# Deviation between spot price and implied spot price of S&P500 mini-futures

From Derivatives Markets (McDonald) it is stated that we may price a financial forward and, equivalently, get an implied spot price from a given futures price: $$F_{0, T}=S_0e^{(r-\delta)T} \implies S_0=\frac{F_{0,T}}{e^{(r-\delta)T}}$$ Applying this to S&P500 mini-futures however, I observed a deviation in the actual and implied spot price when the market was open:

My intuition tells me this may be due to transaction cost as if not I believe there is an arbitrage opportunity, but I am unsure.

Why could this be?

• A small point about the chart: the next 3 fute expirations are mid-june, mid-sep and mid-dec. There is no future expiring in mid-may and therefore that point in the chart is meaningless, should not be there IMO. May 20, 2022 at 20:14
• @nbbo2 The mid-may is the (current) spot-price from yesterday. Apologies for not clarifying. May 20, 2022 at 20:18
• You treat rates and dividends as if they would simply be the same throughout: Dividends are not paid constantly; interest rates are not constant either. so you need a swap curve to get exact rate for the expiry date plus the exact dividends and use appropriate daycount (Act/360 for rates for example). You still have bid and ask to take into consideration for any arbitrage opportunity (plus transaction costs and weather you can borrow invest at the risk free rate if needed). May 20, 2022 at 22:32
• The most obvious indication that your inputs are wrong is that taking r-d with r>d will result in F>S and not F<S as you screenshot suggests. May 21, 2022 at 1:13
• @AKdemy Interest rates and dividends are both transformed to be continuously compounding. Dividends are prone to only some seasonality as we are dealing with an index, and getting the exact interest rate makes little difference. It would be great if you could point more concretely to some factors as these are only marginal. May 21, 2022 at 10:57