# When is Premium Riskier Than Loss?

:::::: :::

::: :::

::: ::::::

## Loss Ratio Time Series by Major Line

### Title decoder: CMP; SD=0.111 (0.0661), cor=0.915 ar fit, r2=0.268, rse0=0.089

• Line; standard deviation
• Down-side semi-deviation is shown in parenthsis (explain)
• Correlation of the line with total on the first line
• (second line) shows the $$R^2$$ and residual standard error of an autoregressive loss ratio model

### Interpretation

• When the rse is much lower than SD it suggests the market cycle is predictable
• Tends to occur in casualty lines (e.g., commercial auto, medical malpractice, private passenger auto, and workers compensation)
• The cycle for property lines tends to be idiosyncratic, for obvious reasons.

### Line Legend

• Thin gray line in each plot shows the total loss ratio, for context
• The horizontal lines show the mean (thicker) and mean $$\pm \Phi^{-1}(22/23)= \pm1.71$$ standard deviations
• If the loss ratios were normally distributed we expect all observations from 22 years (1996-2017) to fall within these tram lines
• They provide a surprisingly good estimate of the range of loss ratio, except for Financial Lines (which uses a different tick spacing, note).

## Direct Premium and Loss Dynamics

posted 2021-11-30 | tags: insurance, risk, pricing, presentations