Yao et al. (2014) discussed that "Fig. 1 illustrates the magnitude of the non-linearity in the dispersion-market return relationship (which is captured by the γ2 coefficients) for the Shanghai B-share market. It is evident that the relationship is far from linear, and as the average market returns become larger in absolute terms, the return dispersions increase but at a decreasing rate. Furthermore, consistent with Christie and Huang's (1995) intuition that herding occurs during periods of market stress, it can be observed from Fig. 1 that as |Rm,t| surpasses a certain threshold, CSSDt in fact tends to become narrower."
My question is: Thus, according to the attached picture, would you please tell me where is the non-linear relationship and where is the return dispersions increase but at a decreasing rate when average market returns become larger in absolute terms?
Hi John,
I have no idea what this is about with regards to content, but I try to explain the relationship I see in this picture:
The relationship is not linear, because the dispersion increases in both directions from the zero-point. It seems to be some kind of quadratic (y²).
When starting at a market return of 0 there is a positive relationship between market return and dispersion. the mean dispersion at a market return of 0 is smaller than the one at a market return of 2 and this is smaller than the dispersion at a market return of 4. But this relationship is also not linear, because the difference between the dispersion at 0 and the dispersion at 2 is greater than the difference between the dispersion at 2 and the dispersion at 4. The growth of the dispersion by ascending market return is negatively accelerated, this means it decreases. It seems to be some kind of log-linear. This is what the authors mean by "the return dispersions increase but at a decreasing rate". The dispersions become greater, but this growth gets smaller, starting at the zero-point.
Hope you understand what I am trying to explain.
Thanks Brian, I really appreciate your answer. It is clear and simple. You are supposed to have a solid background in math or statistics right?