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The Stock Market Index Dow Jones Industrial Average Finance Essay

Introduction

The Dow Jones Industrial Average, also referred to as the Industrial Average, the Dow Jones, the Dow 30, or simply the Dow, is a stock market index, and one of some indices created by Wall Street Journal editor and Dow Jones & Company co-founder Charles Dow. The average is named after Dow and one of his business associates, statistician Edward Jones. It is an index that shows how 30 large, widely owned companies based in the United States have traded during a standard trading session in the stock market. It is the second oldest U.S. market index after the Dow Jones Transportation Average, which Dow also created.

The Industrial part of the name is largely historical, as many of the modern 30 components have little or nothing to do with traditional heavy industry. The average is price-weighted, and to reimburse for the effects of stock splits and other adjustments, it is currently a scaled average. The value of the Dow is not the actual average of the prices of its component stocks, but rather the sum of the component prices divided by a divisor, which changes whenever one of the component stocks has a stock split or stock dividend, so as to generate a reliable value for the index.

Along with the NASDAQ Composite, the S&P 500 Index, and the Russell 2000 Index, the Dow is surrounded by the most closely watched benchmark indices tracking targeted stock market activity. Although Dow compiled the index to gauge the performance of the industrial sector within the American economy, the index's performance continues to be influenced by not only corporate and economic reports, but also by domestic and foreign political events such as war and terrorism, as well as by natural disasters that could potentially lead to economic harm.

800px-DJIA_historical_graph_to_jan09_(log).svg.png

Historical logarithmic graph of the DJIA from the 1890s to the 2010s.

800px-DJIA_2000s_graph_(log).svg.png

Recent logarithmic  graph of the DJIA from Jan 2000 through Oct 2009.

History

The Dow Jones Industrial Average was founded by Charles Dow on May 26, 1896, and represented the dollar average of 12 stocks from leading American industries. Previously in 1884, Mr. Dow had composed an initial stock average called the Dow Jones Averages, which contained nine railroads and two industrial companies that appeared in the Customer's Afternoon Letter, a daily two-page financial news bulletin which was the precursor to The Wall Street Journal. Of the original 12 stocks forming the Dow Jones Industrial Average compiled later in 1896, no longer railroad stocks, but purely industrial stocks, only General Electric is currently part of that index.

When it was first available in the late 1890s, the index stood at a level of 40.94, but ended up beating its all-time low of 28.48 during the summer of 1896 during the depths of what later became known as the Panic of 1896. Many of the major percentage price moves in the Dow occurred early in its history, as the emerging industrial economy matured. A brief war in 1898 between the U.S. and the Spanish Empire might have only had a minor collision in the Dow's way.

The decade of the 1900s would see the Dow halt its thrust as it worked its way through a pair of cataclysmic financial crisis'; the Panic of 1901 and the Panic of 1907. The Dow would be stuck in a trading range of between the 50 and 100 point levels till late 1909. The negativity nearby the 1906 San Francisco earthquake did little to get better the economic climate. International disturbances such as the Russo-Japanese War were few and far between and seemed to have little if any influence on the Dow. The average would end off the decade near the area of the 100 point level.

At the start of the 1910s, the decade would begin with the Panic of 1910–1911 stifling economic growth for a lengthy period of time. History would later take its course on July 30, 1914; as the average stood at a level of 71.42 when a result was made to close down the New York Stock Exchange, and postpone trading for a span of 4½ months. Some historians believe the exchange closed because of a concern that markets would thrust as a result of panic over the onset of World War I. An alternative explanation is that the Secretary of the Treasury, William Gibbs McAdoo, closed the exchange because he wanted to conserve the U.S. gold stock in order to launch the Federal Reserve System later that year, with enough gold to keep the U.S. at par with the gold standard. When the markets reopened on December 12, 1914, the index closed at 54, a drop of 24.39%. Also in trying to describe the huge percentage drop, there was a new recalculation performed on the index in September 1916. Additions to the index raised the number of companies to 20, resulting in a mathematical inconsistency to the average from previous years in the past including 1914. Following World War I, the U.S. would experience another recession in economic activity in what became known as the Post-World War I recession. The Dow's performance would remain practically unchanged from the closing value of the previous decade, adding only around 5%, from about the 100 level to 105.

During the 1920s, specifically in 1928, the components of the Dow were increased to 30 stocks near the economic height of that decade, which was phrased as the Roaring Twenties. The prosperous nature of the economic climate, muted the negative influence of an early 1920s recession plus certain international conflicts such as the Polish-Soviet war, the Irish Civil War, the Turkish War of Independence and the first phase of the Chinese Civil War. The Crash of 1929 and the consequent Great Depression returned the average to its starting point, almost 90% below its peak. By July 8, 1932, following its intra-day low of 40.56, the Dow would end up closing the session at 41.22. The high of 381.17 on September 3, 1929, would not be surpassed until 1954, in inflation-adjusted numbers. However, the bottom of the 1929 Crash came just 2½ months later on November 13, 1929, when intra-day it was at the 195.35 level, closing a little higher at 198.69. For the decade, the Dow would end off with a healthy 173% gain from around the 105 level to a level of 286.

