Use the original paired data
| Period | Benchmark (%) | Asset (%) |
|---|---|---|
| 1 | -2 | -3 |
| 2 | -1 | -0.5 |
| 3 | 0 | 1 |
| 4 | 1 | 2.5 |
| 5 | 2 | 6 |
Retain the fitting definitions
Benchmark mean is zero, asset mean 1.2%, Sxx=10 and Sxy=21 in percentage-point units. The line includes an intercept and uses equal observation weights.
Try the questions
What is the original asset-on-benchmark slope?
- A.
2.1
- B.
0.986666 approximately
- C.
70/151
Answer and explanation
Answer: A
Keep the explanatory return in the denominator.
- A
21/10 uses the benchmark centered squared sum.
- B
This is correlation, with a different denominator.
- C
This is the reverse-regression slope.
Which covariance/variance pair reproduces the original slope?
- A.
5.25 / 2.5
- B.
5.25 / 2
- C.
4.2 / 2.5
Answer and explanation
Answer: A
A common divisor cancels in the ratio.
- A
Both use the n−1 sample divisor.
- B
This mixes sample covariance and population variance.
- C
This mixes population covariance and sample variance.
A constant 0.1% is subtracted from both series. What is the new intercept?
- A.
1.2% automatically
- B.
1.31%
- C.
1.1%
Answer and explanation
Answer: B
Keep raw and excess-return bases distinct.
- A
The slope remains the same, but the intercept shifts.
- B
1.2%+(2.1−1)×0.1% uses the stated constant translation.
- C
This is the new asset mean, not the excess intercept.