I was just reading about the core-satellite approach to constructing portfolios when I came across a note that read (I paraphrase): managers’ total returns will likely have a positive correlation because their portfolio values will go up or down together (depending on the overall market), while their active returns will likely have negative (or zero) correlation because when one manager’s active return is positive another’s is likely to be negative (and vice-versa).
This note is, to put it bluntly, garbage. It demonstrates nothing more than that the author has no understanding of correlation, or of the difference between prices and returns.
I hate it when finance people get things _ so _ wrong. This happens frequently with correlation and frequently with beta. It’s enough to make one tear out one’s hair. (Note: thank goodness I have enough hair that I can tear out some without permanent deleterious effect.)
Negative correlation of returns _ does not mean _ that when one is positive the other is negative. It means that when one is above its mean, the other is likely to be below its mean. But _ both means can be positive _.
Morons!
Saying a manager’s active return is negative is not necessarily saying they have a negative return – but rather that they are just underforming the benchmark. In this case I they are assuming that every managers mean return would equal the market return. Thus, their active returns would have negative correlation (when one is beating the market the other is trailing). Therefore they could both have positive returns and still be negatively correlated.
I know that. That’s not the point.
If you make the assumption that the mean active return for every manager is zero, then their conclusion is correct. But that’s an absurd assumption. If you’re going to make that assumption, you should pursue a passive investing strategy and avoid paying active management fees.
If you make the much more reasonable assumption that their active returns do not necessarily have a zero mean, then the conclusion that they have a negative correlation of returns when one’s active return is positive and the other’s negative is patently false. As a simple example, suppose that the benchmark’s average monthly return is 0.5%. Manager A’s total returns and manager B’s total returns for 12 months are, respectively:
- Manager A: 0.3%, 0.4%, 0.3%, 0.4%, 0.3%, 0.4%, 0.3%, 0.4%, 0.3%, 0.4%, 0.3%, 0.4%
- Manager B: 0.6%, 0.7%, 0.6%, 0.7%, 0.6%, 0.7%, 0.6%, 0.7%, 0.6%, 0.7%, 0.6%, 0.7%
Manager A’s active return is always negative; manager B’s active return is always positive, and their correlation of active returns is +1.0.
Furthermore, the first statement I paraphrased, “managers’ total returns will likely have a positive correlation because their portfolio values will go up or down together” is also patently false. If manager A’s and manager B’s monthly returns were, respectively:
- Manager A: 0.4%, 0.3%, 0.4%, 0.3%, 0.4%, 0.3%, 0.4%, 0.3%, 0.4%, 0.3%, 0.4%, 0.3%
- Manager B: 0.6%, 0.7%, 0.6%, 0.7%, 0.6%, 0.7%, 0.6%, 0.7%, 0.6%, 0.7%, 0.6%, 0.7%
then their portfolio values are going up together (all the returns are positive), but the correlation of returns is -1.0.
There are multiple blanket statements in the books that are BS. That’s why the reading on Biases is so important… 