We document the presence of the random walk effect in stock indices and, at the same time, find that the constituent stocks of the indices are excessively volatile. This gives rise to a paradox in stock markets between the behaviour of the stock index and its constituent stocks. We address this phenomenon in this article and reconcile the seemingly contradictory inferences by extending the Binomial Markov Random Walk (BMRW) model.
BallC.A., & TorousW.N. (1984). The maximum likelihood estimation of security price volatility: Theory, evidence and application to option pricing. Journal of Business, 57(1), 97–112.
2.
BeckerM., FriedmannR., & KlossnerS. (2012). Modeling and Measuring Intraday Overreaction of Stock Prices. Journal of Banking & Finance, 36(4), 1152–1163.
3.
ChowK.V., & DenningK.C. (1993). A simple multiple variance ratio test. Journal of Econometrics, 58(3), 385–401.
4.
CootnerP. (Ed.). (1964). The random character of stock market prices. University of Minnesota, U.S.A: MIT Press.
5.
CutlerD., PoterbaJ., & SummersL. (1989). What moves stock prices?Journal of Portfolio Management, 15(3), 4–12.
6.
FamaE.F. (1970). Efficient capital markets: A review of theory and empirical work. Journal of Finance, 25(2), 283–417.
7.
FuhC.D. (1997). Corrected diffusion approximations for ruin probabilities in a Markov random walk. Advances in Applied Probability, 29(3), 695–712.
8.
GarmanM.B., & KlassM.J. (1980). On the estimation of security price volatilities. Journal of Business, 53(1), 67–78.
9.
JensenM.C. (1978). Some anomalous evidence regarding market efficiency. Journal of Financial Economics, 6(2–3), 95–101.
10.
KunitomoN. (1992). Improving the Parkinson method of estimating security price volatilities. Journal of Business, 65(2), 295–302.
11.
LeRoyS.F. (2006). Excess volatility. The new palgrave dictionary of economics. London: Palgrave Macmillan.
12.
LeRoyS.F., & PorterR.D. (1981). The present value relation: Tests based on implied variance bounds. Econometrica, 49(3), 555–574.
13.
LoAndrew W., & MacKinlayA. Craig. (1988). Stock market prices do not follow random walks: evidence from a simple specification test. Review of Financial Studies, 1(1), 41–66
14.
MaheswaranS., BalasubramanianG., & YoonusC. A. (2011). Post-colonial finance. Journal of Emerging Market Finance, 10(2), 175–196.
15.
MaheswaranS., & KumarD. (2013). An automatic bias correction procedure for volatility estimation using extreme values of asset prices. Economic Modelling, 33, 701–712. DOI: http://dx.doi.org/10.1016/j.econmod.2013.05.019
16.
MalkielB.G. (2003). The efficient market hypothesis and its critics. Journal of Economic Perspectives, 17(1), 59–82.
17.
ParkinsonM. (1980). The extreme value method for estimating the variance of the rate of return. Journal of Business, 53(1), 61–65.
18.
RogersL.C.G., & SatchellS.E. (1991). Estimating variance from high, low and closing prices. Annals of Applied Probability, 1(4), 504–512.
19.
ShillerR.J. (1981). Do stock prices move too much to be justified by subsequent changes in dividends?American Economic Review, 71(3), 421–436.
