The Capital Asset Pricing Model is a single period model which specifies a linear relationship between return on an asset and return on the entire market. The model is widely used in literature as if a portfolio of securities can be designed based on a unique value of systematic risk. In this paper it is shown that in reality it is not possible to design a portfolio based on a unique value of systematic risk and performance index of securities, since both these measures are a function of not only the holding period, but also the values of expected market return and the risk-free rate of return likely to prevail for the period under consideration. Further, using computer simulation the paper captures the extent of impact of the holding period, expected market return, risk-free rate of return and the interaction of the holding period and expected market return together, on the single period measure of systematic risk and performance index of a security. The simulation results also show that other parameters such as the variance of market return, variance of the error term and other combinations of interaction terms do not have any significant impact on the single period measure of systematic risk.