Using a vector autoregression model, the authors demonstrate that serial dependence in stocks (i.e., price momentum) can be exploited by efficiently using the information contained in the variance–covariance matrix. But the method generates significant turnover and is feasible only in an environment with low transaction costs.
The authors use a vector autoregression (VAR) model to capture serial dependence in stock returns. They illustrate the secular decline of returns on momentum-based strategies and the weakening of historical lead–lag relationships between large and small stocks and growth and value stocks. Using an analytical approach, they also use the VAR model to illustrate how it can more efficiently exploit the information contained in the covariance matrix than portfolios constructed using a more simplistic momentum-based or contrarian-based approach.
How Is This Research Useful to Practitioners?
Using the VAR model, the authors illustrate the decreasing strength of serial dependence by plotting the estimated slope coefficients derived from using the ridge regression technique. After the financial crisis, the sign of the coefficients switched, which confirms the changed investment environment and possibly explains why standard quantitative investment processes have generally struggled over the period. The authors also confirm the lead–lag relationship that exists between large- and small-cap stocks and growth and value stocks, which has been discussed in previous research.
Using the same approach with the VAR model, the authors investigate the lead–lag relationships among different industries and find some evidence that technology leads other sectors (except for health) but also that these relationships have weakened significantly over time.
They use an analytical approach to show that expected returns from a zero-cost arbitrage portfolio (constructed using weights derived from the VAR model) incorporate the structure of the covariance and cross-covariance matrix to deliver positive returns. A momentum-based portfolio delivers expected positive returns only if the autocorrelations are positive (cross-correlations negative), whereas a contrarian-based portfolio delivers expected positive returns only if autocorrelations are negative (cross-correlations positive). The authors use principal component analysis to pinpoint the source of the predictability that is used by the VAR model.
Similar analysis is performed on long-only portfolios constructed using constrained mean–variance optimizations. The authors note that the use of the VAR model to construct portfolios leads to elevated turnover levels and is feasible only with low transaction costs.
The portfolios created using the VAR model, as well as the contrarian- and momentum-based portfolio, are based solely on returns in the previous one-month period. A longer window may produce different results.
How Did the Authors Conduct This Research?
Stock returns were predominantly gathered from Kenneth French’s website, with additional return data from the CRSP database. Value-weighted portfolio returns are calculated for the French data as follows: (1) 6 sorted size/book-to-market categories, (2) 25 sorted size/book-to-market categories, (3) 10 industry portfolios, and (4) 48 industry portfolios. Individual stock returns from the CRSP database are randomly selected to construct a 100-stock portfolio that is rebalanced annually. Data are available from 1970.
The authors develop a VAR model that allows for both autocovariance (the standard approach to momentum strategies) and cross-covariance between stocks. They use a statistical technique known as ridge regression to estimate the parameters of the VAR model, which avoids the estimation errors that can arise from using ordinary least-squares techniques.
The authors use an analytical approach to show that expected returns from a zero-cost arbitrage base can be split into three components: (1) a component arising from asset return covariances, (2) asset return autocovariances, and (3) a component that captures the impact of unconditional mean returns. They then apply this framework to three portfolios constructed using a contrarian approach, a momentum approach, and weights derived from the VAR model.
Similar analysis is performed on long-only portfolios that are constructed using a constrained mean-optimization approach. Two portfolios are tested to exploit serial dependence. The first assumes that stock returns are linearly related whereas the second relaxes this assumption.
Momentum-based strategies remain a cornerstone of many quantitative investment processes because they continue to deliver positive albeit volatile returns. But this positive return has become increasingly difficult to achieve because the strategy has become crowded. To mitigate this issue, strategies have evolved and are more complex as portfolio managers strive to remain ahead of their peers. The implementation of VAR models is an example of the sophistication of momentum-based models that are now being used.