long run performance following seasoned equity offering on tunisian stock market

7/30/2019 Long Run Performance Following Seasoned Equity Offering on Tunisian Stock Market

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International Research Journal of Finance and EconomicsISSN 1450-2887 Issue 34 (2009)© EuroJournals Publishing, Inc. 2009http://www.eurojournals.com/finance.htm

Long Run Performance Following Seasoned Equity Offering onTunisian Stock Market: Cumulative Prospect

Preference Approach

Dorsaf BEN AISSIA Higher Institute of Management of Sousse, Rue Abdlaaziz il Behi

Bp 763, 4000 Sousse, Tunisia

E-mail: [email protected]

Slaheddine HALLARA Higher Institute of Management of Tunis, 3 Avenue Jugurtha

Mutuelleville- 1002 Tunis, Tunisia


Hichem ELEUCH Institute for Quantum Studies and Department of Physics

Texas A&M University, College Station 77840

Texas, USA


Abstract

This paper investigates abnormal performance following seasoned equity offeringon Tunisian stock market. Our purpose is to test whether the prospect theory as proposed by Kahneman and Tversky (1992) explain the negative abnormal performance observed following seasoned equity offering in particular when this event reflects future growthopportunities. To do this, we rely on the nonlinearity of the weighting probability function.This function form overweights extreme returns’ distribution and therefore overvaluates positive skewed stocks returns like SEO returns. On Tunisian stock market, SEO event isoften undertaken by managers who want to correct firm’s market valuation. In this case,results show that prospect theory fail to explain negative performance. This is because itimplies a static weighting probability function. An extension of prospect weighting probability function is then proposed in this paper.

Keywords: Abnormal performance following seasoned equity offering, prospect theory,nonlinearity of the weighting probability function

JEL Classifications Codes: G11, G12, G18

1. IntroductionExternal financing of listed companies has long been Seasoned Equity Offering (SEO), by whichcompanies collect funds from stock markets. Admittedly, this type of issue is a source of a long termnegative performance. Recent studies (Loughran and Ritter (1995,1997), Spiess and Affleck-Graves(1995) and Jegadeesh (2000)) show that this negative performance persist over five years after the



International Research Journal of Finance and Economics - Issue 34 (2009) 84

subsequent public issue. One explanation of these negative returns is market optimistic expectations.Indeed, Daniel, Hirshleifer and Subrahmanyam (1999) and Kung and Slutz (1999) show that SEO take place during periods when investors overestimate firms future profits. Investor overconfidence bias canleads to such a behavior. Consequently, gradual adjustment of market valuation to get rid of optimisticexpectations explains long run SEO underperformance.

Our paper extends this existing literature in two ways. First, it presents an explanation for SEOunderperformance based on investor preferences. This suggests that markets anomalies are not only

explained by biases in judgment but also by investor sentiment1. Our paper contends that this sentimentis captured by cumulative prospect function as modeled by Tversky and Kahneman (1992). Under thisfunction, the probabilities of uncertain results do not directly affect the value function as it is the casein expected utility theory. Instead, they are processed in a non-linear way and then integrate the valuefunction. Indeed, investors overweight small events probabilities and underweight median and largeevents. SEO stocks have more extreme returns. Hence, they are overvaluated and accomplish negative performance.

Moreover, relevant research on investors preference function (Sundaresan (1989), Campbelland Cochrane (1999) and Constantinides, Donaldson and Mehra (2002)) often considers that stocksreturns are normally distributed, which can constitute a problem when optimizing preference function,in that law normal is not integrable. Our paper uses an approximation of the normal repartition function

which resolves this problem.Second, most of the previous studies related to long run SEO negative returns were done on

United States markets, few in Europe and emerging countries where market conditions and legalenvironments are very different. These differences in market and legal context under which new stocksare issued, affects investor sentiment. This is, in part, because SEO firm’s managers have differentincentives to issue new stocks on market. An extension of cumulative prospect preference function isthen proposed.

Our paper is organized as follows. Section 2 presents Seasoned Equity Offering context onTunisian stock market. In section 3, we set out the hypotheses of our study, the model and itsresolution. Section 4 analyses empirical results and presents a new model of investor weighting probability function since the market issue environment implications on investor sentiment. Section 5

concludes.

