Today we will look at an example of how asset correlations impact portfolio diversification.
Namely the impact on portfolio risk and expected returns.
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. A non-diversified portfolio.
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 (and other jurisdictions), Chevron is involved with the Ecuadorean government (and others) 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). Not exactly 1.0, as the two companies operate in some different markets, have different product mixes, different management, etc.
I would expect over a long period for the two companies to track each other quite well in share price. Compare the five year performance 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 magic 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. There is almost no correlation between the performance of Exxon and a bunch of paintings. Let us say 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 14.49%.
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 combination than Exxon-Chevron.
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. You want to add assets that are weakly correlated to your existing portfolio. Not simply a “wide variety of assets.”
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.
This sort of gets at the Investopedia claim about how diversification can “yield higher returns.” Say you find a weakly correlated asset that offers higher expected returns to add to your portfolio. You may be able to maintain your portfolio risk at its current level, yet get a bump by adding the potentially higher return asset. Poorly worded by Investopedia.
Next up, a few more thoughts on the benefits of diversification.
