Part A: You Will Construct Two Alpha Factors V And M For The

Part Ayou Will Construct Two Alpha Factors V And M For The Us Market

Part Ayou Will Construct Two Alpha Factors V And M For The US Market

Part A You will construct two alpha factors: V and M for the US market. V is based on the prior 5-day returns and M is the MAX factor discussed in the lecture. The steps to construct factor V are the same as in Assignment 2. For simplicity, ranking is not used to construct V and M. Consider the US market from 2004 to 2023, using the universe defined in the univ_h.csv file. To compute these factors, data from 2003 is needed for initial calculations.

For factor V, first, calculate daily volatility using the prior 21 days of daily log returns, setting return to 0 if data is missing, and enforce a minimum volatility of 0.005. Then, compute the prior 5-day log return for each stock, again assigning zero where data is absent. Next, normalize the volatility by dividing the volatility measure from step one. Finally, subtract the industry average (computed over all stocks in the industry for the given day) from this normalized measure to obtain the factor V value for each stock on each day.

For factor M, begin with the 21-day prior daily returns, subtract the industry average return from each stock’s return, then identify the maximum absolute value among these 21 adjusted returns. Note that for M, normalization by volatility is not applied. Subsequently, compute the industry mean of these maximum values and subtract this industry component from each individual maximum to derive factor M values.

Next, perform a cross-sectional regression of the subsequent day’s return against the factor values for each day t, gaining a time series of the beta coefficients. The industry return is calculated as the simple average return of stocks within each industry for the same day.

From 2005 to 2023, evaluate the two-year rolling averages of the beta coefficients and compute their t-statistics, where T is the number of trading days in the respective years. The average beta and t-statistics over these periods should be tabulated to analyze the statistical significance and stability of the factors.

Paper For Above instruction

The construction of alpha factors as outlined involves a meticulous process of data preprocessing, normalization, industry adjustment, and regression analysis. These factors, V and M, are designed to capture systematic return predictability based on recent returns and volatility patterns, and are well-rooted in asset pricing theory.

The first factor, V, leverages recent volatility and momentum signals. Calculating the 21-day historical volatility provides a measure of recent price variability, adjusted to mitigate the influence of missing data and extreme values by imposing a lower bound. The 5-day return component captures short-term momentum, which is widely documented as a significant predictor of future returns (Carhart, 1997). Normalizing the volatility by dividing the volatility measure standardizes the signal across stocks with different volatility profiles, enhancing comparability. The industry adjustment, subtracting the industry average, ensures the factor measures stock-specific deviations rather than industry-wide movements, aligning with the cross-sectional nature of alpha signals (Fama & French, 1993).

The second factor, M, emphasizes the magnitude of recent price shocks without normalization by volatility, thus capturing extreme movements that might precede reversals or continuation. The step of identifying the maximum absolute adjusted return over the past 21 days highlights recent volatility spikes or significant price shocks, which are believed to contain predictive information about future performance. Removing the industry component further isolates stock-specific information (Haugen & Baker, 1996).

The subsequent cross-sectional regressions of next-day returns on the factors’ values allow estimation of their predictive power. The beta coefficients derived from these regressions quantify how strongly the factors forecast future returns. Calculating the two-year rolling averages and t-statistics assesses the stability and significance of these predictive relationships over time, highlighting periods when the factors are most effective (Koopman et al., 2012).

Overall, constructing these factors involves rigorous statistical processing and industry adjustment, which are essential for creating reliable alpha signals. The stability of beta estimates and their t-statistics over multiple years provides insights into the robustness of these predictors, guiding their practical application in portfolio strategies.

References

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