In a take-home, a stock's monthly returns are regressed on a factor over 60 months, but one month shows a data error of +250%. Compare the slope with and without it, winsorising at the 1st and 99th percentiles against deleting, and choose.

Report the slope with the month corrected or deleted, about 0.94; the raw slope of 2.91 is an artefact and winsorising still leaves 1.79. The +250% is a recording error, almost certainly 2.5% with the decimal moved. With 60 points the 99th percentile is set by the error itself, about 113%, so winsorising shrinks the damage without removing it. Winsorise genuine extreme returns; correct or remove proven errors, and say which you did.

A lot, because of where it sits. The bad month is also the month with the largest factor return, 8.4%, so it is the point with the most leverageIn regression, how far an observation lies from the average of the explanatory variable. A point far out on the x-axis has more pull on the fitted slope. on the slope. Least squares penalises the squared miss, so a single point about 247 points too high drags the line up at the right-hand end, and the slope jumps from 0.94 without it to 2.91 with it, more than three times the true loading. Think of a seesaw with sixty children of normal weight and one elephant sitting at the far end.

Look at how the percentile is computed. With 60 values the 99th percentile sits 0.99 times 59, or 58.41 places along the sorted list: between the second-largest value, 17.2%, and the largest, which is the error. The cap is therefore set by the error itself, about 113%, and a month that should read 2.5% still reads over a hundred. WinsorisingReplacing values beyond a chosen percentile with the value at that percentile, so extreme points are pulled in rather than removed. works when there are many observations beyond the cutoff and each is a real but extreme draw. With one gross error in 60 rows it is the wrong tool.

Decide first whether the point is an error or an event. A +250% month with no news, in a price series that moves a few per cent around it, is a recording error; 2.5% with the decimal shifted fits every fact. Errors are corrected where you can prove the true value and deleted where you cannot; real extreme events are kept and handled with winsorising or a robust regression. Here the correction is provable, so report 0.89 and show the deleted version, 0.94, as a check. A robust flag would have caught it before any regression: the month lies about 58 median absolute deviations from the median, where five or so would already earn a second look.

Write the decision down in the submission. Graders of a take-home read the cleaning notes as closely as the estimate, because a quant who silently drops awkward rows will one day drop the crash month from a risk model. One line is enough: what the point was, why you judged it an error, what you did, and how much the answer moved.