·Standard & Poor's is considering float adjustment of its U.S. indices. This document is a concept paper. No index policy changes are being made now.
· The term 'float adjustment' has become a popular catchphrase as most major indices moved toward this concept in the last three years. Unfortunately, there has been very little critical analysis on how float adjustment fits into the conceptual design and purpose of indices.
· The basic argument for float adjustment is investability. However, the issue of investability is already captured by Standard & Poor's multivariate indexing process. Potential additions have to meet explicit criteria concerning liquidity and public float to be eligible for index admission.
· Float adjustment would not affect the structure of Standard & Poor's U.S. indices, nor would it amend their risk profiles or sector compositions. There would be no improvement in liquidity of the index portfolio. Overall, float adjustment causes little practical change in index properties.
· There are three types of float adjustments: adjustments for investment regulations, adjustments for cross-holdings, and adjustments for strategic holdings.
· Adjustments for investment regulations are not an issue for U.S. equities. Cross-holding adjustments prevent double counting and are conceptually justified. However, strategic-holding adjustments do not fit into the conceptual purpose of indices of being accurate measures of the market. They also introduce agency friction and distortions in asset allocation.
· Standard & Poor's is considering two refinements to its U.S. index methodology.
1) The public float requirement for additions to the S&P MidCap 400 and S&P SmallCap 600 would be raised to 50%. S&P 500 additions already require minimum public floats of 50%. Existing S&P U.S. index constituents that have a public float of less than 50% would not be affected by this change.
2) Shares of its U.S. index constituents having cross-holdings greater than 10% would be reduced, in bands of 10%.
· Based on September 2003 index composition, only four companies in the S&P 500 and nine companies in the S&P Composite 1500 would be affected by this proposal, resulting in small additional turnover of 0.6% and 0.7%, respectively. There would be no impact on the S&P MidCap 400 or S&P SmallCap 600.
The term 'float adjustment' has become a popular catchphrase among those who deal with indices. Ever since the International Finance Corporation (IFC) started adjusting the market capitalization of stocks in its emerging market indices for cross-holdings, strategic holdings by governments and public sector undertakings, and investment restrictions imposed on foreign investors, virtually all index providers have adopted this in some form for their indices. In the last three years, almost all indices, including Standard & Poor's non-U.S. indices, have been adjusted to reflect for available float. Standard & Poor's maintains that it is important to consider any index policy, including float adjustment, from the perspective of how it fits into the conceptual design and purpose of indices.
In this report, we explain the three different kinds of float adjustment. We discuss how Standard & Poor's U.S. index criteria address the issue of float. We then review the practical and theoretical relevance of float adjustment. We explain the difference between U.S. and non-U.S. markets as it pertains to this issue. We also describe proposals for two enhancements to be made to Standard & Poor's U.S. index methodology, and discuss their rationales and impacts. Standard & Poor's will widely consult market participants on these proposals, and will give sufficient notice before announcing any changes in methodology.
Types of Float Adjustment
There are three types of float adjustment.
Float adjustment for investment regulations
In some countries, private investors are not allowed to hold more than a certain percent of stocks in some sectors. Ceilings might also exist for foreign investors. These restrictions do not exist in the U.S.
Float adjustment for strategic holdings
These adjustments involve reducing the market capitalization of a company by the amount held by investors deemed as strategic. These include holdings by officers and directors, founders, and employees, and controlling positions held by private individuals and trusts. In some countries, the government or a quasi-government entity might hold a significant portion of a company, though this is not the case with the U.S. public companies.
Float adjustment for cross-holdings
These adjustments involve reducing the market capitalization of a company by the amount held by other companies in the index. This prevents double counting of that portion of shares of an index constituent held by another index constituent.
In subsequent sections, we will examine the conceptual arguments for strategic-holding adjustments and cross-holding adjustments.
