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This result is still not widely known but a simple equal weighed rule outperforms Markowitz mean variance for most alpha trading strategies i.e. strategies that predict outperformance.

Peter Muller shows this in an original paper in 1993 [1]. Peter Mueller went on to start PDT and make Morgan Stanley billions of dollars in profits.

The same effect can be shown to a limited extent for index portfolios[2] though less scalable because higher cap stocks have more float.

Related is the Kelly Betting criteria - about 50 years old [3] which gives a simple rule for picking and allocating capital to bets.

These 2 ideas - equal weighted portfolios and fractional betting would put a lot of quants out of business.

[1] https://www.semanticscholar.org/paper/Financial-optimization...

[2] https://www.semanticscholar.org/paper/Why-Does-an-Equal-Weig...

[3] https://en.wikipedia.org/wiki/Kelly_criterion

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Decent quants know about the shortcomings of Markowitz allocation. The mean is more or less impossible to measure, and covariances shift over time and are awkward to measure concurrently. So the art is in specifying the parameters. I've used zero mean and block-diagonal covariance in asset allocation before, which isn't far off 1/N allocation.

The issue with Kelly betting is the same as with Markowitz: knowing the parameters of the problem. If you overstate your probability of win by mis-estimating, you'll get ruined. For what it's worth, the version of Kelly betting I'm familiar with is for Bernoulli trials. I think the Gaussian version of the Kelly criterion essentially reduces to Markowitz.

Side note: kelly betting isn't new! Daniel Bernoulli knew about it back in the 1700s. Kelly just connected the formula to ideas in information theory.

>covariances shift over time

This is what I thought when I first ran across the theory in a book. I feel like it's a widespread pattern, there is some big intractable problem, and some genius says "aha, I can reduce this to..." but what they have reduced it to is also an intractable problem, only because of the novelty it feels like progress.

Everybody goes around saying "ha, you can't predict future returns from prior returns, aren't we smart", but how can you predict future covariances from prior covariances any better?

I'm not sure how useful Kelly betting is though, for similar reasons. Isn't it premised on knowing your edge, so knowing how much to bet is not such a valuable secret; you need to figure out how to identify your edge reliably. Particularly that it's not negative.

I eventually decided the way to go is (1) start with every idea or security equal weighted, and (2) basically never rebalance, because things that outperform do tend to continue to do so and the "imbalance" reflects new knowledge disseminated by the market.

I've often wondered about the 1/n strategy. It's simple enough: invest in n assets equally, and rebalance them regularly.

However, there are some questions: how does one know which n assets to pick? Should they be mostly decorrelated? How decorrelated? And shouldn't all n assets have > 50% probability of growth? And what should the number n be? These aren't always easy questions to answer. After all, you could pick n dud assets that are highly correlated, and the strategy would fail.

I'm curious: how do folks apply the 1/n strategy in practice?

Generalizing, there are 3 problems:

1- Alpha prediction (forecasting a return for each asset)

2- Portfolio Construction

3- Portfolio realization - trading

I was referring to problem #2, which assumes you have a priori alpha forecasts and the relative confidence of those forecasts. In the general portfolio construction problem, the past mean returns of stocks is taken to be the future return.

This study [1] does a good job rigorously comparing 1/N to various alternative trading strategies. It also talks about situations where 1/N is more or less likely to dominate.

"Our simulations show that optimal diversification policies will dominate the 1/N rule only for very high levels of idiosyncratic volatility."

[1] http://faculty.london.edu/avmiguel/DeMiguel-Garlappi-Uppal-R...

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