Why Are Derivative Warrants More Expensive Than Options? An Empirical Study

Transcription

1 Why Are Derivative Warrants More Expensive Than Options? An Empirical Study Gary Li & Chu Zhang This version: April, 28 Department of Finance, The Hong Kong University of Science and Technology (HKUST), Clear Water Bay, Kowloon, Hong Kong ( , and , respectively). We would like to thank Du Du, Nengjiu Ju, Ming Liu, Sophie Ni and seminar participants at HKUST for helpful comments on an early version of the paper. Chu Zhang acknowledges the financial support from the HKUST research project competition grant RPC6/7.BM28. All remaining errors are ours.

2 Why Are Derivative Warrants More Expensive Than Options? An Empirical Study Abstract Derivative warrants typically have prices higher than those otherwise identical options. Using data from the Hong Kong market during 22-26, we show that this difference reflects the liquidity premium of derivative warrants over options. Newly issued derivative warrants are much more liquid than options of similar terms. As a result, longer-term derivative warrants are preferred by traders who trade frequently. In spite of higher prices, short-term returns on longer-term derivative warrants are, in fact, slightly higher than the hypothetical short-term returns on options. On the other hand, derivative warrants near expiration are less liquid, more thinly traded, and no more expensive than options of similar terms.

3 1. Introduction Derivative warrants, both call warrants and put warrants, are traded in Britain, Germany, Australia, Hong Kong and Singapore, among other countries. They are like usual call and put options traded in the US and elsewhere, except that they can be issued (i.e., sold short) only by certain financial institutions approved by regulators. They are different from the usual equity warrants issued by the company of the underlying asset in that they are typically cash settled at maturity and there are no additional shares of the underlying asset to be issued when exercised. It has been observed that derivative warrants tend to be priced higher than otherwise identical options. This phenomenon in violation of the law of one price, a central theme in financial economics, is the focus of the current paper. Our objective is to understand what causes derivative warrants and options with identical payoffs to have different prices and how they can coexist. The main thrust of our investigation of the issue in this paper is the difference in liquidity between derivative warrants and options. The effect of liquidity on asset pricing has received considerable attention in the literature in recent years. In their seminal work, Amihud and Mendelson (1986) provide a theoretical argument that the expected return is an increasing and concave function of the bid-ask spread. There are many empirical studies confirming the theory on various financial assets. Amihud and Mendelson (1989) and Brennan and Subrahmanyam (1996) find that illiquid stocks are traded at lower prices and have higher expected returns controlling other factors. Amihud and Mendelson (1991) compare US Treasury notes and bills with less than 6 months to maturity and find that the less liquid Treasury notes have lower prices and higher yields-to-maturity. Dimson and Hanke (24) examine a set of equity index-linked bonds that provide the same payoff as an investment in an equity index, but are relatively illiquid, and show that these securities are sold at a discount relative to their underlying value and hence have higher expected returns. There are also empirical studies on 1

4 the liquidity effect on securities with trading restrictions. 1 We investigate derivative warrants and options on the Hang Seng index in the Hong Kong market, which is the largest market for derivative warrants in terms of trading volume. Our results show that the trading volume and turnover ratios of the derivative warrants are much higher than those of the options, and that bid-ask spreads are lower than those of the options, indicating that derivative warrants are much more liquid than options. The results on turnover ratios imply an average holding period of one day for the derivative warrants and about ten days for the options, so the derivative warrants are more frequently traded than options. We further investigate the returns on the derivative warrants and the options for different holding periods, using bid and ask prices. The one-day holding period returns on the derivative warrants are mostly higher than those on the options. As the holding period gets longer, the return difference between the derivative warrants and the options becomes narrower. Eventually, the returns on options will be higher than those of the derivative warrants. The results are manifestation of the clientele effect, proposed in Amihud and Mendelson (1986), that investors with different holding periods maximize the after-transaction-cost expected returns, which leads to a phenomenon, in equilibrium, that the assets with higher bid-ask spreads are held by investors with longer holding periods. Roughly speaking, long-term investors in the Hong Kong market maximize the long-term returns by investing in options with lower prices and higher bid-ask spreads and short-term investors trade derivative warrants with lower bid-ask spreads despite the higher prices. Our work is related to Chan and Pinder (2) who study the derivative warrants market in Australia and find overpricing of derivative warrants relative to options. They show that the trading volume of warrants relative to that of options can explain some 1 For example, Silber (1991) compares the price of the restricted stocks, which are sold via private placement to sophisticated investors and cannot be resold in the open market, with the price of an otherwise identical class of common stocks traded in the open market. The finding is that the restricted stocks are sold at an average discount of 33.75%. Brenner et al. (21) find that non-tradable options are priced at a mean discount of 18% to 21% to the exchange-traded synthetic options with the same payoff, and conclude that the illiquidity has an effect on the asset prices. 2