Marked by global volatility, the 1930s contended with several consequential European and Asian outbreaks of war, leading up to catastrophic World War II; including the Spanish Civil War, the Second Italo-Abyssinian War, the Soviet-Japanese Border War and the Second Sino-Japanese War. On top of that, the U.S. dealt with a painful recession in 1937 and 1938. The biggest one-day percentage gain in the index, 15.34%, happened on March 15, 1933, in the depths of the 1930s bear market. However, as a whole, the Dow posted some of its worst performance for a negative return. For the decade, the average was down from around the 286 level to 148, a loss of about 48%.

Post-war reconstruction during the 1940s, along with renewed buoyancy of peace and prosperity, brought about a 39% surge in the Dow from around the 148 level to 206. The power in the Dow occurred despite a brief recession in 1949 and other global conflicts which started a short time later plus the latter stages of the Chinese Civil War, the Greek Civil War, the Indo-Pakistani War of 1947 and the 1948 Arab-Israeli War.

During the 1950s, the Korean War, the Algerian War, the Cold War and other political tensions such as the Cuban Revolution, as well as widespread political and economic changes in Africa during the initial stages of European Decolonization, did not stop the Dow's bullish climb higher. In addition, the U.S. would also make its way through two grinding recessions; one in 1953 and another in 1958.

The Dow's bullish behavior began to stall during the 1960s as the U.S. became entwined with foreign political issues such as the Bay of Pigs Invasion involving Cuba, the Vietnam War, the Portuguese Colonial War, the Colombian Civil War which the U.S. assisted with short-lived counter-guerrilla campaigns, and domestic issues such as the Civil Rights Movement. For the decade though, and despite a mild recession between 1960 and 1961, the average still managed a respectable 30% gain from the 616 level to 800.

The 1970s noticeable time of economic uncertainty and troubled relations between the U.S. and certain Middle-Eastern countries. To begin with, the decade happened off with the ongoing Recession of 1969–1970. Following that, the 1973–1975 recession, the 1973 Oil Crisis as well as the 1979 energy crisis began as a prologue to a disastrous economic climate injected with stagflation; the combination between high unemployment and high inflation. However, on November 14, 1972, the average closed above the 1,000 mark (1,003.16) for the first time, during a brief relief rally in the midst of a lengthy bear market. Between January 1973 and December 1974, the average lost 48% of its value in what became known as the 1973–1974 Stock Market Crash. The situation was exacerbated following the events nearby the Yom Kippur War and the series of 1970s Energy Crisis' which followed it soon after. Although the Vietnam War ended in 1975, new tensions arose towards Iran surrounding the Iranian in 1979.

The 1980s saw a quick increase in the average, though severe corrections did occur along the way. The largest one-day percentage drop occurred on Black Monday; October 19, 1987, when the average fell 22.61%. There were no clear reasons given to explain the crash, but program trading appeared to be a major contributing factor. On October 13, 1989, the Dow stumbled into another downfall, the 1989 Mini-Crash which initiated the collapse of the junk bond market as the Dow registered a loss of almost 7%. However, for the rest of the 1980s as a whole, the Dow made a thoughtful of 228% increase from the 838 level to 2,753; despite the market crashes, an Early 1980s recession, and other political distractions such as the Soviet War in Afghanistan, the Falklands War, the Iran-Iraq War, the Second Sudanese Civil War and the First Intifada in the Middle East.

600px-DJIA_Black_Monday_1987.svg.png

The Dow fell 22.61% on Black Monday (1987) from about the 2,500 level to around 1,750. Two days later, it rose 10.15% above the 2,000 level for a mild recovery attempt.

To start off, the markets contended with the 1990 oil price shock compounded with the effects of the Early 1990s recession. Certain influential foreign conflicts such as the 1991 Soviet coup d'état attempt which took place as part of the initial stages of the Dissolution of the USSR and the Fall of Communism; the First and Second Chechen Wars, the Persian Gulf War and the Yugoslav Wars failed to dampen economic enthusiasm surrounding the ongoing Information Age and the "Irrational Exuberance" (a phrase coined by Alan Greenspan) of the Internet Boom. Even the occurrences of the Rwandan Genocide and the Second Congo War, termed as "Africa's World War" that involved 8 separate African nations which together between the two killed over 5 million people; didn't seem to have any noticeable negative financial impact on the Dow either. Between late 1992 and early 1993, the Dow staggered through the 3,000 level making only modest gains as the Biotechnology sector suffered through the downfall of the Biotech Bubble; as many biotech companies saw their share prices rapidly rise to record levels and then subsequently fall to new all-time lows.

On November 21, 1995, the DJIA closed above the 5,000 level (5,023.55) for the first time. Over the following two years, the Dow would quickly tower above the 6,000 level during the month of October in 1996, and the 7,000 level in February 1997. On its march higher into record territory, the Dow easily made its way through the 8,000 level in July 1997. However, later in that year during October, the events nearby the Asian Financial Crisis plunged the Dow into a 554 point loss to a close of 7,161.15; a retrenchment of 7.18% in what became known as the 1997 Mini-Crash. Although internationally there was negativity surrounding the 1998 Russian financial crisis, the Dow would go on to surpass the 9,000 level during the month of April in 1998, making its sentimental push towards the symbolic 10,000 level. On March 29, 1999, the average closed above the 10,000 mark (10,006.78) after flirting with it for two weeks. This encouraged a celebration on the trading floor, complete with party hats. The scene at the exchange made front page headlines on many U.S. newspapers such as The New York Times. On May 3, 1999, the Dow achieved its first close above the 11,000 mark (11,014.70). Total gains for the decade exceeded 315%; from the 2,753 level to 11,497.

