Statistical Arbitrage Week 3

Ideas generation for ALPHA

Definition of Alpha

• Source of expected return over and beyond whtat is explained by beta
• Time-varying \(\rightarrow (T \times n)\) matrix of alphas
  • \(T = \) number of days
  • \(n = \) number of stocks
• Cross-sectionally standardized every day:
  • Mean zero across all (active) stocks
    • Generate long-short signal
  • Variance one across all (active) stocks
    • Normalize volatility across different time point

Winsorization of Alpha

• Substract robust estimate of the mean(such as mean with shrinkage)
• Divide by the standard diviation
• Every alpha > 3 is brought down to 3
• Every alpha < -3 is brought up to -3

Some Sources of Alpha

Value vs. Glamour

Some examples:

• Fama & French: B/M ratio
• Basu: E/P ratio
• Kothari & Shanken: D/P ratio
• Lakonishok, Schileifer & Vishny: C/P ratio
• …
• Long-term Contrarian bucket

General Structure of Value Alpha

• divided by market price
• Not the other way around
• Only market price is guaranteed to be greater than 0

Combining Alphas

• Let \(\alpha_{ti}^1\) be a standardized winsorized alpha for stock \(i\) on date \(t\)
• Let \(\alpha_{ti}^2\) be another alpha
• Aggregate Alpha as: $\alpha_{ti} = w_1 \alpha_{ti}^1 + w_2 \alpha_{ti}^2$
• Winsorize aggregate alpha

Generalization can be made through combining of many flavors of the value alpha to make better aggregate value alpha.

With consensus of analyst forecasts, numerators can also be:

• Analyst forecast of future earnings
• Analyst forecast of future sales
• Analyst forecast of future dividends
• Analyst forecast of future cash flow

The weights for future projections are determined by judgement and backtest.

Momentum

• Straight momentum
  • Jegadeesh and Titman (1993) “Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency” Journal of Finance
  • if high \(\rightarrow\) buy the stock
  • if low \(rightarrow\) sell the stock
• Echo momentum
  • Novy-Marx (JFE 2012) “Is momentum really momentun”
  • Momentum is primarily driven by firms’ performance 12 to 7 months ago
• MomentumConsistency
  • Grinblatt and Moskowitz (JFE 2004) “Predicting stock price movements from past returns: the role of consistency and tax-loss selling”
  • Achieving a high past return with a series of steady positive months generates larger expected return than a high past return achieved with just a few extraordinary months
  • One-year winner (loser) consistency dummy is one if the monthly return of the stock was positive (negative) in at least eight of the one-year horizon’s 11 months
• Industry Momentum
  • Moskowitz and Grinblatt (JF 1999) “Do industries explain momentum?”
    • Industry momentum strategies are more profitable than individual stock momentum strategies.
    • Industry momentum strategies are robust to various specifications and methodologies, and they appear to be profitable even among the largest, most liquid stocks.
  • Industry portfolios exhibit significant momentum, even after controlling for size, book-to-market equity (BE/ME), individual stock momentum, the cross-sectional dispersion in mean returns, and potential microstructure influences.
  • Once returns are adjusted for industry effects, momentum profits from individual equities are significantly weaker and, for the most part, are statistically insignificant.
• Style Momentum
  • Chen and De Bondt (JEF 2004) “Style of momentum within the S&P-500 index”

  • Cap\Type	Growth	Blend	Value
    Small-cap
    Mid-cap
    Large-Cap

  • No-dividend style
• Momentum Acceleration
  • Gettleman and Marks (2006) “Acceleration Strategies”
  • Acceleration is defined as the change in six- month momentum relative to the cross- section of other firms.
  • Trading strategies based on acceleration offer significant abnormal profits of approximately 4.5% annually when controlled for other known regularities in equity returns.

Volume

• Gervais, Kaniel and Mingelgrin (2001) “The high-volume return premium” Journal of Finance
  • Stocks experiencing unusually high (low) volume over a day or a week tend to appreciate (depreciate) over the next month
• Chordia, Subrahmanyam & Anshuman (JFE 2001) “Trading activity and expected stock returns”
  • If stocks had high volume 2 months ago then they tend to go down this month

New issues puzzle

• Loughran and Ritter (JF 1995) “The New Issues Puzzle”
• Companies that issue stock subsequently underperform over the next 5 years
• Worse for IPO’s than for Seasoned Equity Offerings
• Cannot winsorize

Post-earnings announcement drift

• Bernard and Thomas (JAR 1989) “Post-Earnings- Announcement Drift: Delayed Price Response or Risk Premium?”
• Stocks whose earnings are above (below) analyst consensus outperform (underperform) for two months afterwards
• Do not winsorize.

Alpha Aggregation

• Short-term alphas balance long-term alphas
• Technical alphas balance fundamental alphas
• Contrarian alphas balance momentum alphas

	Short-Term	Long-Term
CONTRARIAN	1-month reversal of residuals, MAX factor, idiosyncratic skewness	value , betting against beta (variance)
PRO-CYCLICAL	1-month trading volume, post-earning announcement drift, insider trading, implied volatility	momentum, profitability , disaggregation quality, short interest

Alphas Everywhere

Below are some most important factors for predicting the corss-section of US stock returns

Factor	Definition
Residual Return	last month’s residual stock return unexplained by the market
Cash Flow-to-Price	12-month trailing cash flow-per-share divided by current price
Earnings-to-Price	12-month trailing earnings-per-share divided by current price
Return on Assets	12-month trailing total income divided by most recently reported total assets
Residual Risk	24-month trailing variance of residual stock return unexplained by market return
12-month Return	total return for the stock over trailing twelve months
Return on Equity	12-month trailing earnings-per-share divided by most recently reported book value-per-share
Variance	24-month trailing variance of total stock return
Book-to-Price	most recently reported book value of equity divided by current market price
Profit Margin	12-month trailing earnings before interest divided by 12-month trailing sales
3-month Return	total return for the stock over trailing 3 months
Sales-to-Price	12-month trailing sales-per- share divided by market price