From Largecaps to Microcaps: Stock Herding within ETFs

Even before the Flash Crash on May 6, investors and reporters pondered whether ETFs were raising correlations among stocks. Solely buying or selling ETFs directly does not promote correlation. Instead, differences between the ETF's traded price and the indicative net asset value (INAV) create arbitrage opportunities. That difference in price encourages highly efficient traders ("arbitrageurs") to transact in a large sample of stocks underlying the ETF, either buying or selling the stocks and executing an opposing trade in the ETF. Creation Units and Redemption Units further increase the means of executing such arbitrage strategies.

However, arbitrageurs do perform a very important market function for ETFs: they keep the differences between the ETF traded price and the INAV very small (also known to many as "tracking error"). (A very similar term, "basis risk", is commonly used in the context of derivatives, but Fundometry does not seek to blur the lines between ETFs with derivatives any further.) As a result, an ETF will trade closer to its INAV. Or does the INAV trade closer to its ETF? Arbitrageurs likely do not assess which price (ETF or INAV) reflects the true value of a portfolio of equities, but one can argue at length about whether either price reflects fundamental value or the efficient processing of information.

Instead of focusing on how arbitrageurs make a living, this analysis seeks to slice broad equity sectors, according to each stock's market cap, and observe how stocks correlate to their respective ETFs. Frequently, the S&P 500 is cited as the worthwhile benchmark because its components comprise such a large share of the market's value. However, the herding effect of stocks within an ETF may be more acute among for a smaller company, which does not have much analyst coverage to influence its traded price and where less liquidity can create artificial volatility.

The methodology generating the following results is straight-forward. Four ETFs are selected based on their coverage of different segments of the market based on equity market cap.

iShares S&P 500 Index Fund (IVV)
iShares S&P Midcap 400 Index Fund (IJH)
iShares S&P SmallCap 600 Index Fund (IJR)
iShares Russell Microcap Index Fund (IWC) (holding approx 1300-1400 stocks)

The stocks held by each ETF are monitored on a monthly basis, starting with the first quarter of 2008 (an arbitrary point in time but one which avoids too much data squeezing into one graph). Each month, every stock is classified into a quintile based on its weight in the respective ETF. (This assumes that each stock is a member of only one of the four selected ETFs at any one time.) For example, the 100 stocks with the smallest weights in the S&P 500 Index (hence, the smallest 100 stocks by market cap among the 500 largecap stocks) get classified in the lowest quintile ("quintile 1"). By another example, the 120 stocks with the largest weights in the S&P SmallCap 600 Index (the largest 120 stocks by market cap among the 600 smallcap stocks) get classified in the highest quintile ("quintile 5").

Using daily total returns over a 20-day period, a model computes historical correlations between each stock and its corresponding ETF. These correlations are further classified into segments, identified in the graphs below. These segments help to visually demonstrate the breadth of correlation among stocks inside an ETF. If all of these individual correlations were averaged, an important dimension of the outcome would be missing.Finally, these monthly correlations are aggregated into quarterly periods and presented in the following graphs.

The first graph shows the historical correlations among largecap stocks in the S&P 500 index. (Click on any graph to enlarge.)



Above each stacked bar is a quintile number (1 through 5) at the top of the graph, and a legend provides a definition for each numbered quintile. In the case of the S&P 500 index, each quintile contains 100 largecap stocks. Each vertical stacked bar represents the range of correlations for the 100 stocks, as observed during a quarterly period. Represented by different shades of grey, the correlations are grouped according to where they fall within the distribution. Given the wide variations in correlation, among different stocks and over time, the stacked bars provide a more meaningful picture than a simple average or median. (In case median is easier to follow, a red dot depicts the median correlation for each group.)

More often than not, the smallest 100 stocks (quintile 1) within the S&P 500 index correlate more tightly (as viewed by the full height of the stacked bars) than do the largest 100 stocks (quintile 5). As one moves from left to right, the range of correlation broadens in many of the quarterly periods. As one would expect, the overall tightest ranges of correlations occured in 2008Q4, 2009Q1, and 2010Q2, each characteristic of elevated market volatility. Within each quarter, the median correlations (red dots) did not vary materially from the smallest to the largest quintile.

Why might larger stocks within the S&P 500 index have a broader range of correlation than their smaller peers? Liquidity should be fairly deep for all of these largecap stocks. All of these stocks should have reasonable analyst coverage, although larger stocks probably attract more interest from reporters and analysts. Does the availability of more information cause investors to trade a company according to its specific economic fundamentals, as opposed to a less-publicized company being considered part of another largecap basket trade?

