CORRELATION

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When you put together a grouping of investments through the term asset allocation, you attempt to use those investments that are slightly dissimilar in character and therefore don't always move the same amount at the same time for the same reasons. This is the key reason for the use of foreign investments. However, as the world has gotten smaller due to the ability to communicate almost instantaneously. According to a Financial World article, South Korea, India and Taiwan had extremely low correlations of -0.02, 0.04 and 0.07 between 1991 to 1994 as compared to the U.S. market. (Perfect correlation is 1.0). Portugal was 0.41 as was Brazil. Now that doesn't mean the markets will go up as is evidenced by some Asian countries that have not done that well recently. But, along with growth records, correlation is major focal point for investing.

CORRELATION: (Life Insurance Selling) 1970- 1992
Year 1 2 3 4 5 6 7 8 9 10 11 12
1 Cash 1.0
2 Domestic Stock -0.8 1.0
3 International Stock -0.8 .52 1.0
4 Real Estate .23 -.05 -.07 1.0
5 Domestic Bonds .05 0.4 .25 -.24 1.0
6 NonDollar bonds -.11 .13 .59 -.09 .17 1.0
7 Balanced Funds -.06 .98 .51 -.15 .53 .17 1.0
8 Managed Futures .06 .02 -.07 .11 .04 -.07 0.0 1.0
9 Venture Capital -0.8 .51 .41 .09 .17 .17 .50 .06 1.0
10 Leasing .64 .05 .01 .08 .20 -.01 .09 .03 -.03 1.0
11 Gold -.11 0.0 .26 .15 -.08 .29 0.0 0.1 .04 -.18 1.0
12 Equity REIT .11 .81 .66 -.3 .43 .28 .81 -.14 .89 .13 -.01 1.0

CORRELATION: (1998) This is a relatively "simple" concept but absolutely mandatory in the use of investments. It basically refers to whether or not "different" investments will move at the same time for the same reason and in the same direction. If true, they have a correlation of plus 1. If, on the other hand, they were to move in exactly opposite direction they would have a negative correlation of minus 1. Rarely do portfolios have exactly either- most of the investments have correlations greater than 0 but less than 1.0. In another words, there is some movement of one investment based on the movement of the other(s).

A more specific note is the use of stocks and bonds. Going back 20+ years ago, stocks and bonds were effectively negatively correlated. That's why most investors were told to use some of each- or one instead of the other depending on economic conditions- mostly the movement of interest rates. But as the inflation rate and the interest rates have dropped, the correlations between these two is now maybe 0.8. That's a pretty strong positive correlation Therefore the old 60 % stocks and 40 % bonds-used in a number of supposedly of low-risk portfolios- effectively will not provide the diversification that one might expect. Foreign stocks might provide some of this reduced correlation, but even here one needs to be careful since, if a foreign investment has a negative correlation AND also a negative return, there has been little gained. You also have the increased risk of currency devaluation.

This simply compares how one investment related to another for the particular time frame. The correlations will change due to a myriad of factors.

ASSET ALLOCATION: (Stalla) Below are tables indicating various returns and the associated correlation (1993)
Asset Class Expected Returns Standard Deviation
US Stocks 12% 17.5%
Foreign Stock 11.8 19.5
Venture Capital 18.5 45.0
Dollar Bonds 8.1 7.5
Foreign Bonds 8.2 9.0
Real Estate 10.2 14.0
Cash 6.4 1.5

Figures may vary from other published numbers depending on data used and method of computation (1993)

Correlation Matrix
1 2 3 4 5 6 7
1 US Stocks 1.0
2. Foreign Stock .60 1.0
3 Venture Capital .35 .14 1
4. Dollar Bond .45 .25 .15 1
5 Foreign bond .25 .60 .10 .30 1.0
6 Real Estate .35 .30 .25 .20 .15 1.0
7 Cash -.10 -.15 -.10 -.05 -.10 .20 1.0


Here is another table showing the serial and cross-correlation of historical returns between assets classes (1926- 1987). Serial correlations measure the degree to which the return in one year correlates to the return in the next years. Highly positive serial correlations denote trends (historical projections can be used to make future estimates), highly negative serial correlations suggest cyclical behavior, and low serial correlating suggest randomness in returns (it'd be dangerous to project historical trends into the future).
1 2 3 4 5 6
1 Common Stock 1.0
2. Small Cap .82 1.0
3 Corporate Bonds .19 .08 1.0
4 Government Bonds .11 -.01 .93 1.0
5 T- bills -.07 -.09 .18 .21 1.0
6. Inflation -0.2 .06 -.17 -.17 .01 1.0
Serial Correlations .01 .1 .17 .1 .28 .64

Serial and Cross Correlations of inflation adjusted historical returns between assets classes (1926- 1987)
1 2 3 4 5 6
1. Common Stock 1.0
2 Small Stock .82 1.0
3 Corporate Bonds .27 .11 1.0
4 Government Bonds. .20 .03 .95 1.0
5 T-Bills .09 -.06 .61 .62 1.0
6 Inflation -.22 -0.07 -.61 -.60 -.66 1.0
Serial Correlation .00 .07 .28 .18 .34 .64


The point of the above tables is not to suggest that you understand the nuance of each line item but to simply make you aware of the issue of correlation and how it can impact your total return. Recognize as well that these correlations change repeatedly and may not reflect current economics. That's a major reason why you should consider rebalancing.

