Thomas Cover's Universal Portfolio - Part I, Introduction
Thomas Cover’s Universal Portfolio - Part I, Introduction Another trading methodology similar to Shannon’s Method (aka Shannon’s Demon) is the Universal Portfolio method, advocated by Thomas Cover, a professor at Stanford. Interestingly, he was a Shannon Award winner (the highest award in information theory) along with Elwyn Berlekamp. Cover’s methodology is implemented by Mountain View Analytics, which he is involved with. The Cover method is probably best described in an old (2000) Stanford news article:
To create a universal portfolio, the investor buys very small amounts of every stock in a market — no small task in itself. The New York Stock Exchange, for example, lists 3,025 companies. In essence, the universal investor mimics the buy order of a sea of investors using all possible “constant rebalanced” strategies, in which the amount of money invested in each stock is adjusted each day to achieve a fixed proportion.
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“Imagine we have, for a simple example, two stocks,” Cover explains. “A good constant rebalanced portfolio might invest, say, one-fourth in one stock and three-fourths in the other. At the end of the day, the wealth you have in each stock would not be exactly one-fourth, three-fourths because the prices of the stocks change, so you would do the necessary buying and selling to restore it to one-fourth, three-fourths.”
Cover’s universal portfolio algorithm invests uniformly in all constant rebalanced portfolio strategies. The result is a strategy that is nearly optimal. Cover has shown, for any sequence of stock market outcomes, that this mixture of investments has as high a compound growth rate in the long run as the best constant rebalanced portfolio. Over time, the best strategy (that is, the best constant rebalanced portfolio) fights its way to the top of the fiscal food chain.
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One aspect of information theory is data compression. “The beauty of it is, the mathematics of growth-rate-optimal investment turns out to be parallel to the mathematics for optimal data compression,” Cover says. Thus universal investment algorithms are a counterpart to the universal data compression algorithms used to compress voice, fax and computer files.
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“This is an automatic investment algorithm in the stock market,” Cover says. “The portfolio rides the stocks and lives off the fluctuations. It essentially puts a little bit of money on every possible rebalanced investment algorithm, and the surviving algorithms — the ones that made most of the money — make enough so that your money grows at the same rate as if you had used the best algorithm to start with.”
The algorithm is “somewhat ponderous,” Cover says. “The performance of the algorithm, although good relative to the best portfolio in hindsight, is still slow in responding in an absolute sense. It sometimes requires hundreds of days before the initial conditions wash out, leaving the ‘fittest’ rebalanced portfolio dominating the performance. It’s guiding thinking, but no one’s making money off it yet.”
The Universal Portfolio has quite a bit in common with the Shannon Method:
It’s a Constantly Rebalanced Portfolio (CRP), meaning it it is an extension of Kelly’s optimal long term growth rate formula.
The CRP thrives on volatility. In fact, Thomas Cover coined the term “volatility pumping” to describe the way it makes money. I think “volatility harvesting” is a good description as well. In a crude sense, it’s turning beta into alpha.
The Universal Portfolio is a lot more complicated than the Shannon Method, but I gather by what Cover says, it is proven to outperform it.
In Part II, I’ll list some additional detailed reading on the Universal Portfolio.
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