Moving down the market cap spectrum, the next graph displays the same correlation profile for the S&P MidCap 400 index.



When looking at the range of correlations within each stacked bar, differences between the smallest and largest quintiles (of 80 stocks) begin to blur over time. In 2008Q1 and 2008Q3, the smallest quintile exhibited the tightest range of correlations among the five quintiles. In some quarters, the largest quintile exhibited the largest range of correlations. As with the largecap profile, the median correlations did not vary materially from the smallest to the largest quintile in each quarter.

The next segment of the market cap spectrum, smallcap stocks, is represented by the S&P SmallCap 600 index.



In this case, the median correlations (red dots) in most quarters showed a steady increase from the smallest quintile (of 120 stocks) and incrementally with each quintile of larger stocks. This pattern is a distinct divergence from the correlation profiles of largecap and midcap stocks above. In certain quarters (2008Q1, 2008Q4, 2009Q4, 2010Q1, 2010Q3), the range of correlations for quintile 1 was materially larger than for other quintiles within the same quarter. As seen from this graph, as smallcap companies moved up in the market cap ranks, their stock prices became more correlated to the S&P SmallCap 600 index.

Finally, rounding out the smallest end of the market cap spectrum is the Russell Microcap Index. (iShares did not license a microcap index from S&P.)



The pattern of increasing correlation with increasing relative market cap was even more prevalent among microcap stocks than smallcap or larger peers. In every quarter, the correlation of stocks to the index (whether based on the median or full range from 5th to 95th percentile) increased as the market cap of the stock increased relative to peers. Quintile 1 exhibited the lowest correlation to the index, in terms of the median and the top/bottom (95th and 5th percentiles) of the stacked bars. Quintile 2 exhibited higher correlations than quintile 1, in terms of the median and 95th and 5th percentiles. This pattern continued through quintile 5 and was remarkably consistent throughout every quarter in the sampled period.

Given the different correlation profiles within each ETF, a convenient summary of these results shows the correlation ranges across the market cap spectrum.



In this final graph, we observe that the median correlation (red dots) increased from the smallest quintile of microcap stocks (quintile 1 of the Russell Microcap Index) to the largest smallcap stocks (quintiles 4 and 5 of the S&P SmallCapp 600 Index). Thereafter, midcap and largecap stocks did not correlate significantly more or less with their respective ETF as their market caps increased. What makes micocap and smallcap stocks different from their larger peers?

1. Mathematically, a cap-weighted index and its corresponding ETF should corrrelate to a greater extent with larger companies in the index or portfolio than with smaller companies. The larger the weight of a specific stock, the greater its influence on the returns of the ETF, hence a higher expected correlation with the ETF over time. The correlation profiles of the microcap and smallcap ETFs were consistent with this premise, but not so for the midcap and largecap ETFs.

2. Despite explanation #1, midcap and largecap stocks of varying weights (quintiles) correlated with the ETF, and plausibly with each other, inside a relatively tight range. Overall, midcap quintile 1 stocks and largecap quintile 3 stocks exhibited the narrowest correlation range among their respective peers. Do arbitrageurs have greater influence on the price movements of the smaller quintile stocks, while a larger population of traders contribute to price movements in the larger quintile stocks?

3. Analyst coverage tends to decline as the market cap of a company declines. Therefore, institutional portfolio managers, and even individual investors, need to spend a greater amount of resources and cost to analyze and monitor smaller companies. Therefore, most investors who gravitate toward investing in largecap stocks can utilize analyst reports and press releases to make trading decisions, which implies a notable factor of company-specific criteria influencing price movements. Conversely, microcap and smallcap investors must invest in more companies (a large "basket" of stocks) in order to diversify their risk to any one company which may suddenly go out of business. In fact, one of the greatest appeals of a microcap ETF is the ability to gain diversified exposure to a market segment which would be otherwise quite expensive to trade (i.e. paying bid-offer spreads and commissions across a very large number of stocks).

4. Microcap and smallcap stocks typically have less liquidity (trading volume) than their larger peers. In order for arbitrageurs to profit from small discrepancies between an ETF and its underlying stocks, transaction costs, specifically bid-offer spreads, must be minimized. Trading a certain numbers of shares within a target bid-offer spread is easier with stocks which have greater trading volumes. Therefore, midcap and largecap stocks should be more favored by traders seeking arbitrage profits between the ETF and its underlying stocks. Microcap and small cap stocks (especially quintiles 1 and 2) would not be liquid enough for such traders. (Also see comment below.)

