Take the 2-minute tour ×
Quantitative Finance Stack Exchange is a question and answer site for finance professionals and academics. It's 100% free, no registration required.

Although this is probably a basic question, this is probably also the right forum to post it in :)

I thought I understood beta, but know I am really confused...

The beta between my portfolio (weekly returns) and the benchmark (ACWI in Danish Kroner) is 0,48. So historically my portfolio has had half the volatility of the benchmark. Great.

If I turn the calculation around and look at the benchmark relative to my portfolio (I hope it makes sense) I get a beta of 0,74. So the benchmark has now been less volatile, than my portfolio. I can this be? I would expect the beta of the benchmark relative to my portfolio to be greater than 1...

Here is a link to the data (weekly) if needed:


Kind regards


share|improve this question
add comment

1 Answer

up vote 4 down vote accepted

I did not look at the data, but recall that beta is a parameter in the following equation:

$$ r_A = \alpha + \beta r_B + \epsilon $$ relating two returns (random variables, samples) $r_A$ and $r_B$. To calculate beta you peform $$ \beta = \frac{cov(r_A,r_B)}{var(r_B)}. $$ Thus if assets $A$ and $B$ exchange roles, then only the denominator changes. In your example the variance of your benchmark is smaller than the variance of your portfolio.

Futhermore note that the $\epsilon$ above models all volatility/risk that remains and that is not explained by $r_B$. If $r_B$ and $r_A$ are not too much related then the beta does not tell you too much about risk.

In the CAPM beta plays a more prominent role. But this is a slightly different story.

share|improve this answer
Just wanted to finish your logic to the complete answer: using the formula for beta above, one can see, that beta(A, relative to B) * beta(B, relative to A) = correlation between A and B. So one shouldn't expect them to be inverse of each over. In your example it just means, that the correlation between the returns is sqrt(0.48 * 0.74) ~ 0.59. –  LazyCat Dec 30 '13 at 16:21
Thanks for both insightful comments! I think it makes sense now :) –  user6859 Dec 31 '13 at 7:21
add comment

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.