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

We are given data to compute the M2 measure for Fund A using Modigliani and Modigliani’s approach.
First, recall the formula: M2 = Rf + Sharpe_p × SD_market, where Sharpe_p = (Rp − Rf) / SD_p.
Now, extract the necessary numbers from the table:
- Fund A return Rp = 8.25% = 0.0825
- Fund A standard deviation SD_p = 3.24% = 0.0324
- Market index return Rm = 8.60% is not directly used in the calculation beyond the market benchmark for SDm, but we’ll need the market SD for the final step: SD_market = 3.55% = 0.0355
- Risk-free rate Rf = 4% = 0.04
Compute Sharpe_p:
- Rp − Rf = 0.0825 − 0.04 = 0.0425
- Divide by SD_p: 0.0425 / 0.0324 ≈ 1.31 (more precisely about 1.3125)
Now compute M2 by plugging into the formula with SD_market:
- M2 = Rf + Sharpe_p × SD_market = 0.04 + 1.3125 × 0.0355
- 1.3125 × 0.0355 ≈ 0.0465
- Therefore M2 ≈ 0.04 + 0.0465 = 0.0865
Convert back to percentage: 8.65%
With the computed value in mind, evaluate the answer choices:
- Option D (9.45%): This would require a higher Sharpe_p or a larger SD_market effect; the actual calculation yields about 8.65%, so this is too high.
- Option B (9.29%): Also higher than the calculated 8.65%; not supported by the math.
- Option A (6.95%): This is lower than 8.65%; it underestimates the M2 by a noticeable margin.
- Option C (8.65%): Matches the computed M2 precisely given the inputs.
In summary, the correct approach uses the Sharpe ratio of the fund relative to the risk-free rate, scales it by the market standard deviation, and adds back the risk-free rate. The other options misestimate either the Sharpe ratio, the effect of SD_market, or both, leading to values that do not align with the computed M2.

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