Standard & Poor's U.S. Index Criteria and the Issue of Float
Current addition criteria
- U.S. companies
- Adequate liquidity and reasonable price (the ratio of annual dollar value traded to market capitalization should be 0.3 or greater; very low stock prices can affect a stock's liquidity)
- Market capitalization of $3 billion or more for the S&P 500, $900 million to $3 billion for the S&P MidCap 400, and $250 million to $900 million for the S&P SmallCap 600 (ranges are reviewed from time to time to assure consistency with market conditions)
- Financial viability, usually measured as four consecutive quarters of positive as-reported earnings, which are GAAP net income excluding discontinued operations and extraordinary items
- Public float of at least 50% of a company's total shares outstanding for the S&P 500, and at least 40% for the S&P MidCap 400 and S&P SmallCap 600
- Maintenance of sector balance for each index as measured by a comparison of the GICS sectors in each index and in the market in the relevant market capitalization ranges
- Operating companies and not closed-end funds, holding companies, partnerships, investment vehicles or royalty trusts; Real Estate Investment Trusts are eligible for inclusion in Standard & Poor's U.S. indices
Current deletion criteria
- Companies involved in mergers, being acquired, or significantly restructured such that they no longer meet addition criteria
- Companies that substantially violate one or more of the addition criteria
Standard & Poor's believes that unnecessary and excessive turnover in any given index should be avoided. At times, a constituent may temporarily violate one or more of the addition criteria. However, these criteria qualify a company's viability with respect to gaining admission, not retention of admission once obtained. As a result, an index component that appears to violate the criteria for addition to that index will not be deleted unless ongoing conditions warrant an index change. When a company is removed from an index, Standard & Poor's will explain the basis for the removal.
The issue of float is captured in index criteria
The key rationale supporting float adjustments is investability of the index. This is already addressed by the multivariate criteria used for Standard & Poor's U.S. indices. Specifically, there is a 30% liquidity ratio and a minimum public float requirement for additions to an index. As part of ongoing index maintenance, companies have been removed from indices for reasons of low liquidity or public float.
Float Adjustment Has No Practical Impact on Properties of S&P U.S. Indices
In this section, we will consider the relevance of float-adjusting Standard & Poor's U.S. indices, specifically with respect to resultant changes in liquidity, index structure, sector distribution and risk profile.
Index structure would not change
Float adjustment reduces market capitalization of different stocks by different amounts, and might therefore alter index structure. Exhibits 1, 2 and 3 show the top 30 stocks in the S&P 500, S&P MidCap 400 and S&P SmallCap 600 if those indices were float-adjusted. The ranks of those stocks in the normal, float-unadjusted indices are also shown. As can be observed from the exhibits, the top stocks in the float-unadjusted index largely remain the top stocks in the float-adjusted indices.
To better capture the change in relative weights in the full list of index constituents, we plot the ranks of stocks in each index versus the ranks of the stocks in float-adjusted versions of those indices. These are shown in Exhibits 4, 5 and 6. In aggregate, the plots take the form of a straight, upward sloping line with a 45-degree angle to the X-axis. This indicates that, despite a few individual stocks being affected, in general the ranks of stocks in the float-adjusted index for constituent stocks remain largely in line with ranks in the current index. This is also borne out by the fitted line.
Another aspect of index composition is concentration of individual stocks in the index. Market capitalization-weighted indices, by their very nature, have a few stocks capturing a large percent of index weight. Float adjustment would be welcome if it could reduce concentration of indices. However, as Exhibits 4, 5 and 6 show, float adjustment causes very little change in index concentration.
Index liquidity is not improved
Standard & Poor's indices are among the most liquid and tradable indices in their capitalization segments. Index liquidity is important from the perspective of managing portfolio inflows and outflows, reducing tracking error and keeping transaction costs at a minimum. The primary argument for float adjustment is to improve the liquidity and investability of an index. Therefore, we should compare the liquidity of float-adjusted and normal versions of Standard & Poor's U.S. indices.
First, we consider the liquidity of individual stocks in the index. To do this, we show the numbers of index constituents that become unavailable as attempts are made to turn around a passively indexed portfolio in a single day. Unavailability is defined as trade size exceeding average daily volume. This provides a market capitalization-adjusted measure for the number of less-liquid stocks in the index. The results are shown in Exhibit 10. It can be observed that the float-adjusted indices have very little to add in terms of improving liquidity at the stock level.
To be an appropriate fungible benchmark, an index should facilitate the linking of a large amount of assets to it. There can be various instruments linked to an index, namely futures, exchange-traded funds (ETFs) and passive funds. A large amount of funds linked to an index reinforces its position as an accepted benchmark. Furthermore, a liquid index helps support an active market in futures and ETFs of an index and its sub-components, which provide a convenient and efficient way to buy an index while presenting more crossing opportunities.
