Jim Kopas

Nice writing. You are on my RSS reader now so I can read more from you down the road.

Allen Taylor

Excellent article Jim. During times of normal market market behavior where returns are normall distributed, traditional quantitative measures are important, and most likely investors would find them easiest to understand; however, in my opinion, it is important for wealth managers to understand that asset correlation is a dynamic statistic. Dependence structures between different asset classes have behaved differently in times of market stress with dependence of asset classes increasing during market downturns (phase locking). Negative correlation can turn to positive correlation and vice versa.
An additional problem with interpreting the dependence asset classes on the basis of linear correlation assumes normal distribution of returns. The presence of significant skewness or high kurtosis can under or over estimate the signficance of correlation, especially during extreme periods of volatilty.

I believe that for the average investor, understanding correlation is crucial successful investing over the long term. Risk management during times of extreme volatility is where I believe wealth managers can differentiate themselves by utilizing statistical techniques look beyond linear relationships.

Reducing portfolio risk by investing in assets with negative correlation, while effective in theory, often leads to poor performance. In times of financial distress correlation among seemingly unrelated assets is drawn towards one due to investor activity. In other words, diversification fails exactly when it is needed. My portfolio strategy would be to choose very few investments with strong performance and large margin of safety.
As billionaire Warren Buffett said: “put your eggs in one basket and watch the basket”

Thanks for the comments Allen, Jason and Roman. I completely agree with both of your opinions in regards to how correlations change during times of financial distress. For example, during the liquidity crisis last year all asset classes dropped (except for U.S. Government Securities) which shows that assets tend to be positively correlated during times when investors need negative correlation the most. This just goes to show that in order for investment managers to be successful they must separate themselves from the rest of the pack during times of financial turmoil.

Quoting Yale’s CIO in your article may not be such a great idea. Their endowment lost 24.6% in its fiscal year through June 30,2009. I otherwise agree with your conclusions.

I agree with you, understanding of correlation is very much important. It is not just a number , it contains the information. If we can identify the relation between two independent random variables(stocks) and the degree of the strength of this relationship, then just by observing the behavior of one variable(stock) we can understand the behavior of another variable(stock).Suppose we have two stocks and both have same movements at a given time, then we should not keep these two stocks in our portfolio , because we can get the same return, just by keeping the one stock .So, if return is negative we will have more loss. This means, if we keep the stocks which has opposite movements then loss in one will be managed by another. This does not mean there should be exactly opposite movements, because , in this case return will be zero. Correlation will give you the percentage of movements of one with respect to another. If the correlation is zero , this does not mean there does not exist the relationship between the variables. This means, there does not exist the relationship between the variables by which we are trying to find the correlation. There may exist another relationship between the variables. Generally, we use linear relationship to find the correlation between the variables.

Correlation is a good measure, but just depending on correlation without proper further testing is not a wise move. Also, correlation is based on linear relationship and it means even if there is no correlation, there may be some non-linear relationship.

Most assets have high volatility during market crash. Just considering correlation during a market failure is a statistical bias (time period bias). We need to consider long-term relationship, at least for a full cycle.

Adding negatively correlated assets doesn’t necessarily mean your portfolio produces zero return. Further, even if your portfolio produces zero, it is evaluated compared to a benchmark. The return objective should be producing higher risk adjusted return compare to that of the benchmark (if it is actively or semi-actively managed). Again, there are various measures for this.

Diversification is primarily for reducing risk and increasing risk adjusted return. I don’t know Yale’s asset allocation but loosing 26% does not necessarily mean Yale’s portfolio performed poorly. It may have produced better risk adjusted return than that of the policy statement/market/benchmark/manager universe. If it produced better risk adjusted return, the diversification might have paid off.

Buffet’s portfolio is diversified and there is statistical evidence for that. He has investments in the financial sector, media, retail, consumer discretionary, energy etc. Diversification does not necessarily mean investing in stocks, bonds, emerging markets, alternative investments etc. Diversification can be achieved by investing in different sectors as well.

Commodities, PE funds, direct real estate investments, managed futures etc can produce long-term diversification benefits (strategic asset allocation).

Are you aware of any off the shelf systems for measuring correlation (or lack of)?

Correlation, Beta, and Co-variance are key factor to build up portfolio.
these three can be seen in any financial securities Book.

Correlation- is scaled to be between -1 and +1 depending on whether there is positive or negative correlation, and is dimensionless.
Covariance- the covariance however, ranges from zero, in the case of two independent variables, to Var(X), in the case where the two sets of data are equal. The units of COV(X,Y) are the units of X times the units of Y.
beta- a measure of systematic risk, of a security or a portfolio in comparison to the market as a whole.

The most basic off the shelf system for measuring correlation is microsoft excel. If you are not comfortable using excel to find correlations here is a good video describing the process (the video is not specifically made for calculating asset class correlations but the process would be the same: http://www.youtube.com/watch?v=MLg_EiIUNP8&feature=related @Iain Mitchell

I agree with Jim. Even the smartest investor sometimes does not follow this basic thing.

What is even more important is the change in correlation in asset classes. This can really come around to bite.

