Although many individual route choice models have been proposed to incorporate travel time variability as a decision factor, they are typically still deterministic in the sense that the optimal strategy requires choosing one particular route that maximizes utility. In contrast, this study introduces an individual route choice model where choosing a portfolio of routes instead of a single route is the best strategy for a rational traveler who cares about both journey time and lateness when facing stochastic network conditions. The model is then tested with GPS data collected in metropolitan Minneapolis-St. Paul, Minnesota. Our data suggest strong correlation among link speed when analyzing morning commute trips. There is no single dominant route (defined here as a route with the shortest travel time for a 15 day period) in 18% of cases when links travel times are correlated. This paper demonstrates that choosing a portfolio of routes could be the rational choice of a traveler who wants to optimize route decisions under variability.