The liquidity of an index portfolio may be gauged by showing what percentage of the portfolio becomes unavailable for trade as the size of trade in index-linked assets increases. The results are shown in Exhibits 11, 12 and 13. These exhibits, which compare the normal and float-adjusted versions of the S&P 500, S&P MidCap 400 and S&P SmallCap 600, can be construed as a representation of tracking error versus trade size, given a time constraint. It can be seen that the plots of normal and float-adjusted indices are virtually indistinguishable, showing that float adjustment of Standard & Poor's U.S. indices would not improve liquidity of the index portfolios.
The reason for the inability of float adjustment to contribute liquidity at the individual constituent level or index portfolio level is clear. As we have noted before, liquidity and availability of public float are explicitly included in Standard & Poor's index inclusion criteria. These criteria exclude illiquid stocks, or stocks with very low floats, in which case where float adjustment could improve liquidity.
Risk profile remains unchanged
If the risk profile of the current S&P 500 (or S&P MidCap 400 or S&P SmallCap 600) index portfolio differs from the risk profile of its float-adjusted version, then the two portfolios are measuring different investment opportunity sets. Therefore, we should compare the risk profile of float-adjusted versions of the indices with the current versions.
Fundamental risk factor models use security returns and security characteristics to arrive at fundamental risk exposures based on cross-sectional regressions. The Barra risk model is a commonly used risk decomposition model.
Exhibits 14, 15 and 16 show the risk decomposition and risk index exposures for current and float-adjusted versions of the S&P 500, S&P MidCap 400 and S&P SmallCap 600, respectively. The first part is the decomposition of total risk into explained common factor risk and specific risk. Further, common factor risk is a combination of risk explained by industries and by risk indices. The second part of the exhibits shows risk index exposures, which are sensitivities to shared attributes computed on a monthly basis by combining fundamental and market data. The average stock in the estimation universe has an exposure of zero. The risk index exposure value for each index is the capitalization-weighted average exposure for all of the index constituents.
From the exhibits, it can be seen that there are marked differences in risk decomposition results and risk index exposures of the S&P 500, S&P MidCap 400 and S&P SmallCap 600. However, risk decomposition results and risk index exposures between current and float-adjusted versions of each index are remarkably similar. This suggests that float adjustment would lead to little, if any, difference in risk profile of existing indices.
Sector composition is unaltered
Finally, we compare the sector composition of current and float-adjusted indices. As seen from previous exhibits, sectors are an important component of the risk profile of an index. If the sector composition of an index portfolio differs from that of its float-adjusted version, then the two portfolios are measuring different investment opportunity sets as far as sector exposure is concerned.
Exhibit 17 shows the sector composition of normal and float-adjusted versions of the S&P 500, S&P MidCap 400 and S&P SmallCap 600. The exhibit shows sector weights in the normal and float-adjusted versions largely mirroring each other. Out of the 30 observations, only in three is the difference in sector weight greater than 0.5 percentage points.
Overall, float adjustment has little impact on index properties
From the discussion in this section, we have seen that float adjustment does not affect the structure of Standard & Poor's U.S. indices, nor does it amend the risk profile or sector composition of the indices. There is no improvement in liquidity because the inclusion criteria explicitly screen for float and liquidity. Overall, there is little practical basis for float adjustment. In the subsequent sections, we shall examine the conceptual case for adjustments for strategic holdings and cross-holdings.
Float adjustment would lead to high turnover
There would be one significant practical impact of float adjustment: it would cause one-time market capitalization turnover of 5.91% for the S&P 500, 11.08% for the S&P MidCap 400, 14.84% for the S&P SmallCap 600, and 7.45% for the S&P Composite 1500. This would entail significant transition costs for index managers, without any perceptible change in risk profile, liquidity, index structure, or sector composition. Also, as we shall see in the next section, strategic-holding adjustments would cause unnecessary turnover for long-term investors, in addition to turnover caused by immediate index changes.
Strategic Float Adjustment Does Not Suit the Conceptual Purpose of Indices
We have previously defined strategic holdings. In this section, we will look at the conceptual purpose of indices and investigate whether strategic float adjustment fits into it.
