The paper "A Test on the Location of Tangency Portfolio for Small Sample Size and Singular Covariance Matrix" explores the tangency portfolio's positioning within feasible portfolios under specific conditions: small sample sizes and singular covariance matrices for asset returns. A new test is presented to determine this location, deriving the exact distribution of the test statistic under both null and alternative hypotheses and the high-dimensional asymptotic distribution as both portfolio dimension and sample size increase. The numerical study compares the asymptotic test with an exact finite sample test, showing effective performance. This research is pivotal for understanding tangency portfolio characteristics in challenging conditions, like singularity and limited data, enhancing financial decision-making strategies.