A cost of living index will decrease if the assignee's home currency appreciates against the host currency, or if the price levels of the ECA shopping basket increase more in the home location than the host location – as explained here.
As an example, let's consider a pay review case where relative price levels haven't changed and the index decreases due to the appreciation of the home currency against the host currency. This results in a smaller COLA in home currency terms, but it is important to bear in mind that this lower COLA is converted into host currency at a new, more favourable exchange rate. The decreased index and the new exchange rate cancel each other out, and the COLA amount in host currency – the currency in which COLA is intended to be spent – does not change.
However, if the assignee is receiving the host spendable in home currency, this may be where they are at risk of losing out if there are further exchange rate fluctuations. Having a policy in place to protect assignees from exchange rate changes is the most effective way to guard against this.
But what about the opposite scenario: the exchange rate hasn't changed, but price rises in the home location outpace those in the host location, pushing the index down. This would indeed result in a lower COLA, in either home or host currency. Rest assured, this still doesn't make the assignee “worse off”.
Living costs are increasing for the assignee's peers back home and we need to remember that the index is designed to maintain the same purchasing power they would be experiencing if they were not on assignment. If a company wishes to account for the effect of home inflation on an assignee's pay, generally this is captured by reviewing the assignee's notional home salary – as they would for the assignee's home country peers. A higher notional home salary will mean the COL index is applied to a larger home spendable, consequently increasing the resulting COLA.