Correlation: what is it?
Next: Volatility
 When selecting various assets for your Portfolio, you may be tempted to avoid those with a high Correlation. >Huh? Many think of "Correlation" as being an indication of whether the prices of two stocks move up and down together. The most common flavour of "Correlation" is the Pearson product-moment Correlation Coefficient , applied to two sets of returns ... probably monthly returns, over the past few years. The Pearson Correlation is a number between -1 and +1 and when it's close to +1 one (often) interprets that to mean that the two stock prices tend to move up and down together. In such a case, maybe you wouldn't want both stocks in your Portfolio ... if they move together. However, the Pearson Correlation actually measures whether the two sets of returns tend to be above or below their average together ... and that's a horse of a diff'runt hue. It's quite possible to have one stock go up as the other goes down and still have a Correlation of +1. It's also possible to have both stocks go up yet have a Correlation of -1. NOTE: Sometimes I use a percentage between -100% and +100% to denote correlations. Most people just use a number between -1 to +1. However, there are other measures of "correlation" such as Spearman Correlation. Investors often look at the square of the Pearson Correlation (calling it R-squared). The bad thing about R-squared is that is doesn't distinguish between positive and negative correlation. The good thing about R-squared is that is gives some measure of how far the returns are from being linearly related.
 >Huh? You plot the returns for one stock (stock Y) against the corresponding returns for the second stock (stock X). That'd give you a so-called "Scatter Plot". You can then generate a "best fit line" ... the "Regression Line", shown in red, in the diagram If R-squared were 1 (so Corr'n = ±1), all the points would lie on that Regression Line ... and there would, indeed be a linear relation between the returns.

The interesting thing about that Regression Line is that it has a SLOPE and an INTERCEPT and both have names and are of interest to many.

>INTERCEPT?
Yes. If the equation of the Regression Line is, for example: y = - 0.1 x + 0.2 then - 0.1 is the SLOPE and 0.2 is the INTERCEPT.

If you're plotting returns for some stock versus the returns for some broader market Index (like the DOW or S&P500) then you're seeing if the stock tends to follow "the Market"
... so that Regression Line is interesting and we call the two parameters:
 Alpha = INTERCEPT   and   Beta = SLOPE
Alpha and Beta are also involved in the Capital Asset Pricing Model

See:

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