5 of the overpricing, among other variables such as days-to-maturity and the identity of market makers in the options market. We account for the overpricing of derivative warrants with a full range of liquidity measures. We also go one step further to analyze the holding period returns in derivative warrants and options. Our results indicate more clearly that two assets with identical cash flows but with different prices can coexist in the market if the transaction costs are different, and that the more liquid derivative warrants market caters for the short term trading needs of the investors. There are other studies in the literature of derivative warrants, especially for the Hong Kong market, but they are unrelated to warrant overpricing. 2 The remaining paper is organized as follows. Section 2 describes the Hong Kong derivative warrant and option markets. Section 3 describes the data and provides evidence of overpricing of derivative warrants relative to options. Section 4 presents and discusses the the main results on overpricing and liquidity. Section 5 compares holding period returns on the derivative warrants and the options. Section 6 concludes. 2. The Derivative Warrant and Option Markets in Hong Kong Trading of derivative warrants and options in Hong Kong is conducted in the Hong Kong Exchange and Clearing Limited (HKEx), which is divided into the Securities Market and Derivatives Market. The Securities Market is also known as the Stock Exchange. For historic reasons, stocks and derivative warrants are traded in the Stock Exchange. The Derivative Market is further divided into the Futures Exchange and Stock Options Exchange. Index futures and index options, among others, are traded on the Futures 2 Duan and Yan (1999) use a semi-parametric approach to pricing derivative warrants that substantially improves upon the Black-Scholes model. Several papers in the literature focus on the effect of the introduction of the derivative warrants on the price and the trading volume of the underlying securities, for example, Chan and Wei (21), Chen and Wu (21) and Draper et al. (21). A recent paper by Chow et al. (27) examine the trading records of market makers in the Hong Kong derivative warrant market for their inventory management. 3

6 Exchange, while options on individual stocks are traded on the Stock Options Exchange. As of the end of 27, there were about 5 Stock Exchange Participants (i.e, the brokers and dealer who can trade in the trading system), 144 Futures Exchange Participants, and 57 Stock Options Exchange Participants. There are two types of warrants listed in the Hong Kong Stock Exchange: equity warrants and derivative warrants. 3 Equity warrants, issued by the underlying company itself, entitle holders to purchase the equity securities from the underlying company at the pre-determined price. The exercise of equity warrants usually leads to new issuance of the equity securities of the underlying company, causing a dilution effect. Derivative call warrants are similar to equity warrants except that they are issued by a third party, usually a financial institution. The exercise of derivative warrants does not have a dilution effect on the underlying company s stock. Derivative put warrants, also issued by a third party, entitle holders to sell the equity securities of the underlying company at the pre-determined price to the issuer. The current derivative warrants are all cash settled. In Hong Kong, trading of equity warrants started in 1977, while trading of derivative warrants started in In recent years, the bulk of warrants being traded in the Hong Kong Stock Exchange are derivative warrants. The underlying assets of the derivative warrants are mostly blue-chip stocks. Other underlying assets include stock indexes, a basket of stocks, and some commodities. All the derivative warrants are of European style. 4 The issuers of derivative warrants are typically large and medium sized financial institutions. Several major European and Australian banks are among the most active issuers. Each underlying asset may have multiple issuers who compete 3 The term derivative warrant is used in Hong Kong only. It is called covered warrants in Britain, naked warrants in Germany, and structured warrants in Singapore. In Australia, warrants issued by underlying companies and third party institutions do not have separate names. There, warrants with individual stock as underlying are all called equity warrants and warrants with stock indexes as the underlying are called index warrants. In mainland China, warrants issued by underlying companies and third party institutions are treated the same. 4 There are also more exotic warrants traded in the securities market. These warrants are small in number and trading volume. They will not be discussed in this paper because there are no counterparty options in the derivative markets of the exchange. 4

7 with each other to offer popular contract specifications, lower prices and better liquidity. There is no requirement on derivative warrants issuers to hold the underlying against the derivative warrants they issue. The options trading in Hong Kong started in March Initially, only options written on the Hang Seng Index (HSI) were introduced. Trading of options on individual stocks started in September The index options are of European style and cash settled, while the stock options are of American style with physical delivery of the underlying assets upon exercise. Contract specifications of the options are set by the exchange. A system of market makers has been implemented whereby a handful of market makers are involved. Currently there are 18 market makers in the Futures Exchange and about 3 market makers in the Stock Options Exchange. For each individual stock as the underlying, the number of market makers vary from 5 to 2. The market makers are required to provide liquidity to the trading system. The requirements are not stringent, however. For options expiring in the nearest three months with near-the-money strikes, market makers are required to provide continuous quotes, while for all others, they only need to respond to request for quotes. Figure 1 plots the total trading volume of derivative warrants and options in terms of billion Hong Kong dollars over the period As we can see, the derivative warrants have gained much popularity over time with trading volume increasing from about 85 billion Hong Kong Dollar (HKD) in 22 to 1.56 trillion HKD in 26. By the end of 26, the Hong Kong derivative warrants market had become the largest derivative warrants market in the world in terms of trading volume and it accounted for one third of the total trading volume on the Hong Kong Stock Exchange. The trading volume of options in Hong Kong, though also grew at a moderate pace from about 12.5 billion HKD in 22 to 62.5 billion HKD in 26, pales when compared to the trading volume of derivative warrants. Figure 1 here 5

