Stochastic dominance in stock market 4

However, S&P 500 stochastically dominates NASDAQ 100 at second order implies that risk-averse investors prefer old economy stocks to new economy stocks.. These results suggest that the I

The prices of Internet stocks went up and down at more extreme volatile rates than other conventional stocks between 1998 and 2000 Hence, investments in Internet stocks are likely to either generate big wins or enormous losses Looking at the statistics, the NASDAQ 100 Index increased 140% compared to 33% in the S&P

500 Index from June 1998 to March 2000 After the peak on March 2000, NASDAQ

100 decreased 70% by the end of 2000 while S&P 500 only declined by 14% In 1999, the Dow Jones Industrial Average (DJIA) increased 20%, the NASDAQ was up 86%, and Peter S Cohan & Associates’ Internet Stock Index rose 339% In 2000, however,

the Internet Stock Index had lost 67% of its value, while the DJIA depreciated 6% and the NASDAQ fell 39% Over the two years under analysis, Internet stocks rose by 6%, the DJIA appreciated 18%, and the NASDAQ had gained 13% of its value (Cohan 2001) Demers and Lewellen (2003) reported that 294 Internet firms went public in

1999 and raised more than $20 billion in capital By March 1, 2000, Internet firms had

a combined market value of $1.7 trillion Between January 1999 and February 2000, the Internet Stock Index more than tripled in value However, by 2001, the industry suffered a total decline of 90% (Lewellen 2003)

Academics and analysts started to question this dramatic rise and fall of Internet stocks prices What are the causes of this Internet bubble burst which occurred within a two-year time period? Are new economy stocks overpriced? Is the dramatic rise and fall of Internet stocks due to irrational investors’ behavior or insider action? Will the risk-averse and risk-seeking investors have different preferences on Internet stocks to maximize their utility?

Many studies have attempted to explain the downfall of Internet stocks especially since the bubble burst in the spring of 2000 Although many studies have examined misperceptions on Internet stocks, there is still a persistent lack of literature

on the comparisons between the old and new economy stocks All the literature to date uses individual companies as sample in their studies and none looked at the market from a broader perspective to study the market indices The downfall may be attributed to investors’ behavioral or fundamental account variables, lack of broad picture focus on the risk-based preference of investors Hence, this study tries to fill the gap mentioned here The issue of market efficiency and rationality is not the key

point here as it has been widely discussed in the literature and the imperfect knowledge of the current asset pricing benchmarks The main objective of this study

is to investigate whether investors’ enthusiasm for Internet stocks is consistent with utility maximization A more general framework for analyzing utility choices, stochastic dominance (SD), is used in this study The findings of this study will hold

an important lesson for investors on how to deal with similar bubbles if they arise in the future In addition, the stocks preferences of different types of investors will also

be examined

The empirical results show that neither S&P 500 nor NASDAQ 100 stochastically dominates each other at first order for the whole sample period and the two sub-periods Surprisingly, there is no evidence of the new economy dominance even during the Internet boom S&P 500 dominates at the left-hand (negative returns) side while NASDAQ 100 dominates at the right-hand (positive returns) side However, S&P 500 stochastically dominates NASDAQ 100 at second order implies that risk-averse investors prefer old economy stocks to new economy stocks Furthermore, evidence of old economy stocks dominance is generally stronger at third-order SD than the second-order SD This implies that investors who prefer more positive skewness would also have chosen to buy old economy stocks only These results suggest that the Internet stocks would never be better than the old economy stocks for the entire sample period The evidence of old economy stocks dominating is even stronger after the bubble burst It is also found that risk lovers prefer new economy stocks to old economy stocks while investors with S-shaped or reverse S-shaped utility function have no preference between old and new economy stocks Invertors

may use these findings as a reference for their investment decisions on old and new economy stocks

This chapter is organized as follows Section 2 comprises of a literature review; section 3 describes the SD methodology Section 4 discusses the sample and data; section 5 constructs the SD tests, section 6 reports the SD results, section 7 discusses some special cases and section 8 concludes this chapter

