Konan Chan Fengfei Li National Chengchi University University of Hong Kong

Tse-Chun Lin Ji-Chai Lin

University of Hong Kong Louisiana State University

For Presentation at NTU conference December 7th, 2012

Stock Price Levels and Price Informativeness

What we are interested in knowing…

Does stock price level matter in where informed investors choose to trade? In other words, would high stock price level lead to lower

informed trades in the equity market and make the options market a more appealing trading venue to the informed?

Is this venue switching behavior among the informed more prominent for stocks with more difficulty to attract small investors.

Ultimately, since informed trading carries information, we would like to investigate whether stock price levels affect price informativeness.

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Intuition: High stock price level and informed trading

Uninformed trading is necessary for market making (Kyle, 1985)

Facing budget constraints and limited risk-sharing capacity, uninformed individual investors are likely excluded from participating in trading high-price stocks

When informed traders cannot effectively camouflage their trades among uninformed trades, they cannot gain much from their private information

This would reduce their incentives to collect information and

trade such that the informational role of stock price could diminish.

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Examples of budget constraints on small investors

When companies in Japan reduce the number of shares in a round lot, the number of their individual shareholders significantly increases

Amihud, Mendeslon, and Uno (1999)

When mutual funds split their shares, they experience significant increases in net assets and shareholders

Fernando, Krishnamurthy, and Spindt (1999)

Small trades increase following the splits Schultz (2000)

Stock splits attract more uninformed and informed trades Easley, O’Hara and Saar (2001)

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Our Objectives

We employ the O/S, relative trading volume of options over stock in Roll, Schwartz, and Subrahmanyam (2010), to

Illustrate how does stock price level affect the choice of trading venues by the informed traders.

Help to explain why firms split their stocks.

Shed some light on the nominal share price puzzle.

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Easley, O’Hara, and Srinivas (1998) multi-market sequential trade model

Informed traders move across options market and equity market to maximize trading profits.

The model suggests that more informed trading in options market when Decreasing the depth of the stock market Increasing the depth of the options market

In their model, the market depth is determined by the number of uninformed trades in each market.

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Why is O/S a useful tool for our objectives?

Following Roll et al. (2010), we use O/S to track where informed traders prefer to trade, the options market or the equity market.

If high price causes the depth of the equity market to decrease, then O/S should rise to reflect an increase in traders’ preference to trade listed options.

Conversely, if a stock split is an effective way to attract uninformed traders and increase the depth of the equity market, then O/S should fall after the split.

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Hypothesis 1 and its predictions:

H1: High stock price level would impede informed trading on the stock and

make listed options more appealing to the informed

Predictions: O/S increases with stock price level.

The positive relation between O/S and stock price level is stronger for firms that have more difficulty in attracting small investors.

High stock price level decreases stock price informativeness.

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Hypothesis 2 and its predictions:

For high-priced stocks, managers can use stock splits to attract more uninformed traders to improve informed trading and enhance informational efficiency of stock prices.

Predictions: O/S rises before stock splits. Pre-split O/S is informative about the firms’ future prospects. O/S declines after splits. Stock price becomes more informative after stock splits. Post-split O/S contains less information, compared with pre-

split O/S.

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Why do we care about price informativeness?

It could improve corporate resource allocation. Khanna, Slezak, and Bradley (1994) Subrahmanyam and Titman (2001)

The risk of investing in the stock is lower when stock price reflects more information. Roll, Schwartz, and Subrahmanyam (2009)

We follow Gelb and Zarowin’s (2002) specification for price informativeness: regressing current returns against (current and) future earnings changes.

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Data for testing H1

H1 posits that high stock price level may impede informed trading on the stock and make listed options more appealing to the informed.

To test this hypothesis, we use a comprehensive sample of firms with trading data available on both

listed option (from OptionMetrics) and the underlying stock (from CRSP).

Sample period:1996 to 2010. The number of firms in a given year varies over time,

ranging from 960 in 1996 to 1967 in 2007, with a total of 4702 firms.

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Key variables

Following Roll e al. (2010), we use two measures of O/S: ShO/S based on daily share volume and $O/S based on daily dollar volume.