REBALANCING

This refers to adjusting an investor's asset allocation on a set time period to account for changes in values. For example, an initial portfolio might consist of 40% stocks, 40% bonds and 20% T-bills. Obviously, over time, these ratios will change and periodic rebalancing is necessary to maintain the desired level of risk exposure.

Two professors- Lewis and Stine- found that rebalancing a three asset portfolio whenever any asset is from 7% to 10% above or below the initial allocation produces less exposure than annual rebalancing and requires fewer rebalances and lower transaction costs. But note that this analysis simply uses costs of transactions. It in no way implies- and cannot- that the highest return is available through this process.

MORE CORRELATION: (1995) In the use of asset allocation, one attempts to use investments that, hopefully, will do well, but are independent, at least to some degree, from each other. That is, their movements are not dependent of the same reasons, time or conditions as the other investment(s) in the mixture. From 1985 to 1990, the correlation between international bonds and the U.S. Bond was 0.28- fairly low. But for the five years ending 12/94, the correlation went up considerably to 0.49 and has dropped slightly to 0.45 through May 1995. (Correlation of 1.0 means there is "perfect" correlation between two investments- you look for low correlations most often). The point to note with international bonds-as well as other international investments- the correlation has been going up as more and more financial opportunities are more closely tied to the U.S. dollar. Further, as more analysts analyze foreign investments, fewer inconsistencies and opportunities are noted and therefore much of the uneven playing field is lost.

ASSET ALLOCATION: 3/96 Even in view of the inconsistencies in the European market, asset allocation is still considered a viable process. Admittedly, US stocks significantly outgunned foreign issues in 1994 and 1995- as well as real estate- but a FW article noted that the long term argument for diversifying into foreign issues is valid. Part of the reasons for doing so involve correlation. Correlation essentially represents how much a stock or fund is like another fund. If they move the same amount for the same reason at the same time, they are said to have a correlation of 1.0. What you hope to find is others stocks/funds that may also move up but not for the same reasons. The lower the correlation when compared to each other, the better. Previous articles in many major magazines indicated that foreign issues were becoming more and more correlated with the U.S. market and therefore you weren't really getting the diversification you needed. A study noted in FW through 10/95 indicated that the US market was becoming more correlated with the markets of Australia, Canada, Germany, Hong Kong, the Netherlands and England. However, it was becoming less correlated with the countries of Argentina, Brazil, Mexico, France, Singapore, South Korea and Japan. They indicated one of the major reason of high correlation was how closely the countries monetary policies are tied together. For example, they noted that Hong Kong pegs its monetary policy to the U.S. But they also said that even when the correlation is high, it is NOT that high. Per the past five years versus the S&P 500, the UK and the Netherlands have tracked that index only 60% of the time; Canada about 50%, Germany at 33%; Mexico at 17% and Japan a mere 9%. Even if you did diversify, is it worth the bother? Well, over the last 10 years, foreign stock funds averaged 14.8% and US growth stocks did 13.5%.

For the record, some people say that you can just buy US companies that operate heavily overseas. But "academic studies have shown that the multinationals, even if they get a big chunk of there sales overseas, still track their home market fairly closely".

In summary, most of the charts above represent the fact that various assets do not move exactly in the same manner at the same time or for the same reason. However, the correlation between assets does change over time and it is necessary to rebalance a portfolio to adjust for the economic variables.

THE CORRELATION OF INTEREST RATES AND GDP: 1998 (The Federal the Reserve Board of Philadelphia) When current output rises, the yield curve tends to flatten; when short-term interest rates tend to rise, long-term interest rates move relatively little. Similarly, when current output declines, the yield curve tends to steepen, and short-term interest rates tend to fall with output and long-term interest rates tend remain about the same period

In general, interest rates on bonds of different maturities are highly correlated with each other, with the highest correlations occurring between bonds of similar maturities. Long-term interest rates are "determined" by the average of expected short-term interest rates plus the risk premium for the length of maturity.

Correlation of the Lehman Government/Corporate Bond Index with the S&P 500 Index

(2000)
Annual Quarterly Monthly
1994- 1998 .88 .38 .53
1985- 1998 .63 .22 .38
1979- 1998 .36 .33 .35
1973- 1998 .51 .39 .37

This is one of the best indications of how liars can figure and figures can lie. Look at the annual correlation between 1973 and 1998. Anyone doing analysis with this can clearly show why a bond allocation helps to temper risk, etc., etc., But what the researcher fails to address is that the more recent numbers of .88 show an entirely different focus and one that is, presumably, real life. That's why, once again, numbers starting with 1926 or whatever are mandatory to understand and recognize. But they must be put into context with current economic activities or may be meaningless or even detrimental in putting together an investment\ strategy.

The correlation between technology and financial has fallen. From 1994 to 1999, it was .56. This year, it is .28.

