What kind of return patterns are typical of beginnings and ends of equity bull and bear markets? In his April 2023 paper entitled "Investor Overreaction: Evidence From Bull and Bear Markets", Valeriy Zakamulin examines return patterns of U.S. stock market bull and bear states as a way to decide when investors tend to overreact. He uses the S&P 500 Index as a proxy for the U.S. stock market. He applies a pattern recognition algorithm to: (1) identify index peaks and troughs; and, (2) ensure that a full bear-bull cycle lasts at least 16 months and bear or bull states last at least 5 months, unless the index rises or falls by more than 20%. He then standardizes the duration of each market state to 10 intervals and assumes that the bull or bear return evolves quadratically with state age. Because the available sample is relatively small, he applies bootstrapping to enhance reliability of findings. Using monthly S&P 500 Index returns (excluding dividends) during January 1926 through December 2022, he finds that:
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