4.2 Literature Review

Several researchers have examined investors’ behavior when valuing the Internet stocks Cohan (2001) observes the manifestations of investor’s fear from the stock indices First, investors sell everything and put the earnings into the most rapidly growing sectors because they fear of losing out on rapid growth Panic selling and drops in these rapidly growing sectors then lead the investors to put their money into old economy stocks which they believe of preserving the gains they have made in the fastest-growing sectors

Wheale and Amin (2003) explain the burst from the change of investors’ behavior on valuing the Internet stocks before and after the burst Six measures, namely, return on assets, return on equity, price-sales ratio, price-earnings ratio, book value and free cash flow are selected as indicators of corporate performance They examine the relationship between stock returns and these six indicators before and after the collapse The evidence from their study suggests that only price-sales ratio, price-earnings ratio, book value and free cash flow are value-relevant before the burst However, after the burst, all six indicators are value-relevant Hence, they claim that investors’ valuation on Internet stocks have changed from emphasizing on revenue to profits Therefore, they stress the importance of behavioral finance in classical financial theory

Ofek and Richardson (2003), however, hypothesize on heterogeneous investors with short sales restrictions (via IPO) to explain the Internet bubble burst in Spring 2000 They study various characteristics like volume, share turnover, short interest, rebate rate etc of Internet companies From the beginning of 1998 to 2000, there were many optimistic investors willing to pay high prices for the Internet stocks

On the other hand, there were some pessimistic investors willing to short these stocks

at high prices However, the short sales restrictions lead to the rises of Internet stocks prices During the spring and latter half of 2000, many lockups expired Thus, pessimistic investors and insider sales cause the Internet stocks prices to drop In addition, the holding of retail trader for Internet stocks more than institutional traders shows heterogeneity among investors Hence, the market is more prone to behavioral biases Moreover, retail day traders have driven momentum investing in recent years (Perkins and Perkins 1999)

On the other hand, traditional accounting model does not carry sufficient information about the growth opportunities and intellectual assets that may make up major components of Internet firms’ values Several researchers have studied systematic relationships between stock prices, accounting variables and non-financial measures of resources and performance (see Trueman, Wong and Zhang 2000, Rajgopal, Venkatachalam, Kotha and Erickson 2002) In addition, there are widespread claims that stocks in this sector were overpriced in 1999, and other researchers (for example, Demers and Lev 2001) have investigated the factors associated with the Internet “pricing shakeout” in early 2000, with a focus on non-financial value drivers Existing Internet valuation studies find mixed results when examining the relation between traditional financial measures and market values of Internet firms during 1999 and early 2000 Their results provide some support for the importance of cash availability for Internet firms, particularly after the downturn in Spring 2000 (Keating, Lys and Magee 2003)

Jahnke (2000) discusses new approaches like top-line revenue growth, customer growth, website visits, peer group comparison and momentum to value Internet stocks He points out that the new economy stocks are overpriced The price being set by investors to play the Internet revolution is too high relative to the profits the industry is likely to produce in the future Investors have wrongly assumed that glamour-investing produces superior investment returns He reminds the investors that great technological innovation do not necessarily translate into great investment opportunities for the typical investor Producing high rates of revenue and earning

growth rates over many years is rare As companies get bigger, it becomes harder to grow at above average rates

King (2000) suggests that the best way to value a single e-business company is

to apply traditional valuation methodologies Follow the usual approach of valuation, first, the present value of the future cash flows is determined Then, the projected cash flows are discounted at an appropriate discount rate An indication of the value for an e-business company is the sum of these discounted amounts

Keating, Lys and Magee (2003) show that traditional financial variables and new economy measures can explain much of the cross-sectional variation in prices and returns of Internet stocks in the spring of 2000 However, Lewellen (2003) argues that their results tell more on investor’s irrationality or misperception than as suggested by them on the agency cost and information asymmetries This irrational view suggests why prices rise so dramatically in the first place

