Mixed Approach Between Capital Asset Pricing Model and ARIMA Model for Estimating the Standard and Poor’s Stocks

The Capital Asset Pricing Model (CAPM) uses a formula that calculates a stock's expected return by taking into account the risk-free rate of return, the risk premium, and the stock's beta coefficient. The data on which the assessment is made are considered on an annual basis, or for a given fixed period. At the same time, the assessment of the risk-free yield can be underestimated or overestimated for the specific moment of calculations. The Autoregressive Integrated Moving Average (ARIMA) models, in turn, offer a forecast for a particular observation. This article examines an approach to estimate the expected rate of return on a share from Standard and Poor's 500 (S&P500), which combines the assessment by CAPM and ARIMA models. Amazon's expected rate of return is estimated relative to the S&P500 using the CAPM. A forecast was made with an ARIMA model for Amazon's expected change. A forecast of the S&P500's expected rate of return is then made. This prediction is included in Amazon's CAPM as the expected rate of return in the model. In this way, three results are obtained, which were compared for different dates.