## Examining the Role of Short-Term Correlation in Portfolio Diversification

### Study shows that the nearer and shorter the timeframe, the greater the likelihood an investment will move from uncorrelated to correlated.

From the third quarter of 2008 to the present, the financial markets have “gone to one,” meaning that all investment options have become highly correlated. They have all gone down (with the notable exceptions of cash and government bonds). The benefit of holding uncorrelated assets is that they should not all move in lock step, so that while one goes down, hopefully another will increase. The question that this article attempts to answer is whether the long-term correlations that sales and marketing materials often quote are similar in the short term as well.

Typically, correlation between investment assets and asset classes is calculated over extended time periods, such as 5, 10, or 15 years. But what is of greater concern to the investor is what the correlation will be next month. The use of a low 15-year correlation might obscure more recent data due to the length of time over which the correlation was calculated. Could it be, for example, that the last 12 months would show a much higher correlation between assets than the figure contained in the marketing literature?

This article looks at the near-term issues regarding correlation. Using two series of random numbers (180 observations to simulate 15 years of monthly returns) and running a short (100-trial) Monte Carlo simulation (a process that repeats the same trial), these uncorrelated random series showed significant 36-, 24-, and 12-month correlations. This suggests that investors should also consider short-term correlations between assets when attempting to diversify their portfolios. In addition, correlations should be rebalanced as often as asset allocations because investment strategies, personnel, and so forth change over time.

### What is Correlation?

Most investors have the singular goal of maximizing investment return given a certain level of risk tolerance. Modern portfolio theory holds that returns are maximized in the long run when they are held in a diversified portfolio. A statistical measure of diversification is “correlation,” which is measured on a scale that runs from -1.0 to +1.0. A correlation coefficient of -1.0 or +1.0 is considered perfect correlation, knowing how one series of data moves provides perfect information on how the second series will move.

A negative correlation coefficient signifies that the two series move in opposite directions, for example, as one series increases, the other decreases. This is also known as an inverse correlation. A positive or direct correlation indicates that the series move together, as one increases, the other also increases. It is rare that one comes across perfect correlation, that is, a correlation coefficient of exactly -1.0 or +1.0.

The plus or minus sign indicates whether the relationship is direct or inverse, whereas the calculated value indicates the strength of the relationship. As the correlation coefficient moves from zero toward +1.0, there is an increasingly direct statistical relationship. Conversely, as the correlation coefficient moves from zero to -1.0, there is an increasingly inverse statistical relationship. In addition, a correlation of -0.7, then, is exactly as significant as a correlation of +0.7. A correlation coefficient of zero indicates that there is no statistical relationship between the two series of numbers, the series behave randomly with respect to one another. This is also called “non-correlation,” or, sometimes, the two series are said to be “uncorrelated.”

One important point about correlation is that it does not represent causality. For instance, in school-age children, shoe size is a great predictor of reading ability, not because shoe size has anything to do with reading, but because it is a proxy for age, older children tend to read better.

### Correlation and Investing

Some investors believe that they make only three investment decisions: asset allocation, manager selection, and vehicle choice. Asset allocation is important because it is widely held that diversification is a cornerstone of investing theory. Diversification follows the logic of not putting all of your eggs in one basket. If an investor invests in a single stock, then the portfolio will do as well or as poorly as that single stock. If the investors select two stocks, they would appear to have achieved some level of diversification, but this is only at a company level. If both companies are engaged in the same industry, like Pepsi and Coca-Cola, or American Airlines and Delta, or Ford and GM, then the stock price movements that affect an industry segment will affect both stocks, that is, 100 percent of their portfolio. So, the investors might want also to diversify along company, industry, or geographical lines.

