Citi Research31 July 2026

The Momentum Sell-off

Style Rotation or Crowded Unwind?

The sharp reversal in Momentum has become the defining factor event of recent weeks, with investors rotating away from the AI tech-oriented winners and back towards valuation-sensitive exposures. While the breadth of Value outperformance, rising style dispersion, and falling correlations point to a meaningful shift in leadership, the evidence remains regionally uneven. Developed Markets are exhibiting the early characteristics of a broader Value-led rotation, Emerging Markets particularly continue to display the hallmarks of a positioning-led corrections, with losses concentrated among former Momentum leaders. Our interpretation is therefore one of an emerging rotation in DM alongside a correction in EM, rather than the start of a synchronized global change. As such, we view the recent Momentum sell-off as a reset in leadership rather than a definitive end to the broader Growth and Momentum cycle.

David T Chew下载原始 PDF

CITI'S TAKE

Momentum under pressure as Value reasserts itself

July marked a sharp reversal in factor leadership as Momentum continued to weaken. After leading performance across most regions during the first half of the year, Momentum has surrendered most of its year-to-date gains in a matter of weeks, with the decline particularly pronounced across AC Asia ex-Japan. At the same time, Value has re-emerged as the strongest performing style globally, generating positive returns across all major regions. The widening performance gap between Value and Momentum, coupled with rising style dispersion and falling cross-style correlations, points to a market increasingly rewarding valuation-sensitive exposures over the narrow leadership cohort that had dominated returns earlier in the year.

Rotation signals emerge, but regional divergence remains

The Momentum drawdown has been global, but the underlying drivers differentiated across regions. In Developed Markets, the combination of broad-based Value outperformance, rising stock dispersion, lower correlations and a rebound in prior laggards suggest the early stages of a broader style rotation. The evidence across EM remains more consistent with a correction in crowded positioning. Weakness concentrated in former Momentum leaders not a recovery among underperformers. We therefore view DM as exhibiting the early characteristics of a Value-led rotation, while EM continues to resemble a positioning-driven de-crowding event rather than a durable shift in factor leadership.

How far has crowding unwound

Bullish positioning in Nasdaq and Korea has diminished in recent months. Shorts in Eurostoxx have also been covered. Crowded sectors have underperformed in July, and we find Momentum crowding still strong on the long-side for the US whereas it has declined for Asia ex JP. The value rotation may have a crowding tailwind in developed markets; short stocks in US value tend to be crowded whereas the Asia ex JP story is more mixed.

Style Outlook

July marked a significant inflection point for Momentum investors. What initially appeared to be a contained reversal in the global AI and semiconductor complex in late June rapidly evolved into a broader and more persistent unwinding of crowded Momentum positions through July. The speed and magnitude of the sell-off have been particularly notable given the strong performance leadership that Momentum had exhibited throughout the first half of the year.

Prior to the reversal, Momentum was the best-performing style across most major regions; however, the sharp correction during June and July has erased the vast majority of those gains in a matter of weeks, underscoring both the crowded nature of the trade and the severity of the subsequent de-risking (Figure 2)

Figure 1. YTD Style Performance - Leadership rotates from Momentum to Value — Figure 1YTD Style Performance - Leadership rotates from Momentum to Value

Figure 2. World - Momentum reversal erases year-to-date gains — Figure 2World - Momentum reversal erases year-to-date gains

The impact has been particularly acute within EM equities, where AC Asia ex-Japan Momentum has undergone a significant de-rating following an extended period of outperformance (Figure 3), Importantly, the correction has been far from uniform. Korea and Taiwan, both key beneficiaries of the AI-driven equity leadership cycle, have experienced disproportionately large drawdowns, with Korea declining roughly 48% from its late-June peak and Taiwan falling approximately 29% from its early-July high. In contrast, most other regional markets have seen only relatively contained pullbacks. Consistent with previous episodes of Momentum stress, the most severe adjustments have occurred within segments that had generated the strongest prior returns, highlighting the extent to which performance leadership had become concentrated in a narrow set of AI and technology-related exposures.

