Optimal Portfolio Tutorial




DEFINITION:

An optimal stock portfolio is a stock portfolio consisting of those stocks that an individual wishes to own, configured in such a way that they generate the greatest or optimal return statistically possible for the particular amount of risk an investor is willing to accept.



Do-It-Yourself Optimal Portfolio

At the "heart" of the PMF™ we create for our clients is an OPTIMAL PORTFOLIO containing only those stocks they wish to invest in. In the following do-it-yourself illustration we will construct an optimal portfolio showing you each step so that you get a real "hands on" feel for the PMF™ service we offer.

Let’s suppose you have $10,000 to invest and want us to create a PMF™ consisting of your three favorite stocks - Amce Widgets Ltd., FinBiz Inc and InterNational Blivet. The fundamental question is: " how much of the $10,000 should be invested in each stock to give the best return possible for the risk that you are willing to accept ?". Let’s start to answer this question by constructing 10 random portfolios, each consisting of different proportions of the three stocks and list their RISK/RETURN profiles in Table 1 below.


Acme WidgetsFinBiz Inc.InterNational Blivet
Risk
Return
Portfolio #132%38%30%12.10%11.51%
Portfolio #268%12% 20% 15.54% 12.76%
Portfolio #3 27% 51% 22%12.91% 11.59%
Portfolio #4 20% 20%60% 9.89% 11.00%
Portfolio #5 60% 20%20%14.86% 12.71%
Portfolio #6 12% 74% 14% 13.48% 11.22%
Portfolio #7 15% 80% 5% 14.28% 11.40%
Portfolio #8 38% 19%43%11.76% 11.71%
Portfolio #9 42% 19% 39%12.05% 12.49%
Portfolio #10 74% 10%16% 16.35% 13.06%
RISK / RETURN PROFILE TABLE 1



Interpreting Table 1 is very straightforward. Portfolio #1 consists of an investment of 32% of the $10,000 (i.e., $3,200) in ACME Widgets Ltd., 38% ($3,800) in FinBiz Inc., and the remaining 30% ($3,000) in InterNational Blivet. This particular portfolio configuration carries with it a risk to your capital of 12.10%, and an expected return of 11.51%. The important thing to notice in Table 1 is that each portfolio, due to its different cash/stock allocation, has a unique RISK/RETURN profile.

In order to better visualize the different RISK/RETURN profile of each portfolio we next construct a graph of the data in Table 1.



The number to the right of each red diamond on the graph corresponds to the ID number of the portfolio in Table 1. The graph makes it easy to see that, for the most part, the higher the return associated with a portfolio, the higher the risk - something you've no doubt heard before.

Now let's suppose that you are willing to accept a risk of around 12% on your investment. Which portfolio should you choose? Let's look at the RISK/RETURN graph reproduced below (portfolios #3 and #8 have been omitted to facilitate presentation). You will notice that Portfolios #1 and #9 each have a risk of about 12% but their returns are quite different. Portfolio #9 offers a return of 12.49% whereas Portfolio #1’s return is almost a whole percentage point less at 11.51%. The choice is rather obvious: for the same amount of risk, i.e. about 12%, Portfolio #9 offers a return superior to Portfolio #1. In this illustrative example, Portfolio #9 would be the OPTIMAL PORTFOLIO configuration for an investor willing to accept an investment risk of 12%.



If we continue to generate more random portfolios consisting of different cash/stock allocations a very interesting thing happens. For the sake of illustration let's generate 40 more random portfolios. The graph below is the result.



Perhaps the most striking visual detail in this new graph is the "boundary" (bold dotted line) that is forming. This boundary is known as the EFFICIENT FRONTIER and upon it lie the optimal portfolios we are seeking - those portfolios that statistically guarantee the greatest return for a given risk. With only a total of fifty random portfolio configurations, the boundary is starting to take shape. If this had been an actual client case we would have generated and analyzed the entire "universe" of possible stock portfolio configurations, the end result being an efficient frontier that would be "filled in" allowing our clients to choose the optimal portfolio for every possible risk (within reason!).




Risk/Reward Profile

After a collection of stocks is analyzed as described above, those portfolio configurations that "land" on the efficient frontier are optimal portfolios and are summarized in a Risk/Return Table. This table is a very powerful investment tool that gives investors the ability to choose that optimal portfolio that will give them the greatest return statistically possible for a particular risk they are willing to assume.

For the sake of continuity we'll stick with our illustrative portfolio consisting of Acme Widgets, FinBiz Inc. and International Blivet. After creating and analyzing the entire universe of possible portfolio configurations consisting of these three stocks, the optimal portfolios ( in 0.5% risk increments) are summarized in Table 1. below.


RiskReturnAcme Widgets %
of Portfolio		FinBiz Inc.%
of Portfolio		International Blivet %
of Portfolio
9.0%10.98%10%21%69%
9.5%11.21%18%17%65%
10.0%11.73%21%15%63%
10.5%11.96%28%14%58%
11.0%12.23%22%19%61%
11.5%12.61%30%27%43%
12.0%12.83%28%21%50%
12.5%12.92%37%12%51%
13.0%13.02%30%38%32%
13.5%13.12%26%27%47%
14.0%13.23%21%46%33%
RISK/RETURN Table of OPTIMAL PORTFOLIOS TABLE 1


Let's say that you are a rather conservative investor willing to assume a risk of 9.50%. Looking at the RISK/RETURN Table for 9.50% risk gives the following return and PMF™ cash/stock configuration:


RiskReturnAcme Widgets %
of Portfolio		FinBiz Inc.%
of Portfolio		International Blivet %
of Portfolio
9.5%11.21%18%17%65%
OPTIMAL PORTFOLIO (for 9.50% RISK)



Measured statistically there is no other portfolio configuration containing these three stocks (at this moment in time) that can give you a return higher than 11.21% for a risk of 9.50%.






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