Option Strategy that Bets on S&P 500
In this article, I want to introduce an option trading strategy that bets on the direction of S&P 500 and potentially double your investment every week. Just like what you do in a casino (yes and not really).
The Strategy
The strategy is called credit put spreads. It involves a long position in (buying) a put option and a short position in (selling) another put option with higher strike price. These two strike prices should be close to the current trading price, which is usually referred to as “at the money”. This strategy is bullish — when the price of the underlying assets increases, the strategy will pay a profit.
Let’s take an example to explain how the payoff work. Suppose that SPY is traded at $470.59. A put option that expires in a week and has a strike of $470 has an ask price of $2.85, and a put option that expires on the same date but has a strike price of 471 is traded at $3.23. This strategy will require us to take a long position in the $470 put and a short position in the $471 put. When the position is opened, we buy $470 put at $2.85 and sell $471 put at $3.23. We receive $0.38 per contract, and because we have to trade 100 contracts each time, we will receive $38.
Suppose that a week later, SPY would go up and close at $475. Your long position should expire with no value, as that long position in $470 put gives you the right sell SPY at $470 and you shouldn’t be willing to do that when SPY is actually gonna worth $475. The short position in $471 put shouldn’t worth any thing either for the same reason. So at expiration, the whole position worth $0. What if SPY would go down? What if SPY would stay flat? The cash flows are best summarized in the following table and figure:
From week to week, if SPY goes up, you will earn $38 for every $62 you risk, a return of roughly 61%.
Quite frankly, in the long run, SPY goes up.
In the history, what percentage of weeks do we see SPY go up? SPY has been there for almost 30 years since inception in 1993. The following table summarizes weekly returns (from Friday to Friday) over different time horizons.
Pretty consistent. There is not a valid reason for us to believe the recent higher percentage is going to be persistent. So you have a little better than half of the chance to earn this 61% return. So this is probably gonna work, right? As long as we get more ups than downs, we are more likely to have winning trades.
Can We Optimize it a little?
I will apply the Kelly criterion just as an illustration. There are obviously more mathematics you can use to optimize such a strategy. You can also factoring in possible predictive power of the stock market (note that the probabilities presented in the last section are unconditional). Here I am just taking the probabilities unconditionally.
The Kelly criterion is a criterion for optimal bet size. The optimal percentage of your wealth you should bet on is determined by
where p is the probability of a win, q is the probability of a loss, b is the win/loss ratio. The application of b is a little complicated. b is the wining odds ratio.
In the world of investment, there is an alternative formula:
where a is the fraction that is lost in a negative outcome and b is the fraction that is gained in a positive outcome. We bet $62 and in the case of loss we lose 100% of it, so a = 100%. We will get 61.29% ($38) when price increase. So our optimal size is
Oops, that does not work. A negative result from this criteria means we will need to bet on the other side. If we can improve the winning probability to 65%, Kelly criterion will suggest us to bet about 7.9% of our portfolio each week, but can we?
Verdict
If you are patient enough to reach here, you should probably have seen that this strategy is just not a money printer as we imagined. Or at least it is not as easy as it looks like. Just like what you do in a casino, the odds and winning ratio do not play together to get us the benefit. There are a couple of main “real world problems” that caused this strategy to not work. In “textbook” examples, such a strategy should provide a win/loss ratio of 1, which means investors should lose the same amount as what they win. However, the bid-ask spread in the option market is usually wide, and that takes $12 from us. Just take the $12 as what we pay to play in the casino, and the casino always wins.
