Part 1. Univariate Statistics.
The data below was obtained from Professor Kenneth French’s data library website:
http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html
The table below contains monthly returns of the “Fama/French 5 Factors” and the monthly returns of the “Momentum factor” for the period from July 1963-December 2017 (654 months)
(Double click on the window to access the data on the excel spreadsheet)
- RM-RF The return spread between the capitalization weighted stock market and cash.
- SMB The return spread of small minus large stocks (i.e., the size effect).
- HML The return spread of cheap minus expensive stocks (i.e., the value effect).
- RMW The return spread of the most profitable firms minus the least profitable.
- CMA The return spread of firms that invest conservatively minus aggressively.
- MOM The retun spread of firms with high prior return minus low prior return.
Split the sample in 3 equal periods and compute the average, SD, skew, and kurtosis for each of the six “risk factors” for the full sample and the three different periods. Arrange these values in a table similar to the one shown below. (5p)
| Full Sample: 1963M07 – 2017M12 | ||||||
| MKT_RF | SMB | HML | RMW | CMA | MOM | |
| Mean | 0.531 | 0.250 | 0.345 | 0.250 | 0.287 | 0.659 |
| Std. Dev. | 4.388 | 3.025 | 2.809 | 2.213 | 2.005 | 4.194 |
| Skewness | -0.542 | 0.380 | 0.077 | -0.309 | 0.294 | -1.341 |
| Kurtosis | 2.048 | 3.237 | 2.126 | 12.771 | 1.657 | 10.754 |
| Observations | 654 | 654 | 654 | 654 | 654 | 654 |
| First sub-sample: 1963M07 – 1981M08 | ||||||
| Mean | 0.218 | 0.568 | 0.438 | 0.014 | 0.258 | 0.845 |
| Std. Dev. | 4.419 | 3.263 | 2.607 | 1.617 | 2.027 | 3.698 |
| Skewness | -0.108 | 0.208 | -0.176 | 0.081 | 0.015 | -0.459 |
| Kurtosis | 1.175 | 1.190 | 1.837 | 0.248 | 0.909 | 2.616 |
| Observations | 218 | 218 | 218 | 218 | 218 | 218 |
| Second sub-sample: 1981M09 – 1999M10 | ||||||
| MKT_RF | SMB | HML | RMW | CMA | MOM | |
| Mean | 0.895 | -0.228 | 0.342 | 0.340 | 0.302 | 0.874 |
| Std. Dev. | 4.381 | 2.570 | 2.513 | 1.443 | 1.865 | 2.957 |
| Skewness | -0.929 | 0.165 | 0.274 | -0.035 | -0.240 | -0.554 |
| Kurtosis | 4.403 | 0.905 | -0.034 | 0.178 | 0.577 | 0.997 |
| Observations | 218 | 218 | 218 | 218 | 218 | 218 |
| Third sub-sample: 1999M11 – 2017M12 | ||||||
| MKT_RF | SMB | HML | RMW | CMA | MOM | |
| Mean | 0.480 | 0.412 | 0.256 | 0.396 | 0.301 | 0.259 |
| Std. Dev. | 4.358 | 3.149 | 3.257 | 3.154 | 2.123 | 5.502 |
| Skewness | -0.618 | 0.524 | 0.143 | -0.429 | 0.901 | -1.433 |
| Kurtosis | 1.030 | 6.309 | 2.618 | 8.365 | 2.883 | 9.287 |
| Observations | 218 | 218 | 218 | 218 | 218 | 218 |
- Do the statistics suggest to you that returns for those risk factors come from the same distribution over the entire period? (5p)
- Which factor portfolio gives the lowest and highest future value (full sample)? (5p)
- Which factor portfolio gives the lowest and highest future value (over the five-year period (Jan 2013 – Dec 2017). )? (5p)
- Give a brief explanation of what are the real, macroeconomic, aggregate, nondiversifiable risk that are proxied by the returns of the [RM-RF], SMB, HML, RMW, CMA and MOM risk portfolios. For example, why are investors so concerned about holding stocks that do badly at the times that the HML (value less growth) and SMB (small-cap less large-cap) portfolios do badly, even though the market [RM-RF] does not fall? (5p)