2. Tunisia Reference Context of the Seasoned Equity OfferingOur paper is focusing on companies already quoted on stock exchange and whose capital raise increasetheir equity. These “cash” issues are regulated on Tunisian market by the Council regulation of Financial Markets on public offering. According to this regulation, capital increase in Tunisia stock market gives the right to oldshareholder to participate to stocks subscription in a preferential way. The preferential subscription right is traded on a separate stock exchange. It allows oldshareholders tosubscribe to stocks newly issued or to sell their rights and compensate the dilution that they will suffer in this case.

In this context, we observe on Tunisian stock market that issue prices are different from marketones. On our study period, which runs from January 1998 to December 2007, the difference betweenissue prices and market prices at offering announcement date2 is summarized in the following table:

1 See, e.g., Shleifer (2000), Hishleifer (2001) and Barberis and Thaler (2002) for a review of literature on behavioralfinance.

2 The SEO announcement date considered in our paper is the date of the board reunion at which the terms of the securitiesoffer and the issue price are defined.



85 International Research Journal of Finance and Economics - Issue 34 (2009)

Table 1: Differences between issue price and market price at offering announcement date

(Market price minus issue price)

divided by market price

Average of abnormal returns3 Firms’ percentage relatively to hall

sample

-0.481% -54%

(t=1.05)55%

-0.205%-14% (t=1.34) 45%

Source: Council of Financial Markets

Table (1) show that 55% of firms issuing new securities present an average price discount of 54%. Among these firms, 60% have an issue price of 72% below the market price. Indeed, managers perceive an overvaluation of their firm’s stocks as they know that the market is overestimating the firmfuture performance. To protect their old shareholders against a potential decline in prices, they offer them new shares at prices relatively low.

Moreover, the issue price is close to that of the market in 45% of the cases studied. In thiscontext, the stocks issue is synonymous of a fundraising since it reflects future growth prospects.Consequently and in order to attract more investors, firm’s managers decide to issue new stocks at prices below the market valuation. It is to leave new shareholders a margin of profit. The average pricediscount obtained in this case is about -14%.

Table (1) reports also an underperformance of firms offering new stock on Tunisian stocksmarket. This underperformance is more severe for discounted issue prices firms. This is becauseovervaluation in this case was already begun before the SEO event. The purpose of our paper is toexplain this SEO long run negative returns based on investor preference function.

3. Hypothesizes and Methodology3.1. Literature Review and Hypotheses

One of the key reasons given to explain underperformance realized after SEO event was market

inefficiency. Indeed, Loughran and Ritter (1995, 1997), Spiess and Affleck-Graves (1995) and Denisand Sarin (2000) highlight negative abnormal returns that run over five years after the seasoned publicissue. These authors suggest that this negative performance is explained by the fact that equity issuetake place during periods when investors overreact to past firm’s profit. In fact, they overestimatefirm’s future profitability. This interpretation of negative abnormal returns is known as the assumptionof optimistic expectations, expectations which can be explained by overconfidence bias of Daniel,Hirshleifer and Subrahmanyam (1999). Our paper extends this literature in that it explainsunderperformance based on investor function. The idea behind our study is that under prospect theoryof Tversky and Kahneman (1992), the probabilities of results do not directly affect the value functionas in the expected utility function. Instead, they are processed 4 in a non-linear way and then integratethe value function. In particular, investors overweight a small probability and underweight a median

and large probability. Firms offering seasoned stocks have higher growth opportunities. Consequently,they present a positively skewed returns distribution (Jenkinson and Ljungqvist (2001) and Ma and Shen (2007)), which indicates a low probability of having positive extreme returns. Since low probabilities are overweighted in cumulative prospect theory, firms offering new stocks are overvalued

3 The abnormal returns are calculated using the calendar time portfolio approach of Fama (1998) and adjusted from bad model and heteroscedasticity problems. Details of abnormal returns methodology and results are available for the reader on request. Moreover, average abnormal returns are value weighted abnormal returns calculated over a period of 3 yearsafter SEO events.

