Question

Please define and explain the difference between symmetrical and asymmetrical returns. (Please provide an exaple if appropriate.)

Answer 1

Symmetrical Returns: This the type of distribution of returns in which the values of returns are distributed normally and equally on both sides of the mean return value. The mean and median values of this return distribution are equal and it exhibits Normal distribution characteristics. The sides on each side of mean value are a mirror image of each other. This type of returns distribution does not skew.

Other notable features are-

1. 68% of the values of returns lie between plus and minus one standard deviation from the distribution mean return value.

2. 95% of the values of returns lie between plus and minus two standard deviations from the distribution mean return value.

3. 99% of the values of returns lie between plus and minus three standard deviations from the distribution mean return value.

Asymmetrical Returns: In this type of returns distribution, the sides on each side of mean value are not mirror image of each other. This type of returns distribution does skew. In this type of returns distribution, the values are randomly (not symmetrically) placed on either side of the mean return value. It does not comply with the other features of symmetrical distribution.