I expect many of these are related. I find the difference between odd-dimensional and even-dimensional rotation groups interesting and that has wide-ranging ramifications.
@johncarlosbaez It's not so bad if you have an odd number of socks that are identical though you want to rotate which ones you pick to keep the wear and tear evenly distributed.
@dpiponi@johncarlosbaez : I'm going to use this example to illustrate the fallacy of index funds. The S&P index lists the best performing socks. They regularly unlist the worn out socks, and replace them with brand new socks. It costs them nothing. An index fund, on the other hand, has to buy the socks that have been newly listed, and sell the worn out ones that are exiting the index. So it's buying high and selling low.
@BartoszMilewski@dpiponi@johncarlosbaez For something like an S& P 500 index fund, you're not wrong but the point you're making ends up not mattering very much. The higher capitalization stocks don't turn over often, the ones that do turn over tend to be a very small percentage of the index, and the net effect ends up being on the order of single digit basis points. I'll leave any argument with respect to socks to the experts.
Fund managers try to optimize trading so that returns track their benchmark. The above appears to show they do a pretty good job. They know when stocks are going to enter/exit and plan trading around that.
@BartoszMilewski@johncarlosbaez You're making a testable claim here: that when a stock is listed that it's high, which I have to interpret as meaning you expect it to perform worse, in the future, than other stocks. Do you have some data to justify this claim?
@dpiponi@johncarlosbaez I haven't done the calculations, just some intuitions from physics. I see the stock market as an ideal gas, and index funds an attempt to implement a Maxwell's demon.
@BartoszMilewski@johncarlosbaez If what you said was correct you could buy stocks when they're delisted because that means they are "low". You'd have a sure-fire strategy for beating the market.
@BartoszMilewski@dpiponi@johncarlosbaez Modeling the market (e.g. S&P 500 index) as an ideal gas makes sense. Implementing Maxwell's demon would imply beating the market. Index funds don't attempt that. Rather, they attempt to replicate the market's return, with the expectation of minimal slippage.
@BartoszMilewski@dpiponi@johncarlosbaez I'm still confused. The etf I'm using for comparison didn't begin to trade until 2010.10.01, when it was 108.300003. on 2020.11.01 it was 332.640015. Our data is out of phase, but the return over 10 years is 307% over the period I'm looking at.
For your data, the return is 332%. So, net of the 10 month lag, they appear very much the same.
n.b. You need to use returns, rather than raw data, to get a dimensionless object to analyze.
My understanding is that the raw S&P index includes no dividends and that's what people see. Even if index funds grow at a similar rate, they do it by reinvesting dividends.
@BartoszMilewski@dpiponi@johncarlosbaez I still don't believe it matters. Here's a toy example: Two stocks in an index, both with stocks priced at $1/share, both with 1 million shares outstanding. Index value is $2 million. Assume a fund has 1 share of each. If one of the stocks announces a 10% dividend that has an ex date tomorrow, fund managers expect the stocks to be worth $1/share and $0.90/share tomorrow, yielding an index worth $1.9 million.
If they own equal amounts of the stocks prior to the dividend, they know they need to re balance and have 1 share of the stock without a dividend and 0.90 shares of the stock with a dividend on the ex date. To get there, they sell 0.10 shares of the stock with a dividend immediately prior to the ex date.
If they keep the $0.10 that sale yields, they reinvest on the ex date, at the new ratio: 1 to 0.90 shares. This doesn't guarantee that returns for the index and the fund will be equal but, given that most (?) dividends are reinvested in the market, works out that way in practice. Note again, the sale of the dividend stock results in cash equal to the dividend, which is reinvested at the new prices, with the new balance.
@BartoszMilewski Isn't that analogy implicitly assuming that the system is in equilibrium? Economies tend to grow (in real terms) over the long haul (presumably due to population and productivity growth), so I don't think they are analogous to a system in equilibrium. @dpiponi@johncarlosbaez
@internic@dpiponi@johncarlosbaez In thermodynamics we assume that the system is always reasonably close to equilibrium, but there may be a heater attached to it, or more gas is pumped into it. After all, thermodynamics works for the internal combustion engine.
@BartoszMilewski I'm not saying thermodynamics can't be used as analogy at all (though I'm not convinced it's an apt one); however you were talking about Maxwell's demon, which is usually discussed in reference to extracting work from or creating disequilibrium in closed systems at equilibrium. I guess I'm saying that if anything the stock market is more analogous to a heat engine, where one can perfectly well extract work or bring previously equilibrated subsystems out of equilibrium (through compression or heating), because it is an open system, and part of a larger system that is not even approximately in equilibrium. @dpiponi@johncarlosbaez
Add comment