  We propose and study a simple model of dynamical redistribution of capital in
a diversified portfolio. We consider a hypothetical situation of a portfolio
composed of N uncorrelated stocks. Each stock price follows a multiplicative
random walk with identical drift and dispersion. The rules of our model
naturally give rise to power law tails in the distribution of capital fractions
invested in different stocks. The exponent of this scale free distribution is
calculated in both discrete and continuous time formalism. It is demonstrated
that the dynamical redistribution strategy results in a larger typical growth
rate of the capital than a static ``buy-and-hold'' strategy. In the large N
limit the typical growth rate is shown to asymptotically approach that of the
expectation value of the stock price. The finite dimensional variant of the
model is shown to describe the partition function of directed polymers in
random media.
