Constructing Alpha Factors V and M for the US Market: A Detailed Guide

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.

  1. Consider the US market and the years 2004 to 2023 (you will also need some data in 2003 to calculate the alpha factor). The universe used for each year will be based on the universe from the start of the year (defined in the univ_h.csv file).
  2. To construct factor V
    a) calculate the daily volatility using the prior 21 days of daily returns (use the log return, the return is set to 0 if there is an NA in the adjusted prices). If obtained is less than 0.005, set it to 0.005.
    b) calculate the prior 5-day return; you can use the log-return (again, the return is set to 0 if the prices are not available)
    c) normalize the variable by dividing the volatility obtained in step a),
    d) subtract out the industry component, where is the average of (after step c) over all the stocks in the industry (and in the universe of time t) that the stock i belongs to
  3. To construct factor M
    a) Use the daily returns for the past 21 trading days,calculated in Step 2a).
    b) subtract out the corresponding industry component (calculated using a simple average):
    c) get the maximum value, of the magnitudes of the prior 21 values. The normalization by the volatility is not applied to this factor.
    d) subtract out the industry component, where is the average of over all the stocks in the industry (and in the universe of time t) that the stock i belongs to.
  4. Do a cross-sectional regression of the next day’s return on day t and get the time series of. Here is defined as, where and the industry return is the simple average of over all the stocks in the industry (and in the universe of time t) that stock i belongs to.
  5. From the years 2005 to 2023, calculate the 2-year averages of , and the t-stat, , where T is the number of trading days in the year and the year before (for example, the average obtained for the year 2005 is over the years 2004 and 2005) and and are the standard deviation of calculated using obtained in these two-year periods. List the two-year average betas and the t-stat obtained in a table.

Part B
From the years 2006 to 2023, use the two-year averages calculated (in Part A) from the previous two years (for example, for the year 2006, use the 2-year average of years 2004 and 2005 obtained in Part A) and evaluate the expected returns for all trading days of the year,

Construct and evaluate the portfolio as follows,

  1. On each day t, rank the stocks according to the expected returns, and long (with equal weights) the top 20% of the stocks with the largest values of and short the bottom 20% of the stocks with the smallest values (most negative values) of
  2. Get the portfolio return at each time step t. The return is on the long market value of the portfolio, so it is the sum of the returns on individual positions divided by the number of long positions in the portfolio, where and are the number of long and short positions (both are equal to, is the number of stocks in the universe for that year). is the stock index of the long position j. is the stock index of the short position j. Note that when calculating the portfolio return, the full return without subtracting the market return is used.
  3. For each year calculate the annual return (assuming the cost of trading is 0, and for simplicity simply add up all daily portfolio returns to get the annual return) and the annualized return volatility of the portfolio. List your results in a table. Which are the best and the worst years for the strategy?
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Sample Answer

Constructing Alpha Factors V and M for the US Market: A Detailed Guide

Introduction

In financial analytics, alpha factors serve as vital indicators for stock selection and portfolio construction. This essay outlines the procedure for constructing two alpha factors, V and M, specifically tailored for the US market from 2004 to 2023. Factor V is based on the prior 5-day returns normalized by volatility, while factor M focuses on the maximum returns over a 21-day period. The systematic steps outlined here will help in the effective implementation of these factors in quantitative finance.

Part A: Construction of Alpha Factors V and M

Data Preparation

To begin, data from the years 2004 to 2023 (including necessary data from 2003) should be gathered based on the universe defined in the univ_h.csv file. This data will serve as the foundation for calculating the alpha factors.

Factor V Construction

  1. Calculate Daily Volatility:
    • Use the prior 21 days of logarithmic returns to compute daily volatility.
    • Set the volatility to 0.005 if it falls below this threshold.
  2. Calculate Prior 5-day Return:
    • The logarithmic return is used again, setting it to 0 when prices are unavailable.
  3. Normalization:
    • Normalize the volatility calculated in step 1.
  4. Industry Component Adjustment:
    • Subtract the average value of factor V from all stocks in the same industry for each time period.

Factor M Construction

  1. Calculate Daily Returns:
    • Utilize daily returns from the past 21 trading days as established in step 1 of factor V construction.
  2. Industry Component Adjustment:
    • Similar to factor V, subtract the corresponding industry average from each stock’s returns.
  3. Maximum Value Calculation:
    • Identify the maximum value of the prior 21 days’ returns.
  4. Industry Component Adjustment:
    • Again, subtract the average value from all stocks in the industry.

Cross-Sectional Regression

  • Perform a cross-sectional regression analysis of next-day returns on day t using factors V and M.
  • Calculate time series averages for each factor and their respective industry components.

Summary Statistics

From the years 2005 to 2023, calculate two-year averages, standard deviations, and t-statistics for both factors, compiling results into a table for clarity.

Part B: Portfolio Construction and Evaluation

Expected Returns Calculation

  1. From years 2006 to 2023, utilize previously calculated two-year averages of factors V and M to evaluate expected returns for each trading day.

Portfolio Strategy Implementation

  1. Stock Ranking:
    • On each trading day, rank stocks by expected returns.
    • Create a long position in the top 20% and a short position in the bottom 20%.
  2. Portfolio Return Calculation:
    • Compute daily portfolio returns based on the long positions, averaging out individual stock returns.
  3. Annual Return Analysis:
    • Accumulate daily portfolio returns to calculate annual returns and annualized return volatility.
    • Present results in a structured table highlighting the best and worst performing years.

Part C: Trading Costs Impact Analysis

  1. Incorporate Trading Costs:
    • Assume a trading cost of 5 basis points (bps).
    • Adjust portfolio returns accordingly and compare these results with those obtained without considering trading costs.

Conclusion

The outlined methodology for constructing alpha factors V and M provides a robust framework for quantitative analysis in stock selection and portfolio management. By adhering to these systematic steps, practitioners can derive actionable insights from historical data, facilitating informed investment decisions. Future work could involve exploring additional factors or refining existing ones based on evolving market dynamics.

Results Summary Table (Sample)

Year Annual Return Annualized Volatility Best Year Worst Year
2006 X% Y% 2006 2023
2007 A% B%

This structured approach not only aids in achieving clarity but also enhances reproducibility within financial research methodologies.

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