Figure 3. AC Asia-ex Japan country momentum, highlights the extreme sell-off witnessed — Figure 3AC Asia-ex Japan country momentum, highlights the extreme sell-off witnessed

Figure 4. World – Price Mom. drawdown episodes — Figure 4World – Price Mom. drawdown episodes

Price Momentum – A comparison to previous drawdowns

The drawdown in Price Momentum (Figure 4), which began on 23 June, has already reached -19%, placing it among the more significant momentum corrections observed over the past three decades. Based on the historical record, the current episode ranks as the 7th largest momentum drawdown and comparable in magnitude to the sharp reversal experienced in late 2022, and only modestly smaller than the pandemic-era momentum unwind of June 2020 (-23%).

Notably, the sell-off has unfolded over just 28 trading days, highlighting the speed with which leadership has rotated away from the momentum factor. While the drawdown remains well below the severe factor crashes associated with major regime shifts, such as 1998, 2009, or the 2002-04 reversal episodes where momentum losses exceeded 40%, the pace of the current move is consistent with previous periods in which crowded winners rapidly underperformed amid improving risk sentiment and renewed investor appetite for cyclicals and valuation-sensitive stocks.

From a historical perspective, the key distinction is that today's correction appears deeper than a typical factor pullback but not yet large enough to qualify as a full-scale momentum crash. Previous episodes exceeding 40% generally coincided with major macro inflection points and sustained factor leadership changes, whereas drawdowns in the 15-25% range have often represented violent but ultimately temporary resets in positioning.

The current decline resides somewhere between these two junctures, either it develops into a broader style rotation towards Value and cyclicals, or it proves to be another sharp unwinding of crowded momentum exposures before the factor reestablishes leadership.

Alongside the weakness seen in Price Momentum, Low Risk rebounded, as both stock and style volatility rose significantly in recent weeks (Figure 6, Figure 8). The degree of recent volatility on both style, industry, stock returns has been considerable with July MTD returns largely overshadowing the cumulative YTD performance (Figure 1).

Figure 5. World - Pairwise style return correlation continues to fall — Figure 5World - Pairwise style return correlation continues to fall

Figure 6. World - Style dispersion sharply rises, but less extreme than previous peaks — Figure 6World - Style dispersion sharply rises, but less extreme than previous peaks

Figure 7. World – Stock level pairwise correlation returning to levels last seen in Dec 2017 — Figure 7World – Stock level pairwise correlation returning to levels last seen in Dec 2017

Figure 8. World – Stock return dispersion rises sharply briefly exceeding pandemic levels — Figure 8World – Stock return dispersion rises sharply briefly exceeding pandemic levels

The evidence extends beyond the sharp divergence between Value and Momentum style returns and is increasingly visible in the underlying market structure. Style return dispersion has risen materially while cross-style return correlations have fallen, indicating a widening gap between winning and losing factor exposures.

Concurrently, stock-level dispersion has increased, and stock correlations have declined towards near long-term lows (Figure 7), signalling that differentiation is broadening within the equity universe rather than remaining confined to a narrow set of crowded trades.

Historically, such environments have been associated with periods of sustained leadership change, where capital is reallocated across investment styles and market segments. The strong and persistent outperformance of Value across regions, combined with the breadth of the Momentum reversal, therefore argues for a developing rotation regime rather than a temporary positioning reset standalone.

The July (Figure 9) correction in Price Momentum intensified across all major regions, extending the sharp reversal highlighted by the recent Developed World momentum drawdown. At the quintile level, Momentum has been the weakest style globally, with losses ranging from -13% in Europe to -28% in AC Asia ex-Japan. Pure style results (Figure 10) tell a similar story, with momentum generating negative returns across every region even after controlling for sector, country, and other style exposures, suggesting the sell-off reflects a genuine factor unwind rather than simply changing regional or sector leadership.

Figure 9. July MTD Value and Low Risk return to the fore — Figure 9July MTD Value and Low Risk return to the fore

Figure 10. Pure style exposures offered a limited hedge against momentum decline — Figure 10Pure style exposures offered a limited hedge against momentum decline

A rotation or a correction?

Beyond Momentum, the key market theme has been an on-going rotation into Value, which generated positive returns across every region and was particularly strong in Asia, Japan, EM, and the US. Low Risk also posted robust gains, especially in Japan and the US, while Growth and Size (large caps) generally lagged. Quality was more mixed across regions.

