Is there any reason the semi-variance is phrased as being 'proportional' to variance if returns on assets are symmetrically distributed? Would it be more precise to say half the variance? If semi-variance is proportional to variance, that implies semi-variance = k * variance but here k is specifically 1/2, if returns on assets are symmetrically distributed.
Hi Tess, Yes, you are absolutely correct. Semi-variance is exactly half the variance if the returns on the assets are symmetrically distributed. This is due to the fact that for a symmetric distribution the mean is equal to the median of the distribution. Let me know if this helps. Cheers, Kaustav
