futures questions stock, discount, example, forward

IAmNeil

Questions 1:

Why do we discount dividends at Rf when pricing a forward on stock. For example take a look at example 2 page 30. Is this realy a price that earns the seller the risk free rate? There is a chance they do not get the dividends?
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Questions 2:

a commodity trades at a spot of $100
rf=10%
future val of convenience yeild=$3
according to CFAI, such on page 96
the one year futures price should be
(100*1.1)-3=$107

well wait! if the futures price is 107
a short seller can get $100 now
enter long into the futures
invest at rf for a year and have $110
settle the futures for 107 and net $3 ?????

this would keep happening till the price is 110 ???

Uranus08

To short sell the underlying at the spot you have to borrow the underlying which always has a rate attached to it. Generally when you get the cash for the short it's "restricted" cash that you get paid fed funds on (in the US) which is near nothing (as of right now, never near the RF rate of t-bills). You generally can't trade with this cash unless you want to run a debit/negative margin balance which you'll get charged for.

Essentially, it seems like there would be other costs that would eat away at the $3 until there was no arbitrage.

Edit: Also, I don't know if you can actually short sell commodities (I thought you were talking about stocks above). You'd essentially be buying it from someone at the spot price to sell it at the spot price. I'm not sure if there's an actual commodities lending platform that is based on actual delivery - thus the implementation of futures and forwards.



Edited 1 time(s). Last edit at Monday, March 14, 2011 at 08:11AM by verse214.

maryli

If you sell it short, you have to pay the dividend when it occurs, assuming it's a stock. So, you end up with $107, not $110. Also, you have to put up some margin, so you are not investing the whole $100.