8 The rapid growth of the derivative warrants market owes much to certain regulatory changes made in the late 21. Before these changes, the issuers were required to place at least 85% of a derivative warrants issue to more than 1 investors on the issue date (or more than 5 investors if the size of the warrant issue is small). This exerted substantial pressure on the issuers. The new rule amended on November 28, 21 repealed that requirement, so the issuers can sell the entire issue gradually over time. The new rule requires each issuer to appoint a liquidity provider to input bid and ask prices in the trading system, either continuously or on request. Large issuers tend to appoint themselves as the liquidity providers, while a smaller issuer tends to hire a third party as the liquidity provider. There is no specific requirement on the maximum bid-ask spread on derivative warrants. However, HKEx requires that the issuers provide the information of the maximum bid-ask spread in the listing document. It is common that issuers specify the maximum bid-ask spread as 25 tick size. Other changes in the new rule include simplifying the contents of listing documents and removing some of the restrictions on further issuance of derivative warrants. The new rules substantially improved the liquidity of the derivative warrant market and are one of most important factors for the rapid growth of the derivative warrants market in Hong Kong in recent years. The number of issuers went up from 12 in December 21 before the new rules were implemented to 19 in December 26. The number of derivative warrants outstanding increased from 61 to 1846 over the same period 26. The trading volume became more than eighteen times larger as we see in Figure 1. One factor that contributes to the relative liquidity of the derivative warrants over options is their minimum trading size. While options on stocks are always traded with a round lot equal to that of the underlying stock, set by the exchange, irrespective of how much a round lot of the underlying stock costs. The minimum trading size of the derivative warrants, however, depends on the minimum trading size of the underlying. If one round lot of the underlying stock costs just a few thousand Hong Kong dollars, the round lot of derivative warrants is the same as the underlying. But if one round 6

9 lot of the underlying stock costs tens of thousand Hong Kong dollars, the round lot of derivative warrants is typically one-tenth of that of the underlying stock. This facilitates the speculative trading of many small investors. There are many anecdotal evidence that the majority of traders of derivative warrants are individual investors and they tend to hold warrants only for short terms. A more official evidence is a survey conducted by the Hong Kong Securities and Futures Commission in 25 which reveals that 86.8% of the respondents trade derivative warrants for short-term gains and only.4% of the respondents use derivative warrants for long term investments. As we will argue in the next section, differences in the liquidity between derivative warrants and options cause their prices to be different. The prices of derivative warrants tend to be higher than those of options, other things being equal. For a sample of derivative warrants and options with approximately matched maturity (difference less than 4 days) and strike price (difference less than 1% of the underlying asset price), the median price difference between derivative warrants and options is.4365% of the underlying asset price. This number, in fact, understates the true overpricing of the derivative warrants to options because options on individual stocks are of American type, while derivative warrants are of European type. 3. Overpricing of Warrants Relative to Options A. Data We focus on the derivative warrants and the options written on the Hang Seng Index (HSI) in this paper. A comparison between derivative warrants and options on the index is much cleaner as they are both European style and cash settled. The HSI is the benchmark index in the Hong Kong stock market and the derivatives written on it are the most liquid ones. For the rest of the paper, we will refer to the derivative warrants on HSI as just warrants because the underlying is an index and there will be 7

10 no confusion. Table 1 lists the financial institutions that issue warrants on HSI and the number of call and put warrants they issued during 22 to 26. As we can see, these institutions tend to issue comparable number of call warrants and put warrants. European and Australian banks such as Societe Generale, KBC, Deutsche Bank, BNP Paribas, and Macquarie Bank are the most active in this market. Table 1 here The data of warrants and options on HSI are obtained from the Hong Kong Stock Exchange. The warrants data include daily closing bid and closing ask prices, trading share volume, dollar volume, and other contract specifications such as maturity, strike price, and conversion ratio. 5 From the Hong Kong Stock Exchange, we also obtain the daily trading share volume and dollar volume by the warrants liquidity providers, and the daily amount of warrants outstanding. The options data include daily closing bid and closing ask prices, trading volume, open interest, maturity and strike price of options. The HSI level is from Datastream. The sample period in this paper is from July 15, 22 to December 31, 26. Before the starting date, data on options are not available. One round lot of options is 5 times the index value, which is around twenty thousand during the sample period. One round lot of warrants depends on the issue. The median value is 2.5 times the index value, so the minimum trading size of options is about 2 times larger than a typical warrant. Figure 2 plots the trading volume of warrants and options on HSI during the sample period. The total trading volume of the warrants on the HSI increases from less than 3 billion dollars per month to more than 7 billion dollars per month over the sample period. However, the trading volume of the options on the HSI experiences only a 5 The conversion ratio is the fraction of the shares of the underlying assets the warrant holder is entitled to buy or sell. For example, a derivative call warrant with a conversion ratio of ten entitles the owner to buy one tenth share of the underlying asset at its strike price. 8