Correlation (2001) : In1992, there was a 0.55 correlation between the U.S. and foreign funds. Now it said 0.84. Why? Among the best of reasons- U.S. corporations are doing more business abroad.  

The correlation for REIT's versus the S&P 500 is 0.27 according to Micropal.

The correlation coefficient, a concept from statistics, is a measure of how well trends in the predicted values follow trends in the actual values in the past. It is a measure of how well the predicted values from a forecast model "fit" with the real-life data. The correlation coefficient is a number between zero and one. If there is no relationship between the predicted values and the actual values, the correlation coefficient is zero or very low (the predicted values are no better than random numbers). As the strength of the relationship between the predicted values and actual values increases, so does the correlation coefficient. A perfect fit gives a coefficient of 1.0. The higher the correlation coefficient is, the better.

Some elements of volatility

and Correlation

International correlation: (William N. Goetzmann, Lingfeng Li andK. Geert Rouwenhorst 2004) "we find that international equity correlations change dramatically through time, with peaks in the late 19th century, the Great Depression and the late 20th Century. Thus, the diversification benefits to global investing are not constant. Perhaps most important to the investor of the early 21st Century is that the international diversification potential today is very low compared to the rest of capital market history.

One important question to ask of this data is whether diversification works when it is most needed. This issue has been of interest in recent years due to the high correlations in global markets conditional upon negative shocks. Evidence from capital market history suggests that periods of poor market performance, most notably the Great Depression, were associated with high correlations, rather than low correlations. Wars were associated with high benefits to diversification, however these are precisely the periods in which international ownership claims may be abrogated, and international investing in general may be difficult. Indeed, investors in the past who have apparently relied upon diversification to protect them against extreme swings of the market have been occasionally disappointed.

We find that roughly half the benefits of diversification available today to the international investor are due to the increasing number of world markets and available to the investor, and half is due lower average correlation among the available markets."

Correlations (Malkiel 2004) The EAFE index was not a good index but it’s getting better. I believe in international investing. Let me say one thing about international investing, and then we’ll talk about the details of the particular indexes. With respect to developed countries, I still believe in international investing. But one has to admit that the portfolio theory case for inter-national investing is probably a bit weaker today than it was in the past, the reason being that the correlations of the developed countries of the EAFE index with the U.S. indices have been very close to one in recent years. They’ve gone up. It’s not quite so bad for emerging markets, but in the general inter-national scene I think one has to admit that the case is not as strong as it used to be when the correlations were something like 0.5, when now they’re more like 0.9.

I pretty much gave up on international investments in the mid 90's since the correlations were too close. Further, the FED indicated that there was nothing inherently wrong with the U.S. economy. I don't see how the relevance is much different today. Of course, you can say that the lower dollar has produced some exceptional international returns and I won't disagree. But I have refused to bet on the dollar. I am not going to do so now.  

More correlation: Julia K. Bonafede, CFA Note how close the correlations currently are. The divergence comes when small and mid caps stocks either do exceptionally well or badly           

Even in bad times, the volatility is essentially the same with both.

As of December 31, 2002, the Wilshire 4500 contained 5,168 stocks

Correlation (NY Times 2005) Correlation is essentially a mathematical measure of how two funds perform in relation to one another. If two funds move identically, they have a correlation of 1. If their movements are unrelated, the correlation is 0. The higher the number, the closer the correlation and the worse for investors, since the funds would essentially be moving in tandem -- not what a well-diversified portfolio is designed to do.

A NYU-Emory study, which examined fund returns from 1998 to 2002, says the average correlation among stock funds of similar fund families is 0.77. The average correlation of stock funds from different fund families is 0.73.

Foreign stock correlation: (NY Times 2005) A portfolio holding both domestic and foreign stocks would perform just as well over time as one containing only domestic ones, but with less risk - when risk is defined as volatility of returns.

The key to this idea was the historically low correlation between domestic and international stocks - in other words, their tendency not to move in tandem. Thus, a portfolio with both kinds of stocks would be less volatile than one with domestic stocks alone.

But in the late 1990's, a number of researchers found that the correlations were not constant through the market cycle. As a result, they said, the risk-reducing potential of such diversification was exaggerated.

correlations between domestic and foreign stocks tend to be highest when domestic stocks are declining sharply. Yet those are the very times when correlations need to be low in order to reduce portfolio volatility. And correlations tend to be lowest when domestic stocks are rising, which is when a low correlation is least helpful.

A new study says international stocks do a poor job of reducing risk only when an investor focuses on short holding periods. Over the long term, they deliver precisely what theory says they should.

But here is a major flaw in the article, "The authors don't dispute previous findings that such diversification failed to cut risk over short time horizons. But they say, "So what?" After all, investors should focus on the long term anyway."

The point being is that if you are close to or in retirement, the short term losses can devastate a portfolio. Short term being 2000- 2002. There is not a chance that these people can make up losses of 45%- 60% since they are withdrawing funds. Long term investing is absolute- you must do that during retirement. But the position that you can sustain a one time loss- as identifed by Zvi Bodie in his book, Investments- is anathema to common sense. It does not work and, for most retirees, cannot work since they not amassed huge portfolios on which to draw no matter the economic and market implications.

