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Using Modern Portfolio Theory with Automatic Investor

Posted by | March 2, 2014 | Articles | No Comments

Most investors intuitively see the logic behind diversification. However many don’t practice this important technique or they don’t know how to implement an effectively diversified portfolio. Over the long term, this is a huge mistake.

Diversification is the primary tool investors can use to spread their risk between countries, currencies and markets. It allows us to take advantage of opportunities when they unexpectedly appear and protects us from unseen crises situations. In short, diversification reduces risk and, when properly applied, can increase returns.

How many investors do you know who wouldn’t want to decrease risk and increase returns? Probably none. It follows then, that if investors really sit down and think about it, they will diversify. Those who don’t most likely haven’t thought about it, are gambling rather than investing, or think they know something the rest of the world doesn’t. Experience and research shows that all of these reasons are extremely dangerous to investors’ portfolios.

But how do you diversify properly? What investments should you include? How many different investments should you have in your portfolio? What percentage should each contribute to your portfolio’s overall make up?

These questions must be answered accurately before a portfolio can be properly diversified.

Of course the investments you place into your portfolio must meet your criteria and nobody else’s. You need to accurately assess your risk tolerance, the time left before you will need the money from your investments and a number of other factors. Once you’ve completed your homework, you can then begin to diversify.

Diversification always involves a trade off between risk and return. Let’s say we have two investments: sunglasses and umbrellas. The sunglasses investment pays off for every day that is sunny. It pays nothing on days that aren’t sunny. The umbrella investment pays off for every day that is not sunny. It pays nothing on sunny days. It stands to reason that you would always choose to invest in sunglasses if you were absolutely sure that every day over the next year would be sunny. Similarly you would invest completely in umbrellas if you were certain that each day over the next year would not be sunny. Using this strategy you would realize the maximum possible return on these investments.

However, as we all know, predicting the weather is not 100% accurate. All we know is that at some point within the next year we will have sunny days and we’ll have days that aren’t sunny. Furthermore, we don’t know which days will be sunny and which ones won’t. However we could study the historical weather patterns for our area and come to a fairly accurate prediction on how many days (over the course of a typical year) will be sunny and how many won’t be. As it turns out, this is very similar to the stock market. Short-term, we can’t predict anything with great accuracy. However our accuracy improves over the long-term.

For example, if you were to try to predict IBM’s return over the next year, you might be well off the mark. However if you were to try to predict its return over the next 20 years, you’d probably be a lot closer. Therefore it isn’t unreasonable to use a stock’s history to try to predict its future – as long as you’re doing this over the long-term. (Keep in mind, however, that past performance does not guarantee similar performance in the future.)

And since diversifying correctly requires that you make some predictions, your outlook needs to be long-term.

The rest of this article assumes you’ve decided on the general type of investments that will go into your portfolio (e.g. bonds, mutual funds, small cap equities, large cap equities, and such) as well as the specific securities (e.g. IBM or UOPIX). It further assumes you’ll be investing in equities (and perhaps bonds) rather than other investments such as real estate or treasury bills (although you could use the same techniques to manage any investment). A final note is that a properly diversified portfolio won’t gain anything more by holding more than 40 or so equities. Usually 20 to 40 individual stocks is a good number – but you can get by with less when using mutual funds which are already somewhat diversified.

To begin, I’ll introduce a unique way of looking at investment portfolios.

In 1953, Harry Markowitz developed an ingenious approach to managing investment portfolios that has since been dubbed Modern Portfolio Theory (MPT). Rather than trying to predict individual stock price movements using fundamental or technical analysis, he concentrated on looking at the performance of a portfolio based on the combination of its components’ risk and return.

Unfortunately the underlying calculations required to implement his theory were onerous and not conducive to solving by hand. Therefore it wasn’t until the late 1970s, when computers started to show up everywhere, that MPT took off. Markowitz went on to win the Nobel Prize for Economics in 1990 for his contribution of MPT.