To look at a correlation matrix at an instant in time is an extremely naive and flawed approach. The most recent crisis would indicate that for years cdo’s clo’s had shown very little volatility as they could be immediately repackaged and sold. So if say for example you measured correlation between cdo prices as an asset class and say financials, insurers you may not have witnessed much correlation. However when things unravelled and volatility blew out in the commercial paper market then cdo market the financials and bond re-insurers took huge hits. This is the essential problem with Var and why Var is so dangerous in that in a normal market Var can look benign, correlations which can be highly unstable may appear stable however all of a sudden a huge dislocation reveals that Var has know increased by a factor of ten and the net result was you had no understanding of your risk in the first place. This is why so many firms lost so much money in the early 90′s in commercial real estate only to repeat this with the recent blow up in the housing crisis. I just finished the book “A collosal failure of common sense” about the downfall of Lehman and while it is clear that there were extremely smart and capable people at Lehman aware of what was brewing they did not reside on the 31st floor. So to summarize my comment any institution that relies soley on Var, correlation to compute its risk profile is doomed to failure eventually

Diversification is not possible without understanding how individual assets in a given portfolio move in relation to each other irrespective of their asset class. It is true that a large portion of an individual assets movement is related to the overall sector and industry to which the asset belongs.

However, one must also consider the variation in a individual firm’s earnings for some industries e.g., energy, which is why the correlation between individual assets in a portfolio is at least as important as the correlations between their respective asset classes.

The challenge to achieving true diversification is in finding the right mix of individual assets. If there is a strong negative correlation between ‘all’ assets in a given portfolio then the total return of the portfolio will be sacrificed. Conversely, if there is a strong positive correlation between ‘all’ assets in a given portfolio, diversification will not be achieved. Correlations also change as macroeconomic conditions change. For example, many individual stocks in the energy sector were negatively correlated to the overall market. However, recently the energy sector generally has been positively correlated to the overall market as commodity prices have been generally higher.

Jim, you did a great job in bringing this topic out into the open. Right now high commodity prices make it more difficult to truly diversify. However, in the long run considering correlation will certainly contribute to creating stronger portfolios.

@brian crone

Brian, you pointed out some excellent points about VAR. VAR is good only in normal conditions and it is based on normal distribution assumption. VAR measure fails during crisis. The new administration took some measures to do additional stress testing that may help.

Coming back to the point why even smart investors ignore correlation. Even the father of the modern portfolio theory put his retirement fund mostly in the safer asset, fixed income rather than following his own portfolio efficient theory. We are ordinary people and often show behavioral biases.

Thanks Jim for bringing this topic.

Thank you to everyone that contributed to this discussion. There have been some really great posts here. I noticed that there was some discussion about VAR, my friend Jaime recently sent me a PowerPoint that discusses the drawbacks of VAR and how to correct its flaws. It’s a good read: http://allaboutalpha.com/blog/wp-content/uploads/2009/09/Shadwick-presentation-Sept.-2009.pdf

@Ashok Thomas

@brian crone

@Dave

Well, Swensen is still up double digits and WAY ahead of his competition over any longer period. And, despite his performance, he still knows what correlation is.

Correlation is an enormously powerful statistic when used on a portfolio. Why add a new fund (of any class) when your portfolio has had a 94% correlation to that fund for the past year. I have clients who come to me owning the Vanguard growth, value, and S&P 500 index fund . . . basically, the portfolio correlates 99%+ to the S&P 500, and they claim they are diversified.

Generally, I shift a quarter of assets 3-4 times per year. There’s an example at the link below. The green line results from quarterly rebalancing of 4 Vanguard funds. Note the portfolio correlation to all its components is quite low, 40-70%

http://www.fasttrack.net/charts/vg.png

This kind of active management isn’t hard to do, and keeps the clients happy. I am surprised that so few money managers follow these kinds of strategies. I’d be happy to respond to any questions on this topic.

I include inverse market ETFs and/or inverse market mutual funds in client portfolios. The correlation with the SP500 is between 12% and 19%, depending upon portfolio composition.

Hi,
Thanks for this lucidly written article on co-relation. After this global financial crisis, “co-relation” has got some attention from the investors,investment managers and regulators alike.I would like to add few issues which need to be kept in the mind when using co-relation on portfolio decision making:
(i) Stability of co-relation co-efficient: One may see from your example of S&P 500 and GSCI that co-relation co-efficient is not Constant and may vary (in value and/or in direction) as well.
(ii) Unco-related mean no linear co-relation. There still may be co-relation of higher order. The model generally used in majority of softwares to measure co-relation is “Pearson’s co-relation” which tells about “Linear Co-relation” only.
(iii)Finding a non-co-related asset class is highly unlikely for a general investor and not so easy task for even the big investment firms. Everyone understand age-old statement ” Dont keep all eggs in one basket” but issue is to find really “non co-related” baskets otherwise keeping eggs in even 10 (co-related) baskets wont help.

@Paul Charbonnet

Paul:
It should be pretty easy.

In fact there’s a series of studies, done by Wilshire, i think, which shows tht the biggest reason that institutional investors outperform retail investors is becasue of periodic rebalancing. And, even without regard to forward looking strategies. If all one does is rebalance periodically to an objective/policy allocation, the volatility works for you and you buy low and sell high, which is the real beauty of covariance/variance, or correlations.