Optimal Stock Portfolio Tutorial

What Is A Stock Portfolio?

Simply put: A Stock Portfolio is a collection of diverse stocks proportionately configured to minimize an investor's potential Risk while, simultaneously, providing an acceptable Return for that level of Risk.

Portfolio Return means what you would expect it to - you create a $100,000 diverse stock portfolio today and a year later it is worth $110,000 - your "Return" is $10,000 or 10%.

Portfolio Risk is a little more complex. For the mathematically inclined, Portfolio Risk is the Standard Deviation of the portfolio's Expected Return. In laymen's terms, if a portfolio has a present value of $100,000, a projected annual Return of 10%, and a projected annual Risk of 15%, it means that there is a 68% chance that in the coming year the portfolio's value could be anywhere between $95,000 and $125,000; 34% chance of a value between $95,000 and $110,000, a 16% chance that the portfolio would be worth more than $125,000, etc. The mathematics used to create these probabilities is inconsequential, the important concept here is that you can construct an "Optimal Portfolio", i.e. a portfolio with the highest Return possible for the Risk YOU choose.

Your Personal Risk/Return Profile.

Portfolios have, by their very nature, a trade off between the Risk inherent in the portfolio's stocks due to market uncertainties and the Return those investments generate. Each of us has a different comfort level of Risk due to age, income, assets, core personality, etc. A 45-year-old Oncologist making $400K a year can probability "throw" $100K into a high risk portfolio. A recently retired government worker on a fixed income probably couldn't sleep at night doing the same thing.

If you already have a portfolio it is imperative to determine its present Risk/Return profile. Many portfolios start with the "proper" Risk/Retun profile but, over time, become Riskier then they started out to be. So the fundamental question is: is your portfolio's present Reward worth its present Risk.

For the sake of illustration letís suppose that 2 years ago you invested $100,000 in "MyPort" consisting of your three favorite stocks - Amce Widgets Ltd., FinBiz Inc and InterNational Blivet. The present stock configuration and accompanying Risk and Reward information are listed below in Table 1:
Acme WidgetsFinBiz Inc.InterNational Blivet
74%10% 16% 16.35% 13.06%
MyPort Breakdown with Risk/Return

Table 1

MyPort consists of $74,000 worth of Acme Widgets, $10,000 of FinBiz Inc., and $16,000 of InterNational Blivet (the actual number of shares of each stock owned are immaterial for this analysis).

MyPort's present Risk/Return percentages are interpreted in the following manner: With a projected Return of 13.06% and a projected Risk of 16.35% over the next year, MyPort has a 68% probability of being worth between $97,000 and $130,000 by the end of the year. Perhaps more disturbingly, there is a slighty greater than 21% chance that the value of the portfolio could be less than the original $100,000 invested - a one in five chance of loss.

What Is An Optimal Stock Portfolio?

An Optimal Stock Portfolio is: A stock portfolio consisting of stocks proportionately configured in such a way as to generate the greatest or Optimal Return possible for the particular amount of Risk an investor is willing to accept.

Letís start our search for an Optimal Portfolio by renaming "MyPort" Portfolio #10 and then constructing 9 random portfolios, each consisting of different proportions of the three stocks and comparing their Risk/Return results in Table 2 below:
Acme WidgetsFinBiz Inc.InterNational Blivet
Portfolio #132%38%30%12.10%11.51%
Portfolio #268%12%20%15.54%12.76%
Portfolio #327%51%22%12.91%11.59%
Portfolio #420%20%60% 9.89%11.00%
Portfolio #560%20%20%14.86%12.71%
Portfolio #612%74%14%13.48%11.22%
Portfolio #715%80% 5%14.28%11.40%
Portfolio #838%19%43%11.76%11.71%
Portfolio #942%19%39%12.05%12.49%
Portfolio #10
74% 10%16%16.35%13.06%
Randomly Generated Portfolios

Table 2

The important thing to notice in Table 2 is that each portfolio, due to its different stock proportion configuration, has a unique Risk/Return profile. In order to better visualize this, the data in Table 2 is illustrated in Figure 1 below.

Figure 1

The number to the right of each red diamond on the graph corresponds to the ID number of the portfolio in Table 2. The graph makes it easy to see that, for the most part, the higher the Return associated with a portfolio, the higher the Risk - an investing mantra 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 in Figure 2(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 #1ís 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 more "Optimal" than Portfolio#1 for an investor willing to accept an investment Risk of 12% .

Figure 2

If we continue to generate more random portfolios consisting of different stock percentage configurations a very interesting thing happens. For the sake of illustration let's generate 40 more random portfolios. The resulting graph is illustrated in Figure 3 below:

Figure 3

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 have the highest "guarantee" of the greatest Return for a given Risk. With only a total of fifty random portfolio configurations, the boundary is starting to take shape. Certainly the foregoing procedure can be replicated generating and analyzing the entire "universe" of possible stock portfolio configurations, the end result being an efficient frontier that would be "filled in" allowing you to choose the Optimal Portfolio for every possible Risk (within reason!).

Choosing Your Optimal Portfolio

As stated above, those portfolio configurations that "land" on the efficient frontier are Optimal Portfolios. Let's now create an Optimal Portfolio table using 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 resulting Optimal Portfolios ( in 0.5% Risk increments) are summarized in Table 3 below. For the sake of brevity the interval of Risk Percentages chosen is from 9% to 14% in .5% increments.

Table 3 below is a very powerful investment tool that gives an investor the ability to choose that Optimal Portfolio for a particular Risk they are willing to assume.
RiskReturnAcme WidgetsFinBiz Inc.International Blivet
Optimal Portfolio Table

Table 3

Let's assume you are conservative and willing to assume a Risk to your capital of 9.50%. Looking at the Risk/Return Table for 9.50% Risk gives the following Return and stock configuration Table 4:

RiskReturnAcme WidgetsFinBiz Inc.International Blivet
Optimal Portfolio

Table 4

Measured probabilistically, 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%.

Closing Thought

Unfortunately because the stock market is fluid, its nature constantly changing, even Optimal Portfolios tend to lose their "Optimality" over time. There is no such thing as "buy and forget" in serious portfolio investing. For this reason portfolio owners must regularly monitor the Risk/Return profile of their portfolios and make adjustments when necessary to regain Optimality.