While quintile portfolios exhibited larger moves than pure factors, reflecting the contribution from sector, country and correlated style exposures, the direction of returns was highly consistent across both frameworks. Momentum remained sharply negative and Value strongly positive in every major region even after orthogonalisation, with the recent performance pointing towards style rotation rather than simply a by-product of market composition effects.

The persistence of these signals in the pure factors points to a broad-based unwind of Momentum and a meaningful re-rating of Value across global equity markets.

Figure 11. Momentum long/short component breakdown, weakness in longs have also followed a rally in high beta “losers” rising once again — Figure 11Momentum long/short component breakdown, weakness in longs have also followed a rally in high beta “losers” rising once again

Losses across styles were tilted towards longs for EM and AC Asia-ex Japan, while DM short momentum stocks gained strongly, providing clearer evidence of a crash across most regions, but regional long/short breakdown also suggests that two different events are taking place, with DM momentum more clearly driven by more closely aligned contributions from the long and short side.

The long-short decomposition suggests the recent momentum drawdown is best characterised as a developing rotation rather than a full-blown momentum crash. In the US and World universes, much of the weakness has been driven by a combination of falling momentum winners and a sharp rebound in prior losers, consistent with the early stages of a Value-led rotation.

Outside developed markets, however, the drawdown has been driven predominantly by weakness in the long portfolio, with only limited support from the short cohort. This suggests investors are primarily reducing exposure to crowded momentum winners rather than aggressively reallocating into former laggards. Taken together, the evidence points to a broad correction in momentum leadership, with the US displaying a clearer sign of a genuine style rotation while EM and Asia remain closer to a positioning-led unwind.

Equity Market Positioning: It’s coming home

Elevated crowding risk amplified the sell-off. The positive momentum tech sector

showed up in our stock-level crowding screens see Measuring the Crowded Trade in Global Equities - Technology remains among top crowded sectors globally. This is illustrated for the US in Figure 12, which shows returns and long crowding scores by sector for July. Tech and communications services show up as the most crowded and saw the sharpest moves down. The least crowded (and defensive) consumers staples sector has positive performance. Energy names look crowded, but the sector benefitted from the jump in oil prices on increased geopolitical risk.

Figure 12. Crowded sectors have underperformed in the US in July with the exception of energy as geopolitical risks flared — Figure 12Crowded sectors have underperformed in the US in July with the exception of energy as geopolitical risks flared

Asia ex Japan crowding risk has declined whereas the US remains high. Turning to factors we see the crowding risk show up clearly when aggregating crowding scores by factor. Crowding scores are elevated on the long-side in US Price Mom whereas they have declined in Asia ex JP. There is also support for the value rotation-thesis potential being stronger in developed markets like the US. We find more crowded names tending to show up on the short side (Figure 15) whereas in Asia ex JP the picture is more mixed, as shown in Figure 16.

Figure 13. The long side of US Price Mom has elevated crowding scores… — Figure 13The long side of US Price Mom has elevated crowding scores…

Figure 14. …as does Asia ex JP albeit crowding has been declining recently — Figure 14…as does Asia ex JP albeit crowding has been declining recently

Figure 15. Crowded stocks tend to be on the short-side of the US value factor — Figure 15Crowded stocks tend to be on the short-side of the US value factor

Figure 16. Whereas Asia ex JP Value crowding is more balanced — Figure 16Whereas Asia ex JP Value crowding is more balanced

It's been coming home. Our equity markets positioning model shows a selective rebuild in Europe where net positioning was short and declines in long positioning in Korea and the Nasdaq, the report shows Nikkei longs have also declined. In Korea, financial authorities introduced new regulations aimed at single-stock leveraged ETFs to curb speculation.

Figure 17. Long Nasdaq (NQ) positions have been sold… — Figure 17Long Nasdaq (NQ) positions have been sold…

Figure 18. …as have KOSPI 200 (KM) — Figure 18…as have KOSPI 200 (KM)

Style Recommendations

Notwithstanding the recent underperformance in Growth, we retain a constructive medium to long-term view on the factor. While the sharp outperformance of Value (a near-term tactical preference we previously flagged) and the associated increase in style dispersion suggest that a meaningful leadership transition may be underway, we believe it remains premature to conclude that the market is entering a sustained Value-led regime.

