Last week, we offered a challenge for our readers at Seeking Alpha: "How Would You Exploit the Future for the S&P 500 If You Knew It?"

In that challenge, we presented a scenario for investors that actually took place in the last week of January 2016, which were based on the series of "If-Then" statements we had outlined a week earlier. After discussing those statements, we laid down the challenge.

Getting back to what we really want to get at, do you see how all these changes in the value of the S&P 500 were specifically covered in our If-Then conditions representing how stock prices would be most likely to behave during the fourth week of 2016?

And since they were, the question of how you as an investor could have taken advantage of the foreknowledge of how stock prices would behave under the circumstances we described, but not the knowledge of the exact timing of when the changes in stock prices we described would take place, is a very open question. One where the strategies you might have used in the fourth week of January 2016 would be very similar to what you might do in future weeks when similar circumstances come back into play.

So what would you have done with your investments to maximize your returns given these circumstances (and the benefit of 20-20 hindsight)? If you're reading this article on Seeking Alpha, we'll monitor the responses addressing that question in the comments over the next week and will share the more interesting strategies that are put forward through that venue in our next discussion of our alternative futures model for the S&P 500.

It's been just over a week since our challenge appeared at Seeking Alpha, and we were very pleasantly surprised by the quality of the comments that were provided.

In particular, ghiblinewt picked up on the degree of difficulty in the challenge from a conventional investing perspective:

As I understand it, knowing the market reaction to a set of events which may or may not eventuate is near meaningless, unless you also happen to know that will occur. Perhaps I'm missing the real question being posed here, but the If-Then proposal gives you no real advantage unless you know that the antecedent will occur.

If you know that one of two (n) possible outcomes will definitely occur however then you could decompose the index space into a bi- (n)-nomial tree and then weighted sum over the multiple paths to arrive at some more probable paths.

But I would suggest that attempting to guess market reaction to specific events is very much a losing game- since the market is already continuously integrating these weightings into its prices- I just don't see that as exploitable in any way. the single most significant piece of information you have about the market is where its just been, of course this means that its not IID, but that's pretty well established.

According to conventional finance theory (think Bachelier, Samuelson, Fama, Ross, Tobin and Shiller), ghiblinewt is absolutely correct. However, our futures-based model extracts more information about the likely future for stock prices than any of these market hypothesists were able to consider in their day, opening up the possibility of being able to exploit the additional information to gain greater returns than would otherwise be possible. Here's how we fleshed out that greater potential and re-expressed the challenge (emphasis and links added, spelling errors corrected):

There's an important bit of information to consider with the If-Then conditions as well - where stock prices are currently, with respect to where our futures-based model indicates they would be based upon how far ahead in the future investors are looking.

For example, there are times when we absolutely know that investors are going to shift their attention to a different point of time in the future, which most often happens when investors are focused on the current quarter (the end of which is still in the future), but the clock for which is ticking down, because there is only so much of the current quarter left to play out before investors *have* to shift their focus to a more distant point of time in the future. The classic example from recent years is 2012-Q4 thanks to what we call the "Great Dividend Raid" ahead of the Fiscal Cliff crisis.

Then, there are most other times where investors have to make some kind of determination of how likely an event is (such as the future timing of Fed rate hikes). You're right in assessing that the market is continually doing that, but here, we're seeing in our model that Fed meetings often coincide with investors focusing on a specific future point in time (the time at which the Fed has indicated it plans to next change interest rates), which provides a basis for setting up an investment strategy based on the likelihood of alternative outcomes.

We'll interject here to note that we have come to use Fed meetings and announcements where investors are clearly and nearly universally focused on one particular point of time in the future as calibration events - to check out well our model is providing feedback on the future outlook of investors. It's something we have to do because the scale factor in the basic math behind our model has to be determined empirically.

Resuming our response:

In a sense, it's like the Monty Hall problem from statistics, where you're given three doors to choose from on a game show, behind one of which is the grand prize. The game show host shows you the prize that is behind one of the doors you didn't pick, then gives you the opportunity to choose again from the two unopened doors, so you now have the choice of sticking with your previous choice or switching it.

Statistics says it is very much to your advantage to switch from your original choice.

For our futures based model, the prizes behind the doors you get to choose are the alternative trajectories for stock prices - and unlike the Monty Hall problem, you get to see what the prize is behind each. The model plays the role of Monty Hall and shows you at certain points of time what the prize is behind a particular door is, or rather, the current level of stock prices tells you exactly how far ahead into the future investors are looking.

Unlike the Monty Hall problem, you have the option of sticking with the door through which you can see the prize. Or you can switch to one of the others based on your assessment of how likely it is investors will focus their attention toward the alternative points of time in the future they represent.

There is a probability that attaches to each, so really the question is one of how you can maximize your returns with that knowlege. Or perhaps a better way to ask the question is if you were to make a larger bet on one of those alternatives becoming the focus of investors, how would you hedge your risk if one of the other alternatives turned into the actual outcome?

Armed with that additional information, ghiblinewt proposed the following strategy:

If we take the reductive case that there are just 2 extremal trajectories for the index - say one broadly net up and the other net down over the period of interest. And then we get a peek at the prize - here do you mean that the "prize" is the expected target level for the index +n days into the future? Is it just the current futures level?

Interjecting to answer these questions, from a practical perspective, since the timing of the changes would be unknown, it would the +n days into the future, which may or may not align with the current futures level. Now back to ghiblinewt's proposed strategy:

Then in that case if and only if we had some ex ante probability for those two extremal paths e.g say that they were 70/30 rather than 50/50 probability of eventuating, then we could definitely exploit that difference. Options for example are priced on the "naïve" equal probability distribution at each point in time - so you would be able to exploit any information advantage you had vis vis the standard pricing models. But as I see it when all is said and done you'd still need to gain your advantage via the ex ante probabilities, and whenever these diverge from those priced by the spot and/or futures level then you can exploit that divergence.

So, difficult, but possible.

Meanwhile, Geoffrey Caveney tackled the problem from more of a hands-on, "How could I do this?", perspective:

Well, if you knew the next big move of the S&P 500 will be downward, but you didn't know the exact timing of the move, a safe way to make a big profit would be to sell lots of out of the money call options on SPY. All the premiums you collect would be free money, if you knew that the S&P 500 wouldn't rise enough to make the call options in the money. In real life I would always recommend selling call *spreads* to protect yourself from unlimited losses in the case of an unexpected huge rally.

We would assume that the opposite strategy, buying "in-the-money" put options, would apply in the situation where we expected a decline in prices. Which is coincidentally what Mark Cuban did with his long position in Netflix (NASDAQ: NFLX) back on 5 February 2016.

Altogether, these are what we would consider to be pretty sophisticated strategies. We'll have to tackle the question of what strategy a typical investor might be able to execute in a regular trading account without having to open an options trading account in a future post.

But if you have good ideas, by all means, please share them in the comments to our How Would You Exploit the Future for the S&P 500 If You Knew It? challenge at Seeking Alpha - if you beat us to a workable strategy before we get around to posting our thoughts, we'll give you full credit for devising it!