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.

...

"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.

...

"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.

Comments

[rod.]

Once again, congratulations for your blog. It's hard to find a post here which is not VERY interesting!

I am somewhat intrigued to see that so many information theorists have succeeded in finance. Shannon, Kelly, Berlekamp and Cover. Cover wrote the information theory "bible" (http://www.elementsofinformationtheory.com/) in which he dedicates a full chapter to portfolio optimization and investment. I recently heard that he was taking a sabattical from Stanford to start a hedge fund (or to join one), but it might be a rumor...

Berlekamp is a legend indeed. He was nicknamed "the greatest post-Shannon genius" by the information theory research community. He is insanely smart... in fact, there are some jokes about him on how he can learn many things (not just math) extremely fast:

"do you know what Prof. Berlekamp did last weekend? He learned Russian..."

Hopefully, beating the market requires more than mathematical genius. Hard work, creativity and the ability to think differently might help out.

I must confess that I had an idea similar to your, the CASTrader. It was about February 2006, and after some days of reasoning I just assumed that the required computational power would be way out of proportion. But then, I know very little about implementing CAS algorithms and stuff. I am therefore following this blog with great interest, and hoping you can beat the market using CAS. Good luck!

[Alan J]

Well, thanks again!

Now that you mention it, there does seem to be a powerful concentration of Information Theorists playing and apparently trouncing the market. This sounds like the topic for another post. What's more, they all seem to have known each other.

Mountain View Analytics may be the hedge fund you are thinking about that Cover is allied with.

My personal view is that there are many ways to potentially beat the market, and certainly mathematical genius, hard work, creativity, and thinking differently aren't bad places to start. There are times when genius fails, though: Isaac Newton in the south sea bubble and http://www.bearcave.com/bookrev/genius_fails.html.

As far as computation power, if it can pay for itself and then some, I'll fill a room full of computers!

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