Previous studies in speculative prefetching focus on building and evaluating access models for the purpose of access prediction. This paper investigates a complementary area which has been largely ignored, that of performance modelling. We use improvement in access time as the performance metric, for which we derive a formula in terms of resource parameters (time available and time required for prefetching) and speculative parameters (probabilities for next access). The performance maximisation problem is expressed as a stretch knapsack problem. We develop an algorithm to maximise the improvement in access time by solving the stretch knapsack problem, using theoretically proven apparatus to reduce the search space. Integration between speculative prefetching and caching is also investigated, albeit under the assumption of equal item sizes.