Consider a multiprocessor with k identical processors, executing parallel programs consisting of n processes. Let T$-s$/(P) and T$-d$/(P) denote the execution times for the program P with optimal static and dynamic allocations, respectively, i.e., allocations giving minimal execution time. We derive a general and explicit formula for the following maximal execution time ratio: g(n, k) $EQ max T$-s$/(P)/T$-d$/(P), where the maximum is taken over all programs P consisting of n processes. Any interprocess dependency structure for the programs P is allowed only by avoiding deadlock. Overhead for synchronization and reallocation is neglected. Basic properties of the function g(n, k) are established, from which we obtain a global description of the function. Plots of g(n, k) are included. The results are obtained by investigating a mathematical formulation. The mathematical tools involved are essentially tools of elementary combinatorics. The formula is a combinatorial function applied on certain extremal matrices corresponding to extremal programs. It is mathematically complicated but rapidly computed for reasonable n and k, in contrast to the np-completeness of the problems of finding optimal allocations.