11 moderate increase from about.85 billion dollars per month to 3.5 billion dollars per month over the same period. As we have seen earlier for the whole market, the growth of the warrants on the HSI has been much faster than that of the options on the HSI. Comparison with Figure 1 reveals that more than one third of the total trading volume of derivative warrants is that of the warrants on the HSI and that about one half of the total trading volume of options is that of the options on the HSI. Figure 2 here Out of the entire sample, about two thirds of warrants can be matched with options with the same maturity and strike price. We compare the warrant and option prices using the matched sample. For these matched warrants and options, we also consider two sub-samples. One sub-sample is the sample with positive trading volume of the warrants. The other sub-sample is the sample with positive trading volumes for both warrants and options. B. Overpricing Suppose we denote the value of HSI at business day t as H(t) and the strike price of a warrant or option as K. Let P a w(t, κ, m) and P b w(t, κ, m) be the closing bid and ask prices of a warrant (either a call or a put) on day t with moneyness κ = K/H(t) and maturity m measured in the number of days. Similarly, let P a o (t, κ, m) and P b o (t, κ, m) be the bid and ask closing prices of the option (either a call or a put) on day t with moneyness κ and maturity m. Warrants with the same (κ, m) issued by different issuers are treated as separate observations, but matched with the same option. For simplicity, the dependence of κ on t is suppressed unless it is necessary. The overpricing of a warrant relative to a matched option, D P (t, κ, m), either for calls or puts, is defined as D P (t, κ, m) = [P a w(t, κ, m) + P b w(t, κ, m)]/2 [P a o (t, κ, m) + P b o (t, κ, m)]/2 H(t) 9 1. (1)

12 The reason for normalizing by H(t) is to make the overpricing data comparable across time, as the values of HSI and the values of derivatives written on it contain an upward trend. Defined this way, overpricing is in terms of percentage of the HSI level. On each business day, we observe prices of warrants and options for only a certain moneyness level and maturities, which change with the day. One way to characterize the overpricing of warrants relative to options is through graphs as a function of a moneyness and maturity group. We divide the entire matched sample into several groups according to moneyness and maturity. The moneyness is divided into the groups of.9 κ.95,.95 < κ 1, 1 < κ 1.5 and 1.5 < κ 1. The maturity is divided into the groups of 1 14 days, days, days, days, days and days. For each intersection of moneyness and maturity groups, we pool the time-series and cross-sectional observations and calculate the 25th, 5th, and 75th percentiles of the distribution of D P (t, κ, m), for calls and puts separately. These summary statistics are plotted against the midpoint of the maturity in Figure 3. The left panels are for calls and the right panels are for puts. There are too few contracts outside the moneyness and maturity ranges to calculate meaningful statistics. Figure 3 here Figures reveals that most warrants are traded at higher prices than their option counterparts: the differences are mostly positive. There is an obvious pattern across maturity: the longer the maturity, the greater the overpricing. For some long maturity groups, the median overpricing can be higher than 1% of the underlying HSI value. For short maturities, the overpricing tend to be much smaller and the range of overpricing also tends to be smaller. About 12% warrants actually are quoted at lower prices than the options counterparts. The definition of overpricing, D p (t, κ, m), is based on the bid-ask average prices of the warrants and the options. In fact, for about 62% of the contract/day observations, 1

13 the bid price of the warrants is greater than the ask price of the options. That means, if the warrants were allowed to be sold short, individual investors could sell short these warrants, buy the matched options, and hold the position to maturity to make arbitrage profits. While individual investor can not sell short the warrants, they can sell those they already own. In any case, the warrant issuers can sell more overpriced warrants and hedge them by opposite position in the matched options. In that sense, the phenomenon of overpricing is nontrivial. 4. Overpricing and Liquidity A. Liquidity Measures We employ a number of variables to measure the liquidity of warrants and options contracts: bid-ask spread, dollar trading volume, contract size, turnover ratio and the percentage of trading by liquidity providers. Each variable measures one aspect of the liquidity. The first measure of the liquidity we consider is the bid-ask spread, which is also widely used in the literature. For the purpose of explaining the overpricing issue, we consider the bid-ask spread difference between warrants and options, D S (t, κ, m), defined as D S (t, κ, m) = [P a w(t, κ, m) P b w(t, κ, m)] [P a o (t, κ, m) P b o (t, κ, m)] H(t) 1. (2) Similar to the overpricing measure, the bid-ask spread differences are in the percentage of the HSI value. In Figure 4, we plot the summary statistics of the spread differences. The 25th, 5th, and 75th percentiles of the distribution of D S (t, κ, m) are plotted for each intersection of moneyness and maturity groups. The left panels are for calls and the right panels are for puts. Figure 4 here 11

