<p>The paper provides an explicit derivation to the equivalence between the minimum variance and minimum tracking error portfolios of excess returns on a benchmark. This result relies on the Sherman-Morrison formula. The paper also presents an equivalence of those results to an OLS regression with constrained beta.  Further, the paper uses the first equivalnce result to find a tracking portfolio using the approach of Kempf &amp; Memmel (2006).</p>

In this paper, we study the problem of minimum variance portfolio selection based on a recent methodology for portfolio optimization restricting the allocation vector proposed by Fan et al. (2012). To achieve this, we consider different conditional and unconditional covariance matrix estimators. The main contribution of this paper is one of empirical nature for the brazilian stock market. We evaluate out of sample performance indexes of the portfolios constructed for a set of 61 different stocks traded in the São Paulo stock exchange (BM&FBovespa). The results show that the restrictions on the norms of the allocation vector generate substantial gains in relation to the no short-sale portfolio, increasing the average risk-adjusted return (larger Sharpe Ratio) and lowering the portfolio turnover.