Synthetic Cash Position

Can someone please explain intuitively why we need to compound the portfolio value by the risk free rate in order to determine the number of futures contracts to sell?

I’m talking about this formula:

Number of futures contracts to sell = [Portfolio value x (1 + risk free)^t] / (multiplier x futures price)

Why can’t we just use the portfolio value / (multiplier x futures price)


You have to compound it because if you have a cash position, you would earn the risk free rate.

If you didn’t compound the portfolio value, you would not be earning the cash position. Rather, you would be earning nothing! Out of the market.

Hmm, thanks but maybe I’m still missing something.

When creating a synthetic position, don’t you start out with a portfolio of stocks that resemble the index? You didn’t start out with cash so how come we have a cash position that’s earning the risk free rate?

Its synthetic cash. Remove the risk out of the stock. So short it, so that you are delivered virtually the risk-free rate