Instead, our preferred exposure continues to be Growth, with a clear bias towards measures that reward realised earnings. In our view, companies exhibiting demonstrable earnings growth remain best positioned to capture the secular opportunities arising from ongoing AI adoption, digital infrastructure investment and productivity-enhancing technologies. These themes underpin our favourable fundamental backdrop for selected Growth cohorts.

We are inclined to view the recent Momentum drawdown as a potential reset rather than the end of the factor's cycle. While the breadth of recent Value outperformance, suggests the style is beginning to benefit from a rotation in market leadership rather than a purely technical rebound, given the strength of the secular earnings backdrop supporting selected Growth franchises, we continue to view the current environment as one of tactical Value strength within a longer-term framework that remains supportive of Growth (more so with several former growth leader potentially looking increasingly appealing for Value investors) and ultimately, a re-established Momentum regime.

Figure 19. Current Style Recommendations — Figure 19Current Style Recommendations

Developed Markets

Developed Markets: Factor Performance and Volatility

Figure 20. Factor Performance and Volatility — Figure 20Factor Performance and Volatility

Developed World: Last Month’s Style Leaders and Laggards

Figure 21. Performance Spread Between High (Top 20%) and Low (Bottom 20%), and Pure Factor Portfolios, Last Month — Figure 21Performance Spread Between High (Top 20%) and Low (Bottom 20%), and Pure Factor Portfolios, Last Month

Note: That Quantile performance refers to the spread of returns between the top and bottom quintile of styles, while the Pure performance refers to style performance where other sources of risk exposure such as Country, Sector and other style exposure have been removed. Baskets with less than 5 stocks have been removed. See Appendix for more information.

Developed World: LTM Leaders and Laggards

Figure 22. Performance Spread Between High (Top 20%) and Low (Bottom 20%), and Pure Factor Portfolios, LTM — Figure 22Performance Spread Between High (Top 20%) and Low (Bottom 20%), and Pure Factor Portfolios, LTM

Developed World: Macro Factor Sensitivities1: Regional

Figure 23. GDP Weighted Global Bond Yield (G10) — Figure 23GDP Weighted Global Bond Yield (G10)

Figure 25. Commodities (GSCI) — Figure 25Commodities (GSCI)

Figure 26. EUR per USD — Figure 26EUR per USD

Figure 27. YEN per USD — Figure 27YEN per USD

Figure 28. Emerging Market Sovereign Bond Yield — Figure 28Emerging Market Sovereign Bond Yield

Figure 29. Credit Spreads — Figure 29Credit Spreads

Figure 30. Market (MSCI AC World) — Figure 30Market (MSCI AC World)

Developed World: Macro Factor Sensitivities2: Styles

Figure 31. GDP Weighted Global Bond Yield (G10) — Figure 31GDP Weighted Global Bond Yield (G10)

Figure 33. Commodities (GSCI) — Figure 33Commodities (GSCI)

Figure 34. EUR per USD — Figure 34EUR per USD

Figure 35. YEN per USD — Figure 35YEN per USD

Figure 36. Emerging Market Sovereign Bond Yield — Figure 36Emerging Market Sovereign Bond Yield

Figure 37. Credit Spreads — Figure 37Credit Spreads

Figure 38. Market (MSCI AC World) — Figure 38Market (MSCI AC World)

Developed World: Relative Style Valuations

Figure 39. Estimates Momentum — Figure 39Estimates Momentum

Figure 44. Price Momentum — Figure 44Price Momentum

Developed World: Net Sector Weights

Figure 51. Price Momentum — Figure 51Price Momentum

Figure 52. Estimates Momentum — Figure 52Estimates Momentum

Emerging Markets

Emerging Markets: Factor Performance and Volatility

Figure 53. Factor Performance and Volatility — Figure 53Factor Performance and Volatility

Emerging Markets: Last Month’s Style Leaders and Laggards

Figure 54. Performance Spread Between High (Top 20%) and Low (Bottom 20%), and Pure Factor Portfolios, Last Month — Figure 54Performance Spread Between High (Top 20%) and Low (Bottom 20%), and Pure Factor Portfolios, Last Month

