Abstract: The Sharpe ratio is an important and widely-used risk-adjusted return in financial engineering. In modern portfolio management, one may require an $m$-sparse (no more than $m$ active assets) portfolio to save managerial and financial costs. However, few existing methods can optimize the Sharpe ratio with the $m$-sparse constraint, due to the nonconvexity and the complexity of this constraint. We propose to transform the $m$-sparse fractional optimization problem into an equivalent m-sparse quadratic programming problem. The semi-algebraic property of the resulting objective function allows us to exploit the Kurdyka-Lojasiewicz property to develop an efficient proximal gradient algorithm that converges to a portfolio which achieves the locally optimal $m$-sparse Sharpe ratio. To the best of our knowledge, this is the first proposal that achieves a locally optimal $m$-sparse Sharpe ratio with a theoretically-sound guarantee.