The optimal strategy can't possibly be (b), because it would have the bizarre implication that two investors who have exactly the same preferences and who currently have the same amount of wealth would want to allocate their investments differently depending on how far in the past they started investing.

Edit: I'm quite sleepy right now, but I think the way the mathematics works out is that the risk arising from an asset is a convex function of the amount allocated to it. So by Jensen's inequality it's less risky to invest 50/50 in cash and stocks for two years than to invest for one year in cash and one year in stocks, for the same reward.