I shall start by saying I know little about markets, investing or gambling, but I do know a little bit about probability. This question is prompted by comments to this question, such as "As a personal investor you have no real chance of beating the market." and "You have a chance of beating the market, but it's far more likely you'll lose a lot of money."
Let us compare 2 strategies:
- Put $10,000 in an S&P 500 linked index fund, keep for 1 year and cash out.
- Buy $10,000 of a single S&P 500 stock, randomly selected weighted by market capitalisation, keep for 1 year and cash out.
From a simplistic probabilistic view, I would expect both these strategies to have the same expected return, with the second having a greater variance than the first. If each company had an independent, identically distributed and symmetrical expected return you would expect both to have an equal chance of "winning". If companies have a left skewed expected return, in that you expect some complete failures and fewer to double in value, then you would expect the second to actually win more frequently, but to have a larger chance of losing all your money than of doubling it. A right skewed expected return would have the opposite result.
Another relevant observation is that people differ in their attitude to financial risk. Some people actively avoid risk, for example by hedging their investments and so accepting a lower expected return in exchange for lower variance. Others actively seek out risk, for example playing the lottery, gambling on horses or playing fruit machines. This is accepting a negative expected return for a very high variance, and gaining the "fun" of finding out the result.
Therefore one could conclude that it would be rational for some people, those who favour lower variance, to buy the S&P 500 index. Others, those who favour risk, would be rational in choosing the single stock. They get the same expected return but also gain the "fun" of seeing how their pick did against the market.
Is this analysis approximately correct, or is there something I am missing?