In this article, we analyze the secrecy rate of a physical-layer security (PLS) algorithm using antenna subset modulation (ASM), which requires significantly lower complexity and cost compared to fully digital beamforming. All of the existing studies on the ASM-based PLS provide only approximate secrecy rate by treating random selection of two subsets of antennas for each symbol as independent and identically distributed Bernoulli random variables. To clarify its limitation, we first show that such widely adopted approximation incurs a significant error in the secrecy rate compared to the true value. In addition, we propose a new mathematical approach to derive the exact and closed-form expression for secrecy rate without any approximation. We also show the system optimization using our exact analysis in line with the simulation results, while the existing approximate analysis results in a considerable error.