The industry has done a grave disservice by not recognizing dollar cost averaging down as at least one method of reducing losses of a 2000- 2002 to an "acceptable" level. But, of course, the only place you hear about DCAD is here and in my book. Pity.

Foreign Correlation: (2005) Look at the ratios during the mid 90's and what is going on now.

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The Use of Downside Risk Measures in Portfolio Construction and Evaluation Dr. Brian J. Jacobsen (2006)

What is so efficient about the “efficient frontier?” The standard method of constructing the set of efficient portfolios, from which investors are to choose from, is to use the Markowitz (1952) model which defines risk as the standard deviation of a portfolio. Markowitz (1952) recognized that there are many different ways to define risk, but the standard deviation (or variance) of a portfolio is easier to calculate than alternatives.

All portfolio optimization problems can be described as a sequence of mathematical programming problems. First, an analyst must construct a set of efficient frontiers, which are portfolios that maximize the expected return for any given level of risk over different investment horizons. Second, for each period, an investor’s utility is to be maximized by picking the portfolio that the investor most prefers (in terms of risk-return combinations). This method allows for the efficient frontier to change with time, which suggests that an investor would modify the composition of their portfolio as time unfolds and as expectations are updated regarding the possible return distributions that the investor may choose from.

(I hope every readers takes a real hard look at the comments that the efficient frontier changes over time. It is not static. It does not suggest a buy and hold. It does not say "stay the course". Of course, no one will hardly ever read this stuff so the bulk of American will continue to be swayed by vast and effective marketing rhetoric that you will have enough money for retiement.)

Tough article- only for professional readers

The Dangers of Using Correlation to measure Dependence (2006) Correlation is without doubt the single most important parameter in modern portfolio theory, where it is used to measure the dependence between the returns on different assets or asset classes. The rule is simple: low correlation makes for good diversification and highly correlated assets or asset classes are to be avoided. Fifty years after Markowitz, this way of thinking has become so common that nowadays most people use the terms ‘correlation’ and ‘dependence’ interchangeably. When dealing with the normal distributions that modern portfolio theory is based on there is nothing wrong with this. Unfortunately, however, the returns on most assets and asset classes are not exactly normally distributed and tend to exhibit a relatively high probability of a large loss (known formally as ‘negative skewness’) and/or a relatively high probability of extreme outcomes (known as ‘excess kurtosis’). In cases like this correlation is not a good measure of dependence and may actually be seriously misleading. Another problem is that even in cases where correlation is a valid measure of dependence, people do not seem to fully appreciate its exact nature.

Although it appears quite surprising at first sight, at least part of the finding that the correlation between hedge fund returns and stock market returns is higher in down than in up markets for example can be attributed purely to technicalities. Even a normal distribution with a constant correlation coefficient will exhibit this sort of behaviour.

In a recent book, Lhabitant (2002, p. 171) studies the dependence between hedge funds and the stock market. Using data over the period January 1994 to August 2001 he finds that the correlation between most hedge fund indices and US and European equity is much higher in down markets than in up markets. Overall (as measured by the CSFB/Tremont index), the correlation between hedge funds and US equity is 0.18 in up markets but a whopping 0.53 in down markets.

Correlation:

Correlations are making a lot of noise, but is anybody listening? (James Picerno 2006) I provide his full article. Lengthy but worth the comment about how correlations change.

Modern portfolio theory says correlations matter, but there’s no consensus about what that means for day-to-day money management.

If there’s debate about how to exploit correlation trends in portfolio strategies, the deliberation in mid-2006 comes at a crucial point in the investment cycle. Most asset classes are sitting on tidy gains of recent years, making it easy to look smart. But while almost any asset allocation has impressed of late, the future may not be so forgiving. If so, might paying closer attention to correlations play a bigger role in separating skill from luck?

No matter if you dismiss or embrace them, correlations of returns (along with volatility and expected return) are part of the statistical foundation for building “optimized” portfolios on the efficient frontier. But what happens after the efficient portfolio is built? Should correlations continue to cast an influence over tactical and strategic changes?

In theory, yes. When return correlations change in a material way—as they do from time to time—an MPT-inspired view of the world implies that asset allocation should change accordingly. But theory doesn’t easily coexist with practice when it comes to portfolio management. Everyone talks about correlations, but not every strategist is influenced by them beyond a general recognition that adding asset classes with low or negative correlations relative to existing investments is a good thing.

The time-honored view that most portfolios should hold some mix of stocks and bonds, for example, draws heavily on the history of low correlations between the two. But correlations aren’t written in stone. The reason is that the relationship of returns for the two asset classes—for any two asset classes—are in constant flux.

Consider that the S&P 500 and the Lehman Brothers Aggregate Bond Index post a -0.02 correlation for the 36 months through the end of this past March, according to Morningstar Principia. (Correlation coefficients range from 1.0, a perfect positive correlation, to 0, or no correlation, and down to -1.0 for a perfect negative correlation.) But that’s a single moment in time in an otherwise dynamic relationship, which is to say: Don’t assume the stock/bond correlation dance will remain slightly negative indefinitely.