4 The weighting of probability function was used first by the rank dependant expected utility function theory. This theorywas developed by Quiggin (1981, 1982) and Yaari (1984, 1987).




and have negative returns under such a theory. The hypothesis of our study is then formulated asfollows:

Ho: A firm offering seasoned equity realizes a negative performance because market investorsuse a cumulative prospect function as utility function.

3.2. Data

We obtained the list of firms issuing new stocks on Tunisian stock market, during the period January1998 - December 2006 from the Council of Financial Markets. Moreover, since we examine the performance of issuing firms over a period of 3 years after the SEO event, we impose that issuing firmsdo not have made an equity offering over the preceding 3 years. In other words, once the firm has madean offer SEO, it can’t reintegrate the sample at least 3 years later. Imposing this requirement results ina sample of 22 seasoned equity offerings on Tunisian stock market.

3.3. Methodology

This paper uses as methodology to calculate long run returns of seasoned equity firms investor utilityfunction. In particular, we suppose that investors on market have a cumulative prospect preferencefunction. Moreover, since SEO stocks are positively skewed, they are overvaluated by investors using

such a preference function.To confirm this hypothesis, we make first a skewness test for each SEO firms of our sample.

We calculate then q which corresponds to the probability that SEO stock realizes a positive extremereturn in a preference framework where investor reaches an optimal utility. To do this, we propose tooptimize the function of preference defined by Barberis and Huang (2005). Indeed, this functionintegrates the different elements of the prospect theory in investor utility function. The optimizationconcerns a stocks portfolio composed of market portfolio which is normally distributed and a SEOstock positively skewed. The value of q in hand, we calculate finally, the excess returns registered byeach SEO firm. In particular, we model the SEO excess return in a simple way using a binomialdistribution:

)q1,R ,q,R (R ˆf En − (1)

Where:

nR ˆ is the SEO excess return;

R E is the extreme positive excess return;q is the probability that SEO stock realizes positive extreme returns;R f is the free risk rate.After defining the different steps of our methodology, we propose to explain how returns are

formed after SEO event. To do this, we start from the equilibrium in which investor maximizes theutility of a set of securities normally distributed and a single stock positively skewed. The objectivefunction proposed by Barberis and Huang (2005) is defined as follows:

Max

∫

∞

∞

υ0

0

)R (d))R (P1(w)R (d))R (P(w)R (V (2)

Where:

V is the utility function; w : the probability weighting function ; ( ).. the risk averse function

P: the cumulative probability distribution function;R : the return of the optimal portfolio composed of

MR ˆ : the excess return of market portfolio (normally distributed) and nR ˆ : the excess return of SEO

stock (positively skewed).P(..) , the cumulative probability distribution function is expressed as follows:




)( RP 5 )xR R

(N)q1()xLR

(qNM

Mf

M

M

σ

μ−

σ

μ=

(3)

Where: x is the fraction of the investor’s wealth allocated to new issue stock relative to the

fraction allocated to the market portfolio, N (..) is the cumulative normal distribution, M M and σ are

the mean and the variance of market portfolio.(..)w , the probability weighting function, takes the form6 proposed by Tversky and Kahneman

(1992):

δ

δ

−=

/1))P1(P(

P)P(w

(4)Moreover, Tversky and Kahneman (1992) reported, based on experimental evidence that

65.0≈δ . In this paper, we consider that δ is equal to 2/3 to simplify our optimization resolution.

( ).. , the risk averse function, takes also the form proposed by Tversky and Kahneman (1992):

( )R = R α

, R ≥0

)R ( α− , R<0(5)

The experimental values given by Tversky and Kahneman (1992) for λ and α are respectively

2.25 and 0.88. Nevertheless, in our study, we use as in relevant studies on prospect theory (Barberisand Huang (2006) and Barberis and Huang (2008)), a value of 1 for α 7..

ConcerningM

and M the mean and the variance of normally distributed market portfolio

returnMR ˆ , they take respectively the value of 8.22% and 20.2%, values estimated from Tunisian stock

exchange data.

4. Empirical Tests and ResultsIn this part of our study, we carry out a skewness test for each SEO stock of our sample. This test

justifies our consideration that SEO stocks returns are positively skewed.