The Dow averaged a 5.3% return compounded annually for the 20th century; a record Warren Buffett called "a wonderful century"; when he planned that to achieve that return again, the index would need to close at about 2,000,000 by December 2099.

Even during the height of the dot-com era, authors James K. Glassman and Kevin A. Hassett went so far as to publish a book entitled: Dow 36,000. Their theory was to imply that stocks were still cheap and it was not too late to benefit from rising prices during the Internet boom.

Characterized by fear on the part of newer investors, the uncertainty of the 2000s brought on a significant bear market. There was indecision on whether the cyclical bull market represented a prolonged temporary bounce or a new long-term trend. Ultimately, there was widespread resignation and disappointment as the lows were revisited, and in some cases, surpassed near the end of the decade.

The Dow Jones Wilshire 5000 approximates the shape of the rise in the DJIA during the 1990s acceleration. From a trading low of under 4,000 in 1990 to above the 12,000 mark in the year 2000 with intermittent slides throughout the decade.Dow_jones.png

CALCULATION OF THE INDEX

To calculate the DJIA, the sum of the prices of all 30 stocks is divided by a Divisor, the Dow Divisor. The divisor is adjusted in case of stock splits, spinoffs or similar structural changes, to ensure that such events do not in themselves alter the numerical value of the DJIA. Early on, the initial divisor was composed of the original number of component companies; which made the DJIA at first, a simple arithmetic average. The present divisor, after many adjustments, is less than one (meaning the index is larger than the sum of the prices of the components). That is:

\text{DJIA} = {\sum p \over d}

where p are the prices of the component stocks and d is the Dow Divisor.

Events like stock splits or changes in the list of the companies composing the index alter the sum of the component prices. In these cases, in order to avoid discontinuity in the index, the Dow Divisor is updated so that the quotations right before and after the event coincides:

\text{DJIA} = {\sum p_\text{old} \over d_\text{old} } = {\sum p_\text{new} \over d_\text{new} }.

Hang Seng

Introduction

The Hang Seng Index (abbreviated: HSI) is a freefloat-adjusted market capitalization-weighted stock market index in Hong Kong. It is used to proof and observe daily changes of the largest companies of the Hong Kong stock market and is the main indicator of the overall market performance in Hong Kong. These 45 companies represent about 67% of capitalisation of the Hong Kong Stock Exchange.

Hang Seng Index (HSI) is a value-weighted index of 33 blue-chip common stocks traded on the Hong Kong Stock Exchange. It is considered as the most significant barometer of the Hong Kong stock market. Both futures and alternative contracts on the HSI are traded on the Hong Kong Futures Exchange. Each futures and option contract amounts to HK$50 per index point. The total trading volume on the HSI futures was, for example, 14 433 contracts on 17 June 1999 and the open interest equaled 58 357 contracts at the closing of that day. For the option contracts (calls and puts) of the two nearby months, the daily trading volume was 1748 contracts and the open interest stood at 51 667 contracts on the same day. These derivative contracts play an important role in the Hong Kong financial market and were alleged to be the important instruments used by speculators as an indirect means to attack the Hong Kong dollar during the recent Asian financial turmoil. Moreover, the Hong Kong market is, due to its high liquidity and transparency, often used by international institutional investors and investment banks as a temporary surrogate for reducing or increasing exposure to other East Asian markets. This particular role adds to the significance of the HSI-based derivatives.

HSI was started on November 24, 1969, and is currently compiled and maintained by HSI Services Limited, which is a utterly owned subsidiary of Hang Seng Bank, the largest bank registered and listed in Hong Kong in terms of market capitalisation. It is responsible for compiling, publishing and managing the Hang Seng Index and a range of other stock indexes, such as Hang Seng China AH Index Series, Hang Seng China Enterprises Index, Hang Seng China H-Financials Index, Hang Seng Composite Index Series, Hang Seng Freefloat Index Series and Hang Seng Total Return Index Series.

The objective of this paper is to study how the HSI options are priced. The HSI options have several features worth noting and likely to make a “cleaner” analysis possible. These features include: (1) the HSI options are European-style; (2) both the HSI options and futures are cash settled; (3) the expiration days of the HSI futures coincide with those of the HSI options; (4) the HSI options and futures are traded side by side on the same exchange involving the same clearing house; and (5) buyers of HSI options are not required to pay the full premium initially because the futures-style margining system is used. Therefore, the HSI options can be priced as if they are European-style futures options with both the option and futures share the same adulthood. The last feature allows us to bypass the difficult task of determining the appropriate dividend yield for the index. The Asian financial turmoil in 1997 and afterwards further makes the HSI options interesting in the sense that it provides a test sample for investigating how an option pricing model performs in a turbulent market environment.

Hang Seng Index (HSI), the benchmark of the Hong Kong stock market, is one of the best known indices in Asia and widely used by fund managers as their performance benchmark.

The Hang Seng Index is a market capitalisation-weighted index (shares outstanding multiplied by stock price) of the constituent stocks. The influence of each stock on the index's performance is directly proportional to its relative market value. Constituent stocks with higher market capitalisation will have greater impact on the index's performance than those with lower market capitalisation. The constituent stocks are grouped under Commerce and Industry, Finance, Properties and Utilities sub-indices. 

