# Synthetic Cash position

Hi All, Hope someone may be able to explain a concept to me… LOS42b&c They are saying when you are long a stock and then go and sell futures you will pick up the risk free rate over the futures contract period. I don’t understand this as isn’t the value of a futures index = spot (1+Rf)raised to T minus divs. wouldn’t you have to long the stock and a risk free asset?

Wa_Wa, you may want to check out page 343 (first couple of sentences). I was/am still a bit confused by this too.

The concept is correct… When u long the stock and sell the futures… you are giving up your exposure to the ups and downs of the stock in return for the risk free rate…

By selling the future you are receiving the spot price + RfR that is incorporated into the future’s price for T. Think of it this way: selling the future now > selling the future in 6 months The difference being what the RfR would have earned you. The long position in the stock and the short position in the index should theoretically set each other off. Therefore, you should be left with only the RfR. Edit: excluding dividends

Let’s assume a stock pays no dividends and you initially invest in a stock which price is S0. Futures price is F, expiration T. Notice that the fair price of a future contract should be F = S0*(1+rfr)^T. Now let’s assume that you sell a futures contract and buy a stock, and at expiration the stock price is ST. long futures contract payoff is ST-F, and since you are short it is F-ST for you. long stock payoff is ST. Overall position payoff is F-ST+ST=F-S0=S0*(1+rfr)^T You invest: S0 at time 0 You receive: S0*(1+rfr)^T at time T regardless of ST