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  • Cover's universal portfolio maximizes the wealth growth rate
  • Markowitz's mean-variance model minimizes portfolio variance

Both allocate assets based on historical returns.

How do these two models perform against one another (assuming for Markowitz we use the global minimum variance portfolio by default). How does the universal portfolio compare against the equally-weighted portfolio that is known to outperform Markowitz sometimes? Does the universal portfolio provide portfolio weights in-sample that hold up well out-of-sample compared to the minimum-variance portfolio?

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I personally think that the most appropriate answer is: it depends. Specifically what is "Markowitz's mean-variance model"?

If we consider the more general definition it is an optimization framework and the portfolio is obtained by optimizing according to an objective function and it is expression of the estimated mean/return component and variance/risk component.

First of all the point is how one estimates the inputs (which assumptions, models, statistical techniques etc.) and secondly how one defines performance.

If we only consider the vanilla (no constraints etc.) minimum variance portfolio and vanilla growth optimal portfolio and supposedly we compute the variance component equally all becomes a question of how one estimates the mean component required to obtain the second portfolio.

Finally if we suppose that the estimated mean component is quite close to one's expectation and performance is intended "stability" or "Sharpe-ratio" it happens that the growth optimal portfolio is less diversified and riskier/more volatile (at the same time it compound the invested capital faster thus delivering a higher terminal wealth).

Both Samuelson (1971) and Markowitz (1976) implied that many investors are willing to sacrifice long-term return in exchange for short-term stability.

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  • $\begingroup$ the estimated mean is often far from what we expected, so which of the two portfolios is better then $\endgroup$
    – develarist
    Commented Sep 20, 2020 at 15:01
  • $\begingroup$ The estimated mean component in m.v. optimisation is the vector of expected returns (it is not intended as statistical mean which has been proven to be a poor estimator in this framework). Whatever model one applies if it does not provides good (let it be read as "close to one's expectation") of the expected returns probably it is more rational to consider only minimum variance portfolio simply because there is no need to estimate the mean component. $\endgroup$
    – Nipper
    Commented Sep 20, 2020 at 16:43
  • $\begingroup$ thats why the question only discussed the min var portfolio, not the sharpe portfolio. how does your answer change w.r.t. the min var portfolio? $\endgroup$
    – develarist
    Commented Sep 20, 2020 at 17:14
  • $\begingroup$ Could you please explain me where I referred to the sharp portfolio (which is also called “max sharpe” or “tangency” portfolio)? $\endgroup$
    – Nipper
    Commented Sep 20, 2020 at 20:35
  • $\begingroup$ your 5th paragraph $\endgroup$
    – develarist
    Commented Sep 20, 2020 at 21:17
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All of the models you describe are just that -- models. Any out of sample results could be quite different than one would expect. However, only the equal weight portfolio isn't optimized around some objective, and would be more likely to look similar in performance to the original fitting period . It is similar to Sharpe in that it diversifies from any large number of assets and reduces variance, by diversification.

The Cover portfolio is very sensitive to the assets that make up its portfolio. The underlying assets need to be very volatile, for it to perform well in a short time, and it can take many years to guarantee the best performance of all possible portfolios. So in the long, long run, Cover might be guaranteed to be the best (in terms of terminal wealth). However, you might also have huge drawdowns compared to the other portfolio types.

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