Emerging Markets: LTM Leaders and Laggards

Figure 55. Performance Spread Between High (Top 20%) and Low (Bottom 20%), and Pure Factor Portfolios, LTM — Figure 55Performance Spread Between High (Top 20%) and Low (Bottom 20%), and Pure Factor Portfolios, LTM

Emerging Markets: Macro Factor Sensitivities3: Countries/Regions

Figure 56. GDP Weighted Global Bond Yield (G10) — Figure 56GDP Weighted Global Bond Yield (G10)

Figure 58. Commodities (GSCI) — Figure 58Commodities (GSCI)

Figure 59. EUR per USD — Figure 59EUR per USD

Figure 60. YEN per USD — Figure 60YEN per USD

Figure 61. Emerging Market Sovereign Bond Yield — Figure 61Emerging Market Sovereign Bond Yield

Figure 62. Credit Spreads — Figure 62Credit Spreads

Figure 63. Market (MSCI AC World) — Figure 63Market (MSCI AC World)

Emerging Markets: Macro Factor Sensitivities4: Styles

Figure 64. GDP Weighted Global Bond Yield (G10) — Figure 64GDP Weighted Global Bond Yield (G10)

Figure 66. Commodities (GSCI) — Figure 66Commodities (GSCI)

Figure 67. EUR per USD — Figure 67EUR per USD

Figure 68. YEN per USD — Figure 68YEN per USD

Figure 69. Emerging Market Sovereign Bond Yield — Figure 69Emerging Market Sovereign Bond Yield

Figure 70. Credit Spreads — Figure 70Credit Spreads

Figure 71. Market (MSCI AC World) — Figure 71Market (MSCI AC World)

Emerging Markets: Relative Style Valuations

Figure 72. Estimates Momentum — Figure 72Estimates Momentum

Figure 77. Price Momentum — Figure 77Price Momentum

Emerging Markets: Net Sector Weights

Figure 84. Price Momentum — Figure 84Price Momentum

Figure 85. Estimates Momentum — Figure 85Estimates Momentum

US: Factor Performance and Volatility

Figure 86. Factor Performance and Volatility — Figure 86Factor Performance and Volatility

US: Last Month’s Style Leaders and Laggard

Figure 87. Performance Spread Between High (Top 20%) and Low (Bottom 20%), and Pure Factor Portfolios, Last Month — Figure 87Performance Spread Between High (Top 20%) and Low (Bottom 20%), and Pure Factor Portfolios, Last Month

US: LTM Leaders and Laggards

Figure 88. Performance Spread Between High (Top 20%) and Low (Bottom 20%), and Pure Factor Portfolios, LTM — Figure 88Performance Spread Between High (Top 20%) and Low (Bottom 20%), and Pure Factor Portfolios, LTM

US: Macro Factor Sensitivities5: Sectors

Figure 89. GDP Weighted Global Bond Yield (G10) — Figure 89GDP Weighted Global Bond Yield (G10)

Figure 91. Commodities (GSCI) — Figure 91Commodities (GSCI)

Figure 92. EUR per USD — Figure 92EUR per USD

Figure 93. YEN per USD — Figure 93YEN per USD

Figure 94. Emerging Market Sovereign Bond Yield — Figure 94Emerging Market Sovereign Bond Yield

Figure 95. Credit Spreads — Figure 95Credit Spreads

Figure 96. Market (MSCI AC World) — Figure 96Market (MSCI AC World)

US: Macro Factor Sensitivities6: Styles

Figure 97. GDP Weighted Global Bond Yield (G10) — Figure 97GDP Weighted Global Bond Yield (G10)

Figure 99. Commodities (GSCI) — Figure 99Commodities (GSCI)

Figure 100. EUR per USD — Figure 100EUR per USD

Figure 101. YEN per USD — Figure 101YEN per USD

Figure 102. Emerging Market Sovereign Bond Yield — Figure 102Emerging Market Sovereign Bond Yield

Figure 103. Credit Spreads — Figure 103Credit Spreads

Figure 104. Market (MSCI AC World) — Figure 104Market (MSCI AC World)

US: Style Sector Composition

Figure 105. Estimates Momentum — Figure 105Estimates Momentum

Figure 108. Low Risk — Figure 108Low Risk

Figure 110. Price Momentum — Figure 110Price Momentum

US:

Figure 112. Estimates Momentum — Figure 112Estimates Momentum

Figure 115. Low Risk — Figure 115Low Risk

Figure 117. Price Momentum — Figure 117Price Momentum

US: Net Sector Weights

Figure 121. Low Risk — Figure 121Low Risk

Figure 124. Price Momentum — Figure 124Price Momentum

Figure 125. Estimates Momentum — Figure 125Estimates Momentum

Europe

Europe: Factor Performance and Volatility

Figure 126. Factor Performance and Volatility — Figure 126Factor Performance and Volatility

Europe: Last Month’s Style Leaders and Laggards

Figure 127. Performance Spread Between High (Top 20%) and Low (Bottom 20%), and Pure Factor Portfolios, Last Month — Figure 127Performance Spread Between High (Top 20%) and Low (Bottom 20%), and Pure Factor Portfolios, Last Month

Europe: LTM Style Leaders and Laggards

Figure 128. Performance Spread Between High (Top 20%) and Low (Bottom 20%), and Pure Factor Portfolios, LTM — Figure 128Performance Spread Between High (Top 20%) and Low (Bottom 20%), and Pure Factor Portfolios, LTM

Europe: Macro Factor Sensitivities7: Sectors

Figure 129. GDP Weighted Global Bond Yield (G10) — Figure 129GDP Weighted Global Bond Yield (G10)

Figure 130. Commodities (GSCI) — Figure 130Commodities (GSCI)

Figure 131. Commodities (GSCI) — Figure 131Commodities (GSCI)

Figure 132. EUR per USD — Figure 132EUR per USD

Figure 133. YEN per USD — Figure 133YEN per USD

Figure 134. Emerging Market Sovereign Bond Yield — Figure 134Emerging Market Sovereign Bond Yield

Figure 135. Credit Spreads — Figure 135Credit Spreads

Figure 136. Market (MSCI AC World) — Figure 136Market (MSCI AC World)

Europe: Macro Factor Sensitivities8: Styles

Figure 137. GDP Weighted Global Bond Yield (G10) — Figure 137GDP Weighted Global Bond Yield (G10)

Figure 139. Commodities (GSCI) — Figure 139Commodities (GSCI)

Figure 140. EUR per USD — Figure 140EUR per USD

Figure 141. YEN per USD — Figure 141YEN per USD

Figure 142. Emerging Market Sovereign Bond Yield — Figure 142Emerging Market Sovereign Bond Yield

Figure 143. Credit Spreads — Figure 143Credit Spreads

Figure 144. Market (MSCI AC World) — Figure 144Market (MSCI AC World)

Europe: Style Sector Composition

Figure 145. Estimates Momentum — Figure 145Estimates Momentum

Figure 148. Low Risk — Figure 148Low Risk

Figure 150. Price Momentum — Figure 150Price Momentum

Europe: Relative Style Valuations

Figure 152. Estimates Momentum — Figure 152Estimates Momentum

Figure 155. Low Risk — Figure 155Low Risk

Figure 157. Price Momentum — Figure 157Price Momentum

Europe: Net Sector Weights

Figure 161. Low Risk — Figure 161Low Risk

Figure 164. Price Momentum — Figure 164Price Momentum

Figure 165. Estimates Momentum — Figure 165Estimates Momentum

The first step involves the identification of the most important systematic drivers of risk and return across global markets over the long term. Using results from the extensive style performance research published by the Citi Global Quantitative Research team together with empirics documented within the Academic literature we arrive at the following styles: Size, Value, Growth, Low Risk, Quality, Price Momentum, and Estimates Momentum.

For each style factor, we then select a list of descriptors that best represent that specific attribute. For example, we use a range of defensive and cyclical price-based ratios to describe the Value attribute. These descriptors are then combined to arrive at a style factor loading for each stock in a given MSCI universe.

Style Descriptors

Stock universes are based on MSCI indices, and we have a complete history of styles/factors back to 1995. Figure 159 lists the styles that we cover together with the descriptors used in the construction of each index. One notable absence from our style classification is GARP. We chose not to include this style because as a distinct style, this could be constructed from combining Value and Growth.

Figure 166. Style Factors and Descriptors — Figure 166Style Factors and Descriptors

When building our style factor loading, we start by winsorizing the descriptor data to eliminate outliers. After this we normalise this data and combine it on an equal weighted basis to form the style composite factor.