In fact, a fair absence of arbitrageurs in microcap stocks may explain the steady increase in correlation when moving from quintile 1 to quintile 5. The microcap ETF may provide the best example of how stocks should correlate to an ETF when arbitrage trades are difficult to execute in great frequency, and consequently less profitable. If the microcap segment is the least susceptible to arbitrage trades across a large number of stocks, then it should be the most favorable market segment for traditional fundamental analysts to generate alpha.

Regardless of which explanation, or combination thereof, is the most convincing, stock correlations with an ETF can change significantly depending on company-specific market cap (proxied by weight quintiles) and overall market volatility (proxied by time). One should note that the stocks within a quintile varies from month to month, as their ETF weights change regularly. At the individual stock level, correlations vary substantially from month to month, depending on company-specific news and events. For investors, the more stocks held in a portfolio, the more relevant these results become. For active investors, generating alpha (i.e. outperforming the index) should be more difficult with largecap stocks than with microcap stocks, all else being equal.

From the perspective of public companies, these results probably quantify what CEOs and CFOs already knew. As market cap grows, the more a stock's price becomes influenced by programmatic trading systems supporting index-linked investment vehicles (mutual funds, ETFs, insurance subaccounts, hedge funds, etc). However, at some point, trading volume for a stock may become large enough to dilute the impact of these programmatic factors and increase the influence of analyst coverage and company-specific fundamentals.

This analysis does not dig deep enough to determine how high-frequency trading firms, ETF authorized participants and market structure play a role in the relationship between stocks and their associated ETFs. Hence, the question still remains: "Do ETFs track their INAVs, or is it the other way around?"

Further reading:

The Herd Instinct Takes Over Component Stocks' Correlation to S&P 500 at Highest Level Since '87 Crash (WSJ)

Should ETFs be allowed to include illiquid stocks? (Felix Salmon)

The Real Trend In Fund Flows Will Crush Mutual Fund Managers, And Forever Change The Way Stocks Behave (Clusterstock)

Did nobody ever consider that indexing was dangerous? (FT Alphaville)

Using Leveraged ETFs to Trade during Circuit Breakers

Subtitle: Intraday Correlations between ProShares ETFs and Broad Market Indices

On June 30, 2010, the SEC announced its intention to expand the circuit breaker pilot program to many more stocks and, for the first time, ETFs. Public comments have expressed concern that, when applied to ETFs, circuit breakers may themselves create market disruptions. If a circuit breaker is triggered, whether appropriately or erroneously, for a widely-traded ETF, HFT firms major market participants may pause trading and deprive the market of liquidity when it is most needed. Once an ETF selected for the pilot program triggers a circuit breaker, firms which trade the basket of underlying stocks may also step away for five minutes until trading in the ETF resumes. In such a scenario, the impact on the liquidity of stocks underlying a halted ETF will demonstrate whether the circuit breaker program meets its objectives in practice.

Not all ETFs have been selected for the circuit breaker pilot program. NYSE Euronext compiled a list of 344 ETFs ("piloted ETFs"), as reported by Index Universe, utilizing a volume cutoff:

"NYSE Euronext, the parent company of the New York Stock Exchange, developed the list of 344 ETFs in consultation with other major exchanges and the Financial Industry Regulatory Authority.

"NYSE Euronext winnowed down the universe of U.S. ETFs by excluding products whose average daily trade volume was less than $2 million worth of shares, it said in a press release."

This criteria for selected ETFs produces some interesting and potential trading scenarios. For example, SPY and IVV, two ETF's which track the S&P 500, are included in the proposed expansion of the circuit breaker program. Therefore, if one of these two ETFs triggers a circuit breaker, will the market simply move to trade the other ETF until five minutes passes? What are the odds that both SPY and IVV will simulateously trigger circuit breakers? (This is not a rhetorical question.)

Given the complex trading relationships between an ETF and its underlying stocks, concerns about market disruption resulting from a circuit breaker are difficult to prove in theory and potentially difficult to quantify. A further review of the list of ETFs proposed for the circuit breaker pilot program reveals another interesting scenario: if a broad-market ETF triggers a circuit breaker, can traders utilize leveraged versions of the ETF to continue trading through the duration of the circuit breaker?

To address that possibility, we start with a summary of ETFs which may serve as substitutes (or proxies) for three broad market ETFs: SPY, QQQQ, and IWM.

Those ETFs participating in the circuit breaker pilot program are only unleveraged (long and short) versions of their underlying indices. The obvious choice for trading through the duration of a circuit breaker would be to use a leveraged (long or short) ETF, sponsored by ProShares. The remainder of this analysis studies how effectively these ProShares ETFs followed their stated leverage ratio during 2010 Q2.

