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Portfolio Optimization

Combined Portfolio Divided Portfolio Asset Allocation
 
Conclusions

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 - to reduce the risk, and
  • Asset Allocation - how much money to put into each separate investment within a portfolio in order to obtain the best return


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 well-diversified Divided Portfolio consisting of 14 members (FIGURE 2.2)

After that, one portfolio (Popt) has to be chosen based on the investor's capacity for risk

Popt={f1(r1d1),f2(r2d2),...,fi(ridi),...,fn(rndn)}

were (fi) - is an (i) member of the portfolio; (ri) - return of (fi); (di) - standard deviation of (fi)


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 two-steps approach:

  1. Choose some base solution
  2. Try to improve the base solution

Let's assume the members of the portfolio (Popt) are sorted in the ascending order of return, thus (rn) 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 (fn) with the maximum (rn)

So, our first base solution is

Pbase1={fn(rndn)}

The base 1 solution has two major drawbacks:

  1. We broke the principle of diversification
  2. In the worst case scenario, if the fund (fn) failed we would loose all our investments

Let's try to improve this base solution allocating our capital equally among all the members of the portfolio

Pbase2={f1(r1d1),f2(r2d2),...,fi(ridi),...,fn(rndn)}

The base 2 solution:
  1. Is consistent with the principle of diversification
  2. In the worst case scenario, if the fund (fn) (or any other member of the portfolio) failed we would loose only (1/n) of our investments

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 well-diversified 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.

 

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