To meet the growing interests in the Hong Kong stock market and rising demand for related hedging tools, the Hong Kong Futures Exchange (HKFE) first introduced Hang Seng Index futures contracts in May 1986 followed by the introduction of Hang Seng Index options contracts in March 1993. These contracts provide investors with a set of effective instruments to manage portfolio risk and to capture index arbitrage opportunities. The popularity of Hang Seng Index futures and options has developed step by step with increasing domestic and international investors' participation.

When the Hang Seng Index was first published, its base of 100 points was set equivalent to the stocks' total value as of the market close on July 31, 1964. Its all-time low is 58.61 points, reached retroactively on August 31, 1967, after the base value was established but before the publication of the index. The Hang Seng passed the 10,000 point milestone for the first time in its history on December 10, 1993 and, 13 years later, passed the 20,000 point milestone on December 28, 2006. In less than 10 months, it passed the 30,000 point milestone on October 18, 2007. Its all-time high, set on October 30, 2007, was 31,958.41 points during trading and 31,638.22 points at closing. From October 30, 2007 through March 9, 2008, the index lost 9,426 points or approximately 30%. On September 5, it fell past the 20,000 mark the first time in almost a year to a low of 19,708.39, later closing at 19,933.28. On October 8, 2008, the index closed at 15,431.73, over 50% less than the all-time high and the lowest closing value in over two years. On October 27, 2008, the index fell to 10,676.29 points, having fallen nearly two-thirds from its all-time peak. But stocks passed the 20,000 point milestone again to 20,063.93 on 24 July 2009.

History

There is a agreement among academics and practitioners that the foundation of the modern derivatives pricing theory, i.e., the Black–Scholes option pricing model (Black and Scholes, 1973), consistently exhibits two forms of methodical pricing errors. One well-documented evidences is the “volatility smile/smirk”. This term refers to the observed phenomenon that the volatility of the underlying asset, inferred from the market price using the Black–Scholes model, exhibits a convex relationship (often tilted towards the out-of-the-money call options) to the exercise price of the option (see, e.g., Rubinstein, 1985; Rubinstein, 1994; Sheikh, 1991; Canina and Figlewski, 1993 and Derman and Kani, 1994; Duan, 1996). Another well-documented finding is that the implied volatilities for options of different maturities, but on a same underlying asset, are different (see e.g., Black, 1975; Whaley, 1982 and Heynen et al., 1994; Campa and Chang, 1995). The second phenomenon is commonly known as the term structure of implied volatilities.

Many alternative option pricing models have been proposed to deal with the observed pricing biases associated with the Black–Scholes model. Cox and Ross (1976) proposed the constant-elasticity-of-variance model. Merton (1976) and Naik and Lee (1990) developed the jump-diffusion model where asset returns are allowed to have discrete jumps. Madan and Milne (1991) presented the variance-gamma option pricing model where the variance itself follows a gamma distribution. Hull and White (1987) proposed a bivariate diffusion model where both asset returns and its volatility are governed by diffusion processes. Other stochastic volatility models include Scott, 1987; Stein and Stein, 1991 and Wiggins, 1987, and Heston (1993), among others. In practice, an ad hoc approach has often been used instead to account for these two forms of predictable pricing biases. Specifically, the past Black–Scholes implied volatility of an option is first linked to its strike prices and maturity by, say, a regression. This approximate relationship then serves as the basis for calibrating the future Black–Scholes implied volatility for options with a different strike price and/or maturity. Such an ad hoc procedure has been a ordinary practice among academics and industry professionals.

We focus on the GARCH option pricing framework developed in Duan (1995) and apply the model to the HSI options. The factors that motivate our adoption of this model are two-fold. First, there is a consensus among experiential researchers that both asset return distributions are skewed and leptokurtic, and their volatilities are time-varying and most likely stochastic. Bates (1995) stated that since options are derivative assets, the key to the success of any option pricing model is whether or not the process assumed is consistent with the distributional and time series properties of the underlying asset. The ARCH family of models has in recent years been established as a strongest contender for the asset return generating process (see, Bollerslev et al., 1992). Second, the available evidence suggests that the GARCH option pricing model is able of describing option prices well (for example, Heynen et al., 1994; Amin and Ng, 1994 and Duan, 1996; Heston and Nandi, 2000).

We examine the empirical performance of the option pricing model based on the non-linear asymmetric GARCH (NGARCH) process of Engle and Ng (1993). This form of GARCH requirement is, in the sense of capturing the leverage effect, similar to the exponential GARCH model of Nelson (1990) or the GJR-GARCH model of Glosten et al. (1993). By the result of Duan (1995), the GARCH option pricing model contains the Black–Scholes model as a special case. This class of models must therefore outperform the Black–Scholes model when both of them are calibrated directly against market prices. However, a superior performance may be due to in-sample overfitting. Using the out-of-sample analysis therefore offers a more credible way of determining whether a model that is indeed superior.

