System and method for providing reallocation and reverse optimization of a financial portfolio using a parametric leptokurtic distribution

A computer-implemented system for providing reallocation and reverse optimization of a financial portfolio using a parametric leptokurtic distribution, comprising:

• a memory containing a database configured to store a time series comprising a plurality of risk factors applicable over at least one time horizon, a portfolio comprising a plurality of financial assets, a quantile, and one or more risk adjusted return points for the financial assets;
• an input device to receive input from a user;
• a network operatively coupled and providing communication between the memory, the input device, an output device, and a processor;
• where the processor is programmed to execute program modules, the program modules comprising:
• an association module configured to associate the financial assets with the risk factors;
• a risk determining module configured to generate a subordinated parametric distribution model exhibiting leptokurtic behavior;
• an expected tail loss determining module configured to express a function of expected tail loss for the quantile based on the parametric distribution model exhibiting leptokurtic behavior, wherein the expected tail loss, ETL(x,ε), is defined in accordance with the equation:
• F
• ⁡
• (
• x
• ,
• ζ
• )
• =
• ζ
• +
• 1
• ɛ
• ⁢
• ∫
• VaR
• ⁡
• (
• x
• ,
• ɛ
• )
• ∞
• ⁢
• [
• -
• z
• T
• ⁢
• x
• +
• V
• 0
• -
• ζ
• ]
• +
• ⁢
• f
• q
• ⁡
• (
• z
• )
• ⁢
• ⁢
• ⅆ
• z
• ,
• where the relation holds:
• ETL
• ⁡
• (
• x
• ,
• ɛ
• )
• =
• min
• ζ
• ∈
• ⁢
• ⁢
• F
• ⁡
• (
• x
• ,
• ζ
• )
• ,
• where ζ is a real number, VaR(x, ε) is Value-at-Risk of a portfolio where x=(x1, x2, . . . , xn) is a portfolio structure as a vector of portfolio allocation weights, ε is the quantile, fq(z) is the parametric distribution exhibiting leptokurtic behavior, with the density function of random vector q of future log prices of all portfolio prices one period ahead, vector z, where z=(z—1, . . . , z_n), is in n-dimensional Euclidean space and is over the domain of those z such that the value −zTx+V0 is larger than VaR(x, ε), where zT is the transposed vector of z, and V0 is present portfolio log-value;
• and
• a portfolio reallocation module configured to determine a set of portfolio asset weight changes for each of the financial assets based on the expected tail loss at each such time horizon and for each risk adjusted return point,
• wherein the output device is configured to provide reallocation of the portfolio based on the portfolio asset weight changes for each risk adjusted return point for the portfolio.