from and that will resolve the diffiulty.

Hi, thank you for your answer. I know where it comes from but it does not help.
I will put it another way.

Let's say you have 3 accounts.
If I long a 2 months future for 100 (whatever the underlying and its spot price)
And I short this same contract for 100 at the same moment from another account.

Say one month later it is now trading at 110.

I close my long trade and make an instant profit of 10.
And I long this same contract for 110 on the third account.

So basically I am left with a short contract at 100, a long at 110 and my 10 of profit.
I place my 10 in a bank account and let the 2 futures mature.

After 2 months, at maturation, my futures mature and I make a loss of -10. But I get 10 * (1+r) from the bank.

Conclusion: I made 10 * r of profit without investing any money.

I won't describe it, but if the future price falls to 90 instead of rising to 110 after one month, I do the opposite and get to the free lunch.

I hope I was clear enough ..

#### dgdowney

##### Newbie
6 0
Hello,
I think you are confusing realized and unrealized PNL. When you engage in futures trading you are simply taking on a contingent liability as opposed to buying and asset. Each day the future positions - long and short- are marked to market and is taken from the account holding the position that moved unfavorably into the account of the position that moved favorably. This marked to market variation payment is realized PNL. You are able to remove it from your account and do anything you like with it. It is wise to maintain some cash in the account in case the next day the market moved against you and your account is required to 'pay up' the variation amount.

This is different from buying stock for instance where you can purchase the asset and you don't realize PNL until you sell it.

In your example if you buy at 100 in one account and sell at 100 in a second account your net PNL will be zero at any price point. As the realized pnl combined would exactly offset. Trading against yourself , besides being against the rules, is not very profitable.

Best
David

#### dgdowney

##### Newbie
6 0
....with apologies for my poor grammar and typing.

Best
David

#### El Popino

##### Newbie
3 0
Thanks David,

I see, basically you couldn't place the 10 in a bank account because you need them to offset your loss on the short contract. Got it. Thanks for your help!

Best,

El Popino

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