As the chart above shows, the rolling 36-month correlation of monthly returns between the S&P 500 and the Lehman Aggregate Bond Index was in a range of 0.4 to 0.6 for much of the 1990s. No one should be surprised, given that simultaneous bull markets prevailed in each asset class for much of the decade. The downside was that the diversification value faded for owning stocks and bonds during those years. Of course, no one complained—no one ever does when prices are rising. Bull markets have a habit of banishing over asset allocation’s momentary shortcomings.

Then again, bull markets don’t live forever, which is why asset allocation is valuable over a full cycle and beyond. With that in mind, it’s instructive to recall that the elevated correlations between stocks and bonds declined by the time stocks hit a wall in 2000. In fact, there was a notable drop in correlations well before equities corrected—a warning signal, if you will. More recently, correlations for stocks and bonds have subsequently bounced back, rising to roughly zero for the trailing 36 months through March 2006.

The ebb and flow of correlations is hardly limited to stocks and bonds. Consider the fluctuation with stocks and commodities, everyone’s new favorite asset class. One of the selling points for owning raw materials is the negative correlation with stocks. Measured over various five-year periods, during the 45 years through the end of 2004, an equally weighted mix of commodities posted a negative 0.42 correlation with the S&P 500, according to a study by professors Gary Gorton of the Wharton School and K. Geert Rouwenhorst of Yale.

The long term may look stable in the rear-view mirror, but in the short term there’s a surplus of change unfolding in the stocks/commodities relationship. In fact, some observers worry that the historical negative correlation that commodities post with equities may be diminishing as the masses jump on the raw materials bandwagon.

Comparing the Dow Jones-AIG Commodity Index with the S&P 500 on a rolling 36-month basis reveals a trend that may give pause to proponents of the commodities-as-diversifier argument. Correlations between the two asset classes have recently shot up dramatically, rising to around 0.19 for the 36 months through this past March from negative 0.12 in August 2005. That’s still low, but question is whether the trend will continue.

Perhaps the jump is statistical noise that accompanies the normal cyclical changes that drive correlations in the short run. In support of that view is the history of the stock/commodity performance relationship. Despite the jump in correlations between the S&P 500 and DJ-AIG, the March reading was still well within the recent historical range. In fact, correlations between the two asset classes have been higher, running up to around 0.3 back in 1999.

Still, some skeptics argue that the negative commodities/ stocks correlations may be history going forward, thanks to all the money rolling into raw materials by way of the growing list of exchange traded and mutual funds targeting the asset class.

One sign that hot money is chasing returns in commodities is the fact that oil futures, a dominant factor in commodities benchmarks, have moved into what’s known as contango, says Richard Ferri, president of Portfolio Solutions LLC in Troy, Mich. That means that contracts with later expiration dates are priced higher than those with nearer-term expirations. That’s the reverse of the traditional pricing structure for oil futures, where nearer-term contracts trade at a discount to those dated further out—backwardation, as it’s known.

“People point to the fact that futures have done great,” Ferri notes. The PIMCO Commodity Real Return Strategy Fund, for instance, has racked up impressive gains in recent years by tracking the DJ-AIG index. But that’s partly due to the fact that the fund has been operating in years past, when backwardation of oil futures was the norm, he says. “They made money on the roll [selling a near-term contract to buy a cheaper longer-term contract] for several years. That’s not going to happen going forward. You can expect negative returns from commodity indexes using futures for the next couple of years...until it returns to backwardation,” he predicts.

In any case, the future for the relationship of stocks and commodities may be changing, but watching correlations is no tipoff about what to do in the here and now, warns Bill Bernstein, a principal at Efficient Frontier Advisors, in Eastford, Conn. and author of The Intelligent Asset Allocator. “Changes in correlations over periods of less than 20 or 30 years—or certainly over less than 10 years—are meaningless,” he says.

Bernstein cites the shifts in correlations between REITs and stocks in recent history as an example. As the 1990s progressed, correlations between the two equity groups fell. Bernstein reasons that real estate securities lost some of their allure in the gogo years of the previous decade when technology companies were hot. Investors “thought they didn’t need real estate any more, so they took money out of REITs and put it into ePets or eToys.”

Reflecting the preference, the 36-month trailing correlation between the Dow Jones Wilshire REIT Index and S&P 500 fell from around 0.8 in early 1990 to zero by September 2001. The trend since has been one of rising correlations, reaching 0.42 as of this past March, which coincides with a rebound in demand for REITs.

Interesting, but not necessarily relevant, says Bernstein, who argues it’s all “noise,” and so he ignores the ups and downs of correlations. The drop in the 1990s was a one-time event tied to the peculiarities of the tech boom, he explains. As a result, the bounce-back of recent vintage is a reaction to what he labels a “non-recurring event.”

But not all changes in correlations are dismissed so easily. The increasing tendency of foreign stocks to move in line with U.S. equities is thought to be a byproduct of globalization. Money moves effortlessly across national borders in the 21st century. The impact can be seen in the rising correlations between the S&P 500 and MSCI EAFE (measured in local currency). The two indices have been posting correlations in the range of 0.7 to 0.9 for the last three years, up sharply from the 0.3 to 0.5 during the period from 1993 to 1995.