Practitioners do not apply the Black–Scholes model mechanically in its original form. Normally, the volatility values are adjusted for moneyness and maturity before being fed into the Black–Scholes model. We thus use two ad hoc versions of the Black–Scholes model as our comparison benchmark. First, we allow the volatility parameter of the Black–Scholes model to be updated by backing out the “best” volatility value from the out-of-sample option prices. Second, we allow the Black–Scholes model to use different volatility values for different moneyness and maturity combinations. To make the second benchmark meaningful, we fix the relative values of all volatilities, which are determined by an in-sample analysis, while allowing the overall level of these values to shift up or down by a single constant according to the out-of-sample option prices. In other words, we fix the shape of the volatility smile/smirk but permit the curve to go up or down; depending on how well they fit the out-of-sample option prices. The second benchmark reflects the spirit of how practitioners “live with the volatility smile/smirk”. In terms of the request of the GARCH option pricing model, we obtain the model parameters using the in-sample option prices and keep them fixed in the out-of-sample analysis. In theory, we have penalized the GARCH model because all parameter values are fixed while both evaluation benchmarks are allowed to have one parameter adjusting to fit the market prices. In practice, however, the local volatility of the GARCH model must be estimated for different time points. Therefore, there is also one unknown variable to be determined in the out-of-sample analysis, even though the local volatility is a stochastic variable not a model parameter.

We perform a pragmatic study using fifty-two sets of option data sampled weekly throughout 1997. This data period is chosen to cover the recent Asian financial turmoil, which started in Thailand in July 1997 and began to subside in the early part of 1999. Our empirical results show that the GARCH model clearly dominates the two comparison benchmarks for both in-sample and out-of-sample observations. Although the Asian financial turmoil had resulted in a substantial increase in the market volatility for the second half of our sample, the superior performance of the GARCH model remained unaltered by the onset of the financial turmoil.

Calculation of the index

The current Hang Seng Index is calculated from this formula:

\textrm{Current~Index}= \frac{\sum\textrm{[}\textrm{P(t)}\times\textrm{IS}\times\textrm{FAF}\times\textrm{CF}\textrm{]}}{\sum\textrm{[}\textrm{P(t-1)}\times\textrm{IS}\times\textrm{FAF}\times\textrm{CF}\textrm{]}} \times \textrm{Yesterday's~Closing~Index}.

Descriptions on parameters:

P(t):Current Price at Day t

P(t-1):Closing Price at Day (t-1)

IS:Issued Shares

FAF:Freefloat-adjusted Factor, which is between 0 and 1, adjusted every six months

CF:Cap Factor, which is between 0 and 1, adjusted every six months

Components of Hang Seng

On January 2, 1985, four sub-indices were established in order to make the index clearer and to classify constituent stocks into four distinct sectors. There are 43 HSI constituent stocks in total. As of March 8, 2010, they are:

Hang Seng Finance Sub-index

0005 HSBC Holdings plc

0011 Hang Seng Bank Ltd

0023 Bank of East Asia, Ltd

0388 HKEx Limited

0939 China Construction Bank

1398 Industrial and Commercial Bank of China

2318 Ping An Insurance

2388 BOC Hong Kong (Holdings) Ltd

2628 China Life

3328 Bank of Communications Ltd

3988 Bank of China Ltd

Hang Seng Utilities Sub-index

0002 CLP Holdings Ltd

0003 Hong Kong and China Gas Company Limited

0006 Hong Kong Electric Holdings Ltd

0836 Chinese Resource Power

Hang Seng Properties Sub-index

0001 Cheung Kong (Holdings) Ltd

0012 Henderson Land Development Co. Ltd

0016 Sun Hung Kai Properties Ltd

0083 Sino Land Co Ltd

0101 Hang Lung Properties Ltd

0688 China Overseas Land & Investment Limited

1109 China Resorces Land

Hang Seng Commerce & Industry Sub-index

0004 Wharf (Holdings) Ltd

0013 Hutchison Whampoa Ltd

0017 New World Development Co. Ltd.

0019 Swire Pacific Ltd 'A'

0066 MTR Corporation Ltd

0144 China Merchants Holdings (International) Co Ltd

0267 CITIC Pacific Ltd

0291 China Resources Enterprise, Ltd

0293 Cathay Pacific Airways Ltd

0330 Esprit Holdings Ltd

0386 Sinopec Corp

0494 Li & Fung Ltd

0700 Tencent Holdings Limited

0762 China Unicom Ltd

0857 PetroChina Company Limited

0883 CNOOC Ltd

0941 China Mobile Ltd

1088 China Shenhua Energy Company Limited

1199 COSCO Pacific Ltd

2038 Foxconn International Holdings Ltd

2600 Aluminum Corporation of China Limited (Chalco)

In the future, the number of constituent stocks will be increased to 50 in order to reflect the changes in the Hong Kong stock market and to maintain the index as the most representative market benchmark.

The Hang Seng Composite Index Series was launched on October 3, 2001, targeting on providing a broad standard of the performance of the Hong Kong stock market. Comprising the top 200 listed companies in terms of market capitalisation, it is composed of the geographical series and the industry series. The market capitalisation of these companies accounts for about 97% of the total capitalisation of the stocks in Hong Kong. To ensure fairness in its activities, the HSI Services established the Independent Advisory Committee to give advice on issues pertaining to the indexes. The Committee keeps reviewing the constituent stocks of HSI on a quarterly basis. Usual changes are actually expected.

