Vol 6 page 274 I quote" Performance-based fee structures may also lead to misestimates of portfolio risk. Such fee structures convert symmetrical gross active return distributions into asymmetrical net active return distributions, reducing variability on the upside but not the downside. As a result, a single standard deviation calculated on a return series that incorporates active returns, above and below the base fee, can lead to the underestimation of downside risk"

I do not understand what they are trying to say here. Can anyone explain it better please?.

If you calculate a standard deviation for all returns, positive and negative, then it will be larger than the standard deviation of the positive returns, but smaller than the standard deviation of the negative returns. Therefore, it underestimates the downside volatility.

Let’s say you have hired a fund manager with an active mandate over 6% abs return. Let’s say your fee structure are 2/20.

So long the returns are 6% or less the entire earnings risk is yours. However, the same is not the case if the manager is consistently earning above 6%. Here the variability is shared in the 20/80 ratio. So if the mean abs return is 8%. Your risk around this 8% is limited to 80% of the variability around 8%. Not so, if it is 6% or below mean return.!There the entire variability is your baby.