That is doubling 20 times.
If 100 million people flipped 20 coins, 95 would get 20 heads.
There are approximately 25M millionaires in the US.
If 100 million people flipped 20 coins, 95 would get 20 heads.
There are approximately 25M millionaires in the US.
You can just carry any non-100% gain/loss "swimlane" as a game still-in-progress. Eventually on larger time scale, puchasing power adjusted or not, a swimlane of an investment will certainly hit one of those outcomes.
The outcome is a function of time but a large number of swimlanes guarantees that you can sample any time and observe the same distribution of settled outcomes. You can reasonably assume that the probability of transition from unsettled to settled state at any time is constant. You could model it as markov process. In fact there are many economic agent models doing something like this (OLG models where generations of economic agents overlap in time as child/worker/retiree). Even though these models make sense only on generational scale, with enough agents you can see the micro-structure being consistent in smaller time scales by "ticking" or sampling at smaller time steps the markov process.
The spending power issue could be ignored as "without loss of generality" in most cases or the thesis could be restated in terms of something that preserves purchasing power as part of the coin toss game.
Investment returns mean-revert only if allowed to by policy. Policy can override economic forces for very long generational time scales, thus making it still relevant for individuals.
And I personally don't agree with (or don't understand) these models being used for micro-structure analysis, but I think macro-level interpretations such as wealth distribution may be valid.
Great! Then you will have no problem accepting the following offer: you give me $1000 today, I will give you an arbitrary amount of money that you get to specify (so it has to be computable -- no busy beavers allowed). The catch is that I get to specify when the payout happens (of course with the same proviso: the payout will happen after a computable amount of time).
What a surprise.
> this is the game that represents the economic reality
No, it isn't. Economic reality is nothing like flipping coins, neither for individuals, nor in the aggregate, except insofar as both contain a random element.
> it is still a markov process
So what? Saying "it's a Markov process" is simply making the observation that there is a random element. Yes, flipping coins has a random element, and yes, the market has a random element. It does not follow that flipping coins is a good model of the market. On this logic, coin-flipping would be a "good model" of any non-deterministic process.
The interesting thing about Markov processes is not that they contain random elements. The interesting thing about Markov processes is that you can make reliable predictions about some of them despite the fact that they contain random elements. But coin-flipping is not one of those processes about which interesting predictions can be made. The economy is.
Now suppose of all the crazy investing philosophies in existence, you learn that all N greatest investors (or "N luckiest coin flippers" according to you), suppose you learn all of them have the exact same investing philosophy.
Would this make you reconsider whether your "investing is coin flipping" model is a useful model?
"The Superinvestors of Graham-and-Doddsville"
https://www8.gsb.columbia.edu/sites/valueinvesting/files/fil...
2^20 = 1048576
So roughly 1 in 1 million.
You're off by 100x.
Really? Population of the US is like 350M. Is 7% of US population millionaires? Like, one of out every 14 people out there? I guess that's believable but counter-intuitive.
"The median household wealth in 2021 was $166,900. The 10th percentile of household wealth was zero dollars, meaning 1 in 10 households had wealth of zero dollars or less. The 90th percentile of household wealth was $1,623,000, meaning 1 in 10 households had wealth exceeding $1.6 million."
If they were starting out with $2 million and betting it on a coin flip, they would owe 37% income tax on the winnings of each flip.
And try finding someone to bet you $1 trillion on a coin flip.
Charlie Munger's strategy was not to start out with $2 million and bet it with a 0.0001% chance of winning $2 trillion and a 99.9999% chance of losing it all.
Some people invest money out of each paycheck, study how to best allocate that money between the investment options available to them, do that for many decades, and become millionaires. Some people buy a $2 lottery ticket and become millionaires that day. They both just got lucky, am I right?