Project 2 Exercises

Reader note: The data version, values, negative results, and null results below are retained from the historical study and exercises. They are historical teaching material, not new market results from the current constructed-data run of the I3 reader notebook. The data-authorization branch is skipped by default.

Answer the questions before consulting the solutions. Unless a question says otherwise, returns are expressed as decimals, and the model results come from the fixed 2010–2019 sample.

1. Same-month RF and factor units. In a given month, HiTec’s total return is 2.0%, the same month’s RF is 0.3%, and the published Mkt-RF value is 1.7%. Write down the dependent variable for that month. What would be wrong with subtracting RF from Mkt-RF again? If only the asset’s total return is available and RF is not, can this be called a CAPM excess-return regression?
2. Interpret a conditional Beta. HiTec’s FF3 market Beta is 1.158, with a HAC 95% interval of [1.075, 1.242]. Interpret the linear conditional relationship, in percentage points, when Mkt-RF rises by 1 percentage point in the same month. Does this number prove that a market move causes HiTec’s return to change?
3. Interpret model Alpha. NoDur-CAPM Alpha is 0.2603% per month, with a HAC 95% interval of [−0.1223%, 0.6429%], nominal p = 0.1804, and nine-test Holm p = 1.0000. Explain its unit, interval, and evidentiary limits.
4. Check the sample variance. The total sample variance, fitted variance, and residual variance of NoDur-CAPM excess returns are 0.001039486, 0.000582943, and 0.000456543, respectively (squared decimal returns). Check the numerical identity and convert the fitted and residual shares to percentages. Can this be called a causal decomposition of future risk?
5. Compare FF3 and FF5. HiTec’s R² rises from 0.864 under FF3 to 0.893 under FF5. Give at least two reasons why this difference should not be interpreted directly as the “pure incremental contribution” of the newly added RMW/CMA factors.
6. HAC 3/6/12 sensitivity. Enrgy-FF3 Alpha has the same point estimate, −0.6629% per month, under HAC 3/6/12. The 95% intervals are [−1.2950%, −0.0308%], [−1.3091%, −0.0167%], and [−1.3154%, −0.0104%], respectively. Which quantities change and which stay the same? Is there a reason to treat the three bandwidths as three independent validations?
7. Multiple testing and negative results. Under HAC 6, the Alpha estimates for all three energy models are negative, with single-test p-values of 0.0061, 0.0444, and 0.0249. Their Holm-adjusted values are 0.0549, 0.3111, and 0.1995. How would you state a cautious conclusion? May the report retain only the CAPM nominal p-value?
8. Chronological split. HiTec-FF5 Alpha estimated on 2010–2014 is −0.098% per month, and the 2015–2019 error RMSE is 1.562 percentage points per month. Why is this still not a real-time forecast or a strategy return? List at least three types of information that a future net-Alpha study would need.