Attesting to its validity is the fact that a large number of professional money managers now use MPT to help them with their work.

While the technical details of MPT are very complex, the good news is that there are software packages currently available that allow you to bring the full power of MPT to bear on your portfolio without having to know how the calculations are performed. This means that you can use the same techniques used by some of the top financial minds on your own portfolio – and reap the rewards without having to pay the fees large financial minds usually demand.

Let’s look at how MPT works. Going back to our sunglasses and umbrellas example, we can see that each investment is fairly risky. On any given day you might not make any money. However a portfolio that contains both sunglasses and umbrellas will always pay off – whether the sun shines or not. By adding one risky investment to the other, you’ve effectively reduced the overall risk of your portfolio. (What’s more, if you vary the portion of your sunglasses and umbrellas investment according to the number of days you predict will be sunny or not sunny, your returns might be greater. In essence, you’ve reduced your overall risk and increased your returns.)

The important insight of MPT is that the risk of an individual asset is not too important. What is of prime importance is its contribution to the portfolio’s risk as a whole. And that’s why MPT uses diversification as its primary mechanism.

The first step in using MPT is to predict each investment’s expected return over the long-term (recall that we can generally come up with a good prediction if we’re dealing with long periods of time).

The next piece of information we need is the risk associated with our portfolio. Risk can be defined in a number of ways, however most investors use the standard deviation. For the purposes of this article, we’ll also define risk to be the standard deviation of our particular investment.

The final piece of information we’ll need is the correlation between each investment in our portfolio. Correlation information is usually given as a matrix of correlation coefficients.

All of this information can be obtained from an investment’s historical data. Once we have these data, we can begin our MPT calculations. Our goal is to diversify our investments, in very specific portions, in order to come up with a portfolio that provides a given return at the lowest risk level or the best return for a given level of risk.

MPT assumes that investors will always want the highest return at the lowest risk. In essence it asks, “why would an investor choose an asset that returns 4% a year with a 50% chance of losing some money over an investment that returns the same 4% a year with a 0.001% chance of losing some money?”

The answer, of course, is that a rational investor would not do this. Instead he would choose the investment that returns 4% with the 0.001% risk level. Of course some investors might choose an investment that returns 5% with a 50% risk of losing money over the 4% return, 0.001% risk level investment. And that’s okay with MPT. It doesn’t make assumptions in those cases. If investors are willing to accept greater risk, then they must be compensated with greater returns (no matter how little or how much greater).

In this article, we’ll only look at stocks because studies have consistently shown that they are the most profitable investments over the long-term (however you can use the techniques described with many other investment classes).

In the United States, between 1926 and 1994, small cap stocks have returned 12% annually with a standard deviation (i.e. risk) of 35%. Large cap stocks have returned 10% annually with a standard deviation of 20% over the same period.

Other investments have returned less, but have also been less risky. For example from 1926 to 1994, long-term government bonds returned 5% with a standard deviation of 9% and Treasury bills returned 4% with a standard deviation of 3%.

From these examples, we can see that the larger returns come at the expense of greater risk.

So how does diversifying reduce our risk and increase our returns? It does so by utilizing the way individual investments move with one another. If two investments both return 10% on a sunny day and nothing on a rainy day, then these investments are perfectly correlated (i.e. correlation coefficient is 1). In this case there would be no point in diversifying since owning both would provide exactly the same return as owning just one. (Note that it is a good idea to diversify within investment classes – i.e. investments that are highly correlated – so we eliminate specific, or non-market, risk. However we’ll ignore this in our examples.)

Instead we want to look for investments that aren’t perfectly (or even highly) correlated. Ideally we’d like to find two investments that are perfectly negatively correlated (i.e. correlation coefficient is -1, by the way, no such investments exist – but if they did, we’d be millionaires many times over in a short period of time), however in reality we usually have to settle for low, positive correlation coefficients.

