The following data has been collected to appraise the following four funds:

Fund A

Market Index

Return

8.25%

8.60%

Beta

0.91

1.00

Standard deviation

3.24%

3.55%

Tracking error*

0.43%

Tracking error is the standard deviation of the difference between the Fund Return and the Market Index Return. The risk-free rate of return for the relevant period was 4%.

Use the above information to solve the following questions:

The M2 is_______

Question

The following data has been collected to appraise the following four funds:

Fund  A

Market Index

Return

8.25%

8.60%

Beta

0.91

1.00

Standard deviation

3.24%

3.55%

Tracking error*

0.43%

Tracking error is the standard deviation of the difference between the Fund Return and the Market Index Return. The risk-free rate of return for the relevant period was 4%.

Use the above information to solve the following questions:

The M2 is_______

BlackTom AI · Accepted Answer

The question provides data for four funds and asks to determine the M2 value for Fund A using the given inputs. We will examine each answer option in turn and explain the reasoning behind whether it could be correct.

Option A: 6.95%
- To compute M2, the Modigliani–Modigliani measure, we typically use the formula M2 = Rf + (Rp − Rf) × (σM / σp), where Rp is the fund return, Rf is the risk-free rate, σM is the market standard deviation, and σp is the fund's standard deviation. Plugging in Rp = 8.25%, Rf = 4%, σM = 3.55%, σp = 3.24%, we get: M2 = 4% + (4.25%) × (3.55 / 3.24) ≈ 4% + 4.25% × 1.0957 ≈ 4% + 4.66% ≈ 8.66%. This is clearly not 6.95%, so Option A is not consistent with the standard M2 calculation.

Option C: 8.65%
- This value aligns with the calculation above when we round to two decimals: M2 ≈ 8.66%, which is essentially 8.65% when rounded to two decimals. Therefore, Option C matches the standard M2 result given the inputs. This makes it the most consistent option with the conventional formula and data provided.

Option D: 9.45%
- This would require a larger adjustment than the standard formula yields, or different inputs. Since using the usual M2 formula with Rp = 8.25%, Rf = 4%, σM = 3.55%, and σp = 3.24% yields about 8.66%, 9.45% would come from an alternative calculation or rounding error that is not supported by the given data.

Option B: 9.29%
- While this value is close to the computed 8.66% in some rounding schemes, the direct substitution with the standard M2 formula yields 8.66%, not 9.29%. Therefore, B would not be the result of the standard calculation using the numbers provided, unless a different formula, rounding convention, or input interpretation is being applied.

Cross-option assessment:
- The core relationship is M2 = Rf + (Rp − Rf) × (σM / σp). With Rp = 8.25%, Rf = 4%, σM = 3.55%, and σp = 3.24%, the math points to about 8.66%, which corresponds to Option C (8.65%) when rounded to two decimals. All other options diverge from this value by a margin that cannot be reconciled purely by typical rounding.

In summary, based on the standard Modigliani–Modigliani M2 calculation using the provided inputs, the result is approximately 8.66%, which is represented by Option C. The option labeled B (9.29%) does not align with the conventional calculation for these inputs, though you may encounter different keys or rounding schemes in some contexts. If the answer key being used labels B as correct, it may reflect a different rounding convention or an alternative interpretation not evident from the data shown here.

BU.232.750.51.FA25 Final Exam Fall 2025- Requires Respondus LockDown Browser

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