The constant correlation model is a mean-variance portfolio selection model where, for a given set of risky securities, the correlation of returns between any pair of different securities is considered to be the same. Support for the model is from previous empirical evidence that sample averages of correlations outperform various more sophisticated models in forecasting the correlation matrix, an important input component for portfolio analysis. To enable a better understanding of the constant correlation model, this study identifies some additional analytical properties of the model and relates them to familiar portfolio concepts. By comparing computational times for portfolio construction with and without simplifying the correlation matrix in a simulation study, this study also confirms the model's computational advantage. This study is intended to provide further analytical support for the model as a viable, simple alternative to those portfolio selection models where input requirements and the attendant computations are more burdensome.