Diversification is usually quantified by correlation, that is, the degree to which the movement of one investment or asset class allows for inferences about how another investment or asset class will move. This is not indicative of causality, but simply a statistical relationship that may include causality and that can also occur simply by chance. A portfolio is not diversified if all of its holdings are correlated with one another, meaning that if one holding moves a certain way, we can predict how the other holdings will move. Brokers of commodity-based products (whether futures contracts or hard-asset ownership), infrastructure investments, and real estate funds often cite “uncorrelated with existing asset classes” as a major selling point of their products:

### Issues with Non-Correlation as an Investment Strategy

**Asset classes are too broad**

Individual products within an asset class are not created equal; there are a wide variety of investment choices within any class. For instance, within the “hedge fund” asset class (assuming one considers hedge funds an asset class) there are over 8,000 investment choices. Treating the returns of the asset class as representative of the returns of the underlying components could be erroneous. The same is true of U.S. equities as a whole, or even when dealing with subcategories, such as Small Cap Growth, Small Cap Value, Large Cap Growth, Large Cap Value, and so forth. To be useful, non-correlation should focus on product-level asset holdings.

**Not all portfolios are alike**

Portfolio compositions usually differ among investors in terms of asset allocation and individual investment choices. To claim that a particular product will not be correlated with the portfolio does not give appropriate credit to the diversity of investments and the particular holdings. To be relevant, correlation should be calculated based on the returns of specific portfolio holdings, not generic asset-class returns.

**Different types of non-correlation**

Third, there can be different types of non-correlation. One type of non-correlation is the one people ordinarily think of when they define non-correlation, when one variable changes, the other variable will behave randomly. Another type of non-correlation operates very differently. Two series can have a low overall level of correlation even if they are 100-percent positively correlated half of the time (i.e., they have a correlation of +1.0 for half of the observations) and 100 percent negatively correlated the other half of the time (i.e., they have a correlation of -1.0 for half of the observations). In this situation, the variables clearly have some kind of relationship to one another, although the overall correlation coefficient might indicate otherwise.

Perhaps what makes correlation so interesting is that similar situations can lead to quite different results. Consider the following small series:

Observation | X | Y |
---|---|---|

1 | 1 | 9 |

2 | 2 | 8 |

3 | 3 | 7 |

4 | 4 | 6 |

5 | 5 | 5 |

6 | 4 | 4 |

7 | 3 | 3 |

8 | 1 | 1 |

The overall correlation is -.096, which is not even remotely statistically significant. But within that overall insignificant correlation are two sub-series (observations 1 to 4 and observations 5 to 8). The correlation of observations 1 to 4 is -1.0, and the correlation of observations 5 to 8 is +1.0, which are perfect correlations.

Now consider another small series:

Observation | X | Y |
---|---|---|

1 | 4 | 5 |

2 | 3 | 6 |

3 | 2 | 7 |

4 | 6 | 3 |

5 | 7 | 4 |

6 | 8 | 4 |

The correlation of observations 1 to 3 is -1.0, and the correlation of observations 4 to 6 is +1.0, as in the last series. However, the overall correlation is .72, which is on the border of statistical significance at the .10 level.

In the first case, we had an overall correlation coefficient that indicated there was absolutely no statistical relationship between the two series. However, embedded within that series were two shorter series that had extreme levels of correlation (one positive and one negative). In the second case, the observations were similarly arranged so that the first half of the series had a correlation coefficient of -1.0, and the second half of the series had a correlation coefficient of +1.0, yet the overall result was a nearly statistically significant correlation of .72.

**Even when it operates as we think it does, do we want it?**

If two asset classes (or individual investments) are truly uncorrelated, then when the first asset class increases, the other class may increase, decrease, or remain unchanged. There is no existing statistical relationship that allows us to infer how one class will behave based on the behavior of the other, but is this random effect desirable? We can couch the issue in the following terms: When the first asset class increases, we would like the other class to increase. However, since it is behaving randomly, there is only a one-in-three likelihood that it will do so (with the three possibilities being for it to increase, decrease, and remain unchanged). Similarly, when the first asset class decreases, we would like the other class to increase, though, again, there is a one-in-three chance this will happen. Better odds can be achieved by betting “black” at a roulette table.

### The Experiment

This article examines whether uncorrelated (in the long term) series of numbers (representing investment returns) are also uncorrelated in the short term. While most investment professionals will not be surprised that uncorrelated asset classes (or investments) may have short-term correlations, the question is whether the frequency and duration of the short-term correlations are what might be expected.

This study was exploratory in nature because we could not find empirical research that quantifies the type of short-term correlation that would be considered “normal.” Since we have no basis on which to *a priori* establish whether the short-term series are abnormal, we will quantify and present the results and establish the literature.