Indices should be accurate market barometers
Indices are, first and foremost, market barometers. They reflect a certain size or style of the market, or the total market. Both direct and indirect uses of an index follow from this function. Direct uses involve using index properties in statistical, economic or journalistic representation of the returns of the market, and in benchmarking performance of investment vehicles. Indirect uses involve trading the market using derivatives, or in owning the market through index funds.
Some suggest that adjusting for strategic holdings makes indices a better representation of market. However, the following arguments suggest to the contrary:
· Financial capital consists of equity and debt. As a market barometer, equity indices should reflect the changes in equity capital for the target portion of the market. The portion of capital held by 'strategic' investors is capital, and removing it from index calculation would distort the returns as a measure of equity capital. In fact, if one considers markets to be information-efficient, no adjustments are required. The presence of strategic holdings, and the prospects of their subsequent unloading, is captured in share prices and, consequently, the market capitalization of the company.
· The time horizon for an index is infinite, and an index should be able to accurately track movements in the market over long time horizons. The time horizon for most institutional investors, such as pension plans of going concerns, endowments and open-end mutual funds, is also infinite. Strategic holdings, however, are not of infinite time horizon. These holdings will change as strategic investors divest to diversify their portfolios, or invest elsewhere, or if the companies undergo restructuring. For example, Bill Gates' holdings in Microsoft fell from 26% in 1996 to 11% in 2003. The Roberts family's holdings of Comcast, 33% in 2000, dropped to less than 10% after the AT&T cable acquisition. Over long time horizons, most strategic holdings are not 'off the market.' In the limiting case of infinite time horizon, strategic holdings are very much part of the tradable equity capital of a country.
· Strategic-holding adjustments, as done in practice by most index providers, also impose additional distortions. Since it is extremely difficult, if not impossible, for index providers to find accurate strategic holdings for all stocks in the market, index providers' resort to reverse calculations. For example, with the Russell indices, companies are sorted on the basis of their full market capitalizations. The top 1000 go into the large-cap Russell 1000, while the bottom 2000 go into the small-cap Russell 2000. In 2003, this resulted in companies like Southern Peru Copper (PCU) and MEMC Electronic (WFR) going into the Russell 1000 from the Russell 2000 because their full market caps were $1.2 billion and $2.0 billion, respectively. However, once they got into the Russell 1000, float adjustments resulted in their index market caps being less than $300 million. Thus, they entered a large-cap index with small-cap market caps. The composition and returns of indices are distorted by such post-facto adjustment for strategic holdings.
These arguments are summarized in Exhibit 18.
Indices should serve as investment vehicles for market ownership
Ever since Sharpe and Markowitz suggested that the most efficient portfolio from a risk/reward perspective is the one that holds all stocks in the target market in proportion to their market value, index investment has been a popular vehicle of market ownership. Frictional costs and investability issues result in investors holding optimized portfolios that reflects the market, be it the S&P 500 for the large-cap U.S. market or a mathematically optimized portfolio of Russell 2000 stocks that seeks to replicate the small-cap market. However, these optimizations do not detract from the fact that the market value of a company is its full economic value, not just a portion of the company after reducing the economic value for portions deemed to be 'strategic holdings.' Index ownership should represent ownership in constituent companies in proportion to their economic worth, as reflected by the price discovery process in the share market. However, float adjustments for strategic holdings distort this - an investor ends up owning more of companies with lesser strategic holdings and less of companies with greater strategic holdings.
The issue of agency friction is also important. Ceteris paribus (ignoring liquidity and diversification needs), strategic shareholders will sell their stock at a time when they deem their company holdings less attractive than alternative investments. It is precisely at this time that a strategic float-adjusted index forces an investor to buy more of the company. This is depicted in Exhibit 19. Exhibit 20 summarizes the impact of strategic float adjustment on the goal of market ownership.
Indices should serve as accurate asset-allocation benchmarks
Investor portfolios do not necessarily consist solely of equities. They can also hold significant proportions of bonds, as well as alternative assets. A significant use of indices is in framing asset-allocation policy. For simplicity, let us consider an institution that owns only bonds and equities. Its gains from the bond portion are interest income and capital gains. Its gains from the equity portion are dividend income and capital gains. Bonds and equities represent ownership of debt and equity capital.