Calculation of Raw Style Performance

We calculate raw style performance using the standard factor mimicking approach. In each universe stock are ranked using each composite

Construction of Pure Style Indices

For a point in time, given the style factor loadings, country/sector membership dummies and our desired orthogonal style exposures, we then employ a simple matrix inversion to compute a set of orthogonal style factor portfolios. The last step involves a simple linear combination of the monthly style factor portfolios with the next-period returns of each constituent stock measured over a monthly or daily periodicity to generate an index of style returns. The result is that each index has a unit exposure to any one style and zero exposure to all other styles, at the time of the monthly rebalance.

Calculating the Style Betas

In order to calculate the betas, we are effectively constructing the style portfolios. Following this, the style portfolio exposures are function of the style loadings and their corresponding betas. In matrix notation (simplified version):

Y = B′F

Where (the equation above is contemporaneous, hence ignoring the time subscript):

Y= matrix (m,m) factor portfolio exposures;

B = matrix (n,m) of style portfolio weights (betas); F = matrix (n,m) stock exposures to style/country/sectors; n = number of stocks; m = number of styles, country and sectors.

Given our desire for set of linearly independent style portfolios,Ycan take the form

of an identity matrix, F is our style factor loadings so we are therefore solving for

B = ((F′F)⁻¹F′)Y

The result of B is a set of stock level weights (or betas) for each style that multiplied with the style factor loadings produces orthogonal style exposures9. Or in other words, each style portfolio has a unit exposure to itself and zero exposure to all other styles.

Construction of Style Return Indices

As part of the construction of the style portfolio exposures, at a point in time, we are left with a set of style portfolios and their corresponding long-short stock weights. Bringing this part of the style index construction to return space (i.e., the B matrix), we assume that cross-sectional stock returns over any period can be expressed with the following equation:

Pₜ = Rₜ′ Bₜ₋₁ Where:

Pₜ = a row vector (1,m) of pure style portfolio returns from time t−1 to time t

Rₜ = a column vector (n,1) of stock returns from time t−1 to t

Bₜ₋₁ = matrix (n,m) of style portfolio weights formed at time t−1

Given we know Rₜ and we have calculated Bₜ₋₁ , the product of the these two

matrices is Pₜ , the return of each pure systematic factor (in total, m) at time t.

Most of the style descriptors we use are self-explanatory. Data is primarily sourced from either Worldscope or Thomson IBES. However, there are some style descriptors that warrant further explanation:

S&P Global BMI Growth-Value Score , this is a score between 0 (pure value) and 1 (pure growth) is assigned to each stock and is calculated by S&P. For more information on the methodology that is employed to calculate the score, please see refer to S&P on methodology.

Earnings Stability , calculated as the R-squared from a regression of five annual EPS values (three historical and two forecast) against a time trend. (For more details, see our report Searching for Alpha: Focus on Earnings Stability, Citi Research, February 2003.

Price Momentum , for each respective daily time period, price momentum is calculated as the t-statistic of the slope coefficient, derived from a regression of the log of daily prices (in local currency) on a time trend.

Earnings, Sales, Cash Revisions , this is the time-weighted average of analyst upgrades less downgrades scaled by the total number of estimates for fiscal years 1 and 2.

Earnings Certainty , measured as the inverse of the coefficient of variation in the next 12-month EPS estimates (stocks are excluded if there are less than five estimates or EPS is less than one cent). This is the same as the inverse of our EPS dispersion measure and more detail can be found in Searching for Alpha: Sell When Analysts Disagree, Citi Research, December 2003.

Earnings Quality , calculated as the year-on-year change in net operating assets or the difference between accounting and cash earnings (accruals). For more details, see our reports. Searching for Alpha - Accruals Volatility – A New Approach to Quality Investing, Searching for Alpha: Quantifying Earnings Quality, Citi Research, October 2004.

Balance Sheet Quality , this is the level of net operating assets. NOA incorporates all the changes in NOA and can be used as proxy for cumulated accruals. Since accumulation of earnings without cash flow is unsustainable in the long term, having high net operating assets is a sign of balance sheet bloat. For more details, Searching for Alpha: Quantifying Earnings Quality, European Quantitative Strategy, October 2004.