14 The bid-ask spreads for warrants are mostly lower than those for options: the spread differences are mostly negative, except for the short maturities. The bid-ask spreads of warrants tend to be much smaller than those of options for long maturity groups. This pattern also corresponds well to the overpricing pattern observed in Figure 3. For some of the near-the-maturity groups, the median bid-ask spread difference is positive. The overpricing for these groups is not obvious either. The dollar trading volume is the total daily dollar trading volume per warrant or option contract, a widely used liquidity measure. They are denoted as V w and V o for warrants and options respectively. To summarize the information on this variable, we present statistics for each intersection of the moneyness and maturity groups in figures. Instead of reporting the distribution, we report the total trading volume in each group to highlights the difference in the two markets. Figure 5 and Figure 6 plot the total dollar trading volume for calls and puts, respectively. The left panels are for the warrants and the right panels are for the options. The unit is in billion HKD. Note the scales of the vertical axis for different panels are different. Figure 5 here Figure 6 here It is clear from the figures that warrants are much more actively traded than options for most of the groups. For both of the warrants and options, near-the-money groups have relatively larger trading volume than far in-the-money or far out-of-money groups. The trading volume is distributed differently across maturity groups for the warrants and the options. Most of trading volume of the warrants is concentrated in the medium to long maturity groups. Short maturity warrants are barely traded. For options, however, medium maturity groups tend to have a higher trading volume than the long maturity groups. This pattern corresponds well to the pattern of overpricing in Figure 3 that overpricing is large for long maturities and small for short maturities. 12

15 The third measure we consider is the dollar contract size, which is the price of one lot of warrants or one contract of options. It can be regarded as the minimum capital requirement for investors to participate in each of the market. The contract size matters because there are a large number of small individual investors in terms of personal wealth who trade derivative warrants for increasing leverage. They can participate in the market only when they can afford to buy the minimum amount. A Small contract size facilitates these trades. Figures 7 and 8 plot the 25th, 5th, and 75th percentiles of the distribution of the dollar contract size of the warrants, C w, and of options, C o, for all moneyness and maturity groups. The left panels are for warrants and the right panels are for options. Figure 7 here Figure 8 here The figures show that the minimum dollar amount of buying warrants is typically below five thousand HKD, which makes the warrants market accessible to the small individual investors in Hong Kong. The options contracts, however, typically cost tens of thousand HKD, which is nontrivial amount for small individual investors. Only outof-the-money option contracts with short maturity cost less than ten thousand HKD. The trading in the warrants market is more active than that in the options market evidenced by the difference in the total dollar trading volume between the two markets. Alternatively, we can measure the trading activity in each market by turnover ratio, the frequency of a share changing hands, within a given period. Turnover ratio is widely used in the microstructure literature for measuring one aspect of liquidity for stock markets. The reciprocal of a turnover ratio is usually interpreted as the average holding period by investors. For options and warrants, however, some modifications are needed. The turnover for an warrant contract, T w (t, κ, m), is defined as T w (t, κ, m) = [R w(t, κ t, m) N w (t, κ t, m)] 1 2 [RL w(t, κ t, m) N w (t, κ t, m)], (3) O w (t 1, κ t 1, m) 13

16 where R w (t, κ t, m) is the trading volume of the warrant with (κ t, m) on day t in the number of shares, R L w(t, κ t, m) is the trading volume of the warrant with (κ t, m) on day t by the liquidity provider, O w (t, κ t, m) is the outstanding amount of the warrant with (κ t, m) on day t, and N w (t, κ t, m) = max[o w (t, κ t, m) O w (t 1, κ t 1, m), ] is the new issues of the warrants. The new issues are excluded because turnover ratio is defined for existing contracts. The trading by liquidity providers is excluded to avoid double counting. The liquidity traders do trade for themselves sometimes. Since we do not have data to distinguish the trades by liquidity providers between those for themselves and those for customers, the above definition is based on the assumption that liquidity providers always trade for customers to provide liquidity and, therefore, may underestimate the actual turnover ratio. For the options, the turnover ratio for an option contract, T o (t, κ, m), is defined as T o (t, κ, m) = R o(t, κ t, m) N o (t, κ t, m), (4) O o (t 1, κ t 1, m) where R o (t, κ t, m) is the trading volume in contracts of the option with (κ t, m) on day t, O o (t, κ t, m) is the outstanding amount of the option with (κ t, m) on day t, and N o (t, κ t, m) = max[o o (t, κ t, m) O o (t 1, κ t 1, m), ] is the new contracts of the same terms. Like the definition of turnover ratio for warrants, N o (t, κ t, m) is subtracted to exclude the new option contracts in calculating turnover ratio. However, we do not have the information on the amount of trading by option market makers. We assume that all the trades are between the customers and such a treatment may overestimate the actual turnover ratio for options. Figures 9 and 1 plot the 25th, 5th and 75th percentiles of the distribution of the turnover ratios of warrants and options for all moneyness and maturity groups. Examining the turnover ratio reveals a significant difference between the two markets. For long and medium maturities, the turnover ratio of the warrants is many times higher than that of the options. For the warrants, the long maturity, near-the-money groups have the highest turnover ratio. The 75th percentiles are out of plotted range. 14

