Apply and Test Regression Versions and Extensions of Link Ratios including Mack




The Extended Link Ratio Family (ELRF) modelling framework formalizes average link ratios as regression estimators and extends them to incorporate an intercept term and a constant accident period trend for each development period. These include Mack (Chain ladder) and Murphy (link ratio with intercept).


The resultant benefits include forecast standard errors (instead of just a point value) and the ability to test whether the assumptions made by the model are carried by the data.








* Calculate the uncertainty of your forecast loss reserves

The regression formulation of weighted average link ratios allows you to calculate the standard deviations of your forecasts, so you can quantify how "risky" each line of business is.


* Test the quality of the model

Diagnostic plots allow you to see at a glance whether the link ratio method is appropriate for your data. The plot on the left shows trends that aren't captured by the method. The trend assumed by the method is much higher than that in the data resulting in substantial over forecasting.


Residuals represent the data adjusted for what has been fitted to the data. In this example, the residuals versus calendar year exhibit a strong negative trend. This means that the trend estimated by the ink ratio method is much higher than the trend in the data. Accordingly, the forecasts produced by the link ratio method are much too high.
* Try out the extended modelling features

Other models in the ELRF modelling framework may be able to capture the calendar year trends in your data. Try them, and test thier quality using the diagnostic plots. For the above, a much better fitting model can be found by extending the link ratio model to include a constant accident period trend for each development period. The model better captures the (true) calendar year trends in the data and results in substantially lower forecasts.


Perhaps there are changing calendar period trends. Remove the earlier calendar periods with a few clicks - with a link ratio model, this is equivalent to using link ratios over just the most recent calendar years. Then see if this new model is a better fit to the data. IN many cases, you will find that there is still a trend in the residuals, so the model is not capturing the true trends in the data. Try the Probabillistic Trend Family (PTF) modelling framework.