Therefore many savvy investors diversify by investing in foreign markets as well as different industries and investment classes. The key point is to choose investments that aren’t highly correlated. This happens to be the case with domestic securities and foreign ones.

Once the data are fed into the MPT algorithm, a curve (called the efficient frontier) is plotted. The efficient frontier is the set of portfolios with expected return greater than any other with the same or lesser risk, and lesser risk than any other with the same or greater return.

The efficient frontier is usually plotted on a graph where the x-axis represents the risk level and the y-axis represents the expected return. Each point on the graph represents one particular portfolio that has a specific expected return and a specific level of risk.

This portfolio is composed of the individual investments put together in various portions (each individual investment can range from 0% to 100% of the portfolio).

For example, the point labeled Sample Portfolio (shown below) lies on the efficient frontier and might be composed of 0% T-Bills, 15% EK, 15% IBM, 25% MSFT, 30% AMZN and 15% ICGE. (Note that this is only an example and does not represent an actual portfolio.)


All portfolios that lie on the efficient frontier are called efficient portfolios.

Portfolios that lie below the curve are called inefficient portfolios (i.e. for a given risk level you can obtain a greater return using another portfolio – e.g. the one lying on the efficient frontier – and for a given return you can obtain a lower risk level by using another portfolio).

Portfolios that lie above the curve are not attainable (e.g. you cannot receive a 100% return with no risk).

MPT, therefore, quantifies risk relative to expected return and provides a mathematical model that shows you the best portfolio (i.e. how best to combine the individual investments in your portfolio) to use for a given level of risk or return.

The question naturally arises, “can we do better?” In this case the answer happens to be “Yes.” To see how, let’s introduce Automatic Investor into the equation. Automatic Investor uses an algorithm based on Robert Lichello’s AIM. It balances cash and equity in order to reduce risk and increase returns. This makes it a natural fit for use with MPT. After all, MPT is concerned with returns and risk – as we’ve seen.

By using Automatic Investor to manage each of the individual investments in your portfolio, you’re essentially reducing the risk and/or increasing the return for that investment compared to simply buying and holding that investment. So if the underlying investment has a high volatility (i.e. standard deviation), when Automatic Investor manages it, its volatility goes down significantly. Its return can also be expected to increase.

This causes that investment point to be shifted to the left (i.e. reduced risk) and/or up (i.e. increased return). If you plot the Automatic Investor managed point for each investment, and then calculate the efficient frontier, the curve will be shifted up and to the left.

In effect you’re now able to choose portfolios that were previously unattainable because for a given level of risk, your returns are higher and for a given return, your risk level is lower.

In essence, you are using MPT to manage your entire portfolio (the macroscopic view) and using Automatic Investor to manage each individual investment within your portfolio (the microscopic view). Automatic Investor filters the risk of the underlying investment so that it becomes less volatile at the macroscopic level.

Keep in mind that Automatic Investor thrives on volatility (or a relatively high standard deviation). Therefore using standard deviation as a risk measure at the microscopic level is counter-productive because Automatic Investor manages this risk to wring out higher returns.

However at the macroscopic level, standard deviation is an excellent measure of risk. While you don’t want your entire (macroscopic) portfolio to fluctuate wildly, you do want the individual (microscopic) investments within that portfolio to fluctuate (so that Automatic Investor can produce higher returns with less risk).

A side effect of this is that you can invest in equities that are slightly more risky than those with which you’d normally be comfortable. Since these “riskier” equities are being managed by Automatic Investor at the microscopic level and diversified according to MPT at the macroscopic level, your overall portfolio risk is within your tolerance – and your expected returns can be higher.

Therefore by using MPT in conjunction with Automatic Investor, your returns can be significantly increased and your risk significantly reduced compared with using either MPT or Automatic Investor by itself.

This article was first presented at the AIM 2001 conference in Las Vegas by Mark Hing.

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