The present invention provides for maintaining an approximate absolute risk level for an investment portfolio while minimizing trading necessary to do so. A portfolio of long and short position assets can be obtained that is approximately logarithmic, in the sense that that the value of the portfolio varies in constant proportion to a fractional change in a level of a market. When the market level changes by a specified degree, asset holdings can be adjusted as necessary to the maintain the portfolio as being approximately logarithmic, and total holdings can be adjusted as necessary to maintain a specified level of absolute risk.