Casualty Actuarial Society (CAS) Practice Exam

How is combined risk affected when gains or losses from two risks are correlated?

1. The combined risk decreases

2. The correlation has no effect on combined risk

3. The greater the correlation, the greater the combined risk

4. The correlation reduces overall risk likelihood

The correct answer is: The greater the correlation, the greater the combined risk

When considering how combined risk is affected by the correlation of gains or losses from two risks, it is essential to recognize that higher correlations between risks typically result in greater combined risk. This is due to the fact that when two risks are positively correlated, they tend to move in the same direction; if one risk incurs a loss, the other risk is likely to do the same. Consequently, this synchrony amplifies the potential for greater overall losses or gains, thus leading to an increase in the combined risk. In instances where risks are perfectly correlated, a loss in one risk would correspond directly to a loss in the other, thereby elevating the total risk exposure. The combined risk captures the worst-case scenarios across both correlated risks, and with strong positive correlation, the outcomes are more likely to align negatively, amplifying risk exposure. This relationship clarifies why a higher correlation leads to a greater combined risk, as opposed to options that suggest a decrease in risk or no effect whatsoever. The understanding of correlation's impact on combined risk is critical in risk management and actuarial analyses, reinforcing the need to evaluate not just individual risks, but also how they interact with each other in terms of correlation.