In An Introduction to Diversification, we began our review of the subject.

Knowing something about asset correlations is crucial to better understanding why diversification is important in an investment portfolio.

So that shall be today’s topic.

Asset correlation is a relatively advanced topic. For some of you that means I will not get into it as much as you would like. For others, your eyes may glaze over in boredom quickly.

At the end of the day though, I hope you gain some insight about correlation and how it can help you improve your investment results.

**What is Correlation?**

Correlation is a statistical measure (we cannot seem to escape the world of stats!) of how one asset moves in relation to a second asset.

With investment assets, risk factors can significantly affect performance. We looked at many of these variables in our discussions of nonsystematic and systematic risks. Government policies, inflation, interest rates, hurricanes, company management are a few examples.

The closer in characteristics two assets are, the more they will be affected by the same risk factors. The more divergent the assets, the less impact individual risk factors will have on each at the same time.

Let us use coffee shops to illustrate this point.

Two Starbucks franchises located on the same city block in New York are almost identical in nature. Same clients, same products, same impact from changes in coffee prices, and so on. There may be some minor differences, but not many.

If the city suffers an economic downturn, each shop should suffer equally. If Starbucks is investigated for selling coffee laced with carcinogens, business at both will fall.

Now compare a Starbucks with an Italian espresso shop on the same block.

Many of the same risk factors will be identical because of their physical proximity and product offering. If the local economy falters, both businesses may have difficulties. But if Starbucks is sued for potentially killing customers, Starbucks will suffer whereas there will be no negative impact on the espresso bar.

What about comparing two Starbucks? One in Los Angeles, one in Zurich.

Again, there are similarities between the two, but there are also large differences. If there is an earthquake in Los Angeles that destroys every Starbucks in the city, there will be no problems for the Zurich franchise. If the Swiss economy struggles and customers look for more cost effective coffee options, that has no direct effect on business for a Starbucks in California.

We could look at many more combinations, but I think you get the idea.

**Correlations and Investing**

Like Starbucks’ franchises, some investments share many of the same traits and risk factors. Others have little in common. Some even react in opposite directions to the same risks.

How an investment moves or performs relative to another asset is its correlation.

And this correlation is the reason you want to hold a “wide variety of investments” (per Investopedia) in your portfolio.

When two investments are positively correlated, their performance will move in the same direction. Like two Starbucks on the same street.

When two investments are negatively correlated, if one asset outperforms its expected results, the other will underperform. Perhaps like a pawn shop on the same city street as the Starbucks.

When the economy is great, it’s frappuccinos for everyone. People are making money and not needing to hock their assets. The pawn shop is a lonely place.

But when bad times hit and people become unemployed, there is less money available for a premium priced coffee. Starbucks struggles and may incur losses. Meanwhile, the cobwebs have been cleared off the pawn shop cash register and business is booming. At least until the economy recovers and the Starbucks’ baristas are back at work.

If the movements of two assets are exactly identical, they are 100% positively correlated. If they move in exact opposite directions, they are 100% negatively correlated. If they have no relationship at all, the correlation is 0%.

In investing, correlations range from 1.00 (100% positive) to -1.00 (100% negative).

Most assets are positively correlated to varying degrees. In part this due to increasing globalization and far reaching risk factors that impact most assets. These include inflation, interest rates, government policies, and employment rates.

While most assets are positively correlated, few are perfectly correlated. That is, few assets have correlations of 1.0.

Consider the two Starbucks on the same street. As close in likeness as can be. However, one manager may be better than the other, resulting in customers buying more accessories. Or perhaps the baristas are better in the second shop. They are friendlier, faster, and serve better quality drinks. So although both shops have the same offering, customers over time may increasingly frequent the shop with better service.

Even in a small example like this, there are potential differences between almost identical businesses. This is equally true for investments. And, as we shall see below, these minor differences can play an important role in managing portfolio risk.

Correlations between two specific assets may change over time. As the characteristics and circumstances of the underlying investments shift, so too can the correlations.

**Correlations in Action**

Exxon Mobil is a multinational oil and gas publicly traded company. Let us pretend that your investment portfolio only holds shares in Exxon.

The expected return of Exxon is 15% and the investment risk (i.e. standard deviation) is 10%.

You have read that diversifying your portfolio helps reduce portfolio risk. So you want to sell half your Exxon stock and invest the proceeds in another instrument.

From your research, you find two possible investment options.

Option one is shares of Chevron, another multinational oil and gas company. Option two is the Fine Art Fund; a mutual fund made up of fine art investments. Both have the same expected returns, 25%, and standard deviations, 20%.

If they both have the same risk-return profile, does it really matter which one you select?

Yes!

In many ways, Exxon and Chevron are the same company. They are in the same industries, operate in similar countries, and are affected by the changing price of oil and related commodities. One should expect their share prices to mirror each other to a great degree.

Their performance will not be exact due to company specific risks.

In 1989, faulty equipment, human error, and fatigued crew were factors in the crash of the Exxon Valdez in Alaska. A crash that caused many problems for Exxon.

In Ecuador, Chevron is currently involved with the Ecuadorean government over environmental issues that may result in fines and costs to Chevron.

But for the most part though, in the absence of unique situations, the share prices of major oil companies generally move together up or down.

