Uticaj kovarijanse prinosa dionica na minimalan rizik portfolija
Impact of covariance of stock returns on minimum portfolio risk

Summary/Abstract: Modern portfolio theory is based on multivariable analysis of stocks and portfolio. While the analysis of stocks mostly focuses on returns and risk associated with a given portfolio of stocks, it also needs to assess presence of correlation in a pair of stocks as well as any possible effects of parallel trending of those stocks. This paper looks at the impact of covariance of stocks returns (that is, the impact of correlation coefficients of stocks returns) on minimum risk of portfolio. Graphic and algebraic analysis is performed on a particular portfolio comprised of two stock options. The analysis showed that minimum portfolio risk is a function of correlation coefficient between a pair of stocks. This paper offers mathematical proof of the following hypothesis: (1) The portfolio in its entirety is less risky than any of the individual stocks that it includes, if coefficient of correlation between stocks is less than their individual standard deviations (given that a smaller of the standard deviations is included in the numerator), (2) the efficient portfolio set is a convex function.

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