مقاله Portfolio Optimization Part 1 – Unconstrained Portfolios
We recapitulate the single-period results of Markowitz  and Sharpe 1 in the context of the lognormal random walk model, iso-elastic utility, and continuous portfolio rebalancing. We formally derive the solution to the unconstrained optimization problem and examine the mathematical properties of the resulting efficient frontier and efficient portfolios. We derive the two-fund separation theorem both in the presence of a risk-free asset and in its more general form. We derive and briefly discuss the Capital Asset Pricing Model (CAPM). We present several examples parameterized using market return data for US stocks, bonds, cash, and inflation.