The two key variables for testing H1 are Price, the log stock price level, and Price x Small,

where Small is a dummy variable equal to one if the dollar ownership per shareholder (market cap/number of ordinary shareholder) is greater than the cross-sectional median, and zero otherwise.

We assume that firms with Small=1 have more difficulty in attracting small investors than those with Small=0. If a firm can easily attract small investors, it would have many small investors as shareholders and the dollar ownership per shareholder would be relatively small.

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Table 2. Regressions of O/S on Share Price 13

Table 3. Price Informativeness (Gelb and Zarowin‘s (2002) specification) – full sample

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Model 1 2 3 ERC (Et) 0.018*** 0.012** -0.009 (3.58) (2.41) (-0.65) Future ERC (Et+) 0.082*** 0.246*** 0.197*** (5.54) (9.71) (7.52) Future return (Rt+) -0.073*** -0.065*** -0.121*** (-19.03) (-17.51) (-13.21) Earnings-price ratio (E/P) 0.001*** 0.002*** 0.004*** (8.63) (14.26) (9.78) Asset growth (AG) 0.304*** 0.252*** 0.255*** (16.35) (13.87) (4.53) Size -0.101*** -0.183*** -0.376*** (-25.15) (-35.71) (-28.45) Price (P) 0.230*** -0.144*** (27.30) (-5.71) ERC x Price 0.009 (1.47) Future ERC x Price -0.067*** -0.052*** (-9.43) (-7.29) Future return x Price 0.022*** (6.10) Earnings-price ratio x Price -0.001*** (-6.54) Asset growth x Price -0.002 (-0.11) Size x Price 0.063*** (16.84) Intercept 0.690*** 0.770*** 1.861*** (21.68) (22.03) (22.18) Year fixed effect Yes Yes Yes Adj-R2 (%) 16.59 21.01 23.07 N 30306 30306 30306

Data for testing H2

H2 posits that, for firms whose high stock price levels hinder uninformed traders to enter the market, managers can use stock splits to attract more uninformed traders to Improve informed trading and Enhance informational efficiency of stock prices.

We test H2 using a sample of splitting firms with listed options.

Our split sample includes 1,687 splits, which have a split factor of at least 0.25, over the period of 1996 through 2010.

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Table 5. Cross-sectional Regressions of Pre-split O/S on Pre-split Share Price for Splitting Stocks

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Figure 1. Pre-Split and Post-Split O/S of Split Firms vs. Benchmark Firms

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Table 6. Changes in O/S Before and After Splits 18

Table 7. Cross-Sectional Regressions of Split CARs on O/S

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Table 8. Regressions of SUE on O/S

Pre-split O/S can also predict earnings surprises from one quarter to four quarters after the stock splits, suggesting that option traders prior to stock splits are informed about future earnings surprises.

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Table 9. Long-Run Returns Sorted by O/S

The abnormal returns on the calendar-time portfolios from all three models increase monotonically with pre-split O/S.

The results suggest that option traders prior to stock splits are also informed about split firms‘ future stock performance.

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Table 10 Price Informativeness Before and After Splits (Gelb and Zarowin‘s (2002) specification) 22

Table 11. Predictability of O/S on SUE and Earnings Announcement Returns around Splits 23

Conclusion

The objectives of our paper are to Illustrate how does stock price level affect the choice of trading

venues by the informed traders. Explain why firms split their stocks. Shed light on the nominal share price puzzle.

To achieves the objectives, we propose two hypotheses: H1 posits that high stock price level impedes informed trading on

the stock and reduce the price informativeness about future earnings.

H2 posits that firms can use stock splits to improve informed trading and make their stock price more informative.

We find evidence consistent with our hypotheses.

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Contributions

We extend Roll et al. (2010) to show that stock price level also plays a role in where informed traders

choose to trade.

We also add to the literature on stock splits by showing that stock price level affects the informativeness of stock price

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Thank You

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Table 1. Summary Statistics 27

Table 1. Correlations28

Table 4. Summary Statistics of Stock Splits 29

Table 4. Correlations30