Active share/risk

Don’t judge me. I need to get equity under control.

Can somebody (hopefully) confirm my understanding of active risk/share?

Active risk = tracking error. It’s the difference in the standard deviation of returns on the portfolio vs. that of the benchmark.

Active share = the number of active decisions made by the manager to overweight/underweight securities.

If the over weighing/under weighting of the selected securities have a high correlation with each other, their returns will be similar. Therefore it is possible to have a high active share and low active risk.

The text says this strategy is common for multi-factor based models, but I assume it would also be appropriate for enhanced indexing?

Si?

Active risk = tracking error. It’s the difference in the standard deviation of returns on the portfolio vs. that of the benchmark. Correct

Active share = the number of active decisions made by the manager to overweight/underweight securities. It’s .5 X Sum|portfolio weights - benchmark weights|, but the idea is correct. I’ll also add that the manager has control over active share (but not complete control over active risk) Also, active risk will be due to active share when factor exposure is neutralized wrt the benchmark factor exposure.

If the over weighing/under weighting of the selected securities have a high correlation with each other, their returns will be similar. Therefore it is possible to have a high active share and low active risk. Another way to looking at this is you can have high active share but low active risk when you make diversified stock bets.

The text says this strategy is common for multi-factor based models, but I assume it would also be appropriate for enhanced indexing? No idea about this one.

Two other points__1. Adding cash to your portfolio raises active risk (by increasing deviations from benchmark)

2. Adding securities to your active portfolio that have low correlation with the portfolio lowers total risk. Adding securities to your active portfolio that have high correlation with benchmark lowers active risk.

1 Like

Perfect - thanks for clarifying that.

My only question is around the factor exposure, I’m not sure why but the word “factor” throws me off. Having trouble seeing the concept of “active risk will be due to active share when factor exposure is neutralized with the benchmark exposure”.

So thinking out loud… the factors at play are: market, size, style, momentum, etc. If the portfolio has the same factor exposures as the benchmark then all active risk (tracking error) will be due to the active positions taken by the manager - because all other risks remain the same.

I think that makes sense.

1 Like

Yeah. You could match the benchmark in its allocation to, say the tech sector, and neutralize that factor exposure. But within that factor, you could make concentrated individual security bets that deviate from the benchmark. Here, your sector risk is neutralized, so all active risk is due to active share and idiosyncratic risk.

“If the over weighing/under weighting of the selected securities have a high correlation with each other, their returns will be similar. Therefore it is possible to have a high active share and low active risk.”

This part confuses me. I understand it is possible to have active share and low active risk, but the example shown doesn’t necessarily result in low active risk.

Ative Risk = Stdev (Active Return)

So, if Active Return has been consistently, say always 2% above benchmark, the active risk would be low (0 in this case). To generate consistent active return, the OW/UW bets need to have low correlation with each other. Otherwise, it is hard to generate consistent active return.

If your OW and UW bets have high correlation with each other, that means if you are right, you outperform extremely well, but if you are wrong, you underperform really bad. Then your active return would be very volatile, resulting in high active risk.

Anyone care to comment?

If you have idiosyncratic risk and a relatively large 401k account can you use heuristics to properly 1/n diversify? I am asking for a friend here…

=)

These seem like contradictory statements to me? Now I could be wrong, hence I was asking the question in the first place, but in your second example how would you outperform if your OW/UW bets have a high correlation with each other? If I underweight bank A and overweight bank B, and if they have a correlation of 1, then my portfolio return will not change and my active risk will be low (or zero) while active share increases.

Seems to me that in order to have high active risk my OW/UW bets need to have low correlation with each other - resulting in a return significantly different than the benchmark. Which is in line with your first statement.

Again, I could be wrong. Logic doesn’t necessarily translate well in CFA land.

ok, I hear your logic.

I think I am bogged down on the term “Correlation”. I suppose it means if two securities are highly correlated with each other, they would outperform at the same time and underperform at the same time. If that’s the case, you would net at 0.

If the correlation is -1, that’s the ideal situation, where you have outperform + (short underperform) = 2 outperform.

If the correlation is 0, that would be good as well.

I did a question that says if the correlation is -1, it is highly correlated.

I guess high correlation means the correlation is 1?

True, I would generally assume high correlation = +1, but I suppose we should specify “highly positive correlation” vs “highly negative correlation”.