Universal Portfolios With and Without Transaction CostsUniversal Portfolios With and Without Transaction CostsBlum, Avrim and Kalai, Adam1997
Paper summarycdmurray80The authors give a MUCH simpler description of constantly rebalanced portfolios (CRPs) and of their performance bound than Cover (above). They also begin with a nice example of when a CRP has positive return even though neither stock does. They motivate the problem of performing as well as the best CRP by describing how one can perform nearly as well as the best individual stock (within $1/N$ of the terminal wealth) by simply investing equal-weight initially and holding each stock. They use the same strategy as Cover for performing nearly as well as the best CRP: spread wealth evenly across CRPs and let it grow within each CRP, and get the same bound: the wealth of the strategy is less than the wealth of the best CRP by no more than $(T+1)^{(N-1)}$ over $T$ periods, with $N$ assets. They also consider a case of transaction costs to derive a (slightly looser) bound.
The authors give a MUCH simpler description of constantly rebalanced portfolios (CRPs) and of their performance bound than Cover (above). They also begin with a nice example of when a CRP has positive return even though neither stock does. They motivate the problem of performing as well as the best CRP by describing how one can perform nearly as well as the best individual stock (within $1/N$ of the terminal wealth) by simply investing equal-weight initially and holding each stock. They use the same strategy as Cover for performing nearly as well as the best CRP: spread wealth evenly across CRPs and let it grow within each CRP, and get the same bound: the wealth of the strategy is less than the wealth of the best CRP by no more than $(T+1)^{(N-1)}$ over $T$ periods, with $N$ assets. They also consider a case of transaction costs to derive a (slightly looser) bound.