Systematic modeling of white noise with financial time series in decision making

Abstract

n this study real non - diversifiable (systematic) risk is derived. This risk together with diversifiable (non - systematic) risk is weighted against expectedreturns of certain assets to determine maximum returns of these assets at minimum risk. A Real Risk WeightedPricing Model (RRWPM) is thus developed whichis able to postulate expected returns and risks of assets in the past and in the near future. This enables discounting rates and costs of capitalto be accuratelydetermined. Decisionscan also be madebased on the point estimators determinedfor exampleexpected returns and total risks of assets obtained. Finite investment decision making using real market risk (Non-diversifiable risk) is then undertaken. The Non-diversifiable risks estimates of a portfolio of stocks as determined by the RRWPM are used as initial data. The variance of non-diversifiable risk is estimated as a random variable referred to as random error (white noise). Theestimator is used to calculateestimates of white noise. A curveestimation of the whitenoiseismadeusingKerneldensityestimation. Thisisusedtoderiveprobability estimates of the non-diversifiable risks of the various stocks. This enable comparison among the portfolio of stocks and propagates good decision making. Actual future market risks (systematic or non-diversifiable) of investment portfolios are then determined. Future returns are forecasted using past returns and GARCH (Generalized Autoregressive Conditional Heteroskedastic) models. RRWPM is used to estimate future systematic risk among other point estimators and determines the future costs of the portfolios. Forecasted random error is then calculated as a random variable and used to determine probability density estimates of systematic risk. This enables future actual market risks of portfolio investments to be derived hence facilitating proper future investment decision making