17 The median value for the longest maturity group is greater than 2, meaning that, on average, each contract changes hands at least twice a day. For the other groups, turnover ratio is lower, but still in a order of one tenth, suggesting that warrants are not used for long-term investments. For the options, the median value of the highest turnover ratio group is less than.2, suggesting that most of the investors hold options for more than a week. The 75th percentiles for some far in-the-money groups are zero. Recall that the turnover ratios of warrants may be under-estimated, while the turnover ratios of options may be over-estimated. The actual situation may be more extreme than what we described here. We observe that the turnover ratios of the warrants tend to decrease as the maturity decreases, while the turnover ratios of the options tend to increase as the maturity decreases. We also observe that near-the-money warrants and options are more frequently traded than the out-of-the-money ones. These patterns have some similarity with those of bid-ask spread differences and trading volumes in previous figures. As such, turnover ratio may also have a bearing on the overpricing of the warrants relative to the options. Figure 9 here Figure 1 here A unique measure of liquidity in the warrant market is the percentage trading by liquidity providers, L(t, κ, m), calculated as the share volume traded by the liquidity providers divided by the total share volume for a warrant contract with κ and m on a day t for which trading volume is positive. The higher the value is, the more actively the liquidity providers supply the liquidity to the market by quoting the best bid and ask prices. Figure 11 plots the 25th, 5th, and 75th percentiles of the distribution of L(t, κ, m) for various moneyness and maturity groups. In general, the liquidity providers supply liquidity quite actively. The average L(t, κ, m) for the entire sample is 69.21%. Especially, for the long maturity warrants, nearly all the trading involves the liquidity 15

18 providers. For the short maturity warrants, the liquidity providers supply liquidity selectively, evidenced by a wide distribution of L(t, κ, m). Across moneyness, liquidity providers trade in-the-money warrants more actively than out-of-the-money warrants. Note that for a day with zero trading volume, L(t, κ, m) is undefined. Figure 11 here B. Regression Analysis From the patterns of the liquidity measures, we observe that the long maturity warrants are more liquid than the long maturity options. This corresponds to the observations that long maturity warrants are more expensive than long maturity options. In this subsection, we use regression analysis to quantify the warrants overpricing relative to the options contributed by the liquidity difference between the warrants and the options. We examine the extent to which liquidity differences can explain the cross-sectional and time-series variation in overpricing of the warrants relative to the options. We run regressions of the overpricing on various measures of liquidity, D P = f(d S, D C, D V, T w, L) + ε (5) where D P is the overpricing, D S is the bid-ask spread difference, D C is the contract size difference in 1 HK dollars, D V = log[(1 + V w )/(1 + V o )] is the trading volume difference, T w = log[1+t w ] is the logarithm of warrant turnover ratio, and L = log[1+l] is the percentage of trading from the liquidity providers in the warrants market. 6 functional form f we consider is linear and quadratic ones. The regressions are run over three samples. The first sample includes all the matched contract observations for which the involved variables are defined. Since some of the warrant contract have zero trading volume on some days for this sample, L is not defined and only other four variables are 6 We also try the turnover ratio difference D T = log[(1 + T w )/(1 + T o )], instead of T w. Since the difference between T w and T o is so large, adding T o does not make any difference. It merely reduces 15% of the observations because T o is not defined for zero option open interest. 16 The

19 used. The second sample consists of all matched contracts with positive trading volume of the warrants. This leaves out about one third of observations. The third sample requires positive trading volume of both the warrants and the options. The sample size of the third sample reduces to one half of the second sample. We note that the third sample should be the most important one, as quoted prices without trading are not reliable. Before presenting regression results, we show the correlations of the overpricing D S and the various liquidity measures. Table 2 reports the correlations for the sample of all matched contracts and the sample with positive trading volume of warrants and options. Overall, D P is negatively correlated with D S and D C and positively correlated with D V, T w and L. The correlations are the highest for T w and L. Among the liquidity measures, D V and T w have the highest pairwise correlation. Other than that, the absolute values of correlations among the liquidity measures are below.4. The correlations between the two samples only differ quantitatively, and the signs of the correlations are consistent between the two samples. The correlations for the sample with positive trading volume of warrants are qualitatively the same. Table 2 here In Table 3, we present results of linear regressions. The t-statistics in parentheses are adjusted for a 9-day lag of auto-correlation using the procedure of Newey and West (1987). For the first sample, without explanatory variables, the estimate of the constant shows that there is an average overpricing of.3348% of the index value. All the four explanatory variables are significant with anticipated signs. The R 2 of the univariate regressions indicates the explanatory power of each variable. The constants in these univariate regression models represent the models prediction of overpricing if there are no differences in the liquidity measures, or there is no liquidity providers trading and, therefore, stand for the part of average overpricing remained to be explained. The result 17

