The Effect of Changes in Tick Size Constraints on Changes in Liquidity Table 7 presents the results on the quoted spread The coefficient for the dummy variable

treatment is not statistically significant, implying that there is no difference in the quoted spread

for the control and treatment groups. Also, there is no time trend because the coefficient for the

17 _{Similarly, we need to make the same adjustment for the control stocks both before and after the split, because the} price levels and shares outstanding for the control stocks are similar to those for the treatment stocks’ pre-split levels.

dummy variable after is also not significant. The quoted spread decreases by 6.22 cents after the split. However, the proportional spread does not decrease. The proportional quoted spread increases by 6.5 basis points before adjusting for the fee and by 7.5 basis points after adjusting for the fee, and is significant at the 10% level. Fee structure plays a role in the differences of the changes of the proportionally quote spread before and after adjustment for the fee. For example, suppose a $20 stock has a two-for-one split and a $2,000 transaction has a maker rebate of 29.5 cents (0.295 cents per share*100 shares), but the maker rebate increases to 59 cents after the split (0.295 cents per share*200 shares). Therefore, the maker fee causes a further increase in the proportional quoted spread.

Insert Table 7 about Here

Table 8 presents the results for depth. Before any adjustment, columns 1 and 2 show that depth at the best bid and ask and depth within 10 cents of the bid ask spread increase, implying an increase in the queue for supplying liquidity. However, the results incorporate two mechanical effects: 1) For an n-for-one split, one pre-split share is equivalent to n shares post-split; 2) after the split, one-cent and 10-cent distances from the best ask and bid imply a larger percent deviation from the best bid and ask due to the reduction in the nominal share price. Columns (3) and (4) present the results after adjusting for differences in the shares outstanding. The results show that NDepth decreases whereas NDepth10 still increases. Columns (5) and (6) consider

PDepth and PDepth10, depth within the same deviation percentage from the best bid and ask,

and we find that depth within 10 cents of the best bid and ask increases but depth at the best bid and ask does not increase. Columns (7) and (8) present the results based on PNDepth and

best prices. PNDepth and PNDepth10 actually decrease after the split. Therefore, the results for depth are mixed and depend on the methods of adjustment.

Insert Table 8 About Here

With an increase in the quoted spread and mixed results on depth, the key variable of interest becomes the effective spread, because it measures the transaction cost to traders. Table 9 demonstrates a decrease in the nominal effective spread after the split. However, this decrease in the effective spread is not as large as the decrease in the share price. The proportional effective spread then increases by 2.6 basis points before adjusting for the fee and increased by 3.6 basis point after adjusting for the fee. This shows that the proportional transaction cost increases after the split.

Insert Table 9 About Here

Finally, stock splits lead to an increase in the relative tick size, and the intuition in section 4 suggests that volume should move to the taker/maker market after the split. Therefore, we run two diff-in-diff regressions with the total dollar volume of EDGA and EDGX and the ratio of EDGA volume to EDGA and EDGX volume as the dependent variable.

∗ (15)

∗ (16)

Table 10 demonstrates that the total dollar volume does not change after the split, but the EDGA market share increases by 2.94%, which implies a migration of volume from the maker/taker market to the taker/maker market.

In summary, the results based on a stock-splitting event indicate that an increase in tick size constraints does not improve liquidity and volume. However, the constrained price results in a migration of volume from the maker/taker market to the taker/maker market.

6. Conclusion

This paper provides empirical evidence linking tick size regulation, HFT, and taker/maker fees, which provides a benchmark against which to evaluate the economic consequences of increasing tick size. The JOBS Act encourages the SEC to examine the possibility of increasing tick size, and proponents of wider tick size have offered three rationales for this position (Grant Thornton, 2012). First, they argue, wider tick size controls the growth of HFT. Second, wider tick size increases market-making revenue, supports sell-side equity research, and increases the number of IPOs. Third, wider tick size should increase liquidity. Our empirical results and economic reasoning, however, cast doubt on these rationales.

We show that a one-penny tick size under current regulations has already attracted HFT liquidity provision for low-priced stocks or stocks with high relative tick size. Non-HFTers have a comparative advantage for supplying liquidity for stocks with small relative tick size because of their ability to quote better prices. An increase in relative tick size, however, favors HFTers. Larger tick size constraints eliminate non-HFTers’ ability to undercut HFTers. Therefore, both HFTers and non-HFTers quote the same prices and HFTers can achieve priority because of their speed advantage. An increase in tick size above one cent would further constrain price competition and encourage speed competition. Therefore, instead of controlling HFT, increasing tick size can encourage HFT. 

