In this paper, we study the distributional properties of the tangency portfolio (TP) weights assuming a normal distribution of the logarithmic returns. We derive a stochastic representation of the TP weights that fully describes their distribution. Under a high-dimensional asymptotic regime, i.e., the dimension of the portfolio, k, and the sample size, n, approach infinity such that $k/n\to c\in (0,1)$, we deliver the asymptotic distribution of the TP weights. Moreover, we consider tests about the elements of the TP and derive the asymptotic distribution of the test statistic under the null and alternative hypotheses. In a simulation study, we compare the asymptotic distribution of the TP weights with the exact finite sample density. We also compare the high-dimensional asymptotic test with an exact small sample test. We document a good performance of the asymptotic approximations except for small sample sizes combined with c close to one. In an empirical study, we analyse the TP weights in portfolios containing stocks from the S&P 500 index.

在本文中，我们假设对数收益呈正态分布，研究切线投资组合 (TP) 权重的分布特性。我们推导出 TP 权重的随机表示，它完全描述了它们的分布。在高维渐近机制下，即投资组合的维度k和样本量n接近无穷大，使得$克/n\to C\in (0,1)$，我们提供了 TP 权重的渐近分布。此外，我们考虑了关于 TP 元素的检验，并在原假设和替代假设下推导出检验统计量的渐近分布。在模拟研究中，我们将 TP 权重的渐近分布与精确的有限样本密度进行比较。我们还将高维渐近检验与精确的小样本检验进行了比较。我们记录了渐近近似的良好性能，除了小样本量与接近 1 的c相结合。在一项实证研究中，我们分析了包含标准普尔 500 指数股票的投资组合的目标价权重。