20 of the multiple regression shows that the four variables can explain 15.8% of the total variation of the overpricing, and that T w stands out as the most important explanatory variable, while D S becomes insignificant. For the sample with positive trading volume of warrants, the average overpricing is.3627% of the underlying index value, similar to the previous sample. The univariate regression with L has the highest R 2 among all variables. It seems that L alone explains the average overpricing as the constant in this univariate regression is not statistically different from zero. The model with all the five explanatory variables have a much higher R 2 than any of the univariate regression. Both the coefficients of D S and D C become insignificant. Interestingly, the constant for this model becomes negative. For the sample with positive trading volume of warrants and options, the average overpricing is relatively lower,.2383%. This is due to the fact that some long-term options, for which the overpricing is the highest, are not traded and are excluded from the sample. Except that, the univariate and multivariate regressions results are similar to the ones in the second sample. The model with all the five explanatory variables has a R 2 around 3% with the coefficients of D S and D C being insignificant. Table 3 here While the linear regression models capture the most salient features of the relationship between overpricing of the warrants relative to the options and liquidity measures, the fact that these liquidity measures together appear over-explain the average overpricing is perplexing. It is suspected that overpricing may be not linear in the liquidity measures. We therefore consider adding quadratic terms to capture the possible nonlinearity. We run a regression with all linear and quadratic terms using all the three sample. The results show that some of the quadratic terms indeed play a role in explaining the overpricing. The quadratic terms tend to be more important in the third sample than in the first one. For brevity, we present in Table 4 the model in which only those quadratic terms that are significant in the third sample are included. For the 18

21 first sample, the quadratic term DC 2 and D2 S are significant. Others are less important. The R 2 increases and the constant term reduces. For the second sample with L defined, more quadratic terms become significant. The absolute value of the constant is reduced compared to that in Table 3. For the third sample, in which the added quadratic terms are all significant, we briefly point out the pattern of the nonlinearity. First, overpricing is convex in D S and L and concave in D C and T w. The interaction between D S and T w is positive, while the other three involving D C are all negative. The constant is close to zero and insignificant, suggesting that the functional specification with quadratic terms are more proper. The model with quadratic terms also improves R 2 to 36.54% for the third sample. Table 4 here 5. Overpricing and Holding Period Returns For the matched warrants and options, their payoffs on the maturity date are the same. Therefore, if a warrant has a higher price than the corresponding option and they are both held to the maturity, the return on the warrant must be dominated by the return on the options. From the earlier analysis, we see that long-maturity warrants tend to have very high turnover ratios, which imply very short holding periods. For short holding periods, are returns on the warrants necessarily dominated by those on the options? The answer is not obvious for two reasons. The first reason is transaction costs. The bid-ask spread tends to be smaller for warrants than for the options, especially for long-maturities ones. The second reason is that overpricing is not always monotonic in maturity. If a warrant is bought at a high price, but is also sold at a higher price, then return on the warrant may not necessarily be lower than that on the corresponding option. We examine the difference in short-term holding-period returns between the warrants 19

22 and the options. We consider from a buyer s point of view only because the warrants can not be sold short. The holding-period return is defined over the ask price on day t i and the bid price on day t as R i w(t, κ t, m) = R i o(t, κ t, m) = [ ] Pw(t, b (1/i) κ t, m) 1 (6) Pw(t a i, κ t i, m i) [ ] Po b (1/i) (t, κ t, m) 1 (7) Po a (t i, κ t i, m i) where i = 1 for a one-day return and i = 7 for a one-week return, normalized to be on the daily basis. These returns are hypothetical in the sense that options buyers normally do not trade in such short holding periods. Table 4 reports the average differences in the holding period returns between the warrants and the options for intersections of moneyness and maturity groups using all matched contracts. Panel A is for the average one-day return differences and Panel B is for the average one-week return differences. The t-statistics in parentheses are adjusted for a 9-day lag of auto-correlation using the Newey-West procedure. Table 5 here For the majority of the groups, the one-day holding period return is higher on the warrants than on the options, especially for long-maturity and near-the-money groups, as seen in Panel A. Many of these average one-day returns are significantly positive. On the other hand, the average one-week holding period return differences between the warrants and the options tend to be negative and some are significant, as seen in Panel B. 7 The results indicate that for short holding periods such as one day, the consideration of transaction costs overweighs that of pricing in determining returns. As the holding period gets longer, the convergence of the warrants payoff and the options payoff takes effect and the initial pricing becomes important. The contrast between 1-day and 1-week 7 The sample with positive trading volume of both the warrants and options gives a quantitatively similar results. They are not reported here to save space. 2

23 holding period returns in the warrants and options suggests that investors who have short-term trading in mind should trade in the warrants market because the transaction costs are lower, while investors with longer holding periods should trade in the options market as returns on options tend to be higher due to lower initial prices. 6. Conclusion In this paper, we study the overpricing of the derivative warrants in Hong Kong. We find that the majority of the derivative warrants written on the Hang Seng Index are traded at higher prices than the options with the same underlying asset, strike price and maturity. The derivative warrants are also much more liquid than the options. We use a number of measures for the liquidity difference between the derivative warrants and the options, namely, the differences in the dollar trading volume, the bid-ask spread, the contract size and the turnover ratio. The regression analysis shows that the liquidity difference measured by these three variables explain the overpricing of derivative warrants to a large extent. We also use a unique liquidity measure for the derivative warrants, the percentage of trading volume by the liquidity providers that measures how actively the liquidity providers supply the liquidity for their derivative warrant contracts. This additional variable contributes a large portion of explanatory power in the regression analysis. The relationship between overpricing and the liquidity measures also shows strong nonlinearity. From the turnover ratio of derivative warrants and options, we infer a significant difference in the holding period between the two types of securities. The average holding period for the derivatives warrants is only about one day, while most of options have holding periods beyond one week. We document that taking the bid-ask spread into consideration, derivative warrants have relatively higher returns for the one-day holding period because of their lower bid-ask spreads, while options have relatively higher returns for one-week (or longer) holding periods because of their lower prices. The better 21