Besides investors’ behavior and stock valuation methods, there is literature focus on IPO underpricing in investigating the Internet bubble There is widespread belief among both academics and practitioners that the prices of Internet IPO cannot

be justified by economic fundamentals Managers and bankers are taking the advantage of irrationally high prices to sell Internet stocks Ritter (1991), Loughran and Ritter (1995) and many others show that Internet IPOs significantly underperform

as compared to other stocks of similar size in the same industry for five years after going public

According to Perkins and Perkins (1999), as capital begins to flood the market, companies not only start up faster but also go public sooner A financial food chain includes the entrepreneurs, the venture capitalists, the investment bankers and certain large institutional investors and mutual funds play an important role in IPO In the Internet boom era, venture capitalists are pushed by both their investors and entrepreneurs they invest in to shoot quickly for an IPO On the other hand, the investment banks willing to serve their investors for Internet IPO so they can collect their 7% underwriting fees and engage new clients to manage their follow-on offerings At the end, companies that shouldn’t be public are public

Perkins and Perkins (1999) also state that narrow float which means the limited number of company shares available to public investors drive up the Internet stocks prices When demand is high and the supply is limited, the prices of these stocks skyrocket Furthermore, insiders keep more of the stocks from their Internet startups for themselves In the first half of 1998, these companies offered only 31% of their total capitalization to public investors This allows them to sell their stocks at a greater profit following the significant share appreciation typical in bubble markets

Schultz and Zaman (2001) find that the Internet firms sell smaller proportion

of their equity and insiders sell fewer of their own shares in the IPO This implies that insiders expect prices to remain high for a long time and therefore there is no hurry to sell or they feel the IPOs are underpriced and prefer to sell later

Ljungqvist and Wilhelm (2003) suggest that the unique characteristics on ownership structure and insider selling behavior of firm during the “dot-com bubble”

cause the IPO underpricing The decline of CEO, venture capitalists and investment banks stakes cause the ownership to be more fragmented These changes of ownership then cause the secondary sales to decrease sharply

How true does the media hype sharing market gossip via Internet impact on the Internet stocks prices? Demers and Lewellen (2003) explore the potential marketing benefits of going public and IPO underpricing Internet companies experience high publicity surrounding their IPO They suggest that the marketing benefits of underpricing extend beyond the Internet sector and the “hot issues” market

in the late 1990s If underpricing attracts media attention and creates valuable publicity for issuing firms, this effect should be reflected in an increased number of website visitors following the IPO

Beneath the surface of the statistics, there are unique activities that drive the movement of money in and out of Internet stocks Day traders, message boards, influential analysts and the pervasive influence of the cable-TV network CNBC all have a real impact on the day-to-day flow of money in the markets In some cases, these money drivers are simply new technologies that have speeded up the traditional process of sharing market gossip In other cases, these phenomena are new and surprisingly powerful (Cohan 2001)

Grodinsky (1953) points out that when new industries are born, there often is a rush by many companies to enter the field in this period of initial and rapid growth This is followed by a shakeout period with only a relatively few survivors and by a continuing period of strong growth, although the rate of growth is slower than the

initial period Finally, industries are expected to stop growing, either living a relatively stable existence for an extended period of time or dying Grodinsky points out the great risk of selecting stocks in the pioneering stage, where little information about participants may be available There is little or no past record to guide investors

or aid them in preparing future projections

Any new industry will follow the four stages of industry life cycle Internet companies are in the start-up stage In the long run, this new industry will develop and mature to become old economy and everything will return to normal Although many have suffered from the Internet bubble burst, Koller (2001) advises that investors shouldn’t abandon the Internet stocks Nevertheless, they should understand the basic principles of value creation and generate new insights into the potential value of Internet opportunities Investors should look forward to a better tomorrow

All the literature above try to explain the downfall of Internet stocks attributed

to investor’s behavior, accounting methods, IPO underpricing etc while this study contributes to the literature by looking at different direction that is investor’s utility maximization

4.3 Stochastic Dominance

The SD approach is used to examine whether the new economy stocks dominates the old economy stocks or vice versa in this study The SD approach provides a general framework for studying economic behavior under uncertainty Hadar and Russell (1969), Hanoch and Levy (1969), Rothschild and Stiglitz (1970), Whitmore (1970) lay the foundation of SD analysis Levy (1992, 1998) provides an up-to-date summary

of SD and its applications in economics and finance In finance, the SD approach has been used to study option pricing (Levy 1985), the small-firm effect (Seyhun 1993), portfolio selection (Post 2003) and momentum effect (Fong, Lean and Wong 2004)

