In this paper we solve the problem of static portfolio allocation based on
historical Value at Risk (VaR) by using genetic algorithm (GA). VaR is a
predominantly used measure of risk of extreme quantiles in modern finance.
For estimation of historical static portfolio VaR, calculation of time series
of portfolio returns is required. To avoid daily recalculations of proportion
of capital invested in portfolio assets, we introduce a novel set of weight
parameters based on proportion of shares. Optimal portfolio allocation in the
VaR context is computationally very complex since VaR is not a coherent risk
metric while number of local optima increases exponentially with the number
of securities. We presented two different single-objective and a
multiobjective technique for generating mean-VaR efficient frontiers. Results
document good risk/reward characteristics of solution portfolios while there
is a trade-off between the ability to control diversity of solutions and
computation time.
The mean-value at risk static portfolio optimization using genetic algorithm