First a definition of the term "leverage ratio" as utilized in this analysis. To take an example, the ProShares Ultra S&P 500 (SSO) has a stated objective of going up or down twice as much as the S&P 500 index, on an intraday basis. Hence, the stated target leverage ratio for SSO is +2. Conversely, the stated target leverage ratio for ProShares UltraShort S&P 500 (SDS) is -2 because SDS moves in the opposite direction to the S&P 500. By looking at the returns of leveraged long/short ETFs over 5-minute intervals during 2010 Q2, we compare their returns to the underlying index by utilizing linear regression analysis. These regressions are constrained to have a zero alpha (zero intercept) so that the resulting beta (slope) provides a useful (albeit not perfect) measure of the leverage ratio. Each regression compares a single ETF to its underlying index, ignoring any 5-minute intervals when such ETF did not trade. Otherwise, volume has no impact on the regressions. By constraining the alpha to zero, the following graphs need to display only the slope (termed the "observed leverage ratio").

The closer an ETF trades to its stated target leverage ratio, the better such ETF may serve as a proxy if another related ETF triggers a circuit breaker. How well might various leveraged long/short ETFs of the S&P 500 index serve as proxies to SPY, IVV, or SH? The following graph shows the consistency of the leverage ratio for every trading day furing 2010 Q2.

(For convenient viewing throughout all graphs, those ETFs which will be subject to circuit breakers have markers with yellow centers. For graphs pertaining to the S&P 500, the iShares ETF is excluded so that the higher-volume SPDR ETF is easier to view. On graphs plotting the observed leverage ratio over time, a black line represents the daily standard deviation of 5-minute returns to help compare deviations in the observed leverage ratio to underlying index volatility.)

On a daily basis, the leveraged ETFs appear to trade according to their stated target leverage ratios. As the target level rises to 2x and 3x, the observed leverage ratio for both long and short ETFs exhibits greater variability around the target level. Perhaps the efficiency of instruments used to gain leverage suffers as leverage rises. Liquidity might also play a role. Leveraged ETFs typically have lower trading volume than their corresponding long unleveraged ETFs (discussed in detail further below).

Can one draw the same conclusion by looking at the observed leverage ratio over intraday 5-minute intervals? In this graph, the leverage ratio is computed through a linear regression utilizing all trading days during 2010 Q2 but for a specific 5-minute interval during each trading day.

During certain times of the day, on average, the observed leverage ratio tended to deviate from the stated objective. Most likely (especially between 2:30 and 3:00) these deviations reflected aberrant activity on specific days (e.g. May 6), as opposed to repetitive behavior during most trading days. Interestingly, the interval from 9:30 to 9:34, where 5-minute volatility is highest overall, shows the largest discrepancy in observed leverage ratio. Currently, the SEC does not apply circuit breakers during the beginning and end of regular trading hours (9:30 to 9:45 and 3:45 to 4:00).

Switching from a time-based perspective, the next graph shows the observed leverage ratio according to the return in the underlying index during 5-minute intervals.

(For clarification, the horizontal axis shows return bands, each spanning 0.10%. The return band labelled -0.30% includes any 5-minute intervals when the underlying index dropped by 0.3000% to 0.3999%. The return band labelled +0.30% includes any 5-minute intervals when the underlying index rose by 0.2001 % to 0.3000%. The return band labelled 0.00% includes any 5-minute intervals when the underlying index dropped by -0.0999% to 0.0000%. Furthermore, since the return bands are based on the underlying index, and not the ETFs, circuit breakers might have triggered if they had been in effect for ETFs at that time.)

All ETFs based on the S&P 500 traded close to their stated target leverage ratios as long as the underlying index did not rise or fall more than 0.40% within any 5-minute interval. As the underlying index became more volatile, the observed leverage ratio tended to shrink. Note that as the magnitude of change increases, the number of historical data samples drops, which may in turn reduce the regression quality and increase the standard error of the slope (beta).

In the same manner, we can determine how well various leveraged long/short ETFs of the NASDAQ 100 index served as proxies to QQQQ or PSQ. The following two graphs plot the observed leverage ratio over time, first daily followed by intraday, and roughly follow the patterns seen in the graphs for the S&P 500. For the ProShares triple-leveraged ETFs, SQQQ and TQQQ, the observed leverage ratios deviated from the stated target levels more so than for the corresponding ProShares ETFs tracking the S&P 500 .

According to the return in the NASDAQ 100 during 5-minute intervals, the following graph shows that the observed leverage ratios for the related ETFs tracked their stated target levels most of the time. Only when the Nasdaq 100 index rose or fell by more than 0.40% did the observed leverage ratio begin to decline. In this case, the spike in standard error which we observed for the S&P 500 is not present among the ETFs which track the NASDAQ 100.

