  This paper studies the portfolio optimization problem when the investor's
utility is general and the return and volatility of the risky asset are fast
mean-reverting, which are important to capture the fast-time scale in the
modeling of stock price volatility. Motivated by the heuristic derivation in
[J.-P. Fouque, R. Sircar and T. Zariphopoulou, \emph{Mathematical Finance},
2016], we propose a zeroth order strategy, and show its asymptotic optimality
within a specific (smaller) family of admissible strategies under proper
assumptions. This optimality result is achieved by establishing a first order
approximation of the problem value associated to this proposed strategy using
singular perturbation method, and estimating the risk-tolerance functions. The
results are natural extensions of our previous work on portfolio optimization
in a slowly varying stochastic environment [J.-P. Fouque and R. Hu, \emph{SIAM
Journal on Control and Optimization}, 2017], and together they form a whole
picture of analyzing portfolio optimization in both fast and slow environments.
