What effect does the size of an insurance pool have on actual versus expected losses?

The size of an insurance pool plays a significant role in the relationship between actual losses and expected losses. As the pool of insured individuals becomes larger, the principle of statistical probability comes into play. When a larger and more diverse group is pooled together, the law of large numbers suggests that the actual losses will average out more closely to the expected losses calculated based on the collective risk of the entire group.

This occurs because with a larger pool, extreme variations in losses from individual members are less impactful on the overall results. The randomness in loss events tends to balance out; thus, the collective experience of many insureds leads to more predictable outcomes. Consequently, larger pools provide insurers with better data and a clearer projection of loss trends, allowing actual losses to more closely match the anticipated figures.

In contrast, smaller pools can lead to more variability and unpredictability, as a few high-loss events can skew results significantly. This highlights the importance of having a sufficiently large risk pool in insurance, where the effects of randomness diminish and the insurer can more accurately predict the likelihood of claims.