Factor Library IL

Version 1.1.0

Methodology

The library is grounded in the Fama–French and Carhart factor models. Those models were built to explain the variation in asset returns through systematic factors. In practice they are also used to isolate the return that remains beyond those factors (alpha). The library keeps the economic reasoning established in the literature, while adapting the portfolio construction rules to the smaller and more concentrated structure of the Israeli equity market.

The research universe covers the broad layer of the Israeli equity market, smaller companies included, and holds about 185 stocks at a typical date. Each period includes every company that met the eligibility conditions, judged on the information available at that time (point-in-time).

The market portfolio (MKT-RF) is weighted by market capitalization, while the factor portfolios give every stock equal weight. Holdings are held unchanged until the next rebalance; daily returns are recorded, and the monthly return is compounded from the daily series. Returns are total returns, including dividends.

RF: Risk-Free Return

The risk-free series represents the return on a short-term, shekel-denominated asset. It is based on the Bank of Israel’s official yield-to-maturity series for three-month MAKAM.

The MAKAM yield is quoted on an annualized basis. For each trading day, it is converted into a holding-period return using the actual number of calendar days since the previous observation. Interest accrued over weekends and holidays is therefore included in the next published daily return.

Monthly RF is not derived from a separate monthly yield series. It is the compound return of the published daily RF observations within each calendar month.

Yₜ is the annualized yield expressed as a percentage, and Δdₜ is the calendar-day gap between consecutive daily observations.

Daily

RFₜ = (1 + Yₜ / 100)^(Δdₜ/365) − 1

Monthly

RFₘ = Π(1 + RF_d) − 1
MKT-RF: Market

MKT-RF represents the return of the eligible Israeli equity universe in excess of the risk-free rate.

Each stock is weighted by its full market capitalization at the end of the preceding period. The calculation uses full market capitalization rather than free-float capitalization.

Because the Israeli market can be highly concentrated, no single stock may account for more than 7% of the portfolio. Any weight above the cap is redistributed among the remaining stocks in proportion to their market capitalization. This process is repeated until every stock is within the limit.

The cap reduces dependence on a small number of companies without changing the eligible universe. Without it, a single stock would historically have represented as much as 35% of the universe’s total market capitalization.

After the capped market return has been calculated, the corresponding risk-free return is subtracted:

MKT-RFₜ = Σᵢ(wᵢ,ₜ₋₁ × Rᵢ,ₜ) − RFₜ
SMB: Size

The size factor (SMB) measures the return gap between small and large companies.

SMB and the value factor (HML) are built from a single combined sort at the end of June each year (t):

  • Size: two groups split at the median market capitalization, small and large.
  • Value: three groups by the ratio of book equity to market value, the bottom 30%, the middle 40%, and the top 30%.

Crossing the sorts produces six portfolios, held for twelve months.

The book-to-market ratio uses book equity for year t−1 over market value at the end of December t−1, which keeps a neutral six-month window, while the size sort uses market capitalization at the end of June t.

Financial statement figures enter on the date they were actually published.

Unlike the source literature, which computes the breakpoints from New York Stock Exchange listings alone, in Israel they are computed from the broad market index. Including the whole market lets the smaller stocks pull the median down, and can even affect the sign of the factor’s return.

Averaging the returns of the value groups neutralizes the value effect and isolates the size premium:

SMBₜ = ⅓[R(S/H)ₜ + R(S/M)ₜ + R(S/L)ₜ] − ⅓[R(B/H)ₜ + R(B/M)ₜ + R(B/L)ₜ]
HML: Value

The value factor (HML) measures the return gap between companies with a high ratio of book equity to market value (value companies) and companies with a low ratio (growth companies).

The factor is built from the same six portfolios and the same annual formation at the end of June. Averaging the two size groups neutralizes the size effect and isolates the value premium, while the middle group (medium value) is excluded from the calculation.

HML is the difference between the average return of the two high-value portfolios and the average return of the two low-value portfolios:

HMLₜ = ½[R(S/H)ₜ + R(B/H)ₜ] − ½[R(S/L)ₜ + R(B/L)ₜ]
MOM: Momentum

The momentum factor (MOM) measures the return gap between the stocks with the strongest performance over the past year (the winners) and those with the weakest (the losers).

Stocks are ranked at the end of each month (t) by their cumulative return over the eleven months that have passed, from t−12 to t−1. The formation month itself (t) is excluded from the measurement, to avoid the bias that short-term reversal would introduce. The top 30% are classified as winners, the bottom 30% as losers, and the middle 40% are excluded from the calculation.

To neutralize the size effect, stocks are split in parallel into small and large at the median. Crossing the two sorts produces four equally weighted portfolios — small winners, large winners, small losers and large losers — rebalanced monthly.

MOM is the difference between the average return of the winner portfolios and that of the loser portfolios:

MOMₜ = ½[R(S/W)ₜ + R(B/W)ₜ] − ½[R(S/L)ₜ + R(B/L)ₜ]
Regression and performance evaluation

The regression model splits a portfolio return into two parts: exposure to broad market risks, which are the factors, and the excess return that remains — alpha (α).

The full model equation:

Rₚ,ₜ − RFₜ = α + βₘ(MKT-RF)ₜ + βₛSMBₜ + βₕHMLₜ + βₒMOMₜ + εₜ

The risk-free return (RF) is subtracted from the portfolio return before the analysis, and the market factor (MKT-RF) is included in every specification.

Technical notes

  • Annualization: daily alpha is multiplied by 252 and monthly alpha by 12 to give an annual figure.
  • Standard-error accuracy (Newey–West): the calculation corrects for bias from persistent trends and from changes in volatility over time. The lag length (L) is set by:
    L = min(floor[4 × (n / 100)^(2/9)], n − k − 1)
  • Significance (p-value): a two-sided test based on the normal distribution, to check that a result is not down to chance.

Goodness-of-fit measures

  • Adjusted R²: the main measure for comparison. Unlike plain R², which always rises when variables are added, the adjusted measure charges a penalty for each factor added, which makes comparison between model specifications reliable.
  • Incremental contribution (ΔR²): how much unique explanatory power a given factor adds, found by comparing the full model with the same model estimated without it. Because the factors are related and correlated, the incremental contributions do not sum to the overall R².
Revisions

Material data or methodology changes are recorded in the changelog with their effective version and date.