Assuming that I dedicate 2% of equity to the premium of a long call or put option (Options on SPY), how do I calculate the option parameters (date, strike) so that my position would reflect a 100% equity spot position in the Underlying (SPY)? This would be a way to limit risk per trade to 2% while still having larger market exposure.
As you know, there are many choices of how to arrange such a trade, which is why you posted this question. As you probably also know, there is no universal formula to guide selection among the strikes and expirations, as the decision depends on your market forecast and preferred risk-reward profile. Each possible trade has different exposures to price, time, and volatility risks. Here are a couple of illustrations of factors to consider when making your decision. The current SPY price is (roughly) 92. Suppose you have 92,000 in equity, and you want to risk 2%, or 1,840, on a SPY option trade. You expect SPY to rise in the short term, so you decide to buy call options. With this forecast, you want to benefit from a move upward while reducing time decay. Delta tells us how much the option price will change for a one point change in the share price. The higher the delta, the more the option price gains (or loses) with share price movement. High delta options also have less time premium. You decide to select options with a delta of approximately 0.80. For every 1.00 gain in SPY, your option contract will gain 0.80. Looking at the option table, you see the closest match is the SPY July 86 option, with a delta of 0.79 at an ask price of 6.90. To get the number of contracts to buy, you divide 1,840 by 6.90 to get 2.67. Rounding up, you buy 3 contracts, representing 300 shares, for a total premium of 2,070. Another choice, more risky, is to approximate with options the full amount of equity. First compute the number of shares by dividing the equity by the share price. Dividing 92,000 by 92 gives 1,000 shares. To buy enough option contracts to control 1,000 shares, divide the number of shares by 100 (number of shares per option contract). The result is 10 contracts. The strike price to buy can be calculated by dividing the 2% risk amount, 1,840, by 1000, giving us 1.84. Consult the options table to find a call option priced at approximately 1.84. The closest price in July is the 93 strike, with an ask price of 1.97 and a delta of 0.44. Ten contracts, representing 1,000 SPY shares, will cost 1,970. Note the option price is all time premium. These out-of-the-money options have more risk of time decay, but greater reward in the event of a big move upward. The larger the move, the more closely will the option position approximate full equity of 1,000 shares. To illustrate profit and loss at expiration, if SPY closed unchanged at 92, the first trade would lose 270, whereas the second trade would lose 1,970, the total amount invested. If SPY closed at 97, the first would make 1,230, whereas the second would make 2,030. Buying 1,000 shares would make 5,000. You can, of course, sell your options before expiration. If the price rises soon after you buy, the profit will be higher than the profit at the same price later, at expiration. Obviously these illustrations hardly scratch the surface. Beyond simple call options, spreads offer further flexibility to tailor trades to forecasts.
Is your 2% max a barrier, or are you looking at holding the package - no matter what - until expiration even if the instantaneous loss is more (maybe much more) than 2%? Over what time frame do you want to do this? If I'm making the right assumptions about what you want, it may not be possible, as 2% is far lower than the volatility of pretty much anything worth trading, and you will have trouble finding strikes with that granularity.
The idea was to practially bake the 2% risk per trade rule right into the option premium. This way, a stop loss would not be needed and a trade (days - weeks) would have a chance to run its course. Taking advantage of a longer term trend without having to time the market precisely would be the potential benefit.
Thank you for taking the time to write such a detailed response. It would be too risky to simulate 100% of equity. Best would probably be to start with an analysis of the greeks. It seems that delta > .80 is a must requirement in order to replicate the movement in the underlying.