Arbitrage on Futurs - Stocks with Dividends

[Tim Hortons]

Jam C-14

For this example to work, aren't we assuming that the stock does grow at r-d to calculate the dividend payout (the integral part)? Because that may not happen, this does not seem to me to be a risk free profit.

[FoxtrotFool]

I think the idea is that arbitrage is only based on the pre-conditions. In the example, the assumption of dividends is build in.

A similar example is binomial pricing tree. Let's say that you have build a arbitrage based on a specific tree, you can't turn around and say that this is not risk free because the stock might not ended up as one of the two prices pre-determined by the tree.

For a stock, the dividend amount doesn't really mean too much, other than you are realizing some of the stock price (by converting into cash). So any stock model has to specify dividend conditions in order to be useful.

[chucky almendinger]

You've bought the index at time 0. You do nothing with it but hold it and invest any dividends you recieve from it. You're risking that the dividends and investment income won't accumulate to 5.23 - the amount you'd have to add to the 510 from future sale to pay back the loan. I agree, it aint a sure thing, but in some of these "arbitrage free" models, we have to treat it like it is. See the whole Arbitrage Pricing Th in investments ch 11. I tried to follow some of those, and they assume that beta determines everything with a portfolio.

[zapped]

i have feared that this type of question would come up on the exam. but the more i think about it, the more it seems too time consuming. any time you have to pull something out of the sky to create an arbitrage opportunity, it takes too much time to create the thought. hopefully the SoA is aware of this. besides, i don't remember may problems like this in the text. and they don't test from the JAM (unless Carmody writes the question - and he's on the exam committee). they did have some arbitrage problems in the text, but the solutions were far more obvious.