Up to my knowledge, I believe this is the first study that uses SD approach to study Internet stocks

Suppose there are two assets, X and Y, the probability of exceeding any return

in X is always at least as high as in Y For a non-satiation investor, he will prefer asset

X to asset Y An investment decision can be made without having the particular

mathematical form of investor’s utility function SD is generally described by the determination of an order of preference between two assets It is not dependent on

distributional assumptions and risk measures For case here, X can be referring to the

returns of the new economy stocks with cumulative distribution function (CDF) F

and Y refers to the returns of the old economy stocks with CDF G Assuming that

investors prefer more to less, an investor who want to maximize his expected utility

would prefer F which lies below G Chances to earn higher returns are always greater with X than Y; regardless the investor likes or dislikes risk More explanation

of SD can be found in the previous chapters

4.4 Sample and Data

S&P 500 and NASDAQ 1001 are used to represent the old and new economy stocks respectively S&P 500 can be called “old economy stocks index” or simply the “old stocks” and NASDAQ 100 can be called “new economy stocks index” or simply the

1 CRSP and @Net Index have also been examined as proxies to old and new economy stocks As the results are similar, only the results for S&P 500 and NASDAQ 100 are reported in this chapter

“new stocks” The NASDAQ 100 Index includes 100 of the largest domestic and international non-financial companies listed on The NASDAQ Stock Market based on market capitalization The index reflects companies across major industry groups including computer hardware and software, telecommunications, retail/wholesale trade and biotechnology It does not contain financial companies including investment companies Both daily indices are obtained from Datastream

With the assumption that the history is likely to repeat by itself in the future and hence analyze the past will help us to make inference for the future The sample for this study covers the period from January 1998 to December 2003 The sample period starts from 1998 because there is a clear upward trend for Internet stocks around this period This sample period spans a period of intense IPO and secondary market activities for Internet stocks The sample is further divided into two sub-periods to look at the effect of bubble burst The first sub-period is a bull run for Internet stocks from 1 January 1998 to 9 March 2000 (before crash) and the second sub-period is a bear market for Internet stocks from 10 March 2000 to 31 December

2003 (after crash) For simplicity, the first sub-period is called “bull sub-period” and the second sub-period is called “bear sub-period”

NASDAQ 100 which translate to annualized returns of 2.6% and 7.8% respectively

The mean returns for NASDAQ 100 is three times higher than S&P 500 for whole

sample period Hence, by using means alone, everybody will prefer to long new stocks

Table 4.1: Descriptive Statistics of Daily Returns for Indices in

Whole Sample Period and Two Sub-Periods

Note: * significant at 1% level.

However, when we look at each sub-period, a different conclusion is drawn:

investors will prefer new stocks in the bull sub-period and prefer old stocks in the bear sub-period Compared to the old stocks, new stocks go up more in the bull

market and down more in the bear market Before crash, the annual mean returns are 15.6% for S&P 500 and 70.2% for NASDAQ 100 which is nearly five times higher It seems the returns of new stocks are too high while the returns of old stocks are too low during the two-year’s market boom However, after crash, the annual mean returns are -5.2% for S&P 500 and -28.6% for NASDAQ 100 which is more than five times lower than S&P 500! This implies that the new economy stocks generate big wins and enormous losses within a short period of two years This divergence between the old and new stocks suggests that investors tend to put their money into the new stocks when they are afraid of losing out on growth opportunities and they scramble into old stocks when they fear a drop as they want to preserve the gains they made in their new stocks (Cohan 2001)

