I have picked three ETFs, collected 5 year historical data and calculated the correlation of daily end prices. I calculated the following correlations:

  A     B     C
A 1    
B 0.77  1
C 0.49  0.72  1

How do I read this result?

Update: This is my retirement (in 25 years) portfolio where I just wanted to use ETF A. As an improvement I want to mitigate the risk by splitting equally on three ETFs. With the given correlations is the risk lowered at all?

  • 3
    What is your goal? Try to be specific. – JTP - Apologise to Monica Jan 15 '17 at 17:13
  • My goal is to reduce the risk of ETF A. – user52195 Jan 16 '17 at 8:24
  • Without more info, we can't answer. We have no way of knowing if correlation is due to actual shared responses (eg all three holding some of the same stocks) it was completely due to random numbers. – keshlam Jan 17 '17 at 2:53

Correlation is a measure of how two variables move when one of them changes. Correlation takes values between -1 and +1 where negative correlation means there is a general inverse relationship (i.e. prices move in opposite ways) and positive correlation means there is a general positive relationship (i.e. prices move in the same way). I say "general" because, for example, a positive correlation does not imply it is impossible for ETF prices to move in different ways at some points in time.

Now, your table has only values between 0.49 and 0.72, omitting the obvious 1s (a variable always moves perfectly with itself), which means that all ETFs in your portfolio are positively correlated. We can further qualify this correlation and say that the 0.49 is "moderately" correlated whereas 0.72 and 0.77 are quite strongly correlated to A. Therefore, your portfolio will tend to follow dips in the market (as well as upward movements) at the same time but to different extents.

Finally, with regards to risk, correlation tells you about portfolio risk rather than individual security / ETF risk. High correlation between all securities in a portfolio means that if a large dip in the market occurs, the entire portfolio will sink. This does not mean that dips will occur often (i.e. riskiness). Some measures that can be interesting to measure riskiness of ETF A are variance (which measures volatility) and Sharpe ratio which calculates the pay-off for taking risks.

  • The correlation is the portfolio risk and Sharp ratio the individual pay off. Is there something like the portfolio Sharpe ratio? – user52195 Jan 16 '17 at 11:20
  • Sharpe is essentially a measure of reward vs risk. Reward here is defined as the excess return of a portfolio over a risk free asset (such as treasury bills) and risk is the volatility of the portfolio. So yes, Sharpe works for portfolios. – ApplePie Jan 16 '17 at 12:44