Testing adaptive market efficiency under the assumption of stochastic volatility

Master Thesis


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University of Cape Town

This dissertation explores the adaptive market hypothesis (AMH) first proposed by Lo (2004) which incorporates the efficient market hypothesis (EMH) of Malkiel and Fama (1970) and its behavioural exceptions. The AMH differs from the EMH, in that it assumes that the efficiency level of a market can fluctuate over time, whereas the EMH does not. The original test of evolving efficiency (TEE) was developed by Emerson et al. (1997) and Zalewska-Mitura and Hall (1999) and has an underlying GARCH-M model. Later, the generalised test of evolving efficiency (GTEE) was developed by Kulikova and Talyor (in progress), which has an underlying stochastic GARCH-M model proposed by Hall (1991). In this dissertation, the stochastic volatility test of evolving efficiency (SV-TEE) is developed using an underlying Stochastic Volatility-in-Mean (SVM) model introduced by Koopman and Uspensky (2002). The QMLE technique introduced by Harvey (1989) and the classical and Extended Kalman Filter techniques are described so that the TEE, the GTEE and the SV-TEE can be calibrated together with the hidden volatility process estimation. The empirical study tests the adaptive efficiency of four markets - two developed (London Stock Exchange and New York Stock Exchange), a mature developing (Johannesburg Stock Exchange) and an immature developing (Nairobi Stock Exchange). The best-performing tests were selected for each market and it was observed that there were constant and adaptive efficiencies in the developed and mature developing markets, and constant inefficiency in the immature developing market. The SV-TEE was not selected as the best-performing test for any of the markets - possibly because the time period considered for each market was too short.