Does the trend mean that it’s time to ditch foreign stocks? That may be a bit excessive. Indeed, even if high correlations are now the norm among these two slices of the equity market, some of the diversification benefits are still intact. The reason: The forces that drive earnings in Europe, Asia and elsewhere aren’t identical to what’s unfolding in Chicago and Silicon Valley.

One quick example comes by way of Europe and Japan, the primary developed-market alternatives to the United States. Each is said to be emerging from economic slumps, Japan in particular. In contrast, the United States has enjoyed a robust expansion in recent years, but may be facing a slowing economy now, according to some economists. In 2004 and 2005, for instance, gross domestic product in America rose by 4.2 percent and 3.5 percent, respectively, according to the IMF. That was comfortably above Europe’s roughly 1 to 2 percent range, or Japan’s 2 to 3 percent.

Is the gap closing? Yes, or so the IMF forecasts, predicting recently that U.S. GDP will slow a bit to 3.4 percent for all of 2006, while the pace of growth in Europe is expected to rise to 2.0 percent. Ditto for Japan, which is said to be on track for a slight increase to 2.8 percent GDP growth this year.

Perhaps that explains why the MSCI EAFE’s local currency-based returns have left the S&P 500’s gain in the dust for the three years through this past March. EAFE, which is heavily weighted with European and Japanese stocks, posts an annualized total return of 24.9 percent for the 36 months through this year’s first quarter, far above the 17.2 percent for the S&P 500.

Yes, both indices have posted healthy gains over the past three years, and so it’s no surprise to learn that correlations between the two benchmarks are relatively high of late. But just because correlations are high doesn’t mean that performance will be comparable in absolute terms.

Still, the question remains: Does the high correlation between domestic and foreign stocks thwart the case for investing overseas?

To a degree, yes, says Jerry Miccolis, senior financial advisor at Brinton Eaton Associates in Morristown, N.J. “International equities are getting more and more correlated with domestic equities,” which convinces him to avoid allocations to foreign equities in developed markets. Instead, he favors emerging markets stocks, which post correlations that are still fairly low relative to domestic equities. Even so, the advantage won’t last forever since correlations are likely to rise between the U.S. and developing markets, he predicts.

In fact, Miccolis monitors the correlations between asset classes for clues about how to structure portfolios. “The real differentiator turns out to be correlation,” he says of picking and choosing which slices of the capital markets to own and by how much. As an example, he compares the tech sector of large-cap stocks with commodities. Both have fairly high expected returns, but Miccolis uses commodities and shuns big-cap tech stocks as a separate and distinct investment. The reason: Tech is highly correlated with the stock market generally. “So there are two asset classes that individually look pretty attractive, but only one makes the cut and the other doesn’t, and it’s entirely because of the correlation,” he says.

Miccolis routinely analyzes three-, five- and ten-year trailing correlations for various asset classes for clues about what comes next, a task that he argues offers much insight for crafting portfolio strategy. But it’s a bear of a chore. The shifting correlations tend to trigger changes in asset allocation, he explains, but uncovering the trends comes at a price. “It’s not easy to do because you’ve got to look at correlations of each asset class with every other asset class.”

For a strategist looking at, say, 10 asset classes, that’s a lot of number crunching. Of course, if the effort yields strategic intelligence, the work is worthwhile. Otherwise, it’s a colossal waste of time, or worse if it promotes unnecessary portfolio tinkering.

Deciding which view is accurate varies depending on whom you talk to. Modern portfolio theory has been widely hailed as bringing science into the world of money management. But even after 50 years of MPT-inspired enlightenment, there’s still plenty of art driving decisions in the money game.

The Volatility of Correlation -Important Implications for the Asset Allocation Decision  Excellent article by William Coacker (2006)

The severity of how much correlation changes, even over longer periods of time, has not been adequately understood.

This paper analyzes the changing correlation of 15 asset classes measured against the S&P 500 over a 35-year period, and the impact of those changes on asset allocation decisions. It measures the correlations in rolling one-, three-, five-, and ten-year time series, from 1970 to 2004.

The article also evaluates whether 15 asset classes have helped or hurt in years the S&P 500 has declined, and whether growth or value styles are more correlated to the index.

The average variance in correlation measured 0.98 over one year and 0.25 over ten years. In short, the relationship among many of the asset classes appears to be inherently unstable.

Large value provides more diversification benefits than large growth, and small value provides more diversification than small blend or small growth. Emerging markets may provide higher returns and greater diversification than developed nations. But the low correlations of small value and real estate may not hold up during the next broad market decline.

Correlations exhibit uniqueness, meaning periods are distinct from previous time periods. For example, international stocks' correlation to the S&P 500 was 0.48 from 1970 to 1997, but 0.83 from 1998 to 2002.

Rather than rely on historical correlations, a more comprehensive and dynamic approach is needed in making asset allocation decisions.

Observations

Most relationships of these 15 asset classes to the S&P 500 were unstable:

The average variance in correlation over one year was 0.99.

The average variance over three years was 0.57.

The average variance over five years was 0.43.

The average variance over ten years was 0.27.

