A trading puzzle: how much would you pay to know the closing price of SP500 in one month?

I can tell you where the SP500 will settle in one month. How much would you pay for this information? (And then, what would you do with it?)

Let's say you give a number like $ 10 million, and I accept it. The S& P 500 is currently at 1000. I gaze deeply into your eyes and tell you the truth: in one month, the S& P 500 will close that day's trading at a level of…. 1000. Oops! Now what? How are you going to make money? You owe me $ 10 million in a month, and I will collect. There is no point in buying or selling futures at the same price at which you expect them to expire. So what can you do? [He doesn't mention the strategy of announcing your shot on social media and using it to gain followers. The value of this will depend on whether you have something to monetize or follow it up with...and if you do not already have a following it's likely you don't have skill in monetizing one so again the value of the follower windfall depends on its beneficiary]

All you can do is hope the market moves in the meantime, and it really is a hope, because you have no other information about what is going to happen over the course of the next month, not the volatility, nor the volume, nor the highs and lows. All you know is that it will be at 1000 again a month from now.

So how do you time your entry points? Say you have $1 million of liquid assets and say that this much money would let you support up to $10 million in notional, because futures have a haircut of about 10 percent.

Suppose you are very lucky and the S&P 500 jumps down to 900 before you even have a chance to put in your order. Now you would want to buy. But how much? Do you put your entire amount on the line, such that even a single tick against you triggers a margin call?

Ultimately you can perhaps do best if you are able to buy and sell options, but there won't always be a liquid options market at every strike you need at the asset that you want to trade, and besides, we haven't really discussed options yet. [Kris: This is actually the key — you could use options to structure a bet on terminal value but this riddle in general is insightful because it shows just how much you are missing if you don’t understand options]

These kinds of practical issues are ignored in standard textbook discussions of riskless profit opportunities but they are precisely the issues that financial hackers worry about most. And you will almost surely never experience anything with this level of certainty at any time in your career. There will always be doubts about your model, your inputs, and your forecasts…According to standard theoretical concepts of arbitrage, none of those questions matters. According to real-world practical experience, you can't even begin to trade until you have answered all of them.