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In a financial derivatives lecture that I'm watching, the professor brings up an example of where someone might want to use futures. A hedge fund holds a large proportion of Company ABC's shares, which are trading at $100 a piece. They want to clear their position and replace them with zero-coupon bonds that mature in 2 years. So they short a forward contract that expires in 2 years of the appropriate amount.

The professor then mentions that whichever bank is taking the other end of this deal might charge a premium on the forward because they know this hedge fund is smart. One, is that true? And two, why is that true? Isn't there only one formula for the future on equities (the P0 * e^(rt) one)? If there's a deviation, can't someone do the standard arbitrage here and make profit?

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    I have personally never seen a premium being charged for a forward. That's why there is a bid ask spread. You can have margin or collateral requirements but generally, a premium for a froward is something that one would only pay for an unfair forward (that isn't priced at the ATMF), typically throughout the existence of the forward if the counterparty wants to offset the contract.
    – Alex
    Commented Jan 5 at 15:07

2 Answers 2

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That formula is the fair value of a future, which implies no credit risk. A forward is an over-the-counter product where counterparty risk is something to consider - e.g. what happens if the hedge fund goes bankrupt and can't fulfill their side of the forward?

The charge a premium because they can. The hedge fund can either accept or refuse the premium, and can shop around with other banks that might give them a better price. It could be an arbitrage for the bank if they can take an offsetting position with no premium with another counterparty or an exchange.

I'm not sure about the "they know this hedge fund is smart" comment other than that they assume that the hedge fund is taking (or getting out of) their position because of their prediction of the market, so they might try to squeeze a bit of the profit out of their position.

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Because banks are in the business of making money. They provide a service (taking the other side of the forward the hedge fund wants) in return for making a little bit of money on the deal.

Imagine for a moment that I have a $100 bill but I really want to have $100 in my bank account. If we're friends, you'd potentially be willing to help me out and Venmo me $100 in exchange so I don't have to run down to the bank branch to deposit cash. But if you were a business, you'd want to charge a premium. Maybe you'd offer to send me $99.50 for the $100 bill because you expect that the convenience of getting the money in my account immediately is worth $0.50 to me. There would be no business sense in sending me $100 for the $100 bill unless you were offering that service as a loss leader for other services that you were going to charge for. But loss leaders are a problem when dealing with "smart" customers. If I'm running a retail bank dealing with random customers, it makes sense to offer some services for free knowing that customers that have no-fee checking and savings accounts with my bank are likely to get loans from me too without a lot of shopping around. Big hedge funds, though, are always going to shop around to get the best price they can get. If I offer service X for free hoping to build up business for service Y where I charge fees, the hedge fund is going to use me for X and go to someone else that charges for X but has lower Y fees when they need service Y. So if you're dealing with a "smart" customer, it's more likely that you're going to want them to pay as they go.

In this case, there are additional risks that the bank needs to cover in order to make it worth it to take the other side of the deal. The hedge fund might go bankrupt and be unable to make good on its side of the deal so the bank either needs to take on some counterparty risk or pay someone to take on that risk. The bank either needs to hold the forward contract or, more likely, find some other investor that wants to buy the bank's side of the deal. They want to charge something for doing that matchmaking and for the risk that the market moves against them in the time between when they do the initial deal with the hedge fund and the subsequent deal with whoever they sell their side of the contract to. And the bank has to pay the bankers making the deal, rent offices, buy computers, etc. Those are all things the bank would want to make sure they were compensated appropriately for. In our $100 bill example, the "convenience fee" you'd charge would have to cover the risks that my bill was counterfeit, the expenses of running the business, etc.

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