However, there is a significant difference when the institution's equity benchmark is adjusted for strategic holdings. In this case, while the bond portion will be ownership of liability of the entire bond-issuing entities, the equity portion of the portfolio will be ownership of only a fraction of the equity-issuing entities. Thus, there is a mismatch between the asset and liability ownership of an investor. Exhibit 21 explains this.
The simplest example of this is when one is holding stocks and bonds of a corporate entity. One might argue that significant proportions of the liability positions are not held in equity-issuing entities, but in government or quasi-government positions. However, if one takes a macroeconomic perspective and considers equity capital as ownership of productive capacity of the economy, this simple example can be generalized into the broad realm of all financial capital assets.
Indices should be investable
In essence, the major argument for float adjustment is investability. In order to be an efficient investment vehicle, as well as to support a market in derivatives, it should be possible to buy or sell all the stocks in the index in proportion to their index weights. Many single-variable indices simply sort stocks once every three to 12 months to arrive at size-based indices that might have constituents that are simply not liquid enough to buy. Therefore, these indices have to adjust for float to make them investable. Despite float adjustments, exceptions like Berkshire Hathaway crop up, which they address through one-off rules.
Standard & Poor's believes that a multivariate approach to index construction is more appropriate to address investability issues, rather than the institution of structural changes that would distorts an index's composition and returns. As we have noted above, liquidity and availability of public float are explicitly included in Standard & Poor's index inclusion criteria. Therefore, Standard & Poor's index constituents with significant strategic holdings (for example, Wal-Mart or Microsoft in the S&P 500, or Washington Post in the S&P MidCap 400) are still liquid enough to trade without difficulty.
Float Adjustments for Cross-Holdings Are Conceptually Justified
As defined before, cross-holding adjustments seek to prevent double counting of that portion of shares of an index constituent held by another index constituent. If cross-holding adjustments are not made, an index represents the cross-held portion of constituents twice over. Therefore, Standard & Poor's accepts the proposition that cross-holding adjustments are conceptually justified.
Proposed Refinements to Standard & Poor's U.S. Index Methodology
Standard & Poor's is considering two refinements to its U.S. index methodology. These are described below.
Public float requirement for S&P MidCap 400 and S&P SmallCap 600 additions
Standard & Poor's is considering raising the public float requirement for additions to the S&P MidCap 400 and S&P SmallCap 600 to 50%, from the current 40%. S&P 500 additions already require a minimum public float of 50%. When the S&P MidCap 400 and S&P SmallCap 600 were established in the early 1990s, most mid- and small-cap companies did not have a majority of their shares in public hands. However, Standard & Poor's has recently seen the availability of more companies that meet the more stringent 50% criterion.
The companies currently in the S&P Composite 1500 that have public floats of less than 50% would not be affected by this change. They would retain their index memberships unless ongoing conditions warranted changes. The list of companies with public floats of less than 50% appears in Appendix 1.
Standard & Poor's is also considering reducing shares of U.S. index constituents that are cross-held.
· Cross-holding adjustments would be made only for those index constituents that have more than 10% of their shares held by another index constituent(s).
· Shares of companies with cross-holdings would be adjusted in bands of 10%. The reduction in index shares would be the lesser multiple of 10%. For example, if an S&P 500 constituent has 17% of its shares held by another S&P 500 constituent, its shares would be reduced by 10%. In other words, its investable weight factor would be 90%. The 10% band should prevent unnecessary turnover caused by small changes.
· Changes for cross-holding adjustments would be made annually to coincide with one of the quarterly shares adjustments, which are typically done at the close of the third Friday of a quarter-ending month. Cross-holding adjustments would be announced on Index Alert, as well as at http://www.standardandpoors.com/.
· If a company being added to a U.S. index required a cross-holding adjustment, Standard & Poor's would announce the percent adjustment (or investable weight factor) at the time of the addition announcement.
Impact of cross-holding adjustment
To evaluate the impact of Standard & Poor's indices being adjusted for cross-holdings, we examined the turnover based on September 2003 index composition. There are only nine companies in the S&P Composite 1500 that have cross-holdings of more than 10%. These are shown in Exhibit 22.
All the cross-holding companies are in the S&P 500; therefore, no adjustments would be required to the S&P MidCap 400 and S&P SmallCap 600. In the S&P 500, four constituents would require adjustments, and in the S&P Composite 1500, nine constituents would require adjustments. These potential cross-holding adjustments are shown in Exhibit 23 on the next page.
