So you’ve been told you should diversify your portfolio for stock investing, you’ve been told it makes for good stock portfolio management, but how can you know whether one of the potential stock investment strategies you’re considering is aiding you in diversifying your personal stock portfolio. Well, one way is to simply invest in different sectors, like Health Care, Technology, Construction, Financials, Real Estate, etc. But, are Health Care and Real Estate really that diversified? How can you know if you really have a good stock trading strategy?
Correlation
One-way to determine stock trading diversity is through correlation. If two investments are correlated, then generally they will not be considered diversified, and is probably not considered good stock portfolio management, on the other hand, if two investments are not correlated, then they may be good candidates for diversification.
How to Calculate
But, you say, “how do I calculate the correlation between two investments?”. If you use spreadsheet software or have access to spreadsheet, then the ability to calculate the correlation between various investments for aiding in good stock portfolio management is right at your fingertips.
Example
For example, let’s consider Health Care and Real Estate, and let’s assume a good proxy for the Health Care industry is the Health Care Select Sect SPDR (XLV) and maybe a good proxy for the Real Estate sector is the ETF (Exchange Traded Fund) iShares Dow Jones U.S. Real Estate Index Fund (IYR). Retrieving the data for these two symbols from Yahoo!’s Finance web site (a good web site for stock market research) and then using Microsoft’s Excel spreadsheet software with the Tools/Data Analysis/Correlation capability, a correlation coefficient of 0.735 is calculated for XLV/IYR indicating a fairly high correlation between the Health Care and Real Estate sectors. So, adding a health care investment to a portfolio of Real Estate investments is probably not very much diversification. (With respect to correlation, a correlation coefficient of -1.0 represents highly uncorrelated and a correlation coefficient of 1.0 represents highly correlated. For the purposes of this article, it will be assumed that a correlation coefficient of less than approximately 0.5 is a good threshold for determining diversification.)
OK, so now let’s throw in a bunch of sectors and see what happens:
| XLV | IYR | XLE | XLF | XLB | XLY | XLP | XLI | XLU | XLK | |
| Health Care (XLV) | 1.00 | |||||||||
| Real Estate (IYR) | 0.74 | 1.00 | ||||||||
| Energy (XLE) | 0.72 | 0.79 | 1.00 | |||||||
| Financials (XLF) | 0.82 | 0.78 | 0.83 | 1.00 | ||||||
| Materials (XLB) | 0.76 | 0.94 | 0.77 | 0.85 | 1.00 | |||||
| Cons. Discret (XLY) | 0.81 | 0.88 | 0.73 | 0.89 | 0.95 | 1.00 | ||||
| Cons. Staple (XLP) | 0.26 | 0.05 | 0.46 | 0.52 | 0.21 | 0.31 | 1.00 | |||
| Industrials (XLI) | 0.67 | 0.52 | 0.81 | 0.88 | 0.63 | 0.68 | 0.76 | 1.00 | ||
| Utilities (XLU) | 0.53 | 0.48 | 0.85 | 0.76 | 0.53 | 0.56 | 0.79 | 0.90 | 1.00 | |
| Technology (XLK) | 0.09 | -0.35 | 0.11 | 0.12 | -0.27 | -0.16 | 0.50 | 0.47 | 0.36 | 1.00 |
From the correlation matrix generated by the spreadsheet, it appears Health Care, Real Estate, Energy, Financials, Materials and Consumer Discretionary are all fairly highly correlated with each other.
Now let’s go back to our original quandary, suppose your personal stock portfolio is invested in Health Care and you want to diversify. Well, from the correlation matrix generated by the spreadsheet, we can see that Consumer Staples, Utilities and Technology are fairly well uncorrelated with Health Care, so those sectors might be good additions for diversification of your personal stock portfolio. Or, suppose we’re invested in Real Estate, in this case attractive sectors for diversification might be Consumer Staples, Industrials, Utilities and Technology.
