Asian Journal of Pure and Applied Mathematics

In this paper, system of asset pricing models were used to study stock market price changes by implementing the Ito’s method; measures which could influence the volatility, the expected rate of returns and asset values which follows multiplicative effects were established through the impressions on Tables to demonstrate different price changes. In terms of generalizing the system a Geometric Brownian motion theorem were developed and proved as a deterministic concepts which does not depend on random factors. However, stochastic vector Differential Equation were considered by constraining the stochastic part of the system which is function of volatility where covariance matrix solutions were obtained to measure overall volatility or risk, by selecting assets with low or negative covariance. From the covariance matrices of each corporate investor positive and negative eigenvalues were obtained showing the assets in the portfolio are experiencing both gains and losses over time; positive eigenvalues indicates that the assets are increasing in value, which is beneficial for investors. Whereas negative values indicates that the assets are losing value, which is detrimental for investors too. More so, the mix of positive and negative eigenvalues provides important information about the risk and diversification of portfolio. To this end, a fundamental matrix were also adopted to construct portfolios that are diversified in terms of risk and predicted asset returns which is informative to investors in terms of informed decision making.