These adjustments would cause a marginal one-time turnover. The market capitalization turnover associated with these changes would be 0.6% for the S&P 500 and 0.7% for the S&P Composite 1500. There would be no turnover for the S&P MidCap 400 or S&P SmallCap 600.
Standard & Poor's Global Indices
This proposed change pertains to Standard & Poor's U.S. indices only. Standard & Poor's non-U.S. indices would not be affected by any proposed change.
From a conceptual perspective, Standard & Poor's non-U.S. indices are float-adjusted to reflect the following facts:
1. Some countries might have regulations disallowing private investors to hold more than a certain percent of stocks in some sectors. Ceilings might also exist for foreign investors.
2. In some countries, the government or a quasi-government entity might hold a significant portion of a company.
3. Standard & Poor's non-U.S. indices do not have specific criteria addressing both minimum public float and liquidity limits for index eligibility. Most global markets also lack the liquidity associated with U.S. markets.
From a practical perspective, U.S. companies have a much higher degree of public float than non-U.S. companies. This is shown in Exhibit 24, which plots the average available float for different regional components of the S&P Global 1200.
The average available float in the U.S. is 94%. In contrast, the average available floats for large-cap companies in two of the largest non-U.S. markets, Europe and Japan, are 82% and 75%, respectively. These are even less than the average available floats for the S&P MidCap 400 and S&P SmallCap 600, which are 90% and 86%, respectively.
U.S. stocks also have greater liquidity among developed markets. Exhibit 25 shows the turnover of major global markets. As can be seen, turnover of U.S. stocks is higher than turnover in other major markets, indicating greater liquidity in the U.S. market.
In sum, Standard & Poor's indices attempt to balance market representation with investability, and full-float adjustments are necessary in most non-U.S. markets to make indices investable.
The term 'float adjustment' has become a popular catchphrase as most major indices moved toward this concept in the last three years. Unfortunately, there has been very little critical analysis of how float adjustment fits into the conceptual design and purpose of indices.
The basic argument for float adjustments is about investability. However, the issue of investability is already captured by Standard & Poor's multivariate index inclusion process. Potential additions have to pass minimum liquidity and public float requirements to be eligible for index admission. This is a far simpler solution to the issue of investability than making adjustments that introduce distortions in index composition and returns.
Float adjustment would not affect the structure of Standard & Poor's U.S. indices, nor would it amend their risk profiles or sector compositions. There would be no improvement in liquidity, since Standard & Poor's U.S. index inclusion criteria already address float and liquidity. Overall, there is little practical impact on index properties.
There are three types of float adjustments: adjustments for cross-holdings, adjustments for investment regulations and adjustments for strategic holdings. Adjustments for investment regulations are not an issue for U.S. equities. Cross-holding adjustments seek to prevent double counting of that portion of shares of an index constituent held by another index constituent, which is conceptually justified.
Adjustments for strategic holdings do not fit into the conceptual design and purpose of indices. Indices should serve as accurate market barometers. However, strategic float adjustment distorts the returns as a measure of equity capital. In fact, if one considers markets to be information-efficient, no adjustments are required. Strategic-holding adjustments introduce mismatches in the time horizons of indices and index investors. Most pension plans, funds, and endowments have infinite time horizons. Over long time horizons, most strategic holdings are not 'off the market.' Indices should serve as investment vehicles for market ownership, but float adjustments for strategic holdings distort this - an investor ends up owning more of companies with lesser strategic holdings and less of companies with greater strategic holdings. Strategic-holding adjustments also introduce agency friction into the index investing process.
Standard & Poor's is considering two enhancements to its index methodology. First, the public float requirement for additions to the S&P MidCap 400 and S&P SmallCap 600 would be raised to 50%. S&P 500 additions already require a minimum public float of 50%. Second, Standard & Poor's is considering reducing, in increments of 10%, shares of U.S. index constituents that have cross-holdings of greater than 10%. Only four companies in the S&P 500 and nine companies in the S&P Composite 1500 would be affected by this move, resulting in additional turnover of 0.6% and 0.7%, respectively. There would be no impact on the S&P MidCap 400 and S&P SmallCap 600. Standard & Poor's will consult market participants and give adequate notice before announcing any changes in methodology.
Appendix 1: S&P Composite 1500 Members With Public Float Less Than 50%