Assuming a variance of 0.20 or greater as lacking consistency, then 13 of 15 asset classes over three years, 12 of 15 over 5 years, and 9 of 15 over 10 years had inconsistent relationships to the S&P 500. If the assumption were tightened to variances of 0.15 as lacking consistency, then 14 of 15 asset classes over three years, 12 of 15 over 5 years, and 12 of 15 over 10 years had inconsistent relationships to the index.

Relationships in down markets have also been inconsistent. Among equities, large value was most likely to outperform the S&P 500 in down years, but not always. Small value and mid-value also tended to outperform the index in down years, but not with reliable consistency. All growth styles usually lost more than the index in down years, but not always. International and emerging markets had an equal occurrence of losing less and losing more than the index.

Correlation: A 2006 report from Merrill Lynch & Co. found that as of February this year, small stocks were 94% correlated to the broad Standard & Poor's 500-stock Index -- which means, in simplified terms, in a year when the S&P 500 rose, an index of small stocks also rose 94% of the time. By contrast, as recently as six years ago, the figure was just 62%.

The MSCI EAFE index, which measures emerging markets, now shows 96% correlation to the S&P, up from just 32% six years ago.

Even commodities like oil and precious metals are increasingly moving in tandem with stocks. The Goldman Sachs Commodity Index, which tracks 24 commodities, moved from a correlation of negative 14% in 2000 -- in other words, it tended to fall when stocks rose, and vice versa -- to a positive correlation of 33% at present

Asset Prices and Asset Correlations in Illiquid Markets  Professional article pdf

 Correlations (2007)

                                        U.S. Equity International      Emerging Mkt Equity   Absolute Return   Equity     Hedge Funds  Venture Capital   Private Equity   REITs     Real Estate  Commodities     U..S. Bonds Govt     U.S. Bonds All        U.S. Bonds TIPS  Cash

                                                        Equity

U.S. Equity                      1.00       0.65                 0.45                      0.50                                0.85            0.35                 0.70           0.55           0.10          -0.25                    0.35        0.30                  0.35                0.35

International Equity           0.65      1.00                 0.60                       0.55                               0.55            0.30                 0.60           0.40           0.15          -0.10                    0.20        0.20                   0.20                0.20

Emerging Mkt Equity        0.45      0.60                 1.00                        0.50                               0.65            0.35               0.30            0.20           -0.30         -0.05                   -0.20       -0.15                 -0.10              0.00

Absolute Return              0.50       0.55                  0.50                      1.00                              0.65              0.10                0.35            0.55            -0.05         -0.05                  0.10         0.15               0.15                 0.20

Equity Hedge Funds       0.85        0.55                  0.65                     0.65                              1.00               0.50                0.60             0.50           0.00          -0.05                   0.10         0.15               0.25                 0.35

Venture Capital              0.35       0.30                  0.35                       0.10                              0.50               1.00               0.65             -0.05          0.15           0.20                  -0.30        -0.25              -0.15                0.05

Private Equity                 0.70        0.60                0.30                       0.35                               0.60              0.65               1.00              0.20            0.20          -0.05                 -0.15        -0.10               0.05                0.25

RE ITs                           0.55        0.40                0.20                       0.55                               0.50               -0.05              0.20            1.00            0.00           -0.20                 0.35         0.30                 0.30                0.20

Real Estate                    0.10        0.15                 -0.30                     -0.05                             0.00               0.15               0.20             0.00            1.00            -0.05                  0.00       0.00                  0.20               0.40

Commodities                 -0.25      -0.10                -0.05                     -0.05                            -0.05              0.20              -0.05             -0.20           -0.05          1.00                   -0.20       -0.10              -0.20               -0.20

U.S. Bonds Govt           0.35       0.20                 -0.20                      0.10                              0.10             -0.30               -0.15            0.35              0.00          -0.20                  1.00        1.00               0.75                  0.50

U.S. Bonds All              0.30       0.20                 -0.15                       0.15                             0.15             -0.25                -0.10            0.30            0.00           -0.10                  1.00        1.00               0.75                  0.45

U.S. Bonds TIPS          0.35       0.20                 -0.10                      0.15                              0.25               -0.15              0.05             0.30             0.20           -0.20                   0.75        0.75            1.00                  0.75

Cash                            0.35 0.     20 0.               00 0                       .20                                 0.35               0.05                0.25             0.20           0.40            -0.20                  0.50         0.45             0.75                  1.00

These estimates, which are drawn from Leibowitz and Bova (2004), are used for illustration only and may or may not reflect current expectations for any or all asset classes. Source: Morgan Stanley Research

EFM- Of course, that is the problem with correlations. It takes at least a year to get valid numbers. But once they complied, the correlatoins have already changed.

Correlation (2008) The authors find that stock and bond returns tend to move substantially together during periods of lower stock market uncertainty. However, stock and bond returns tend to exhibit little relation or even a negative relation during periods of high stock market uncertainty.

