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Modigliani modigliani measure

What Is Modigliani Modigliani Measure?

The Modigliani Modigliani Measure, also known as the M2 Measure or RAP (Risk-Adjusted Performance), is a financial metric used to evaluate the risk-adjusted return of an investment portfolio by comparing it to a benchmark portfolio. It falls under the broader category of portfolio performance evaluation metrics and aims to present risk-adjusted performance in easily interpretable percentage terms. The M2 Measure standardizes a portfolio's volatility to match that of a chosen benchmark, allowing for a more direct comparison of returns for a given level of risk.

History and Origin

The Modigliani Modigliani Measure was jointly developed in 1997 by Nobel laureate economist Franco Modigliani and his granddaughter, Leah Modigliani. Originally named "RAP" for risk-adjusted performance, it aimed to provide a more intuitive and readily understandable measure of portfolio performance than existing metrics. The development of the M2 Measure built upon earlier work in portfolio theory, particularly by addressing certain interpretational limitations found in the widely used Sharpe Ratio. Their goal was to quantify how well an investor is compensated for the risk taken in a portfolio, relative to a benchmark and the risk-free rate.17

Key Takeaways

  • The Modigliani Modigliani Measure (M2) evaluates a portfolio's risk-adjusted performance in comparison to a benchmark.
  • It presents the risk-adjusted return in percentage terms, making it more intuitive than dimensionless ratios.
  • The M2 Measure adjusts the portfolio's return to match the risk level of the benchmark, allowing for direct comparisons.
  • A higher M2 value indicates superior risk-adjusted performance.
  • It helps investors understand the added value of active management by accounting for both return and risk.

Formula and Calculation

The Modigliani Modigliani Measure is derived from the Sharpe Ratio. The formula for the M2 Measure is:

M2=SRP×σB+RfM_2 = SR_P \times \sigma_B + R_f

Where:

  • (M_2) = Modigliani Modigliani Measure
  • (SR_P) = Sharpe Ratio of the portfolio
  • (\sigma_B) = Standard deviation of the benchmark
  • (R_f) = Risk-free rate

To calculate (SR_P), the formula for the Sharpe Ratio is first applied:

SRP=RP−RfσPSR_P = \frac{R_P - R_f}{\sigma_P}

Where:

  • (R_P) = Portfolio return
  • (R_f) = Risk-free rate
  • (\sigma_P) = Standard deviation of the portfolio's excess return15, 16

The M2 Measure essentially scales the portfolio's Sharpe Ratio by the benchmark's volatility and then adds back the risk-free rate, converting the dimensionless Sharpe Ratio into a percentage return figure that is directly comparable to the benchmark's return.

Interpreting the Modigliani Modigliani Measure

The Modigliani Modigliani Measure provides a percentage figure, which represents the risk-adjusted return of a portfolio as if it had the same level of total risk as the benchmark. A higher M2 value indicates that the portfolio has achieved a better return for the amount of risk taken, relative to the benchmark. For instance, if a portfolio has an M2 of 15% and its benchmark has a return of 10%, the portfolio has outperformed on a risk-adjusted basis. This allows for clear comparisons between portfolios, even if they have different risk profiles, because the M2 Measure normalizes their risk to that of a common benchmark.13, 14

Hypothetical Example

Consider an investment scenario with the following hypothetical data for a Portfolio A and a Market Benchmark:

  • Portfolio A:
    • Return ((R_P)): 12%
    • Standard Deviation ((\sigma_P)): 15%
  • Market Benchmark:
    • Return ((R_B)): 9%
    • Standard Deviation ((\sigma_B)): 10%
  • Risk-Free Rate ((R_f)): 3%

Step 1: Calculate the Sharpe Ratio for Portfolio A

SRA=RP−RfσP=0.12−0.030.15=0.090.15=0.60SR_A = \frac{R_P - R_f}{\sigma_P} = \frac{0.12 - 0.03}{0.15} = \frac{0.09}{0.15} = 0.60

Step 2: Calculate the Modigliani Modigliani Measure for Portfolio A

M2,A=SRA×σB+Rf=0.60×0.10+0.03=0.06+0.03=0.09 or 9%M_{2,A} = SR_A \times \sigma_B + R_f = 0.60 \times 0.10 + 0.03 = 0.06 + 0.03 = 0.09 \text{ or } 9\%

In this example, Portfolio A has an M2 Measure of 9%. This means that, after adjusting for risk to match the market benchmark's volatility, Portfolio A would have yielded a 9% return. Since the Market Benchmark itself returned 9%, Portfolio A performed similarly on a risk-adjusted basis. This measure provides a clear picture that transcends simple comparisons of raw returns, offering a deeper insight into performance metrics.