4-1 Skewness test

The skewness of returns in our sample is calculated as suggest Bickel and Doksum (1977) who define

it as equal to ∑=

⎟⎠

⎞

⎜⎝

⎛

σ−N

1i

2

iR

ii )R (ER

N

1 where N is the number of stock’s monthly returns and R i is the

average monthly return.For the 22 SEO firms of our sample, we find that 8 firms have a positive skewness, 12 have a

negative skewness and only 2 firms have a very low skewness. In table 2, we present the skewness signof our sapmle of SEO stocks which are divided into 3 groups according to the difference between issue

price and market price at offering announcement date. We present also in table 2 the sign of the longrun performance of each SEO stocks groups.

5 )R R ˆxR ˆ(P)R (P nM = )f xR R MR ˆPr()f R NR ˆPr()ExR R M

R ˆPr().ER nR ˆ(P +

)M

Mf xR R (N)q1()

M

MExR R (qN

σ

μ−

σ

μ= .

6 See Gonzalez and Wu (1999), Abdellaoui (2000), and Jullian and Salanie (2000) for a review of the other forms of theweighting probability function proposed in related literature.

7 This value of 1 for α

allow us also to simplify our optimization resolution.




Table 2: Skewness and long run performance of SEO stocks

Firms’ percentage

relatively to hall sample

(Market price minus issue price) divided

by market price Average skewness sign SEO returns sign

55% -54% Negative Negative45% -14% Positive Negative

Table (2) lends support to the evidence that:

• cumulative prospect theory can be verified only for positive skewness returns in that under this theory positive skewness corresponds to future negative return ;

• returns obtained theoretically according to prospect theory are at odds with market realitywhen returns distribution is negatively skewed. Indeed, prospect theory preview positivefuture returns when return distribution is negatively skewed since investors overvaluated extreme negative returns.

Therefore, our study suggests first to estimate returns of positive skeweness SEO returns usingcumulative prospect function (by optimizing Barberis and Huang function). Second, it tries to explainwhy this function can’t explain abnormal performance of negatively skewed stocks.

4-2 Study of long run negative performance of SEO stocks

The results of Barberis and Huang (2005) goal function resolution8 are presented in table (3).

Table 3: Results of q, the probability of extreme returns achievement

Positively skewed SEO Firms q

1 0.0672 0.0123 0.0574 0.0635 0.0966 0.013

7 0.0128 0.065

Table (3) indicates that for positive skewed SEO Stock, q, the probability of reaching extremereturns belongs to the interval [0.01; 0.09]. This result supports the evidence that investor preferencestructure can explain future short run underperformance of SEO stocks since under the cumulative prospect preference a low probability is overweighted.

The value of q must be then updated during the next two years to obtain 3 years of returnsafter SEO event. This study suggests that:

• q 2, the probability of realizing extreme returns the second year after SEO event is equal toq*(1+ cumulative return of the first year after SEO event);

• q 3, the probability of realizing extreme returns the third year after SEO event is equal toq 2* (1+cumulative return of second year after SEO event).

Indeed, after the arrival of public information the first year after SEO event, investors correcttheir overvaluated forecasts of future returns. In particular, R E, the extreme return will decrease.Consequently, the probability the reach such a return will increase witch lead to eliminate abnormalreturns.

To calculate returns over 3 years after SEO events, we use the equation (1) and replace eachtime q by its corresponding values according to the firm and the year after issuing studied.

In table (4), we present the results of average abnormal returns for positively skewed stocks.

8 The methodology of the resolution of Barberis and Huang (2005) optimization is presented in the appendix of our paper.




Table 4: Results of average abnormal returns calculated according to the cumulative prospect preference for positively skewed SEO stocks

1 st year 2 nd year 3 rd year

Average9abnormal returns calculated according to the cumulative prospect preference

-0. 094% -0.044% -0.006%

-0.234% -0.356% -0.205%Average abnormal returns

(t=2.05) (t=1.67) (t=1.34)

