Modigliani Risk-Adjusted Performance

Modigliani risk-adjusted performance (M-squared) takes any fund’s historical return and asks: “What would this fund have earned if it held the same volatility as the benchmark?” By levering or deleveraging the fund’s returns to match the benchmark’s risk, M-squared produces apples-to-apples return comparisons. A conservative 8% fund and an aggressive 12% fund become directly comparable once volatility is standardized.

The core insight: volatility as the common denominator

Imagine two portfolio managers. One runs a conservative fund with 10% annual volatility, earning 7% returns. The other runs an aggressive hedge fund with 25% volatility, earning 9% returns. Which manager is better?

The 25% volatility fund looks superior by raw return: 9% beats 7%. But that manager is taking 2.5 times more risk to earn 28% more return. The conservative manager is doing more with less. Without adjusting for risk, the comparison is incomplete.

Alpha and beta try to answer this, but they depend on correlation to a specific benchmark. M-squared sidesteps that complexity. It rescales both funds to the same volatility level—say, the benchmark’s 18% volatility—and asks: at that risk level, how much would each fund earn?

If the conservative fund’s 7% return at 10% volatility scales up to 12.6% at 18% volatility, and the aggressive fund’s 9% at 25% volatility scales down to 8.1% at 18% volatility, the conservative manager has revealed superior risk-adjusted skill. The comparison is now apples-to-apples.

The mechanism: scaling returns to a standard risk level

M-squared uses the Sharpe ratio—the fund’s excess return divided by its volatility—to measure efficiency per unit of risk. That ratio is then applied to the benchmark’s volatility to produce the adjusted return.

M² = Fund return + Sharpe ratio × (Benchmark volatility − Fund volatility)

If a fund earned 12% with 15% volatility (and assuming a risk-free rate of 2%, a Sharpe ratio of 0.67), and the benchmark has 18% volatility:

M² = 12% + 0.67 × (18% − 15%) = 12% + 2.01% = 14.01%

The message: at the benchmark’s 18% volatility, this fund’s methodology would have delivered 14.01%. Compare that figure directly to another fund’s M² figure, and risk is already accounted for.

Why Modigliani matters for portfolios of different styles

Modigliani is especially useful for comparing portfolios that deliberately differ in risk level. A stable-value fund and a growth fund shouldn’t be ranked by absolute return alone; they serve different purposes. M² lets you ask: if the stable-value fund were levered to growth-fund volatility, would it outperform?

Similarly, when evaluating a low-volatility ETF against a standard equity ETF, M² converts the low-volatility fund’s modest returns into an equivalent return at benchmark risk. If the low-vol fund earned 6% at 10% volatility, and the benchmark returned 10% at 18% volatility, M² would show the low-vol fund’s equivalent return at 18% volatility. That adjusted figure reveals whether the low-vol manager’s security selection is genuinely skilled or just riding the low-volatility factor.

The lever assumption: a source of controversy

M-squared rests on a critical assumption: that a fund’s return scales proportionally with volatility. If you lever a fund’s portfolio by 1.5x (taking 50% more risk), the theory assumes returns also scale by 1.5x.

In practice, that’s only partially true. Leverage is costly. A fund that levered its holdings would bear financing charges, widening bid-ask spreads, and potential margin calls during market stress. These frictions eat into returns, so a levered portfolio underperforms the theoretical scaling.

Conversely, the assumption breaks down during market dislocations. A fund’s volatility measured over calm years may spike during crashes when correlations shift and tail risk activates. An M² figure calculated from historical calm-period data could overstate the fund’s risk-adjusted returns in a true stress scenario.

M-squared versus other risk-adjusted metrics

M-squared differs meaningfully from alpha, which is return beyond what beta would predict for a given benchmark. Alpha assumes a linear relationship to the benchmark; M² abstracts away the benchmark entirely, using volatility alone.

It differs also from Sharpe ratio, which measures return per unit of risk but doesn’t convert to an actual dollar return—it’s a ratio, not a return percentage. M² converts that ratio into a return figure, making it more intuitive for side-by-side fund comparisons.

And it differs from down-capture ratio, which ignores upside entirely and focuses on loss severity. M² weights both upside and downside equally through volatility.

For a complete assessment, pair M² with up-capture ratio and down-capture ratio to understand whether the fund’s risk comes from large rallies (benign) or potential crashes (concerning).

The evergreen problem: past volatility is not future volatility

M-squared is a historical metric. It answers: “Based on what this fund did, here’s its risk-adjusted return at benchmark volatility.” It doesn’t predict what the fund will do forward.

A fund’s volatility can shift for many reasons: strategy changes, manager departure, market regime shift, or growth in asset size. A small, nimble fund with 12% historical volatility might swell to billions under management and end up with 18% volatility as manager skill matters less. The M² figure would be stale.

Institutional investors often recompute M² using rolling windows (e.g., the trailing three years) to catch shifts in fund behaviour. Even so, M² remains a backward-looking snapshot, not a forward covenant.

When to use M-squared, and when to dig deeper

M² shines when comparing two funds with materially different risk profiles serving different purposes. Should a retiree use this low-volatility equity fund or that standard equity fund? M² translates both to the same risk level and compares returns directly.

It’s less useful when comparing funds already matched to the same benchmark and risk profile—two large-cap growth funds, for instance. In that case, up-capture ratio and alpha are more relevant because they measure outperformance within the same environment.

It’s also incomplete without context. A 12% M² is stellar if earned over 10 years; it’s suspicious if earned over 18 months of a bull market. Pair M² with the fund’s Sharpe ratio, R-squared to the benchmark, down-capture ratio, and absolute return history to build a full picture.

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