The spreadsheet used for this analysis:
http://www.poweropt.com/Diversification.xls
A free Excel viewer may be downloaded from Microsoft’s web site to view it at www.microsoft.com (search for Excel viewer).
Note: For this article, the analysis was performed over a five-year historical time span.
[tags]investment diversification, exchange traded fund, etf, stock investing, stock portfolio management, stock investment strategies, stock market research[/tags]
Erwin
I would like to get your comments on the correlation coefficient calculation that you made. Specifically, whether the calculation should not be made between average annual returns, instead of the data you used. It seems to me that if you are planning to use Modern Portfolio Theory tools, you need the information on the same basis, if returns are annual and the risk is computed as the standard deviation of the annual returns, then the same should be done on the correlations. Erwin Rosen
admin Post author
I think I’ll avoid following the bunny down the Modern Portfolio Theory trail, but the correlations were recalculated using annual returns as mentioned in the blog response and the following are the results:
As can be seen from the data, the basic conclusions of the article still hold using the annual correlation data. One interesting difference between the two results is Consumer Staples (XLP) is fairly correlated (0.84) with Technology (XLK) using the annual correlation data and fairly uncorrelated (0.50) using the daily return correlation data. So are Consumer Staples correlated or uncorrelated with Technology? Well Consumer Staples consist of “stuff†that is purchased regardless of the economy, people still eat even in economic downturns, maybe a few more peanut and butter sandwiches and fewer steaks, but people still eat. But, on the other hand, Technology is very business cycle sensitive, people and especially the corporate world cut back on Technology purchases in an economic downturn. So from a 50,000-foot level Consumer Staples and Technology should not correlate very well, so the daily correlation results seem to make more sense than the annual correlation results from this perspective. Personally, when performing correlation studies, regression analysis, etc. I prefer to have more data points and finer resolution than vice versa. And, after putting a bunch of numbers in the “blender†we should ask ourselves, “Does the resulting outcome really make sense?†Modern Portfolio Theory is just that, it’s a theory, nice to think and ponder about, but when it comes to real money it doesn’t hurt to have some of our own theories.
Ryan
This is very interesting, but how would you determine if your portfolio as a whole is correlated to a single security? What I am thinking is perhaps two uncorrelated investments could combined to be correlated to something else.
What I would like to do is create a portfolio of multiple securities that would be uncorrelated to the market as a whole. Is it possible to even do this?
admin Post author
it is possible to determine how well a security is correlated as an investment strategy to a personal stock portfolio by using a similar procedure as outlined in the article. Instead of using the prices of indexes as the inputs to the correlation calculation as outlined in the article, the prices of the individual stocks in the personal stock portfolio would be used, along with the candidate stock or stocks for addition to the personal stock portfolio. As a rule of thumb if a stock has a correlation coefficient less than 0.5 with another stock then it would be considered uncorrelated. For example supposed we have four existing securities in a personal stock portfolio, AA, BB, CC, and DD, and we are considering adding EE and FF. After calculating the correlation coefficients between EE/FF and the existing positions in the personal stock portfolio, we determine EE has correlation coefficients of 0.8, 0.9, 0.6 and 0.7, and FF has correlation coefficients of 0.55, 0.4, 0.5 and 0.45. From the correlation results, it is clear FF is less correlated than EE with the existing positions in the personal stock portfolio and if we are seeking to diversify our investments, then EE might be the better position to add to the personal stock portfolio. With larger portfolios and/or larger potential candidates to add to a personal stock portfolio, it becomes difficult to see better candidates by inspection, and one possible solution is to simply analyze the average of the correlation coefficients for stock investing. For our simple case, the average correlation coefficients for EE/FF would be 0.75 and 0.475 respectively, again FF has a lower average correlation coefficient and appears to be less correlated than EE. Another method might be to choose a candidate based on having fewer correlation coefficients less than 0.5, in this case EE has 0 and FF has 2, and again FF appears to be less correlated with the personal stock portfolio.