Correlation and Time Periods
Motivated by a comment by NormR

So I read, in a discussion forum, a comment that
"Correlations will change depending on if you use yearly, monthly, or daily data "
and I think ...

>You think he's all wet, eh?
Well, I think it's unlikely that they're the same, but they're probably very close, so I ...

>You decide to test it, eh?
Stop interrupting!
Yes, I decide to demonstrate that the correlation calculated on the basis of daily or monthly or annual returns ... they won't be so different. So I do this:

  1. I download 10 years worth of daily stock prices for two stocks.
  2. I look at the prices every N market days, for each stock (where N is some number between 1 and 250).
  3. I calculate the N-day returns, for each stock (that'd include daily, weekly, monthly etc.).
  4. I use these N-day returns to calculate the Correlation (and expect they won't be much different).
  5. I repeat 2 to 4, going from N = 1 to N = 250 (the latter being about one year).
When the smoke has cleared, I get this:

>Mamma mia!
You took the words right outta my mouth! Anybuddy wanna play? The spreadsheet is here. (Click on the picture to download.)

You just type in the Yahoo symbols for a couple of stocks in cells K6 and L6 ... and click the Download button.
You can also move that slider to pick a time period from N = 1 to N = 250 to see the Correlation for that number of days.
You can ...

>What's that other do Correlations button?
I was getting to that!
If you click it, you can see the right charts materialize before your eyes. It's very pretty.
>That's your opinion ...

Here are some others:

>So when people talk about correlation, what one do they mean?
Beats me ... but I think it's common practice to use monthly returns over the past three years.
However, I note that most discussions of correlation between assets make statements like so ... without indicating what returns are to be used:
      "The correlation coefficient of two stocks characterizes the price interdependence between them."
      "We've also seen that if a pair of stocks have a correlation of -1 then their risk cancels out, so this may be a particularly interesting pair of stocks to own."
      "Correlation analysis attempts to measure the strength of relationships by means of a single number varying between -1 to 1 called the correlation coefficient."
      "... these products have a very high correlation with the stock market and therefore make lousy diversifiers."

Correlation means ... what?
Besides having a value that depends upon the time period (as indicated above), there's another interesting feature of "correlation":
When we speak of Correlation between two assets, we usually expect that high positive correlation (near 1.0 or 100%) means their returns tend to be positive (or negative) together.

>Yeah, so?
So, don't be so sure. Take a gander at this chart
You may think that there's a fairly high correlation. In fact, the correlation is -1.0 (or -100%).

The following returns have a correlation of -1.0 (or -100%).

The Y-returns are obtained from the X-returns via: Y = 20% - X/10

>What about correlation between prices?
It's 98% (or 0.98, if you prefer).

>So when people talk about correlation, what do they mean?
I've already answered that question.