0

Imagine you want to use periodic cashflows to purchase deep-in-the-money LEAPS (>1yr expiration calls) on SPX, but the size of the cashflows are too small to do so consistently (the cost of such a call is too high). Is it possible to effectively lower the cost of the LEAPS? In other words, could you approximate a call on XSP (which is 1/10th the size of SPX) using only SPX options?

Please note that this question is purely academic. If I were actually buying LEAPS I would almost certainly use SPY calls. So answering “just use XSP/SPY/ES options” is not helpful; this question is about the math. Assume SPX is the only option chain you have access to. I am also not looking to increase or decrease relative risk or return profiles, the aim would be to pay 1/10th of the price for 1/10th of the return, much like a call on XSP.

Let’s also ignore transaction costs and commissions. Here is what I have come up with, but I have no idea if it would actually work:

I’m sure there’s a better word for this, but basically it’s a “synthetic synthetic call”. My understanding is as follows—a synthetic call is created by combining shares of the underlying with a long put for the same amount of shares. So you wind up with unlimited upside, and downside protection to a degree determined by the cost of the premium of the put, much like a call option (but with way less leverage for the buyer).

Meanwhile a synthetic long is created by going long a call and short a put at the same strike. The price of that position moves almost in tandem with the underlying (but with way more leverage for the buyer). Since SPX is a cash-settled index, though, there is no actual underlying.

So this position would be composed of three legs: a synthetic long and a long put. The long put would be at a slightly lower strike than that of the two contracts composing the synthetic long.

So I think the maximum loss should be proportional to the spread between the synthetic long’s strike and the strike of the put. And by placing cash collateral into the account equal to that maximum loss (and including that collateral in the in the calculation of the overall position’s size), you’d have limited your downside to 100% of the investment without capping your upside, much like a call, but you could scale the size of the position by adjusting the spread between the strike of the synthetic long and the protective put.

This has started to come together in my mind, but I can’t shake the feeling that there’s a fatal flaw somewhere in my logic, because I haven’t been able to find reference to a strategy such as this one (I might just not know the right terms to search for, though). Thoughts?

1 Answer 1

1

Your "synthetic synthetic call" is just equivalent to a plain SPX call (at the strike of your long put). It does not succeed in "scaling down" to the equivalent of an XSP call.

So I think the maximum loss should be proportional to the spread between the synthetic long’s strike and the strike of the put.

This is incorrect. The maximum loss is the spread between the current SPX price and the put strike (plus the put premium). The strike of the long call and short put in the synthetic long is irrelevant to the risk profile. Any strike (as long as it's equal between the long call and short put) creates the equivalent of a long SPX position.

Here is a somewhat related question.

2
  • Ah, of course! A synthetic long doesn’t care about the strike. Right. That makes this really obvious in retrospect. Really appreciate the response. I don’t actually trade options and it shows! Just interested as I learn more about markets. ~~But what about adjusting the spread between the current price of SPX and the put? Could it actually work to scale it that way?~~ Nevermind, I’m still asking silly questions. I guess it should net to exactly the same cost as a long call at the equivalent strike?
    – Thomas
    Dec 2, 2023 at 21:58
  • Oh yeah, I’m dumb. I just re-discovered adjusting leverage by adding cash and somehow thought it was different.
    – Thomas
    Dec 2, 2023 at 22:46

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .