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Correlation is symmetric: the amount that $X$ is correlated with $Y$ is the same as the amount that $Y$ is correlated with $X$. What you're talking about is the regression coefficient, which is in a sense anti-symmetric: the coefficient of $X$ with respect to $Y$ is the reciprocal of coefficient of $Y$ with respect to $X$ (well, almost; you actually get ...

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Should have been a comment as there are already brilliant answers, but posting as an answer only because it is a bit lengthy! Ignoring the sample/population nuances, here is a simple illustration that correlation is an indicator of the strength (and direction) of the linear relationship but not the 'magnitude' : \$\text{Correl}(Y,X)= \frac{\text{Cov}(X,Y)}{\...

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High correlation between the prices of two stocks is an indication of relative percentage changes at around a certain ratio in the same direction most of the time, but not necessarily in similar percentages or magnitudes. If a stock’s price moves, for example, one-fifth of another stock’s price in percentage terms in the same direction most of the time (...

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Notice that linear correlation is just a standartized measure of variability for two variables around their mean values, loosely speaking. In your concrete case of a linear correlation between stock returns, it won`t say anything about magnitude because the mean of each return series go into the computation. You can only say those stock returns have a strong ...

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