Other Related Hang Seng Stock Indices

Hang Seng China AH Index Series

Hang Seng China Enterprises Index

Hang Seng China H-Financials Index

Hang Seng Composite Index Series 

Hang Seng Freefloat Index Series

Hang Seng Total Return Index Series

Hang Seng Composite Industry Indexes

The Hong Kong stock market is the second largest (only after Japan) in Asia and sixth or seventh largest in the world in terms of market capitalization. The HSI consists of 33 constituent blue-chip stocks, which account for roughly 70% of total market capitalization and trading activities. The HSI options were introduced in March, 1993 by the Hong Kong Futures Exchange and they are actively traded. They are European-style options settled by cash on contract end and subject to the futures-style margining system. Daily HSI option data from 1 January 1997 to 27 January 1998 are obtained from the Hong Kong Futures Exchange. We construct weekly data sets using the official resolution prices on Wednesdays. If a Wednesday happens to be a non-trading day, the nearest business day data in the same week are used. Altogether, there are 56 sets of weekly data. For each set of weekly data, it includes three dissimilar maturities: the current month, the next month, the month after next. To keep away from liquidity-related biases, we keep out options with maturity less than 14 days from our sample. We also exclude deep-in-the-money and deep-out-of–the-money options because those options are finely traded and may supply distorted information on volatilities. For each weekly data set, we include options with maximum 14 different strike prices, with seven being above and seven being below the current HSI futures if the quotes are available. Under the contract specification, strike prices are set at intervals of 200 index points when the HSI is above 8000 level which was the case during our sample period.

As discussed before, the HSI options are successfully index futures options using the futures-style margining system. Under such circumstances, arbitrage trades can be easily executed with minimal costs if the put–call parity situation is violated. Indeed, our investigation shows that the put–call parity holds extremely well. The unspoken futures prices from the put–call parity condition are almost identical to actual market futures prices throughout our entire sample period. After extracting implied futures prices, we just concentrate on call options in following empirical investigations because put options add no useful information when the put–call parity holds extremely well. We use first 52 weeks of data for estimating 52 sets of in-sample model parameter values. For each set of in-sample model parameter estimates, following four weeks of data are used to examine one- to four-week out-of-sample performance. Call options are classified as long-term or short-term depending on whether the maturity is greater or less than 50 days. Along the moneyness length, they are grouped into in-the-money (ITM, if (F−X)/X>2.5%), near-the-money (NTM, if −2.5%(F−X)/X2.5%) or out-of-the-money (OTM, if (F−X)/X<−2.5%). Table 1 shows the number of call option contracts broken down by moneyness and maturity in our empirical investigation. The “In-sample” row refers to the data used for the in-sample calibration. The rows corresponding to “Week 1” to “Week 4” refer to data used in one- to four-week out-of-sample investigations.

Table 1. The number of HSI call option contracts by moneyness and maturitya

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FTSE

The FTSE 100 and FTSE 250 Short Indices aim to replicate the payoff to a shorting investment strategy. They are derived from the underlying headline FTSE 100 and FTSE 250 Total Return Indices respectively. As a result, corporate actions and dividends are reflected in the FTSE Short Indices as they occur and as they are captured in the underlying FTSE Indices. The FTSE 100 and FTSE 250 Short Indices attempt to replicate the inverse returns experienced by an investor attaining the negative daily performance of the underlying headline index i.e. by short selling the index with a daily rebalance. The cost of dividends and benefit of earning interest for the short position are taken into account in the index calculation of the short index. These indices can serve as benchmarks for the creation of ETFs, structured products or other passive investment vehicles that enable investors to gain short exposure to the market or hedge portfolio exposure without the need to short or use derivative instruments. The short indices are derived from the existing underlying headline FTSE 100 and FTSE 250 Total Return Indices. As a result corporate actions and constituent changes are reflected in the short indices as they occur. Dividends used in the index total return calculations are those declared by the company and applied on the ex-dividend date. Treatment of dividends and the calculation of the underlying total return indices can be found in the Guide to Calculation Methods of the UK Series of the FTSE Actuaries Share Indices which can be found on the internet www.ftse.com/Indices/UK_Indices/Downloads/uk_calculation.pdf.

The objective of the FTSE 100 and FTSE 250 Short Indices is to replicate the payoff to shorting investment strategies. The FTSE 100 and FTSE 250 Short Indices take into account the three main components of the payoff to the shorting investment strategies. In practice points 1 and 2 are captured in the Total Return Indices of the underlying indices:

1. Capital gains associated with the underlying equity securities

2. Cash dividends paid by the underlying securities

3. Interest earned on the initial capital as well as the proceeds of the short sale

Constitutions FTSE Index 100

This reflects the quarterly review effective 21 June 2010 in which African Barrick Gold and Essar Energy replaced London Stock Exchange Group and Thomas Cook Group. The index consists of 100 companies, but a total of 102 listings as two classes of shares are included for Royal Dutch Shell and Schroders.

