SAAM Algorithm

Configuration of parameters

The difficulty of estimating \(\mu\) well enough for the plug-in portfolio to have reliable performance was pointed out by Black and Litterman (1990), who proposed the following pragmatic quasi-Bayesian approach to address this difficulty. Black and Litterman’s approach basically amounted to shrinking an investor’s subjective estimate of \(\mu\) to the market’s estimate implied by an “equilibrium portfolio.” The investor’s subjective guess of \(\mu\) is described in terms of “views” on linear combinations of asset returns, which can be based on past observations and the investor’s personal/expert opinions. More details can be seen in the article: MEAN–VARIANCE PORTFOLIO OPTIMIZATION WHEN MEANS AND COVARIANCES ARE UNKNOWN.

And the estimation of the covariance matrix can be gain by resampling.

Reference

Lai, Tze Leung ; Xing, Haipeng ; Chen, Zehao MEAN–VARIANCE PORTFOLIO OPTIMIZATION WHEN MEANS AND COVARIANCES ARE UNKNOWN Ann. Appl. Stat. 5, no. 2A (2011), 798-823