Finally, we can determine how well various leveraged long/short ETFs of the Russell 2000 index serve as proxies to IWM or RWM. The following two graphs plot the observed leverage ratio over time, first daily followed by intraday.

In this case, the observed leverage ratio of the ETFs fluctuated even more from their stated objective than for the ETFs which track the NASDAQ 100. Could these fluctuations be the result of lower trading volume in the ETF and its component stocks? Additional analysis further below should address this question.

According to the return in the Russell 2000 during 5-minute intervals, the following graph shows that the observed leverage ratios tracked (and many times exceeded) the stated target levels most of the time. Only when the Russell 2000 index rose or fell by more than 0.50% did the observed leverage ratio decline significantly.

Thus far, the leveraged ETFs corresponding to the S&P 500, NASDAQ 100, and Russell 2000 appear to maintain an observed leverage ratio consistent with expectations, except during sharp price movements. However, brief periods of sharp price movements would be most likely to trigger circuit breakers, outside of erroneous trading activity. Might the participation of unleveraged ETFs in the circuit breaker pilot program prompt a change in how leveraged ETFs behave during extreme price volatility? In other words, can leveraged ETFs attract more volume, and in turn achieve observed leverage ratios consistent with stated levels, if any of their corresponding unleveraged ETFs triggers a circuit breaker?

The following three graphs compare the daily volume of the ETFs listed above (except for IVV). When selecting ETFs to include in the pilot program, the SEC focused on the highest-volume ETFs for the three broad-market indices. In addition, the corresponding unleveraged inverse ETFs had respectable volumes but lower than some of their leveraged counterparts. (Note the log scale for the vertical axis.)

In fact, for all three indices, the double-leveraged ETFs (both long and short) traded with materially higher volumes than their corresponding unleveraged short counterparts. The same conclusion can be drawn from the following three graphs, which plot average intraday volume during 5-minute intervals according to the 5-minute return in the underlying index. (Note that the graph plots average, not total, 5-minute volume because not all ETFs traded during every interval in every trading day of 2010 Q2.)

Once again, the double-leveraged ETFs consistently traded in greater volumes than their unleveraged short counterparts but less than their unleveraged long counterparts. Furthermore, these three graphs exhibit a very consistent "smile" shape, indicating that 5-minute interval volume does increase as 5-minute price movement (positive or negative) increases. While the overall shape is intuitive, the consistency among all ETFs (across different leverage ratios and long vs short) demonstrates the potential for a leveraged ETF to attract more volume should an unleveraged long or short ETF trigger a circuit breaker. However, these graphs do not and cannot prove how the observed leverage ratio of leveraged ETFs might behave during such a market scenario in the future.

In conclusion, the above analysis demonstrates some key aspects of leveraged ETFs which require careful consideration during normal and volatile periods of intraday trading.

1. As intraday (5-minute interval) price volatility of an underlying index increases, the observed leverage ratio drops significantly below stated levels. If an underlying index rises or drops by more then 0.50% in a 5-minute interval, then the leveraged ETFs may not trade at a predictable correlation to the undering index within the same interval.

2. As intraday price volatility of an underlying index increases, the corresponding volume also increases, confirming that ETFs are popular among traders who seek to rapidly gain market exposure or hedge existing positions. Both leveraged and unleveraged ETFs exhibit the same pattern of trading volume, which demonstrates that a leveraged ETF may be a viable proxy for an unleveraged ETF which has triggered its circuit breaker.

3. Both the NYSE and SEC appear to have postponed determining how leveraged ETFs may be included in the circuit breaker program. Most likely, the embedded leverage of such ETFs increases their chance of triggering a circuit breaker at times when other similar ETFs may trade inside their trigger levels. Such a potential scenario is further complicated by past behavior of observed leverage ratios, as shown above. (Currently, the SEC is not granting exemptive relief to ETFs which request to make significant investments in derivatives.)

4. The SEC is already concerned with the performance of leveraged ETFs, specifically due to their daily resets (which should not be pertinent to intraday leverage ratios). Might the exercise of identifying circuit breaker trigger levels create further scrutiny on a product where FINRA states "typically are not suitable for retail investors who plan to hold them for more than one trading session, particularly in volatile markets"?

Once the proposed ETFs are rolled out into the circuit breaker pilot program, leveraged ETFs will be put to a potentially new test . How might leveraged ETFs behave empirically should a related ETF trigger its circuit breaker?