Abstract: A method of applying a substantially constant leverage to a value of a log-normal distributed asset includes providing an underlying log-normal distributed asset having an original volatility ? and an original yield q. The asset includes an associated value S denominated in a currency having an associated interest rate r. The method and system also include applying a leveraging factor L to produce a modified value, volatility and/or a modified yield.

Abstract: A method is applied for improving performance of constant leverage assets (CLAs) by establishing a CLA approximated portfolio of assets having investment options in relation to an original portfolio. The investment options are allocated to predetermined increments whereby they are subsequently monitored in view of the CLA approximated portfolio. The performance of the CLA approximated portfolio is evaluated based on the monitored leverage in comparison with a desired level of leverage, and analyzed in view of underlier trends correlated to options exchanges. Readjustment occurs by incorporating new strikes upon the determination of the underlier trends fluctuating up or down, and thereby altering an approximate payoff function which ultimately varies the leverage of the CLA approximated portfolio to a level marginal to the desired level.

Abstract: Several methods are applied for providing an investor performance evaluation analysis of certain investments. A Continuous-Time method, Taylor Series expanding and compounding method and a Monte Carlo with Brownian Bridges simulation method produce useful statistical answers per each investment during a multitude of periods, including the expected performance, standard deviation around the expected performance, various confidence intervals, and even an estimate of the actual distribution of future returns. Additionally, important features such as the dependence of such an investment on market volatilities, correlations, dividends, and interest rates are made apparent to the investor and sometimes precisely quantified.

Abstract: A method of applying a substantially constant leverage to a value of a log-normal distributed asset includes providing an underlying log-normal distributed asset having an original volatility &sgr; and an original yield q. The asset includes an associated value S denominated in a currency having an associated interest rate r. The method and system also include applying a leveraging factor L to produce a modified value, volatility and/or a modified yield.