The Factor InVe(nn)stigator is a series of case studies that discuss how to interpret factor analysis results, both the intuitive and surprising, for various well-known investments and indices.

Our first subject is The MSCI World Small Cap Index. This index is comprised of small capitalization stocks across 23 developed countries.1 Let’s view and interpret the factor analysis results using the Two Sigma Factor Lens since the index’s inception in mid 2004.


Exhibit 1: MSCI World Small Cap Index Factor Exposures2

Source: Venn. August 24, 2004 - August 22, 2019, using daily data.

Factor Exposures (ß) - MSCI World Small Cap Index


Notable Positive Exposures:

  • Equity: The index has exhibited a positive Equity beta of 1.1 over this period. It comes as no surprise that this is the largest factor exposure. After all, the index is made up of stocks!
  • Small Cap: As one might intuit, there was also a positive exposure to the Small Cap factor because the index is focused on stocks with smaller market caps. In fact, the average market cap of the index’s constituents as of July 31, 2019 was only $1.4 billion3 (versus $25.1 billion in the MSCI World Index).4
  • Foreign Currency: The positive beta to the Foreign Currency factor (which is designed to be short USD and long the other G10 currencies) likely results from the index’s exposure to stocks throughout the world (more than 40% of the weight as of July 31, 2019 was in countries outside the U.S.).5 Additionally, this index does not hedge the resulting currency exposure.
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Notable Negative Exposures:

  • Local Equity: For reasons similar to the Foreign Currency factor, the index has a small negative exposure to the Local Equity factor (which is intended to capture home bias, or exposure to U.S.-specific equities). This implies that the index has meaningful international representation.
  • Emerging Markets: There is a small negative exposure to the Emerging Markets factor. This likely stems from the fact that the index only contains stocks from developed countries. There is no emerging market country representation.

Note that the two negative exposures discussed above are not bolded in Exhibit 1 like the three positive exposures. While both Local Equity and Emerging Markets are statistically significant (meaning their t-statistics are less than -2), they are not economically significant, as they do not contribute meaningfully to the risk of the index, as demonstrated in Exhibit 2.


Exhibit 2: MSCI World Small Cap Index Factor Contributions to Risk6

Source: Venn. August 24, 2004 - August 22, 2019, using daily data.

Factor Contributions to Risk - MSCI World Small Cap Index


Finally, we can break down the index’s annualized 8.4% return by each factor. Exhibit 3 shows that the Equity factor contributed most to returns, unsurprisingly. The other large contributor was the Risk-Free Rate, which is the return an investor receives for investing in a risk-free asset (learn more here).


Exhibit 3: MSCI World Small Cap Index Factor Contributions to Return7

Source: Venn. August 24, 2004 - August 22, 2019, using daily data.

Factor Contributions to Return - MSCI World Small Cap Index


Overall, Venn’s factor analysis holistically explained the risk and return for the MSCI World Small Cap Index. Over 96% of the index’s risk over this period can be explained by the Two Sigma Factor Lens (as evidenced by the 3.6% residual risk component in Exhibit 2), and only 17 basis points of the index’s annual return resulted from this unexplained risk (as displayed in Exhibit 3). 

Further, the factor analysis results for the index are very intuitive and jive with the index’s general objective: to deliver long exposure to global, developed, small cap stocks, where:

  • long exposure and stocks translate to a positive Equity beta
  • global translates to the positive Foreign Currency and negative Local Equity betas
  • developed translates to a negative Emerging Markets beta
  • small cap translates to a positive Small Cap beta

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1 Source:

2 Factor exposures, otherwise known as factor betas, measure the sensitivity of the index to the various factors. All else equal a factor beta of 0.5 means that for every 1% the factor returned, the index returned 0.5% on average.

3 Source:

4 Source:

5 Source:

6 Factor contributions to risk are calculated using the correlation-adjusted, weighted factor risk divided by the index’s risk.

7 Factor contributions to return are roughly calculated by multiplying the factor exposures by the factor returns.


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