This improvement in geometric returns is an illusion, it does not add to final returns (what you can eat with the money). Read that paper, it explains pretty well
Its very counter-intuitive because the finance industry teaches everyone to think in terms of geometric returns (compound rates) but as the paper says "Expected portfolio values are governed by arithmetic means, not geometric means or volatility."
I have the opposite experience; for over a decade working in finance I never looked at geometric mean, because we were working in target risk space with leverage, all our backtests had the same expected risk so we only looked at arithmetic means. I only started looking at geo-means a couple of years ago after I retired. So I found geo-means more counter intuitive to begin with... GAT
You probably won't agree with me but I've written up my rebuttal: http://qoppac.blogspot.co.uk/2017/02/can-you-eat-geometric-returns.html Thanks again for showing me the paper. Was interesting and useful. GAT
I wouldn't call it a rebuttal at all. You essentially agreed with the main points of the paper. The paper basically says: diversification decreases volatility but does not add dollars to the investor. It reduces risk but does not add to expected returns The problem is that you changed the definition of ' expected returns' (dollars). Expected value, that I know of, has always meant an average figure. You argue that a median figure is superior, you say that its better due human nature and risk aversion. So you essentially came up with a new definition of expected returns THAT ADJUSTS FOR RISKS. Is it any surprise that you found that diversification helps that metric? That's exactly what the paper is arguing, that diversification helps risk averse people, but does not add dollars to the investor Take your lottery ticket example, if risk aversion lead one not to buy the ticket, the person is giving up 100 pounds. Its giving up pounds in the bank due risk aversion. Does that mean its a bad decision? No, its an excellent decision but the fact remains that pounds where given up in the process. Does that mean the diversification is bad? No, but it does mean that one MIGHT give up returns in the process Imagine a father with $1M in the bank he wants to give to 2 sons. He gives 90% to one and 10% to another. One son is risk loving, he puts it all in the stock market, the other one is risk averse and puts it all in T-Bonds. Call this situation, Situation A Now imagine both sons are risk loving, they both put all the money in the stock market. Call this Situation B. The father might tell himself "In Situation A, the median outcome is better for me" but is there any doubt that the 'pool' of both son's wealth will grow faster in situation B? The son's money are not 'interacting with one another' (there is no rebalancing). In Situation A dollars in the bank were given up in order to improve the 'median' outcome (since the son with bonds will grow wealth more slowly than the one with stocks), but that is a RISK adjusted return. Its not an actual return. Diversification helps risk adjusted returns, not ACTUAL returns (the ones that you can eat with) I love diversification but I'm fully aware that a lot of the time, I give up money in the process. Or at the very least, returns stay the same. I sure heck know I ain't making any more from it (unless I rebalance)
One situation where it might seem that diversification is adding to returns is when someone neglected an asset class and ends up investing in it. Say someone is 100% in US equities, if he puts 75% in US equities and 25% in EM equities, usually there will be an increase in returns (Since EM equites tend to return more in the long-run). But the increase in returns comes from the fact that a higher return asset class was added, not because of some 'diversification return'
What is more amazing about this is that the author of the paper shows quite clearly that Eugene Fama made a serious error when he talked about a 'diversification return' in his paper. So the guy who wants to convince the world that markets are efficient shows that he doesn't understand the basic mathematics of how markets work
That is a great approach. My question is what criteria can one uses to select the 11 stocks? Thanks in advance.
Another question: Do you have any easy back of the envelop calculation method that can show that? And what does that means? I will in general get 1.2% less in expected return compare to holding the full diversified index?