The Effects of Federal Funds Target Rate Changes on S&P100 Stock Returns, Volatilities, and Correlations  We study the impact of FOMC announcements of Federal funds target rate decisions on individual stock prices at the intraday level. We find that the returns, volatilities and correlations of the S&P100 index constituents only respond to the surprise component in the announcement, as measured by the change in the Federal funds futures rate. For example, an unexpected 25 basis points increase of the target rate leads on average to a 113 basis points negative market return within five minutes after the announcement. It also increases market volatility during the 60-minute window around the announcement with 147 basis points. Positive surprises, meaning bad news for stocks, provoke a stronger reaction than negative surprises. Market participants also respond differently to good and bad news. In case of bad news for stocks the fact that there is a surprise matters most, whereas in case of good news the magnitude of the surprise is more important. Across sectors, Financials and IT show the strongest response to target rate surprises.



2/19 

Start and stop dates for below are 1970 - 2004







CORRELATION LINK:
High Correlations
These four relationships have been consistently strong:
1. The S&P 500 and large growth have had a long-term correlation of .96. Over rolling three-year periods, their correlations have been .90 or higher 100 percent of the time (Table 1 and Table 4, Panel 1).
2. Small blend and small growth have had a long-term correlation of .98. Over rolling three-year periods, their correlations have been .90 or higher 100 percent of the time (Table 1 and Table 4, Panel 8).
3. Large value and mid-value have had a long-term correlation of .96. Over rolling three-year periods, their correlations have been .90 or higher 100 percent of the time (Table 1 and Table 4, Panel 3).
4. Mid-blend and mid-growth have had a  long-term correlation of .93. Over rolling three-year periods, their correlations have been .90 or higher 93 percent of the time (Table 1 and Table 4, Panel 5). The author believes it is not helpful to invest in assets with similar return expectations and consistently strong correlations.
A better use of an investor’s risk budget is to invest in assets with lower correlations that still meet return objectives.
Low Correlations
Five assets have had low correlations to all the other assets in this study. Here is a summary of each:
1. Natural resources have had a correlation of less than .20 to all 17 other assets in this study, with the highest being just .19, for both small growth and small value. Natural resources have had the lowest average correlations—and the most consistently low correlations—to every asset in this study, including every category of stocks, bonds, and alternatives. Hence, natural resources have provided more diversification benefits than every other asset in this study. Of special note, natural resources have had a negative correlation 83 percent of the time to U.S. bonds, due to their inverse relationship to inflation.
2. Long-short has had an average correlation of .30 or less to all 17 other assets in this study, including negative correlations to all three U.S. growth styles, ranging from –.22 to –.33. Long-short has provided very strong risk-reduction benefits to all other assets, though it has had a mild association to value styles (high of .30 to large value) and real estate (.27).
3. U.S. bonds (the Lehman Brothers Government/Credit Index was used as the proxy for U.S. bonds) have had an average correlation of .30 or less to 15 of the 17 assets in this study, with the exceptions being mild connections to global bonds (.38) and cash (.34). U.S. bonds have had a very low correlation to all nine U.S. equity styles (ranging from .02 to .24), international stocks (.13), and emerging markets (–.06). But the correlation of U.S. bonds to U.S. equities has been less consistent than investors might expect, which will be discussed later in the study.
4. Global bonds have had an average correlation of .30 or less to 15 of the 17 assets in this study, with mild connections to international stocks (.44) and U.S. bonds (.38). Global bonds have had a negative relationship to all nine U.S. equity styles, with correlations ranging from –.03 to –.12. Interestingly, global bonds have had lower correlations and lower standard deviations in their correlations to U.S. equities than U.S. bonds. In other words, when mixed with U.S. equities, global bonds have provided more diversification benefits than U.S. bonds.
5. Cash has had an average correlation of .30 or less to 16 of the 17 assets in this study, with the exception being a mild relationship to U.S. bonds (.34).

Correlation (Wired 2009)

To understand the mathematics of correlation better, consider something simple, like a kid in an elementary school: Let's call her Alice. The probability that her parents will get divorced this year is about 5 percent, the risk of her getting head lice is about 5 percent, the chance of her seeing a teacher slip on a banana peel is about 5 percent, and the likelihood of her winning the class spelling bee is about 5 percent. If investors were trading securities based on the chances of those things happening only to Alice, they would all trade at more or less the same price.

But something important happens when we start looking at two kids rather than one—not just Alice but also the girl she sits next to, Britney. If Britney's parents get divorced, what are the chances that Alice's parents will get divorced, too? Still about 5 percent: The correlation there is close to zero. But if Britney gets head lice, the chance that Alice will get head lice is much higher, about 50 percent—which means the correlation is probably up in the 0.5 range. If Britney sees a teacher slip on a banana peel, what is the chance that Alice will see it, too? Very high indeed, since they sit next to each other: It could be as much as 95 percent, which means the correlation is close to 1. And if Britney wins the class spelling bee, the chance of Alice winning it is zero, which means the correlation is negative: -1.

If investors were trading securities based on the chances of these things happening to both Alice and Britney, the prices would be all over the place, because the correlations vary so much.

But it's a very inexact science. Just measuring those initial 5 percent probabilities involves collecting lots of disparate data points and subjecting them to all manner of statistical and error analysis. Trying to assess the conditional probabilities—the chance that Alice will get head lice if Britney gets head lice—is an order of magnitude harder, since those data points are much rarer. As a result of the scarcity of historical data, the errors there are likely to be much greater.