The text demonstrates out-of-sample performances of minimum variance portfolios in the German stock market in the period 2002-2015. Because of two huge drawdowns on equity markets in the period 2000-2010, scholars and professionals have tried to find an alternative to the marketcap weighted investing; potentially the minimum variance investing approach. The paper presents the construction of minimum variance portfolios, the description of their compositions and empirical risk-return characteristics under various holding periods. As anticipated, minimum variance portfolios have lower risk vis-à-vis the CDAX index, but they have also higher returns. Finally, minimum variance portfolios have better risk-adjusted performance figures in comparison with equal-weighted alternatives.

The article shows properties of risk-based portfolios in the German stock market. Those systematic strategies use different approaches to weight stocks in portfolios. We present theoretical and empirical characteristics of five risk-based equity investments: the equal-weighted, minimum variance, maximum diversification and risk parity (equal risk budgeting and equal risk contribution) portfolios. Risk-based portfolios outperformed the market-cap weighted CDAX index with a lower level of risk in the period 2002-2015. Their excess returns relative to the CDAX index can be explained with Scherer's five-factor model; with Fama-French and low-risk anomaly factors. R 2 s of different strategies range from 77% to 92%.

ÚvodZákladním stavebním kamenem finančních teorií je positivní vztah výnosu a rizika. Jeden z prvních, který formálně modeloval tuto souvislost, byl Markowitz (1952), když demonstroval hranici efektivních portfolií v prostoru očekávaný výnos -riziko. Racionální investoři by měli maximalizovat očekávaný výnos při daném riziku nebo minimalizovat riziko při daném očekávaném výnosu. Zakomponováním bezrizikového aktiva rozšířili Markowitzovu teorii portfolia např. Tobin (1958)