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Other Resources:

• Investment Dictionary: A mathematical term describing how closely related the price movement of different securities or asset classes is. More...
   
• Pathtoinvesting: In investment terms, correlation is the extent to which the values of different types of investments move in tandem with one another in response to changing economic and market conditions. More…
   

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2.
 

• The CPA Journal: In statistics, correlation measures the relationship between two entities. A correlation of 1.0 means that the two entities move in perfect tandem with each other. More…
   

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3.
 

• Wikipedia: The correlation ρ_{X, Y} between two random variables X and Y with expected values μ_X and μ_Y and standard deviations σ_X and σ_Y is defined as:
  
  

  Since μ_X = E(X), σ_X² = E(X²) − E²(X) and likewise for Y, we may also write:

  
   

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4.
 

• Correlation Coefficient
• Data Mining
• Covariance
• Standard Deviation
• Diversification
• Variables
• Modern Portfolio Theory
• Linear Relationship
• Portfolio Management
   

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5.
 

Other Resources:

• Path To Investing: The extent to which the returns of various asset classes tend to be driven by the same market forces is called correlation, and most, though not all, traditional asset classes tend to be quite highly correlated. More…
   
• The CPA Journal: The Long View. No one can predict market performance over any time period, short or long, but the study of correlations shows that, over time, different asset types have not performed in line with the stock market. More…
   

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6.
 

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7.
 

While all things being equal, historical non-correlation is important measure to consider, the following are some of the misinterpretations of correlation analysis that are pivoted in the simple fact that past correlation is not necessarily indicative of future results.

Some of the reasons for this is 1) the past is finite and the future is infinite 2) Certain conditions in the future that may cause investments to correlate is very likely to have not occurred in the past 3) Correlation studies are frequently done based on monthly numbers and not daily numbers and thereby hiding possible high degrees of historical intra-month correlation, 4) Even if the past could be indicative, frequently the data is limited; a correlation study of one year obviously does not carry the same weight as 10 years yet rarely is the period covered mentioned 5) frequently two records disparate in length are be compared; the measure can of course only reflect the period in common 6) two investments may be highly "non-correlated" 99.9% of the time but correlate to the extreme under historical stressful events that occur .1% of the time and which may be the most important time to have non-correlation 7) events such as a liquidity crisis can cause previously uncorrelated investments to correlate 8) managed investments are managed by people and not computers; the unpredictability and diversion from the past decision making behavior may deviate for a variety reasons  9) because non related events appear to be correlated (ie. the stock market and the winner of the Superbowl) does not mean that there is a predictive basis for the future. and 10) correlation studies in of themselves do not quantify the qualitative aspect of trading.

Other Resources:

• Financial Sense University: One of the most common errors of analysis occurs when correlation is assumed to imply causation. More…
   
• Wikipedia: Correlation implies causation, also known as cum hoc ergo propter hoc (Latin for "with this, therefore because of this") and false cause, is a logical fallacy by which two events that occur together are claimed to be cause and effect.
  
  For example:

  Teenage girls eat lots of chocolate.

  Teenage girls are most likely to have acne.

  Therefore, chocolate causes acne.

  This argument, and any of this pattern, is an example of a false categorical syllogism. One observation about it is that the fallacy ignores the possibility that the correlation is coincidence. But we can always pick an example where the correlation is as robust as we please. If chocolate-eating and acne were strongly correlated across cultures, and remained strongly correlated for decades or centuries, it probably is not a coincidence. In this particular case, the fallacy ignores the possibility that there is a common cause of eating chocolate and having acne (e.g. being young).

  Another important factor which should be considered is the presence or absence of a known mechanism which may explain how one event causes the other. Using the above example, if chocolate contains large quantities of hydrogenated fats, or trans-fatty acids, and if those have been shown to clog pores and thus cause acne, then the link between chocolate and acne is more believable. A counter-example would be astrology, where there is no convincing known mechanism to describe why personality would be affected by the position of the stars. Of course, the absence of a known mechanism doesn't preclude the possibility of an unknown mechanism.

  For one event to be the cause of another, in the normal world, it must happen first. In some cases the precipitating event may happen so quickly before the result, or may overlap the result in time, so they are said to occur simultaneously. However, the precipitating event can't happen after the result, for example, by concluding that a current increase in population caused a baby boom many years ago.

  Another example:

  Ice-cream sales are strongly (and robustly) correlated with crime rates.

  Therefore, ice-cream causes crime.

  The above argument commits the cum hoc ergo propter hoc fallacy, because in fact the explanation is that high temperatures increase crime rates (presumably by making people irritable) as well as ice-cream sales.

  Another possibility is that the direction of the causation is wrong and should be the other way around. For example:

  Gun ownership is correlated with crime.

  Therefore, gun ownership leads to crime.

  The facts could easily be the other way round: increase in crime could lead to more gun ownership with concerned citizens. See wrong direction.

  The statement "correlation does not imply causation" notes that it is dangerous to deduce causation from a statistical correlation. If you only have A and B, a correlation between them does not let you infer A causes B, or vice versa, much less 'deduce' the connection. But if there was a common cause, and you had that data as well, then often you can establish what the correct structure is. Likewise (and perhaps more usefully) if you have a common effect of two independent causes.

  But while often ignored, the advice is often overstated, as if to say there is no way to infer causal structure from statistical data. Clearly we should not conclude that ice-cream causes criminal tendencies (or that criminals prefer ice-cream to other refreshments), but the previous story shows that we expect the correlation to point us towards the real causal structure. Robust correlations often imply some sort of causal story, whether common cause or something more complicated. Hans Reichenbach suggested the Principle of the Common Cause, which asserts basically that robust correlations have causal explanations, and if there is no causal path from A to B (or vice versa), then there must be a common cause, though possibly a remote one.

  Reichenbach's principle is closely tied to the Causal Markov condition used in Bayesian networks. The theory underlying Bayesian networks sets out conditions under which you can infer causal structure, when you have not only correlations, but also partial correlations. In that case, certain nice things happen. For example, once you consider the temperature, the correlation between ice-cream sales and crime rates vanishes, which is consistent with a common-cause (but not diagnostic of that alone).

  In statistics literature this issue is often discussed under the headings of spurious correlation and Simpson's paradox.

  David Hume argued that any form of causality cannot be perceived (and therefore cannot be known or proven), and instead we can only perceive correlation. However, we can use the scientific method to rule out false causes.
   

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