cab691

02-25-2012, 07:26 PM

Hi, I have a pretty basic question about the parallelogram method.

Let's say there's a single rate change of 8% at 7/1, and we want to put the earned calendar year premium on level. Naively, I'd guess that if seven eighths of the premium comes from policies written before 7/1, we'd use an overall rate factor of

\frac{7}{8}1.08 + \frac{1}{8},

the weighted average. But that's not what the parallelogram method prescribes! Instead, we use the harmonic weighted average:

\frac{1.08}{\frac{7}{8} + \frac{1}{8}1.08}.

Why is the harmonic weighted average better than the ordinary weighted average here?

Let's say there's a single rate change of 8% at 7/1, and we want to put the earned calendar year premium on level. Naively, I'd guess that if seven eighths of the premium comes from policies written before 7/1, we'd use an overall rate factor of

\frac{7}{8}1.08 + \frac{1}{8},

the weighted average. But that's not what the parallelogram method prescribes! Instead, we use the harmonic weighted average:

\frac{1.08}{\frac{7}{8} + \frac{1}{8}1.08}.

Why is the harmonic weighted average better than the ordinary weighted average here?