The purpose of this article is to demonstrate the effect of investment time horizon on the choice of risky assets in a portfolio when the investor in question is optimizing a Safety-First (downside risk-aversion) utility function. It is shown, under standard assumptions, that although shortfall risk decreases exponentially with investment time horizon, the portfolio asset allocation proportions remain invariant. In fact, in some instances, the optimal allocation will not even depend on the drift of the underlying assets. Thus, we extend the classical results of Samuelson and Merton, derived under conventional utility assumptions, to an individual optimizing an A.D. Roy Safety-First objective; a discontinuous utility function that has been extolled as conforming to observed investor behaviour. A numerical example is provided.