# Hedge

I have question of “complete hedge strategy” as described in FRM books. Optimal number of contracts to short sell is calculated as follows: if you have 1,000 USD portfolio, Beta is 1.3 and S&P index price is assume 50\$ and multiplier is 2 and If you would like to make “complete hedge” (i.e. aim for beta of zero) you should short 13 contracts (calculated as = 1,000*1.3/30*2) but I don’t see how this works in practice. Let’s assume risk free rate (RF) is 5% and Market return (KM) is 11%, then without applying any hedge, my return applying CAPM model would be: 1,000*(5%+(11%-5%)*1.3) = 128 USD. Now, assuming I have shorted 13 contracts i.e. 1,300 USD (calculated as 13*50*2) and assuming my market return is 11%, then my loss will be 143 USD (1,300 * 11%) which I will have to pay because I shorted 13 contracts (I placed bet that share price would be constant and in reality market returned 11% growth). Bottom line is that I have gained 128 USD on my portfolio and lost 143 USD on my futures hedge. My net loss is 15 USD. My question is - how is the loss of USD 15 a “complete hedge”? Should not it be the case that compete hedge leads to 5% return - which is the risk free rate of return?