% of abnormal returns explained by Cumulative prospect theory 40.59% 12.50% 2.9%

Results presented in Table (3), show that when SEO stocks are positively skewed, thecumulative prospect utility function explains 40.59% of abnormal returns the first year after new issue.This overvaluation is quickly corrected. Indeed, abnormal returns the second and third years after SEOevent are not significant. This is explained by the fact that this type of firms needs funds in order toseize future growth opportunities. It is not surprising then that investors anticipating firm’s futurereturns attribute a low probability for a potential extreme positive returns achievement. This low probability is overweighed under cumulative prospect theory. During the months that follow, more public information arrives and investor perceived future extreme return will consequently decrease.SEO stocks prices are then adjusted gradually from their overvaluation. Figure (1) summarizes the

scenario of our explanation:

Figure 1: Average price as function of prospect theory preference

However, a new stocks issue does not necessarily means a financing need for future growth

projects. In this study, we show that seasoned equity offering reflects in 55% of the studied cases adesired and a controlled action made by firms’ managers (see table (1)). These managers judging thattheir firms’ values are overestimated by market and in order to protect their oldshareholders against prices’ decline, decide to make new stocks issues at prices relatively low. In this paper, we find thatthis type of issue corresponds to negatively skewed stocks for which cumulative prospect theory isunable to explain long run negative performance (see table (2))

Indeed, in prospect theory, market equilibrium is based only on investor utility function and doesn’t include other market participants’ utility such as firms’ managers. Our paper suggests that the

9 Average abnormal returns are SEO stocks abnormal returns scaled by firm’s size at the announcement date (ie. valueweighted returns).




integration of managers’ utility in investor preferences affects primarily the probability weightingfunction. The idea is to use a dynamic function. This dynamic is defined by the following proposition:investor overvaluates positive skewness returns and undervaluates negative skewness returns. Whereas,under prospect theory, investor overvaluates both positive and negative skewness returns.

Our proposition can be explained by the presence in investor behavior of cognitive biases suchas over-optimism or over-confidence. These biases lead to excessive reaction when investor holds positive new information and to slowly adjustment when new information is negative (see, e.g, Odean,

1998, 1999; Dieter et al., 2003). The skewness of returns is a significant information for investor onstock market which justifies their overreaction to positive skewness and their underreaction to thenegative skewness. Figures (2) and (3) summarize our proposition:

Figure 2: Overweighting of positive skewness

Figure 3: Underweighting of negative skewness




Thanks to our probability weighting function proposition, we can explain underperformance of negatively skewed SEO stocks especially when SEO event was initiate to protect old shareholdersagainst market prices decline. This underperformance is summarized in table (5).

Table 5: Average abnormal returns for negatively skewed SEO stocks

Average abnormal returns

1 st

year 2 nd

year 3 rd

year-0.628% -0.604% -0.481%(t= 5.03) (t=12.88) (t=1.05)

Figure (4) illustrates the evolution of this long run underperformance realized by discounted SEO stocks.

Figure 4: Average price of discounted SEO stocks

Figure (4) show that the discounted issue prices SEO event takes place after a significantmarket overvaluation of firm’s stocks. Nevertheless, on the Tunisian market, investors continue tooverweight future returns increasing market price the first months after issue since they hope realizingextreme returns. As more public information arrives, firm’s price decreases to converge to itsfundamental value. Investors looking at the continuous and persistent decline in prices expect negativeskeweness in future returns. The undervaluation of this negative skewness explains then long rununderperformance of SEO stocks.

5. ConclusionThe objective of our paper is to explain SEO long run performance based on cumulative prospectfunction of Tversky and Kahneman (1992). Results show that this utility function explains market over optimistic expectations observed in prices the first year after the announcement event. However, itcan’t explain returns when firm’s managers use SEO event to correct their firm’s valuation frommarket mispricing. This is because weighting probability function under prospect function is a staticfunction. Our paper extends cumulative prospect theory in that it considers a dynamic weighting probability function. This dynamic is conditioned by returns skewness sign and gives a moreappropriate explanation of the observed reality of the market.




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[5] Barberis, N. and R. Thaler, 2003. “A Survey of Behavioral Finance”, In G. Constantinides, M.Harris et R. Stulz (´ed.), Handbook of the Economics of Finance, Elsevier Science.

[6] Campbell, J.Y. and Cochrane J.H., 1999. “By Force of Habit: A Consumption Based Explanation of Aggregate Stock Market Behavior”, Journal of Political Economy 107(2), pp.205-251.

