You may have seen this already: https://arxiv.org/abs/1101.4548 https://arxiv.org/abs/1101.4548 Funny stuff. They predict that in aggregate 100% of the wealth

You may have seen this already: https://arxiv.org/abs/1101.4548 https://arxiv.org/abs/1101.4548 Funny stuff. They predict that in aggregate 100% of the wealth is invested in stocks and investing more than that would be suboptimal: the optimal leverage is 1. They "submit the hypothesis to a rigorous test" and find that the optimal leverage for the S&P 500 is around 1, given its volatility. There is a small problem with their rigorous test. They forgot to include dividends: "a real investment in the S&P500 outgrew federal deposits at only 2.0% p.a". Including dividends would bring the optimal leverage to 2 or 3. But that's ok. It's close enough to 1 for them, apparently. Even better: ignoring dividends was not so wrong anyway because the S&P 500 overestimates the return of a real equity investment due to survivorship bias. "The S&P500 is an index of five hundred large companies, listed publicly in the United States. We use it as a proxy for a generic diversified investment in US stocks, but we note some caveats. Firstly, the index does not account for dividends paid to stockholders. This means it will tend to underestimate the performance of a real investment. Secondly, the index suffers from survivorship bias, representing a portfolio of the largest and most successful companies in the US, in which less successful companies are routinely replaced. This acts in the opposite direction to the first caveat."