
Home  Portfolio Optimization  0/1 Knapsack Problem  About Us  Contact Us 

Problem Description
The investor's objective is to get the maximum possible return on an investment with the minimum possible risk.
This objective led to the development of two investment strategies:
Portfolio Diversification
Most investment experts suggest the size of the portfolio in range 6 to 30 funds, and it is largely depends on the Fund Manager's preferences.
Once the size of the portfolio is chosen, the selection of the best members of the portfolios (Combined Portfolios) or (Divided Portfolios) is next.
As a result of these selection procedures, we created a set of the optimal portfolios consisting of 10, 15, and 20 members (FIGURE 2.1), and welldiversified Divided Portfolio consisting of 14 members (FIGURE 2.2)
After that, one portfolio (P_{opt}) has to be chosen based on the investor's capacity for risk Asset Allocation
Once the portfolio is chosen, the asset allocation procedure is next  how to determine the separate investments within a portfolio in order to obtain the best tradeoff between risk and return along with applicable constraints (e.g. we are not allowed to put more than 10% of the portfolio into one fund).
Let's use the next twosteps approach:
Let's assume the members of the portfolio (P_{opt}) are sorted in the ascending order of return, thus (r_{n}) has the maximum value among all the members of the portfolio.
Clearly, we can potentially obtain the maximum return allocating all the money into the fund (f_{n}) with the maximum (r_{n}) So, our first base solution is The base 1 solution has two major drawbacks:
Let's try to improve this base solution allocating our capital equally among all the members of the portfolio
Any other attempts to improve the base 2 solution require to allocate resources unequally (to assign the unequal values to the eggs in our baskets), or to shrink the size of the portfolio (the number of the baskets), or both.
All of them inevitably lead to bigger losses in the worst case scenario, and cannot be considered as optimal. Final Thoughts
Equal allocation of the investment capital among all the members of the portfolio has obvious benefits.
It doesn't mean this approach is the Fund Managers' only possible choice.
Fund Managers may try their own methodologies, strategies, and preferences to obtain a better tradeoff between risk and return allocating investment unequally.
In any case, the starting point is the selection of the optimal welldiversified portfolio based on the investor's capacity for risk.
And the best way to do it is by using our Combined Portfolio and/or Divided Portfolio software.

Home  Portfolio Optimization  0/1 Knapsack Problem  About Us  Contact Us 