Practical Applications

The Modigliani Modigliani Measure is a valuable tool in various financial contexts for assessing and comparing investment performance.12 Fund managers and institutional investors commonly use it in portfolio construction and evaluation to determine how effectively a portfolio has generated returns relative to the risk assumed. It is particularly useful for evaluating mutual funds, hedge funds, and other managed accounts, as it provides a standardized way to compare their risk-adjusted performance against market indices or peer groups.11 Financial advisors may also use the M2 Measure to explain to clients how different investment strategies have performed when accounting for risk.

Furthermore, the M2 Measure aids in the selection of appropriate benchmarks for performance appraisal. The CFA Institute emphasizes the importance of selecting relevant benchmarks to accurately assess a portfolio's performance.9, 10 By translating risk-adjusted performance into a percentage, the Modigliani Modigliani Measure makes it easier for investors to grasp the concept of being rewarded for risk, aligning with practical investment goals and preferences.8

Limitations and Criticisms

While the Modigliani Modigliani Measure offers a more intuitive interpretation of risk-adjusted returns, it is not without its limitations. One significant critique is its reliance on standard deviation as the sole measure of risk, which assumes that returns are normally distributed. In reality, financial returns often exhibit skewness and kurtosis, meaning they are not perfectly symmetrical or may have "fat tails" (more extreme positive or negative events than a normal distribution would predict). This can lead to an inadequate capture of true risk, especially for portfolios with asymmetric return distributions.6, 7

Another limitation is its dependency on the choice of benchmark. An inappropriate or poorly chosen benchmark can lead to misleading M2 Measure results, as the measure provides a relative comparison, not an absolute one. If the benchmark does not accurately reflect the portfolio's investment strategy or market risk exposure, the assessment of risk-adjusted performance may be flawed.5 Furthermore, like other performance metrics, the M2 Measure relies on historical data, which may not always be a reliable indicator of future performance.4 The Morningstar Rating for Funds, while distinct from M2, also grapples with the challenges of risk adjustment and investor intuition, highlighting the complexity of capturing "risk" in a universally appealing manner.3

Modigliani Modigliani Measure vs. Sharpe Ratio

The Modigliani Modigliani Measure (M2) and the Sharpe Ratio are both widely used metrics in risk management to evaluate risk-adjusted returns, but they differ primarily in their presentation and interpretability. The Sharpe Ratio, developed by William F. Sharpe, calculates the excess return per unit of total risk (standard deviation). It provides a dimensionless figure, meaning it is a ratio without a percentage unit, which can make direct comparisons between different investment options less intuitive for some investors. For example, knowing that one portfolio has a Sharpe Ratio of 0.8 and another has 1.2 indicates the latter is better on a risk-adjusted basis, but it doesn't immediately tell an investor the percentage difference in return.2

The M2 Measure addresses this by converting the Sharpe Ratio into a percentage return that is adjusted to the volatility of a chosen benchmark. By scaling the portfolio's risk to match the benchmark's risk, the M2 Measure allows for a more direct and easily understood comparison. Essentially, if a portfolio and its benchmark have the same risk level, their M2 Measure would directly compare their returns. This makes the Modigliani Modigliani Measure particularly advantageous when communicating performance to a broader audience, as it expresses the result in a familiar unit (percentage return) rather than an abstract ratio. While the M2 Measure offers improved interpretability, the rankings of portfolios based on the M2 Measure will be the same as those based on the Sharpe Ratio, as it is a direct transformation of the latter.1

FAQs

What does a higher Modigliani Modigliani Measure indicate?

A higher Modigliani Modigliani Measure (M2) indicates superior risk-adjusted performance. It means the portfolio generated more return for the level of risk taken, relative to the benchmark, or achieved the same return with less risk.

Can the Modigliani Modigliani Measure be negative?

Yes, the M2 Measure can be negative if the portfolio's performance is poor, even after adjusting for risk. A negative M2 would imply that the portfolio underperformed the risk-free rate on a risk-adjusted basis.

How is the Modigliani Modigliani Measure different from Jensen's Alpha?

While both are performance measures, the Modigliani Modigliani Measure focuses on the total risk (standard deviation) and adjusts a portfolio's return to match a benchmark's volatility for direct percentage comparison. Jensen's alpha, derived from the Capital Asset Pricing Model (CAPM), measures a portfolio's excess return relative to what would be expected given its beta (systematic risk). M2 compares total risk-adjusted returns against a benchmark's total risk, whereas alpha looks at the "skill" of the manager in generating returns beyond what market exposure alone would provide.

Is the Modigliani Modigliani Measure suitable for all types of portfolios?

The Modigliani Modigliani Measure is best suited for diversified portfolios where total risk (volatility) is a relevant measure. Its effectiveness may be limited for highly concentrated portfolios or those with non-normally distributed returns, as the underlying assumption of standard deviation might not fully capture all aspects of risk. It also requires a relevant benchmark for meaningful comparison.