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Appendix: Methodology of the resolution of Barberis and Huang (2005) preference

functionThe goal function of Barberis and Huang (2005) is defined as follows:

Max ∫∞

υ

∞

υ

0

)R (d))R (xP1(w

0

)R (d))R (xP(w)R (V (6)

Where:

V is the utility function; w: the probability weighting function; ( ).. the risk averse function P:

the cumulative probability distribution function; R : the return of the optimal portfolio composed of

MR ˆ : the excess return of market portfolio (normally distributed) and nR ˆ : the excess return of SEO

stock (positively skewed).P(..) , the cumulative probability distribution function is expressed as follows:

)R R ˆxR ˆ(P)R (P nMx = (7)

)xR R R ˆPr()R R ˆPr()xR R R ˆPr().R R ˆ(P f Mf NEMEn + (8)

)xR R

(N)q1()xR R

(qNM

Mf

M

ME

σ

μ−

σ

μ=

(9) Where: x is the fraction of the investor’s wealth allocated to new issue stock relative to the

fraction allocated to the market portfolio, N (..) is the cumulative normal distribution, M M

and σ are

the mean and the variance of market portfolio.(..)w takes the form proposed by Tversky and Kahneman (1992):

δ

δ

−=

/1))P1(P(

P)P(w

(10)3/265.0 ≈ .

and ( ).. , the risk averse function, takes also the form proposed by Tversky and Kahneman (1992):

( )R = R α

, R ≥0

)R ( α− , R<0(11)

In this paper, we consider that 25.2 and α =1

Replacing )P(w and ( )R by their respective values in the goal function, we get:

∫∞

∞ +−

+−

0

3/23/23/2

3/20

3/23/23/2

3/2

)R (d)P)P1((

)P1()R (d

))P1(P(

P)R (V

(12)where

P )xR R

(N)q1()xR R

(qNM

Mf

M

ME

σ

μ−

σ

μ=

and N=

2te

2

1 −

π ;




As R M follows a normal distribution and normal distribution is not integrable, we approximateits integral by a square whose area is equal to 1. This implies that we consider the extent of the normal

law is equal toσ2

1. Hence, we replace the expression

2te2

1 −

π by

σ2

1(see the following figures).

Figure 5: Normal law function

σ

2

2

1 t e−

π

Figure 6: Normal law function approximation

2σ

1

2σ

Furthermore, in our study on Tunisian stock market, we have:

• %22.8M = ;

• R f = 1; Indeed, we consider that excess return is measured relatively to investor initial

wealth. In particular, we consider that 1R ˆ =(W1-W0)/ W0 =(W1/W0)/-1= 1R ~

-1.

• ER = [ ]2 ;

• and %2.20M =.




Consequently,

0xR

M

ME <σ

μ

and

0xR

M

Mf f

σ

μ

or

0xR

M

Mf <σ

μ

Thus, the integration of M

MExR

σ

μis done over a negative interval. Nevertheless, the

integrationM

M

xL

σμ

is done on two types of interval according to which it is positive or negative.

Figure 7: Utility integration on positive and negative interval

So,

∫∞

+

−+

∞ −

λ

0

)R (d3/2

)

3/2

P

3/2

)P1((

3/2)P1(0

)R (d3/2

)

3/2

)P1(

3/2

P(

3/2P)R (V

(13)

=

∫

∫

σ

σ

σ

μ

μ

σ

σ

−+

σ

−−

σ

−−

+

σ

−+

σ

−−

σ

−

λ

σσ

σλ

MxRf m

MxRf m

Mf mMExR m

)R (d

))2

q1(())

2

q1(1((

))2

q1(1(

)R (d

)))2

q1(())

2

q1(1((

)2

q1(

)R (d

)))2

q(1()

2

q((

)2

q(

3/23/23/2

3/2

0

xr 3/23/23/2

3/20

3/23/23/2

3/2

(14)

To obtain the optimum of this equation, we calculate:

• 0dq

dV=

(15)• 0

dx

dV=

(16)

For the expression of q and x obtained from the goal function optimization, we replace M , R f

and M by its values. This operation is repeated for each extreme return ER of SEO stocks.

long run performance following seasoned equity offering on tunisian stock market

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