New math cracks portfolio selection when data is scarce and messy
Researchers have solved a decades-old problem in portfolio management: how to reliably pick winning asset combinations when you have fewer observations than assets to choose from—a common real-world constraint. The breakthrough enables fund managers and risk officers to make statistically sound investment decisions even with sparse or correlated data.
Originaltitel: A test on the location of tangency portfolio for small sample size and singular covariance matrix
<p>The test for the location of the tangency portfolio on the set of feasible portfolios is proposed when both the population and the sample covariance matrices of asset returns are singular. The particular case of investigation is when the number of observations, <em>n</em>, is smaller than the number of assets, <em>k</em>, in the portfolio, and the asset returns are i.i.d. normally distributed with singular covariance matrix <strong>Σ</strong> such that rank(Σ)=r<n<k+1rank(Σ)=r<n<k+1. The exact distribution of the test statistic is derived under both the null and alternative hypotheses. Furthermore, the high-dimensional asymptotic distribution of that test statistic is established when both the rank of the population covariance matrix and the sample size increase to infinity so that r/n→c∈(0,1)r/n→c∈(0,1). Theoretical findings are completed by comparing the high-dimensional asymptotic test with an exact finite sample test in the numerical study. A good performance of the obtained results is documented. To get a better understanding of the developed theory, an empirical study with data on the returns on the stocks included in the S&P 500 index is provided.</p>