Authors: T.C Urama, C.P Nnanwa and P.O. Ezepue
Abstract: We analyze the cross-correlation matrix C of the stock index returns in the Nigerian Stock Market (NSM) from the period 2009 to 2013 using the concept of random matrix theory. We test the eigenvalues of the selected assets from the exchange and use their respective eigenvector to determine the stocks that drive the market through the analysis of their inverse participation ratios. We also proffer a method of obtaining a realistic implied correlation matrix for a hypothetical portfolio of some given assets selected from those considered in the empirical correlation matrix of the assets considered. We discover that the implied correlations matrix is positive meaning that the corresponding assets move in the same direction. Hence, portfolio diversification is not an optimal investment strategy, rather investment on derivative assets like call and put options is recommended.
Keywords: Random matrix, cross-correlations, implied volatility, portfolio weights, a basket of options.