Many thanks to @rene for his ideas in the comments to the question.

Here is the query that calculates the user's reputation for posts no older than 365 days.

select posts.owneruserid [User Link]
     , sum( case votes.votetypeid
            when 1 then 15
            when 2 then 10
            when 3 then -2
            else 0
            end
        ) [estimated rep.]
from posts
inner join votes on votes.postid = posts.id
where posts.creationdate > dateadd(dd, -365, getdate())
and posts.owneruserid = ##userId##
group by posts.owneruserid