I am trying to compare ratio backspreads vs naked long options. It easier to work on puts since puts have an upper bound for the gain that is the strike price when the stock drops to 0. I want to compare the fund efficiency: the maximum gain over money put in. With a naked long put, the max gain the the strike and the price of the put is the cost: Kb/Pb, strike of the buy over the buy price. With a backspread, suppose the ratio is 1:2 and the credit/debit is 0. The max gain is Kb and the margin requirement is (Ks-Kb), which is the money tied up, the effective cost, or the investment. The ration is Ps/Pb = Nb/Ns, where N is the number of contracts bought or sold. The return on investment of the backspread is delta*Kb(Ps-Pb). The ratio of returns on investment of the backspread over the long put is therefore simply the delta between the two strikes. That is, as far as return on investment is concerned, the backspread underperforms the naked put since delta < 1. Has someone arrived at a similar conclusion?