1. A computer implemented method for maintaining a leveraged or reverse exchange traded product, comprising: electronically monitoring, with a computer, changes in value of a product sold on an exchange, Electronic Communication Network (ECN), or Alternative Trading System (ATS); in response to said monitored changes in value during a trading day, calculating, with a computer, a target number of shares in the product and/or derivatives based on the price of the product required to provide a target return that is one of a multiple of a return of the product, a negative of the return of the product, or a negative multiple of the return of the product, the target number of shares changing as a function of the monitored changes in value of the product during the trading day; buying or selling shares in the product to obtain the target number of shares; wherein the step of calculating further comprises calculating a leverage ratio, wherein the leverage ratio is dg(r)/dr=c(1+r) c−1 , and wherein r is a current, cumulative return of the product during a current trading day, and c is a constant, and wherein the leverage ratio is equal to the number of underlying shares required to provide the target return with respect to one share of the product; wherein c=ln(1+r′*)/ln(1+r′), and wherein r′* is the target return for a return, r′, of the product, and In(x) is the natural logarithm of x; and wherein, regardless of a timing of an investment in the leveraged or reverse exchange traded product and recent return history of the product, a forward looking return of the leveraged or reverse exchange traded product is fixed relative to the return of the product.