Validity Testing of Classical Asset Allocation Models: An Empirical Study

Abstract

This paper uses a 20 years of daily total return data for the S&P 500 Index (ticker symbol SPX) and 10 stocks, make all the necessary calculations to plot a portfolio area that gather an efficient boundary, a minimum risk or variance boundary, and a minimum return boundary together for a given set of constraints. Analyze all the outcomes in order to compare the various restrictions for each optimization issue (MM and IM), as well as the two solutions to the same optimization problem. The Excel solver was the primary tool utilized during calculation to resolve optimization issues for each point on the minimal risk or variance border. Also, this paper use an Excel solution table to calculate a large number of multipoints on any desired boundary. Through calculation and research, we found that, Markowitz model makes full use of covariance matrix to generate excellent portfolio. However, the results are numerically unstable. At the same time, the hypothesis of normality, stationarity and mean square error are verified. The exponential model simplifies the Markowitz model and produces more robust results. However, it introduces additional assumptions about the independence, normality, and homoscedasticity of the regression residuals, which are also invalid. The reduction (CDaR) model is hypothesis-free. The numerical stability can be obtained by transforming the nonlinear optimization problem into a linear programming problem.