By the EMH I mean this practical form: People cannot systematically outperform simple strategies like holding VTSAX. Certainly, you cannot expect to have a higher expected value than max(VTSAX, SPY). Opportunities to make money by active investing are either very rare, low volume, or require large amounts of work. Therefore people who are not investing professionally should just buy broad-based index funds.
This isn’t the right way to formulate an EMH. You can trivially get higher expected return than any investment by simply leveraging that investment. 1.1x leveraged SPY has higher expected return than SPY, and 1.2x SPY has even higher expected return and so on. As long as the borrowing rate is lower than the expected return on SPY, leveraging will always improve your return.
A better formulation would be that no strategy has a better risk-adjusted return than the market portfolio, which is the capital weighted portfolio of all securities held by everyone. If you restrict your investment universe to US equity only, the market portfolio is VTSAX (or SPY, they’re close enough). Then you could formulate the EMH as saying no portfolio of US equities will consistently outperform VTSAX in risk-adjusted terms, meaning, if we normalize the beta of the first portfolio to 1, then it won’t outperform VTSAX (which has a beta of 1 by virtue of being the market portfolio). Now my argument with leverage does not contradict this formulation, because a 1.1x leveraged VTSAX will have beta = 1.1. So if your normalize it to beta = 1, you get back VTSAX, which does not outperform VTSAX.
As long as the borrowing rate is lower than the expected return on SPY, leveraging will always improve your return.
Maybe not what you meant, but this wording is too strong. If you leverage high enough to exceed the Kelly bet size by 2x or more, then your long-run portfolio value will be zero.
Yes, you’re right. I’ll weaken the claim to 1.1x SPY will beat SPY in expected return historically and in almost all reasonable contexts. Certainly often enough to invalidate the incorrect EMH stated above.
My statement was motivated by the single time period investment model, as is considered in the standard mean-variance diagram of modern portfolio theory. On that diagram, as long as the risk free rate is below the market portfolio, you can draw a straight line between them and once you go beyond the market portfolio, you’ll always have higher expected return all the way to infinity. But a single time period is not the best way to model long-term investing.
This isn’t the right way to formulate an EMH. You can trivially get higher expected return than any investment by simply leveraging that investment. 1.1x leveraged SPY has higher expected return than SPY, and 1.2x SPY has even higher expected return and so on. As long as the borrowing rate is lower than the expected return on SPY, leveraging will always improve your return.
A better formulation would be that no strategy has a better risk-adjusted return than the market portfolio, which is the capital weighted portfolio of all securities held by everyone. If you restrict your investment universe to US equity only, the market portfolio is VTSAX (or SPY, they’re close enough). Then you could formulate the EMH as saying no portfolio of US equities will consistently outperform VTSAX in risk-adjusted terms, meaning, if we normalize the beta of the first portfolio to 1, then it won’t outperform VTSAX (which has a beta of 1 by virtue of being the market portfolio). Now my argument with leverage does not contradict this formulation, because a 1.1x leveraged VTSAX will have beta = 1.1. So if your normalize it to beta = 1, you get back VTSAX, which does not outperform VTSAX.
Maybe not what you meant, but this wording is too strong. If you leverage high enough to exceed the Kelly bet size by 2x or more, then your long-run portfolio value will be zero.
Yes, you’re right. I’ll weaken the claim to 1.1x SPY will beat SPY in expected return historically and in almost all reasonable contexts. Certainly often enough to invalidate the incorrect EMH stated above.
My statement was motivated by the single time period investment model, as is considered in the standard mean-variance diagram of modern portfolio theory. On that diagram, as long as the risk free rate is below the market portfolio, you can draw a straight line between them and once you go beyond the market portfolio, you’ll always have higher expected return all the way to infinity. But a single time period is not the best way to model long-term investing.