What sort of market prediction is decided by coin flip though? This makes more sense in the context of a binary outcome like sports betting in which you are betting on a team either winning or losing.
It doesn't matter that it's not a binary choice to pick a stock, you can convert it into a binary choice at will. For example, you can send out 1M emails with stock recommendation for some large stock with "buy" or "sell" as a 50/50 coin flip. You didn't pick the stock, you chose between buy/sell, the outcome will be the same: your market prediction skill will look fantastic to a select few.
The scheme definitely could get foiled if people were just told that a certain stock would go up (without hedging against the market), because if it's a red day for the market the whole e-mail list could get wiped out as all the stocks go down.
I would think that there is approximately a 50% chance of most stocks beating the market on any given day though.
If you send a bunch of e-mails saying "${ticker} will go up more than the market tomorrow, I'd recommend you invest and hedge with a bet against the market" for a variety of random tickers, I'd guess around half of them would pay off.
I'm not sure if that is truth (today). The majority of stocks have been doing a massive nose dive within the past year. I own stocks of approximately 10 different companies. All, except AAPL, under water. So - 90%. In contrast, defense and healthcare stock market has seen a different trend. I own zero of these.
That's why I included the part about hedging against the market. There may be days where almost every stock goes down, but generally only around half will every go down more than the market.
That's why I included the part about also hedging against the market.
Not that it's particularly easy to do, but if you took out an equal weighted short position on the $SPY while going long on some ticker, it would pay off if that ticker outperformed the market.
You could get close to a binary output with an option spread with a tight range of strikes (e.g. buying a call at price X, and selling a call at price X+1). If the stock price goes above the high strike it is a maximal payout one way, and below the low strike maximal payout the other way. If the strikes are close compared to movements of the stock and near the current price of the stock, the outcome is likely to be nearly binary. If the stock settles between the strikes the payout would be partial and continuous, but that window is very small.
It doesn't matter for this hypothetical scheme. It'll always be one or the other outcome, and you will thus look prescient to one half or the other half of the victims. Each day your pool of victims cuts in half but you don't care which half it is. The scheme works regardless of how often the stock actually goes up or down. At the end, there will always be one victim who was given exactly the correct series of predictions by you ahead of time.
If the two outcomes don't have equal probability there are no two halves here. In a bull market with everything being green saying that something will go up is not an interesting prediction.
There are two halves because you told half the victims one prediction and the other half the opposite prediction. It does not come from the probability of the outcomes. The probability of the two outcomes doesn't matter at all for this thought experiment's goal: that you can appear to correctly make N yes-or-no predictions in a row to one victim if you have 2^N-1 other victims that you can tell incorrect predictions to. This process guarantees that one of the victims in the pool ends up getting the correct series of predictions.
I'm not sure how else to explain this but please ask again if you feel like this isn't making sense; any failure here is mine, not the thought experiment's. This is an extremely well-known thought experiment. This wasn't thought up by anyone here.
One way to overcome this is to calculate the percentage change of a stock compared to the percentage change of the median performing stock in the market. 50% will be perform better than the median stock while 50% will perform worse.