What you are describing is a conditional value list. An unstored calculation field with Year ( Get ( CurrentDate ) ) could be used as the match field in a relationship to limit the values in the the list to just those where a year field in Activities just shows the activities for this year. Please note that while this does what you have requested, your list on January 1st each year, will be empty.
Here are some links on conditional value lists.
There's a lot of overlap between the first two links so you can read one and skim the other. The demo file gives you several examples of different conditional value lists so you can examine them to see how they are set up. If you are using FileMaker 12 or later, you can open this demo file from your File menu to get a converted copy of the demo file that you can examine in your version of FileMaker.
The next to last link discusses how to set up a chain of conditional value lists where the value selected in each conditional value list controls the values listed in the next value list and the very last link is a fairly new addition that describes how to use ExecuteSQL to produce conditional value lists that aren't easily possible with the other methods described here.
Forum Tutorial: Custom Value List?
Knowledgebase article: http://help.filemaker.com/app/answers/detail/a_id/5833/kw/conditional%20value%20list
Hierarchical Conditional Value lists: Conditional Value List Question
Using ExecuteSQL to produce a conditional value list: Using ExecuteSQL to Produce a Conditional Value List
Feel free to post follow up questions here if those links aren't enough to get your value lists working correctly.