The Markowitz Bullet does not build when I change the 4 stocks for 25 S&P 500 stocks and 4 ETFs, (see attached). I want to replicate one of my academic papers - 'Modelling risk reduction in equity portfolios using exchange-traded funds with multiple variance-covariance (VCV) matrices."
Have you tried a Shrinkage method on the VCV matrix? Ledoit and Wolf (2004) state that it improves the accuracy of the tangency portfolio and the GMVP when compared to the Markowitz (1952) matrix or the Single Index Model (Sharpe, 1963) matrix. My example will be looking at minimising portfolio risk by using the GMVP coupled with a weighting in the risk-free rate. This will allow us to be along the Capital Allocation Line.
Please see these journals;
Ledoit, O. and Wolf, M. (2003) ‘Improved estimation of the covariance matrix of stock returns with an application to portfolio selection’, Journal of Empirical Finance 10 (5), 603-621.
Ledoit, O. and Wolf. M. (2004). ‘A-well conditioned estimator for large-dimensional covariance matrices’, Journal of Multivariate Analysis 88 (2), 365-411.
Ledoit, O. and Wolf. M. (2004) ‘Honey, I shrunk the sample covariance matrix’, Journal of Portfolio Management 30 (4), 110-119.
Markowitz, H. M. (1952) ‘Portfolio Selection’, Journal of Finance 7 (1), 77-91.
Markowitz, H. M. (1959) ‘Portfolio Selection: Efficient diversification of investment’, Edition 2.
Sharpe, W. F. (1963). “A Simplified Model for Portfolio Analysis,” Management Science 9 (2), 277-293.
Sharpe, W.F. (1964) Capital Asset Prices: A Theory of Market Equilibrium, Journal of Finance 19 (3), 425-442.