The other rationale for increasing tick size is that constrained price competition leads to better service in areas such as stock research. The general argument that controlling prices leads to non-price competition is valid. However, we doubt that non-price competition would take the form of competition over stock research. Most HFT market-making firms do not have research arms, and a more natural form of non-price competition would be speed competition. A recent article in the Wall Street Journal states that “investment banks and proprietary trading firms spend millions to shave ever smaller slivers of time off their activities . . . [as] the race for the lowest ‘latency’ [continues], some market participants are even talking about picoseconds— trillionths of a second.”18 We believe one of the drivers for such aggressive investment is the desire to establish time priority when price competition is constrained, and the rents originating in tick size constraints facilitate such investment. We also expect that traders would migrate to trading venues where tick size constraints can be bypassed, and the taker/maker market is one such market. In summary, we believe that HFT and the taker/maker market are more immediate and natural responses to an increase in tick size than improving stock research.

Finally, we find that an increase in relative tick size after stock splits does not improve either the quoted spread or the effective spread. Depth increases mechanically, but it does not increase when we adjust for an increase in number of shares or a decrease in nominal price. The dollar trading volume also does not increase.

Our paper can be extended in various ways. First, current theoretical work on speed competition focuses on the role of information. Our paper points out another channel for speed competition: tick size constraints. Models using discrete prices can be constructed to indicate the value of speed and the impact of tick size constraints on market quality. Second, we explain the

market share of taker/maker fees based on tick size constraints, and theoretical models can be built to understand why there exist separate equilibria for traders on separate trading platforms and how exchanges set fee structures in both taker/maker and maker/taker fee markets to maximize total profits. Empirically, the relationship between tick size constraints, HFT, and maker/taker versus taker/maker fees can be further explored. For example, the SEC recently announced a pilot program for increasing tick size for a number of small stocks, and it would be interesting to see the impact of this shock on speed competition and the taker/maker fee market.

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Table 1. Sample Summary Statistics

This table presents summary statistics on the sample data used in the paper. Panel A presents summary statistics on the 117-stock sample as of October 2010 using CRSP market data. Panel B presents descriptive statistics on both the split sample and matched firms 30 days prior to the split execution day using both CRSP and NASDAQ (Total View-ITCH) data.

Panel A: CRSP Summary Statistics of 117 Stocks as of October 2010

Market Cap Avg Closing Price Avg Daily Volume

($Million) ($) (1000s) Mean 19352 41.5 5095 Medium 2032 27.22 573 Std 42246 64.41 11176 Min 282 5.72 24 Max 275000 575.94 67028

Panel B: Summary Statistics of Split Sample & Matched Firms

Mean

N Sample Match

Split Factor 83 2.23 -

Pre-split Price ($) 83 79.19 76.61

CRSP

Market Cap ($Million) 83 6937 7110

Avg Closing Price ($) 83 78.42 76.09

Avg Daily Volume (1000s) 83 895 1046

NASDAQ (Total View-ITCH)

Avg Quoted Spread ($) 83 0.132 0.128

Avg Effective Spread ($) 83 0.1 0.115

Avg Best Depth 83 436 445

Table 2. Who Provides the Best Quotes?

This table displays the percentage of time HFTers and non-HFTers provide the best bid and ask quotes to the NASDAQ limit-order book. The sample includes 117 stocks in NASDAQ HFT data from October 2010. Stocks are sorted first into 3-by-3 portfolios by average market cap and then by average price from September 2010. For each portfolio and each trading day, we calculate the percentage of time that HFTers are the sole providers of the best quotes, the percentage of time that non-HFTers are the sole providers of the best quotes and the percentage of time that both provide the best quotes. Column (1) presents the average percentage of time that HFTers are the sole providers of the best quotes and column (2) presents the average percentage of time that non-HFTers are the sole providers of the best quotes. Column (3) presents the average percentage of time that both HFTers and non-HFTers provide the best quotes. Column (4) shows the ratio of column (2) figures to column (1) figures. Column (5) shows the difference between column (1) figures and (2) figures. t-statistics of column (5) based on 21 daily observations are presented in column (6). *, ** and *** represent statistical significance at the 10%, 5%, and 1% level, respectively.