That is why I would anticipate the correlation between Exxon and Chevron being close to 1.0 (i.e. 100% positive). It would not be exactly 1.0, because the two companies do operate in some different markets, have different product mixes, different management, etc.

But I would expect over a long period for the two companies to track each other quite well in share price. I just looked at a five year performance comparison between Exxon (stock symbol: XOM) and Chevron (stock symbol: CVX) – you can compare companies using Yahoo Finance Interactive Charts – and the similarities over time are striking.

But although they are close, they are not exact matches. That is good for diversification.

But not great.

**The Importance of Correlations**

Anytime the correlation between two assets is less than 1.0, there is an advantage in reducing overall risk by adding the new investment to one’s portfolio.

That is because of the portfolio risk-return calculations.

In (very) short, by adding assets that are not perfectly correlated to each other, one receives the cumulative impact of the expected returns, but only a reduced impact on portfolio risk.

I have re-read the Investopedia definition of diversification a few times.

I do not really understand what they mean when they state diversification will “yield higher returns and pose a lower risk than any individual investment found within the portfolio.”

I agree with the latter part of the statement, but have trouble with the first section.

**Correlations and Portfolio Expected Return**

While diversification allows you to invest in assets with high expected returns, diversification does not give the portfolio any bump.

In an investment portfolio, the expected return of the portfolio is simply the sum of each individual investments’ weighted averages in the portfolio.

For a simple, two asset portfolio:

ERp = (Wa)(ERa) + (Wb)(ERb)

Where:

ERp = Expected return of the portfolio

Wa = Weight in percentage of investment “A” in total portfolio (“b” for investment “B”)

ERa = Expected return of investment “A” in the portfolio

In our example, the expected return of Exxon is 15% and 25% for Chevron. If you invest 50% of your portfolio in each asset, the portfolio’s expected return should be 20%.

ERp = .50(15) + .50(25) = 20%

Pretty easy.

Remember that expected returns are just weighted averages of all the individual investments.

Correlations between assets do not impact the expected returns of the portfolio.

**Correlations and Portfolio Risk**

However, it is not that simple a calculation for the risk of the portfolio.

You need to factor the assets’ correlations into the equation. In a two asset (A and B) portfolio:

℺²p = (W²a)(℺²a) + (W²b)(℺²b) + (2)(Wa)(Wb)(℺a)(℺b)(pab)

Where:

℺ = Standard deviation

Wa = Weight in percentage of investment “A” in total portfolio (“b” for investment “B”)

pab = Correlation between investments “A” and “B”

The first part of the equation looks a lot like the expected return calculation. In that sense, there is a weighted average effect from risk.

But let us see how the second part of the equation alters the equation’s impact.

**Diversification Impact of Strongly Correlated Assets**

In our example, the standard deviation for Exxon was 10% and for Chevron 20%. Because the two companies are quite similar, I shall say that the correlation coefficient is 0.85. Not quite 1.0, but close.

If we crunch the numbers we see that the portfolio standard deviation is 14.49%. Slightly less than if we simply took the weighted average (15%) as we did with expected return.

The difference is due to the fact that the two assets are not perfectly correlated. However, because the correlation of 0.85 is very high, the reduction in risk is relatively small.

**Diversification Impact of Weakly Correlated Assets**

Now let’s consider our other potential investment; the Fine Art Fund. It had the same expected return (25%) and risk (20%) as Chevron. Therefore, we would expect an Exxon-Fine Art portfolio to yield the same expected return and risk as the Exxon-Chevron combination.

Actually, no we would not expect that in the slightest.

Here’s why.

In the real world, the correlation between fine art and oil companies is negligible. In fact, there is no correlation between the performance of Exxon and a bunch of paintings. So we shall say that the correlation between Exxon and the fund is 0.002.

Now for the numbers.

The expected return of a portfolio consisting of 50% Exxon and 50% Fine Art Fund would be 20%. The same as with the combined Exxon-Chevron portfolio.

This is because both Chevron and the Fine Art Fund have the same expected returns. And, as we saw above, expected return calculations are simply weighted averages of the portfolio’s individual investments.

But the portfolio risk is a different story.

If we crunch the numbers we see that the portfolio will have a risk of only 11.2%. Much less than a pure weighted average of 15% and significantly less than the Exxon-Chevron combination of 14.5%.

Yet the expected returns of both a portfolio of Exxon-Chevron or Exxon-Fine Art Fund are identical at 20%.

From a risk-return aspect, the Exxon-Fine Art Fund is the much better investment choice.

**Why is Option Two Superior?**

Because of the correlation between the assets.

Assets with high correlations receive some impact through diversification. But as you move toward a perfect correlation of 1.0, the risk reduction benefits from diversification lessen.

If you really want to reduce portfolio risk, you need to add assets that have low, or even negative, correlations to the assets already in the portfolio.

Investopedia states that diversification “mixes a wide variety of investments within a portfolio”.

True.

But to make it worthwhile, be certain you consider the correlations between assets as well as expected returns and risk levels in your investment selections.

The impact on your portfolio’s efficiency could be huge.

As for the optimal mix, there are many other variables that need consideration. We will look at them down the road in asset allocation and portfolio construction.

Next up, a few more thoughts on the benefits of diversification.

I often read your blog, I just thought I would say to keep the good work!