How can I estimate the probability distribution of the profit on investment if I put my money in, say, S&P 500?

Beyond knowing my expected return, I want to know such things as: What are the chances my investment will be below 50% at the end of 5 years? What is the median expected value (the value at which I can be 50% sure my investment will be above that)?

  • Are you asking for someone to provide you with research? You would estimate this by gathering the data and working up the statistics. – quid May 25 '17 at 23:08
  • @quid: I would have thought this is a very common thing and was hoping that someone could either link me to the probability distribution or explain to my why I'm wrong. – Zaz May 25 '17 at 23:29
  • The Personal Capital website does this for you and takes many factors into account. – gaefan May 26 '17 at 13:07
  • While you may not be aware of this, you are basically asking how to value your asset, and also forecast various possible events. When a question asks something like "I want to know such things as...", it is an indication that it is too broad to be answered here. If you have a specific question that is answerable, you may want to re-ask, but even the most concrete: "What is the probability that the S&P500 will be down 50% in 5 years?" is going to be very technical & opinionated, and already veering into the arena of "should I invest in the S&P500?" – Grade 'Eh' Bacon May 26 '17 at 15:33
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    @Grade'Eh'Bacon: I think that "what is the probability of being down X% in Y years" is likely too broad. But I think "how do I calculate the probability of being down X% in Y years" is on topic, and it seems to me like that is what this question is asking (although it could be asked better). I think it's legitimate to ask how to approach the question of estimating future returns, although the answer may be complicated. – BrenBarn May 26 '17 at 18:31

There is no simple answer to that, because no one knows exactly what the probability distribution of S&P 500 returns is.

Here is a sketch of one possible way to proceed.

  1. Get data on past stock prices from something like Yahoo Finance or Google Finance.
  2. Run a bunch of simulations where you pick a random date in the paste and see what the return was 5 years later.
  3. Compute whatever stats you want on this (e.g., median return, chance of being down 50%).
  4. Cross your fingers.

Don't forget step 4! The problem is that the stock market is full of surprises, so this kind of "backtesting" can only reliably tell you about what already happened, not what will happen in the future. People argue about how much you can learn from this kind of analysis. However, it is at the least a clearly defined and objective process. I wouldn't advise investing your whole nest egg in anything based just on this, but I do think that it is relevant information.

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