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They say that it's impossible (for ordinary men, with simple statistics and math) to predict future stock price based on the past stock price.

But that's not exactly true. As you still can predict something, and with quite a high certainty.

You can predict future volatility based on past volatility. You don't need complex math to conclude that there's a good chance (maybe not >90% but probably >60%) that next month for highly volatile stocks in past and recently like AMD, Tesla or Shopify going to be more volatile than for less historically volatile McDonald's or Procter & Gamble.

  • So, volatility is one thing you can predict from the past.
  • The head part of the probability distribution could be predicted. The shape of the tail of the distribution may be not very precise, but the shape of the head should be more or less close to reality.

What else statistical or other properties of the future prices could be predicted based on past prices?

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    I think you are falling for a fallacy. Could you have predicted the March volatility by looking at Jan and Feb?
    – Aganju
    Jul 25, 2020 at 16:37
  • @Aganju you can predict that 90% of the time stocks that have higher volatility in past year would also have higher volatility in the next month.
    – Alex Craft
    Jul 25, 2020 at 19:43
  • @Aganju I can't say for sure, but even if you just take average last year volatility as prediction for the next month volatility, you probably would be close to being right >50% time.
    – Alex Craft
    Jul 25, 2020 at 19:45
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    The basic fallacy of your argument is that yes, you can predict something maybe 60% of the time - except that the 40% times you are wrong will cause bigger losses than the 60% you are right, especially if you ignore the tails of the probability distribution. But you may have a great future as an economist or a financial advisor, because most of them have been telling this fairytale for decades, and there are always some more suckers (oops, clients) who want to believe in magic..
    – alephzero
    Jul 26, 2020 at 1:33
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    Consider one inconvenient mathematical truth: suppose your volatility distribution has infinite variance (and there are quite simple mathematical distributions with that property.) Any attempt to estimate the variance numerically will produce a finite variance, and is therefore 100% guaranteed to be wrong.
    – alephzero
    Jul 26, 2020 at 1:35

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You are correct that a probability distribution of future prices can be stated. In fact, the market prices of options on a given stock imply such a distribution -- including the tails (far-from-the-money options).

The statement that it's "impossible...to predict future stock price" is shorthand for it being impossible to do so in a way that beats the market on average. The main parameters governing the market-consensus distribution are the current stock price, which determines the mean of the distribution, and the current expected or "implied" volatility, which determines the standard deviation of the distribution. And yes, volatility is empirically "persistent", so the past "realized" volatility in a stock plays a big role in how market participants arrive at the implied volatility number.

The key point is that if the market (including the options market) is "right" about the probability distribution (i.e., if future stock prices behave as if they're drawn randomly from it, and have no further predictability), there is no way to beat the market. An investment strategy that you believe will beat the market corresponds to a belief that the market is wrong in some way about this future price distribution. It's like how betting on a coin flip at even odds can make money, on average, only if the coin is biased (the odds are wrong).

For example, if you think the mean of the future price is significantly higher than the current price (or in plain language, the stock is likely to go up), then you would overweight a long position in that stock. If instead you think the standard deviation of the future price is significantly higher than the implied volatility in the options market, you would use an options strategy like a straddle that bets on a large move but is neutral on direction.

The fact that a given stock is likely to have high, or low, volatility is only profitable information if it is not already the consensus reflected in (options) market prices.

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  • Thanks, I see, I had wrong understanding of what people mean by predicting the stock price "impossible...to predict future stock price" is shorthand for it being impossible to do so in a way that beats the market on average" - that's a valid point.
    – Alex Craft
    Jul 25, 2020 at 20:13
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You don't need complex math to conclude that there's a good chance (maybe not >90% but probably >60%) that next month for highly volatile stocks in past and recently like AMD, Tesla or Shopify going to be more volatile than for less historically volatile McDonald's or Procter & Gamble.

Your hypothesis is that it's likely that stocks like TSLA and SHOP which have had significantly higher current and historical volatility than MCD and PG are likely to continue to have higher volatility next month? Really?

Not only do you not need complex math to conclude this but my unsubstantiated guess is that this will always be true until the day that MCD has a nationwide E-Coli burger problem or PG is found to be selling carcinogenic Tide detergent.

You can predict future volatility based on past volatility. So, volatility is one thing you can predict from the past. The head part of the probability distribution could be predicted.

OK, I'm going to give you the benefit of the doubt that you can predict volatility for next month. Feel free to pick the securities of your choice. Please post your volatility predictions for 10 stocks and/or ETFs for August. Please also include what you're going to do with that predicted volatility. Are you going long? Going short? Doing something more complex? Looking forward to some insight. TIA.

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