Contracts: Long and Short Positions

[tukeywilliams]

I know that the payoff from a long position in a forward contract on one unit of an asset is ( S_T - K ) and the payoff from a short position in a forward contract on one unit of an asset is ( K-S_T )

I am not sure that I really understand this. Why, for example, does the value of a long position become positive, and the value of a short position become negative if the price of the asset rises sharply?

Thanks

 

[Christian]

First, it's important to understand what a short position is. You are borrowing a security from a broker, and selling it, then hoping the later you can buy it back for a cheaper price to pay back the broker and keep the difference.

For example, let's imagine that we have an account in US dollars. Let's say that presently, one contract of euros costs $130,000, but we think that in the future, the cost of one contract will go down to $120,000. So, we borrow one contract from our broker, and sell it at the current market price. Lo and behold, our speculations were correct, and one week later the cost of one contract has dropped to $120,000.

Since we owe our broker (who we originally borrowed the contract from) one contract, we buy it at the market price of $120,000 to return to him, and pocket the $10,000 difference.

Now, imagine if one week later the price had actually RISEN to $140,000. We still owe our broker one contract, and now it's going to cost us an additional $10,000 to buy it in the market.

That is why the value of a short position decreases as the price of the asset increases.