Revisiting the duration dependence in the US stock market cycles

There is a big controversy among both investment professionals and academics regarding how the termination probability of a market state depends on its age. Using more than two centuries of data on the broad US stock market index, we revisit the duration dependence in bull and bear markets. Our results suggest that the duration dependence for both bull and bear markets is a nonlinear function of the state age. It appears that the duration dependence in bear markets is strictly positive. For 93% of the bull markets, the duration dependence is also positive. Only about 7% of the bull markets, those with the longest durations, do not exhibit positive duration dependence. We also compare a few selected theoretical distributions on their ability to describe the duration dependence in bull and bear markets. Our results advocate that the gamma distribution most often provides the best fit for both the survivor and hazard functions of bull and bear markets. However, our results reveal that none of the selected distributions accurately describes the right tail of the hazard functions.publishedVersionPaid open acces

Trend following with momentum versus moving averages : a tale of differences

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Time series momentum in the US stock market: Empirical evidence and theoretical analysis

There is much controversy in the academic literature on the presence of short-term trends in financial markets and the trend-following strategy’s profitability. We restrict our attention to studying the time series momentum in the S&P Composite stock price index. Our contributions are both empirical and theoretical. On the empirical side, we present compelling evidence of the presence of short-term momentum. For the first time, we suppose that the returns follow a -order autoregressive process and evaluate this process’s parameters. On the theoretical side, we develop a tractable theoretical model that contributes to our fundamental understanding of the trend-following strategy’s risk, return, and performance. Using our model, we also estimate the power of statistical tests on the trend-following strategy’s profitability and find that these tests suffer from the low power problem.publishedVersionPaid open acces

Predictable Dynamics in the Small Stock Premium

We start this paper by providing a detailed study of how the mean monthly return on the Small-Minus-Big (SMB) Fama-French factor is affected by the January effect and the stock market return during the preceding month and preceding calendar year. We then proceed to building a predictive model for the monthly SMB factor return that incorporates the January effect and the dependence on both the market return during the preceding month and preceding calendar year. Our findings suggest that a positive small stock premium appears mainly during the years following the years with a negative return on the market as the result of a delayed and stronger reaction of small stocks to good news and a stronger January effect. We also argue that the January effect constitutes a much lesser part of the size effect than it was previously supposed

Sharpe (Ratio) Thinking about the Investment Opportunity Set and CAPM Relationship

In the presence of a risk-free asset the investment opportunity set obtained via the Markowitz portfolio optimization procedure is usually characterized in terms of the vector of excess returns on individual risky assets and the variance-covariance matrix. We show that the investment opportunity set can alternatively be characterized in terms of the vector of Sharpe ratios of individual risky assets and the correlation matrix. This implies that the changes in the characteristics of individual risky assets that preserve the Sharpe ratios and the correlation matrix do not change the investment opportunity set. The alternative characterization makes it simple to perform a comparative static analysis that provides an answer to the question of what happens with the investment opportunity set when we change the risk-return characteristics of individual risky assets. We demonstrate the advantages of using the alternative characterization of the investment opportunity set in the investment practice. The Sharpe ratio thinking also motivates reconsidering the CAPM relationship and adjusting Jensen's alpha in order to properly measure abnormal portfolio performance

Stock earnings and bond yields in the US 1871–2017 : The story of a changing relationship

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Stock earnings and bond yields in the US 1871–2017 : The story of a changing relationship

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