(1) (2) (3) (4) (5) (6)

Relative Tick Size _Only HFT Non-HFT_{Only Non-HFT} HFT & Ratio

Non-HFT minus HFT t-stat Large Cap Large (Low Price) 1.6% 2.5% 95.9% 1.55 0.9%*** 7.27 Medium (Medium Price) 11.9% 18.6% 69.6% 1.57 6.7%*** 14.01 Small (High Price) 16.8% 37.7% 45.5% 2.25 20.9%*** 37.81 Middle Cap Large (Low Price) 18.0% 15.2% 66.8% 0.84 -2.9%*** -3.52 Medium (Medium Price) 20.0% 56.6% 23.4% 2.83 36.6%*** 36.03 Small (High Price) 20.7% 63.7% 15.7% 3.08 43.0%*** 67.15 Small Cap Large (Low Price) 11.3% 54.7% 34.1% 4.86 43.4%*** 27.55 Medium (Medium Price) 20.2% 55.8% 24.0% 2.77 35.7%*** 30.11 Small (High Price) 18.6% 70.7% 10.7% 3.80 52.1%*** 66.79 Total 15.4% 41.7% 42.9% 2.62 26.3%*** 18.31

Table 3. Market Share of BBO Depth Provided by HFTers

This table presents percentage of depth at NASDAQ best bid and offer (BBO) provided by HFTers. The sample includes 117 stocks in NASDAQ HFT data from October 2010. The stocks are sorted first by average market cap and then by average price from September 2010 into 3-by-3 portfolios. Panel A presents share-weighted BBO depth provided by HFTers and Panel B presents equal-weighted BBO depth provided by HFTers. To calculate the share-weighted average for each portfolio on each day, we aggregate the number of shares provided by HFTers at BBO and then divide it by the total number of shares at BBO for that portfolio. Panel A presents the average daily share-weighted BBO depth provided by HFTers. t-statistics are calculated based on the 21 daily observations. To calculate the equal-weighted average, we first compute, for each stock on each day, the depth provided by HFTers relative to total depth. The daily equal-weighted average for each portfolio is the average of the percentage of depth provided by HFTers for stocks in the portfolio. Panel B presents the average daily equal-weighted BBO depth provided by HFTers. t-statistics are calculated based on 21 daily observations. *, ** and *** represent statistical significance of large-minus-small differences at the 10%, 5%, and 1% level, respectively.

Panel A: Percentage of BBO Depth Provided by High-frequency Traders (Share-weighted)

Large Medium Small Large-Small

Relative Tick

Size Relative Tick Size Relative Tick Size Relative Tick Size t-stat (Low Price) (Medium Price) (High Price) (Low-High Price)

Large Cap 55.66% 45.44% 35.07% 20.59%*** 22.10

Middle Cap 39.73% 29.24% 24.61% 15.13%*** 22.88

Small Cap 25.78% 23.02% 20.78% 5.00%*** 3.18

L-S Cap 29.88%*** 22.43%*** 14.29%***

t-statistics 18.84 17.92 16.80

Panel B: Percentage of BBO Depth Provided by High-frequency Traders (Equal-weighted)

Large Medium Small Large-Small

Relative Tick Size Relative Tick Size Relative Tick Size Relative Tick Size t-stat (Low Price) (Medium Price) (High Price) (Low-High Price)

Large Cap 50.22% 42.70% 30.81% 19.41%*** 30.55

Middle Cap 43.10% 26.37% 24.79% 18.30%*** 30.28

Small Cap 22.64% 25.48% 21.04% 1.59% 1.50

L-S Cap 27.58%*** 17.22%*** 9.77%***

Table 4. Percentage of Volume with HFTers as the Liquidity Providers

This table presents the trading volume percentage due to HFTers as liquidity providers. The sample includes 117 stocks in NASDAQ HFT data from October 2010. The stocks are sorted first by average market cap and then by average price from September 2010 into 3-by-3 portfolios. Panel A presents the volume-weighted percent of volume due to HFT liquidity providers and Panel B presents the equal- weighted percent of volume due to HFT liquidity providers. To calculate the volume-weighted average