Mean-variance criterion uses both “mean” and “variance” (or “standard deviation”) together to make inference It is well-known that risk averters prefer stock with higher mean and smaller variance while risk lovers prefer stock with higher mean and higher variance As the means are 0.03% and 0.01% and the standard deviations are 2.65% and 1.3% for the new and old stocks respectively, risk averters have no preference between the old and new stocks while risk lovers prefer new to old stocks in the whole period One will draw the same conclusion in the bull sub-period However, in the bear sub-period, the means are -0.11% and -0.02% and the standard deviations are 2.89% and 1.35% for the new and old stocks respectively Hence, risk averters prefer old stocks while risk lovers have no preference between the old and new stocks in the bear sub-period

The standard deviations for NASDAQ 100 are always higher than the standard deviations for S&P 500 before and after the crash This clearly shows that invest in Internet stocks are anytime riskier than in old economy stocks Furthermore, the standard deviation for NASDAQ 100 increases after crash while the mean returns reduce This implies that it is riskier to invest in the new economy stocks after the bubble burst

4.5 Stochastic Dominance Tests

In order to investigate in detail why risk averters / risk lovers have / no preference between the old and new stocks, the SD approach is used to study the entire range of returns Please refer to chapter 2 for several methods of testing SD used in the econometrics literature Since no single SD test dominates so far, both the DD and KS tests are applied here Evidence that both tests produce similar results would give us a greater degree of confidence about the results Detail explanation of DD and KS tests can be found in previous chapters

4.5.1 Davidson and Duclos Test

Consider an N Q observation of q i random sample, i = 1, 2… N Q from a population of

new economy stocks with distribution function F Q (.) Let

.3,2 , )()

(

and ,)

Q

Q

Q

Suppose there is another N P observation of p i random sample, i = 1, 2… N P from the

population of old economy stocks with distribution function F P (.) Let

(

and ,)

P

P

P

The DD test statistics are implemented over a grid of pre-selected points, x i , i

= 1,…, k as shown in chapter 2 Their corresponding statistics T s(x i)for i = 1, 2… k

are used to test the following hypotheses:

but ,somefor , )()

(

:

,, ,2,1, , )()

x F x

F

H

k i

x x F x

i i

s Q i

s

P

A

i i s Q i

2 3

1 2

1

du u D dvdu v F x

D

du u D du

u F x

D

x F x

D

x Q

x y Q Q

x Q x

Q Q

Q Q

Let{ }P , 1, 2, , i i= N be an i.i.d sample of returns to S&P 500, with CDF, F P( )x Define D P s( )x as the function that integratesF P to order s - 1 That is,

,,

2 3

1 2

1

du u D dvdu v F x

D

du u D du

u F x

D

x F x

D

x P

x y P P

x P x

P P

P P

Please refer to chapter 3 for the test statistic proposed by Barrett and Donald (2003)

4.6 Stochastic Dominance Results

This section reports the results of DD and KS tests Figures 4.1 to 4.3 show how the

DD statistics changes over the distribution of returns in the grid for the whole sample period and two sub-periods respectively The first-, second- and third-order DD statistics are denoted as T1, T2 and T3 in the figures below

Figure 4.1: DD Statistics of S&P 500 and NASDAQ 100 for Risk Averters

from January 1998 to December 2003 (Whole Period)

The plots show that T1 are positive for the negative returns and negative for the positive returns Most of the T1 are significant for both sides of returns This implies that the non-satiation investors prefer old economy stocks when the returns are negative On the other hand, when the returns are positive, they would prefer new economy stocks This can be attributed to some investors prefer old economy stocks because of less downside risk Ang, Chen and Xing (2001) define “downside risk” to

Figure 4.2: DD Statistics of S&P 500 and NASDAQ 100 for Risk Averters

from 1/1/1998 to 09/03/2000 (Bull Sub-period)

Figure 4.3: DD Statistics of S&P 500 and NASDAQ 100 for Risk Averters

from 10/03/2000 to 31/12/2003 (Bear Sub-period)

be the risk that an asset’s return is highly correlated with the market when the market

is declining Markowitz (1959) raises the possibility that agents care about downside risk, rather than about the market risk If investors dislike downside risk, then an asset with greater downside risk is not as desirable as, and should have a higher expected return than an asset with lower downside risk On the other hand, all T2 and T3 are positive and most are significant at 5% significant level for the whole sample period and bear sub-period However, it is noted that T2 is negative and significant in the last 15% of the distribution in the bull sub-period This last 15% of the returns’ distribution is with daily returns of more than 3.8% Hence, this infers that with very high returns, the new economy stocks can attract risk-averse investors even they know

it involves high risk to invest in Internet stocks

Table 4.2: DD Test Results for Risk Averters in Whole Sample Period and

Note: % DD < (>) 0 denote the percentage of DD statistics which are significantly negative (positive)

at the 5% significance level, based on the asymptotic critical value of the studentized maximum modulus (SMM) distribution.