24 liquidity and higher short-term returns of derivative warrants make them a good tool for the purpose of short-term speculation. Our findings enhance the understanding of how the two markets serve different needs for different investors. 22

25 References Amihud, Y. and H. Mendelson, 1986, Asset pricing and the bid-ask spread, Journal of Financial Economics, 17, Amihud, Y. and H. Mendelson, 1989, The effects of beta, bid-ask spread, residual risk and size on stock returns, Journal of Finance, 44, Amihud, Y. and H. Mendelson, 1991, Liquidity, maturity and the yields on U.S. government securities, Journal of Finance, 46, Black, F. and M. Scholes, 1973, The Pricing of Options and Corporate Liabilities, Journal of Political Economy, 81, Brennan, M. J. and A. Subrahmanyam, 1996, Market microstructure and asset pricing: On the compensation for illiquidity in stock returns, Journal of Financial Economics, 41, Brenner, M., R. Eldor and S. Hauser, 21, The price of options illiquidity, Journal of Finance, 56, Chan, H. W and S. M. Pinder, 2, The value of liquidity: evidence from the derivatives market, Pacific-Basin Finance Journal, 8, Chan, Y. and K. C. J. Wei, 21, Price and volume effects associated with derivative warrant issuance on the Stock Exchange of Hong Kong, Journal of Banking and Finance, 25, Chen, K. C. and L. Wu, 21, Introduction and expiration effects of derivative equity warrants in Hong Kong, International Review of Financial Analysis, 1, Chow, Y., J. Li and M. Liu, 27, Making Hong Kong s derivative warrants market, working paper. 23

26 Dimson, E. and B. Hanke, 24, The expected illiquidity premium: Evidence from equity index-linked bonds, Review of Finance, 8, Draper, P., B. S. C. Mak and G. Y. N. Tang, 21, The derivative warrant market in Hong Kong: relationships with underlying assets, Journal of Derivatives, Summer, Duan, J. C. and Y. Yan, 1999, Semi-parametric pricing of derivative warrants, working paper. Newey, W. and West, K., 1987, A Simple, Positive Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix, Econometrica 55, Silber, W., 1991, Discounts on restricted stock: The impact of illiquidity on stock prices, Financial Analyst Journal, 47,

27 Table 1 Derivative warrant issuers The table lists the codes, names of issuers, and the numbers of call warrants and put warrants on the Hang Seng Index from July 22 to December 26. Code Name Call Put AA ABN Amro 7 6 BP BNP Paribas CA Calyon 4 2 CG Citigroup 2 2 CL Credit Lyonnais 5 2 CS Credit Suisse 1 DB Deutsche Bank GS Goldman Sachs JP J.P. Morgan 2 KC KBC MB Macquarie Bank MS Morgan Stanley SG Societe Generale UB UBS

28 Table 2 Correlations The table reports the correlations of the overpricing D P, and the various liquidity measures in the regression analysis, D S, D C, D V, Tw and L. D S is the bid-ask spread difference, D C is the contract size difference, D V = log[(1 + V w )/(1 + V o )] is the trading volume difference, Tw = log(1 + T w ) where T w is the turnover ratio of the warrant, L = log(1 + L) where L is the percentage of trading by the liquidity providers in the warrants market. The upper triangle is for the sample of all matched contracts, and the lower triangle is for the sample with positive volume of warrants and options. D P D S D C D V Tw D P D S D C D V T w L

29 Table 3 Overpricing and liquidity: linear regressions The table reports the coefficients of the following regression of overpricing on various measures of liquidity. D P = β 1 + β 2 D S + β 3 D C + β 4 D V + β 5 Tw + β 6 L + ε where D P is the overpricing, D S is the bid-ask spread difference, D C is the contract size difference, D V = log[(1+v w )/(1+V o )] is the trading volume difference, T w = log(1+t w ) where T w is the turnover ratio of the warrant, L = log(1 + L) where L is the percentage of trading by the liquidity providers in the warrants market. Panel A is for the sample of all matched contracts/day. Panel B is for the sample with positive trading volume of the warrants. Panel C is for the sample with positive trading volumes for both the warrants and the options. n is the number of observations. The t-statistics in parentheses are adjusted for a 9-day lag of auto-correlation using the Newey-West procedure. The sample period is from July 22 to December 26. A. Sample of all matched warrants and options, n = Const. D S D C D V Tw L R ( 19.84) ( 2.13) ( -2.5) ( 14.32) ( -6.31) ( 11.84) ( 9.56) ( 16.65) ( 18.32) ( 9.89) ( -.58) ( -4.42) ( 3.4) ( 14.12) 27