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?"
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)