Universal PortfoliosUniversal PortfoliosThomas M. Cover1991

Paper summaryjyang772Cover's Universal Portfolio is an information-theoretic portfolio optimization algorithm that utilizes constantly rebalanced porfolios (CRP). A CRP is one in which the distribution of wealth among stocks in the portfolio remains the same from period to period. Universal Portfolio strictly performs rebalancing based on historical pricing, making no assumptions about the underlying distribution of the prices.
The wealth achieved by a CRP over n periods is:
$S_n(b,x^n) = \displaystyle \prod_{n}^{i=1} b \cdot x$
The key takeaway:
Where $\mathrm{b}$ is the allocation vector. Cover takes the integral of the wealth over the entire portfolio to give $b_{t+1}$. This is what makes it "universal". Most implementations in practice do this discretely, by creating a matrix $\mathrm{B}$ with each row containing a combination of the percentage allocatio, and calculating $\mathrm{S} = \mathrm{B\dot x}$.
Cover mentions trading costs will eat away most of the gains, especially if this algorithm is allowed to rebalance daily. Nowadays, there are commission-free brokers. See this summary for Universal Portfolios without transaction costs: \cite{conf/colt/BlumK97}

Cover's Universal Portfolio is an information-theoretic portfolio optimization algorithm that utilizes constantly rebalanced porfolios (CRP). A CRP is one in which the distribution of wealth among stocks in the portfolio remains the same from period to period. Universal Portfolio strictly performs rebalancing based on historical pricing, making no assumptions about the underlying distribution of the prices.
The wealth achieved by a CRP over n periods is:
$S_n(b,x^n) = \displaystyle \prod_{n}^{i=1} b \cdot x$
The key takeaway:
Where $\mathrm{b}$ is the allocation vector. Cover takes the integral of the wealth over the entire portfolio to give $b_{t+1}$. This is what makes it "universal". Most implementations in practice do this discretely, by creating a matrix $\mathrm{B}$ with each row containing a combination of the percentage allocatio, and calculating $\mathrm{S} = \mathrm{B\dot x}$.
Cover mentions trading costs will eat away most of the gains, especially if this algorithm is allowed to rebalance daily. Nowadays, there are commission-free brokers. See this summary for Universal Portfolios without transaction costs: \cite{conf/colt/BlumK97}