Rational Valuation Formula (RVF) and Time Variability in Asset Rates of Return

The present study examines the long-term relationship between aggregate price and dividend data and the corresponding mechanism for short-term error correction using the rational valuation formula and time-varying cointegration and based on Muth's (1961) theory of rational expectations and price movements. The study assumes the variability of asset rates of return and tests the null hypotheses of errorcorrection mechanisms for time-constant cointegration vectors and inequality between fundamental value and share price. The series used were provided by Shiller (2005) and refer to aggregate price and dividend data for the U.S. stock market over the period 1871 to 2010. The data were analyzed using Johansen’s cointegration models with the use of restricted variables resulting from the combination of the variables studied with the Chebyshev time polynomial, as proposed by Bierens and Martins (2010). The results indicate rejection of the null hypothesis of constancy of cointegration vectors as well as the non-rejection of the null hypothesis of inequality between fundamental value and share price. These results are consistent with those obtained by Bierens and Martins (2010) and do not corroborate Muth's (1961) theory of rational expectations. It is therefore concluded that investors have different expectations of return for different future periods. The results suggest the validation of the model used and that there is a possibility of the occurrence of speculative movements supported by rationality or rational speculative bubbles.