3i

Admiral Group

African Barrick Gold

Aggreko

Alliance Trust

AMEC

Anglo American

Antofagasta

ARM Holdings

Associated British Foods

AstraZeneca

Autonomy Corporation

Aviva

BAE Systems

BG Group

BHP Billiton

BP

BT Group

Barclays

British Airways

British American Tobacco

British Land Company

British Sky Broadcasting Group

Bunzl

Burberry Group

Cable & Wireless Worldwide

Cairn Energy

Capita Group

Capital Shopping Centres Group

Carnival

Centrica

Cobham

Compass Group

Diageo

Essar Energy

Eurasian Natural Resources Corporation

Experian

Fresnillo

G4S

GlaxoSmithKline

HSBC

Hammerson

Home Retail Group

ICAP

Imperial Tobacco

Inmarsat

InterContinental Hotels Group

International Power

Intertek Group

Invensys

Investec

Johnson Matthey

Kazakhmys

Kingfisher

Land Securities Group

Legal & General

Lloyds Banking Group

Lonmin

Man Group

Marks & Spencer

Wm Morrison Supermarkets

National Grid

Next

Old Mutual

Pearson

Petrofac

Prudential

RSA Insurance Group

Randgold Resources

Reckitt Benckiser

Reed Elsevier

Rexam

Rio Tinto Group

Rolls-Royce Group

Royal Bank of Scotland Group

Royal Dutch Shell

SABMiller

Sage Group

J Sainsbury

Schroders

Scottish and Southern Energy

SEGRO

Serco Group

Severn Trent

Shire Pharmaceuticals Group

Smith & Nephew

Smiths Group

Standard Chartered Bank

Standard Life

Tesco

TUI Travel

Tullow Oil

Unilever

United Utilities

Vedanta Resources

Vodafone

WPP Group

Whitbread

Wolseley

Xstrata

Market capitalisation

The following table lists the 40 FTSE 100 companies which had a market capitalisation of £6 billion or more on the 3 October 2009.

Rank↓

Company↓

Business type↓

Capitalisation (£m)↓

(from stock exchange listing)

1

HSBC

Financial (bank)

119,036

2

Royal Dutch Shell

Energy (Oil/Gas)

107,824

3

BP

Energy (Oil/Gas)

100,364

4

Vodafone Group

Telecommunications (mobile)

72,739

5

GlaxoSmithKline

Pharmaceuticals (inc. research)

63,224

6

AstraZeneca

Pharmaceuticals (inc. research)

40,027

7

Barclays Bank

Financial (bank)

39,351

8

British American Tobacco

Tobacco

38,730

9

Rio Tinto Group

Mining

38,174

10

BHP Billiton

Mining

35,908

11

BG Group

Energy (Oil/Gas)

35,576

12

Tesco

Consumer goods/drinks

30,960

13

Standard Chartered

Financial (bank)

29,728

14

Royal Bank of Scotland

Financial (bank)

26,291

15

Lloyds Banking Group

Financial (bank)

25,736

16

Xstrata

Mining

25,033

17

Anglo American

Mining

24,704

18

Diageo

Consumer goods/drinks

23,873

19

SABMiller

Consumer goods/drinks

23,845

20

Unilever

Food production

22,756

21

Reckitt Benckiser

Consumer goods/household

21,666

22

Imperial Tobacco Group

Tobacco

18,387

23

National Grid

Energy (distribution)

14,772

24

Prudential

Financial (insurance)

14,483

25

Centrica

Energy (consumer distribution)

12,753

26

Aviva

Financial (insurance)

12,397

27

BAE Systems

Aerospace and defence

11,786

28

Cadbury Plc

Food production

10,996

29

Scottish and Southern Energy

Energy (consumer distribution)

10,420

30

ENRC

Mining

10,379

31

BT Group

Telecommunications

9,961

32

British Sky Broadcasting

Media (broadcasting)

9,886

33

Tullow Oil

Energy (oil and gas)

8,957

34

Rolls-Royce Plc

Aerospace and defence

8,360

35

Morrisons

Consumer goods/food

7,307

36

Antofagasta

Mining

7,098

37

Compass Group

Travel and leisure

7,000

38

Associated British Foods

Food production

6,618

39

WPP Group

Media

6,594

40

Pearson

Media

6,116

Constitutions of FTSE Index 250

This reflects the replacement of VT Group with Melrose Resources effective 9 July 2010.

In alphabetical order:

3i Infrastructure

Aberdeen Asset Management

Aberforth Smaller Companies Trust

Aegis Group

Afren

Amlin

Aquarius Platinum

Arriva

Ashmore Group

Ashtead Group

WS Atkins

Aveva

BBA Aviation

BH Global

BH Macro

BSS Group

BTG

Babcock International Group

Bankers Investment Trust

A.G. Barr

Balfour Beatty

Barratt Developments

Beazley Group

Bellway

Berkeley Group Holdings

Big Yellow Group

BlackRock World Mining Trust

Bluebay Asset Management

Bluecrest Allblue Fund

Bodycote International

Booker Group

Bovis Homes Group

Brit Insurance Holdings

British Assets Trust

British Empire Securities and General Trust

Britvic

N Brown Group

CPP Group

CSR

Cable & Wireless Communications

Caledonia Investments

Capital & Counties Properties

Carillion

Carpetright

Catlin Group

Centamin Egypt

Charter International

Chemring Group

Chloride Group

City of London Investment Trust

Close Brothers Group

COLT Group

Computacenter

Connaught

Cookson Group

Cranswick

Croda International

Daejan Holdings

Daily Mail and General Trust

Dairy Crest Group

Dana Petroleum

Davis Service Group

De La Rue

Debenhams

Derwent London

Dexion Absolute

Dignity

Dimension Data Holdings

Domino Printing Sciences

Domino's Pizza UK & IRL

Drax Group

DSG International

Dunelm Group

Eaga

EasyJet

Edinburgh Dragon Trust

The Edinburgh Investment Trust

Electra Private Equity

Electrocomponents

Enterprise Inns

EnQuest

Euromoney Institutional Investor

F&C Commercial Property Trust

Fenner

Ferrexpo

Fidelity China Special Situations

Fidelity European Values

Fidelity Special Values

Fidessa Group

Filtrona

FirstGroup

Foreign & Colonial Investment Trust

Forth Ports

GKN

Galiform

Game Group

Gartmore Group

Gem Diamonds

Genesis Emerging Markets Fund

Genus

Go-Ahead Group

Grainger

Great Portland Estates

Greene King

Greggs

HSBC Infrastructure Company

Halfords Group

Halma

Hansen Transmissions

Hansteen Holdings

Hargreaves Lansdown

Hays

Helical Bar

Henderson Group

Heritage Oil

Hikma Pharmaceuticals

Hiscox

Hochschild Mining

Homeserve

Hunting

IG Group Holdings

IMI

ITE Group

ITV

Imagination Technologies Group

Impax Environmental Markets

Inchcape

Informa

Intermediate Capital Group

International Personal Finance

International Public Partnerships

JD Sports Fashion

JKX Oil & Gas

JPMorgan American Investment Trust

JPMorgan Asian Investment Trust

JPMorgan Emerging Markets Investment Trust

JPMorgan European Fledgling Investment Trust

JPMorgan Fleming Mercantile Investment Trust

JPMorgan Indian Investment Trust

Jardine Lloyd Thompson Group

Keller Group

Kesa Electricals

Kier Group

Ladbrokes

Laird

Lamprell

Lancashire Holdings

Law Debenture

Logica

London Stock Exchange Group

MITIE Group

Marston's

McBride

Meggitt

Melrose

Melrose Resources

Merchants Trust

Michael Page International

Micro Focus International

Millennium & Copthorne Hotels

Misys

Mitchells & Butlers

Mondi

Moneysupermarket.com Group

Monks Investment Trust

Morgan Crucible Co

Mothercare

Murray Income Trust

Murray International Trust

National Express Group

Northumbrian Water Group

PZ Cussons

Pace

Paragon Group of Companies

PartyGaming

Pennon Group

Perpetual Income & Growth Investment Trust

Persimmon

Petropavlovsk plc

Polar Capital Technology Trust

Premier Farnell

Premier Foods

Premier Oil

Promethean World

Provident Financial

Punch Taverns

QinetiQ

RIT Capital Partners

RPS Group

Rank Group

Rathbone Brothers

Redrow

Regus

Renishaw

Rentokil Initial

Resolution

Restaurant Group

Rightmove

Robert Wiseman Dairies

Rotork

SDL International

SIG plc

SSL International

SVG Capital

Salamander Energy

Savills

Scottish Investment Trust

Scottish Mortgage Investment Trust

Senior

Shaftesbury

Shanks Group

Smith (DS)

SOCO International

Spectris

Spirax-Sarco Engineering

Spirent

Sports Direct

St. James's Place

St. Modwen Properties

Stagecoach Group

SThree

Stobart Group

SuperGroup

Synergy Health

TalkTalk Telecom Group

Talvivaara Mining Company

Tate & Lyle

Taylor Wimpey

Telecity Group

Temple Bar Investment Trust

Templeton Emerging Markets Investment Trust

Thomas Cook Group

Tomkins

Travis Perkins

TR Property Investment Trust (two listings, both ordinary and sigma shares)

Tullett Prebon

UK Commercial Property Trust

Ultra Electronics Holdings

Unite Group

United Business Media

Victrex

W H Smith

Weir Group

Wellstream

Wetherspoon (J D)

William Hill

Witan Investment Trust

Wood Group

Xchanging

Yell Group

How to calculate FTSE

UK INDEX CALCULATION METHOD

The FTSE Actuaries UK Share Indices are arithmetic weighted indices where the weights are the market capitalisation of each company. The price index is the summation of the market values (or capitalisations) of all companies within the index and each constituent company is weighted by its market value (shares-in-issue multiplied by share price multiplied by investability weighting, which is usually 1.00). The price movement of a larger company (say, representing five per cent of the value of the index) will, therefore, have a larger effect on the index than a smaller company (say, representing one per cent of the value of the index).

The formula used for calculating the indices is straightforward. However, determining the capitalisation of each constituent company and calculating the capitalisation adjustments to the index are more complex. The index value itself is simply a number which represents the total market value of all companies within the index at a particular point in time compared to a comparable calculation at a starting point. The daily index value is calculated by dividing the total market value of all constituent companies by a number called the divisor. The divisor is an arbitrary number chosen at the starting point of the index to fix the index starting value (say, at 100.0). The divisor is then adjusted when capitalisation amendments are made to the constituents of the index allowing the index value to remain comparable over time.

Total market value of all companies = Index Value

Latest index divisor

A simple example of the calculation method is as follows. Please note, these calculations are to be used only as examples and where necessary numbers have been rounded for simplicity. Actual index calculations are undertaken to sufficient significant figures to ensure these do not occur.

Step 1 - Calculate the capitalisation of constituent companies at starting

Step 2 - Set starting value of index (say, 100)

Step 3 - Calculate index divisor on the starting date

Index divisor = Total Market Value

Index Value

Step 4 - Calculate the capitalisation of constituent companies on the end date (day 2)

Step 5 - Calculate index value at end date

Index Value = Total Market Value

Index Divisor

The index divisor can be used to quickly calculate the impact of an event on an

index. The effect of a change in the price of a constituent company expressed in

index points is calculated as follows:-

( Shares-in-Issue /Index Divisor X Change in Share Price X Free Float Factor) /100

Similarly, the market value of a rise or fall in an index can be calculated using the

index divisor as follows:-

Change in Index Points x Index Divisor

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