We began with two series of 180 random numbers representing 15 years of monthly returns. Correlations were calculated for the last 36, 24, and 12 months of the series, since these timeframes were representative of the effect that will be introduced into the portfolio. In other words, the relevant correlation is the most recent one, not the one that was evident 15 years ago. A hundred iterations of this experiment were performed.

**Exhibit 1: Frequency of observed correlations resulting from 100 trials**

Each trial had 180 monthly observations (15 years). During the 100 trials, the overall correlation was .20 one time, and less than .20 the other 99 times.

The correlation for each trial was recalculated over the last 36, 24, and 12 months, and the correlations for these shorter periods are indicated:

Correlation (+/-) | 0.2 | 0.3 | 0.4 | 0.5 |
---|---|---|---|---|

Overall | 1 | – | – | – |

Last 36 months | 27 | 9 | 2 | – |

Last 24 months | 33 | 18 | 6 | 2 |

Last 12 months | 61 | 39 | 21 | 10 |

### The Results

The test revealed that, overall, the two series were uncorrelated. In the 100 trials, the overall correlation of .20 was only obtained once. When we reviewed the correlations of the last 36, 24, and 12 months, some startling results were evident. In the last 36 months of each trial, the correlation was 0.2 or more 27 percent (27/100) of the time, 0.3 or more 9 percent of the time, and 0.4 or more 2 percent of the time.

For the last 24 months, a correlation of 0.2 or more occurred 33 percent of the time, a correlation of 0.3 or more resulted 18 percent of the time, a correlation of 0.4 or more was obtained 6 percent of the time, and a correlation of 0.5 or more occurred 2 percent of the time.

The last 12 months, however, may be the most relevant period because this timeframe is the most likely to impact a portfolio. A correlation of 0.2 or more occurred 61 percent of the time, a correlation of 0.3 or more was evident 39 percent of the time, a correlation of 0.4 or more occurred 21 percent of the time, and a correlation of 0.5 or more was found 10 percent of the time. An investor adding an investment and expecting it to be uncorrelated (based on 15 years worth of data) could very well be surprised at the resultant effect.

### Conclusion: Do Your Short-Term Correlation Home-Work

Our findings suggest that if an investor is adding an investment to his or her portfolio with the goal of aiding diversification, he or she should parse the long-term correlation into shorter-term metrics. The nearer and the shorter the timeframe, the greater the likelihood that the investment will move from uncorrelated to correlated. As the correlation that will be added to the portfolio is more reflective of the 180th month than the first month of the series, the additional calculation of a near-term 36-, 24-, and 12-month correlation could prove useful. Perhaps there is an investment that can be added to the portfolio that, over the long term, will provide uncorrelated returns and, therefore, aid in diversification. However, if the return stream is presently correlated to the portfolio, the investor should wait a couple of periods before adding the investment, thereby mitigating the short-term effects of correlation.

**Review Investments Periodically for Correlation Shifts**

An additional implication from this study concerns investments that are already in the portfolio. Once an investment is added, there is usually no further attention devoted to the correlation. This study suggests, however, that the correlations of the existing investments should also be reviewed periodically. Manager changes, style drift, and so forth may mean that the original correlation that made the investment attractive is no longer accurate.

### About the Author(s)

Jeffry Haber, PhD, is an associate professor of accounting at Iona College, where he teaches undergraduate and graduate classes in a variety of accounting areas. He publishes in the areas of investments, anti-money laundering and terrorist financing, earnings quality, ethics, bankruptcy prediction, and other areas of financial and managerial accounting. Haber received bachelor's and master's degrees from Syracuse University and his doctorate from Rensselaer Polytechnic Institute. He is active on a number of professional committees and is a frequent speaker at investment conferences. He is also controller of a private foundation.

Andrew Braunstein, PhD, is a professor of business economics in the Hagan School of Business at Iona College in New Rochelle, New York, where he has recently completed his 31st year of fulltime service. The majority of his research and publication activity has involved the application of econometric techniques to issues in business, economics, and education.

Issue: 2009 Volume 12 Issue 3

Topic: Finance / Investing / Accounting

Tags: asset management, investments, portfolio management, risk, Strategy, study