Results of the DD test are shown in Table 4.2 Recall that the DD test rejects the null hypothesis if none of the DD statistics is significantly positive and at least

some (even one) of the DD statistics are significantly negative (DD 2000) However,

this is too restricted as in some situations when X dominates Y in a small range but most risk averters will prefer Y to X (Leshno and Levy 2002) To overcome this

limitation, a 10% cut off point is used in this study That is, new economy stocks dominate old economy stocks if at least 10% of the DD statistics are significantly negative and no DD statistics are significantly positive Alternatively, if at least 10%

of the DD statistics are significantly positive and no DD statistics are significantly negative, it is inferred that old economy stocks dominate new economy stocks

The results show that neither S&P 500 nor NASDAQ 100 dominates each other at first order for the whole sample period and the two sub periods Surprisingly, there is no evidence of NASDAQ 100 dominance even during the Internet boom These results are interesting because they indicate that new economy stocks may not

be consistently profitable even in the boom market There are about half of negative returns for NASDAQ 100 in the sample period (Table 4.4) On the other hand, the old economy stocks are more attractive after the crash suggests that (a) investors believe that old stocks are still better than new stocks and (b) investors have learned from the earlier period concerning the high risk of Internet stocks

Table 4.3: KS Test Results for Risk Averters in Whole Sample Period and

Note: Qfs P means New Economy dominates Old Economy at the s order and vice versa

* significant at 1% level, ** significant at 5% level, *** significant at 10% level.

Results of the KS test are shown in Table 4.3 The table reports p-values of the

KS test for first-, second- and third-order SD respectively Along the row of Qfs P

shows p-values for testing the hypothesis that new economy stocks weakly dominate old economy stocks at order s = 1, 2, 3, while the row Pfs Q tests the opposite

hypothesis All p-values are computed by simulations based on the procedure in

Barrett and Donald (2003)

The significance of both hypotheses at first-order SD invalidates the hypotheses that new economy stocks dominate old economy stocks and vice-versa

The p-values for Pf2 Q and Pf3 Q are well above 5% (except for second-order

SD in the bull sub-period) while p-values for the opposite hypotheses are virtually

zero across all periods Thus, there is strong evidence of old economy stocks dominance over the entire sample period at the second and third orders These results strongly indicate that all risk-averse investors would have preferred old economy stocks over the entire sample period and after the bubble burst Evidence for old economy stocks dominance at third-order SD implies that investors who prefer more positive skewness would also have chosen to buy old economy stocks to maximize their utility

Consistent with the DD test results, the KS test shows clear evidence of old economy stocks dominance This may imply that there are some rational investors who prefer old economy stocks than the new economy stocks which are undervalued

by the irrational investors Although the market has attracted many inexperience investors or speculators during the extraordinary asset pricing period, the evidence of old economy stocks dominates even stronger after the bubble burst

Recall that S&P 500 dominates at the negative returns while NASDAQ 100 dominates at the positive returns Therefore, it is intended to analyze the descriptive

of negative and positive returns for each index respectively Table 4.4 displays the descriptive statistics of daily negative and positive returns for S&P 500 and NASDAQ

100 Both indices have been observed to represent about half of the daily negative and positive returns respectively for the whole sample period and also during two sub-periods S&P 500 has smaller mean (in absolute value) of negative returns and positive returns respectively than NASDAQ 100 for all periods The means of negative and positive returns for NASDAQ 100 are about double the mean returns for S&P 500 This appears that new economy stocks earn more and lose more than the