This paper addresses problems prevailing for life insurance companies in their asset-liability management when there are heterogeneous levels of the minimum guaranteed rate of return to the policyholders. The problems are analysed in a setting with a «bearish stock market» where the buffer accounts are empty. Some life insurance companies say that they use their assets to hedge the aggregated guarantee to their customers. If an insurance company has two types of customers, one with a high minimum guaranteed rate of return and one with a low, we show that if the insurer hedges the aggregated guarantee, the customer with the low guarantee will always get a return that is above the minimum guaranteed rate of return. The reason that the authorities in Norway have reduced the minimum guaranteed rate of return from 4% to 3% is to reduce the probability of the life insurance companies defaulting on their liabilities. We argue that this reduction may in fact increase the probability of default.