Size, Book-to-Market, Volatility and Stock Returns: Evidence from Amman Stock Exchange ... · 2016....

Electronic copy available at: http://ssrn.com/abstract=1727280

90

Size, Book-to-Market, Volatility and Stock Returns: Evidence from Amman Stock Exchange (ASE)

Walid Saleh

Abstract

Fama and French (1998) investigated the superiority of value-glamour strategy in 13 developed markets as well as in 16 emerging markets. They confirmed the value premium in 12 out of 13 developed markets. However, they hesitated to give a reliable conclusion concerning the emerging market returns for two reasons. First, they used a short time period sample, nine years. Second, they argued that such emerging market returns suffer from high volatility. This paper aims to investigate the value premium using data from Amman Stock Exchange during the period 1980-2000. In particular, this study seeks to examine the validity of value-glamour strategy using book-to-market equity and explore the effect of stock volatility on portfolio returns. This contribution to the extant literature is significant since it introduces stock volatility as a potential explanation of value premium. The study provides evidence suggesting that the value-glamour strategy does not work in Amman Stock Exchange. Consistent with Fama and French's (1998) prediction, stock volatility has an impact in explaining the difference in returns between value and glamour stocks. In addition, the study shall provide evidence showing that the underperformance of value-glamour strategy in Amman Stock Exchange is mainly related to stock volatility. Keywords: Contrarian strategies, book-to-market, behavioral finance, stock volatility, emerging market returns. JEL classification: G15 Walid Saleh is an Associate Professor of Corporate Finance. Arab Open University, Jordan Branch, Department of Business, P.O.Box 1339, Amman 11953 Jordan. E-mail: [email protected] or [email protected]

Electronic copy available at: http://ssrn.com/abstract=1727280

Walid Saleh - Size, Book-to-Market, Volatility and Stock Returns: Evidence from Amman Stock Exchange (ASE)- Frontiers in Finance and Economics – Vol. 7 No.2 – October 2010, 90 – 124

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1 - Introduction

Over the past two decades an extensive body of empirical research has provided evidence suggesting that the cross-sectional pattern of stock returns can be predicted using some value measures such as market value of equity, book-to-market equity, cash flow yield, earnings-to-price ratio as well as intrinsic value to price ratio1. Examples are, Fama and French, 1992, 1993, 1998; Lakonishok, Shliefer, and Vishny, 1994; Gregory, Harris, and Michou, 2001, Cai, 1997; Danial and Titman, 1997; LaPorta, 1996; Jaffe, Keim, and Westerfield, 1989, amongst others.

More than one explanation has been introduced to explain the superiority of “value” stocks over “glamour” stocks2. Firstly, the risk model, which asserts that value stocks outperform glamour stocks because they are riskier in some aspects (e.g. Fama and French, 1992, 1993, 1996). Fama and French proposed a three-factor model to explain the cross-sectional of stock returns. They provided evidence suggesting that the CAPM is unable to explain the cross-sectional returns anymore. Therefore, they modeled two more factors to the market factor: book-to-market equity and size.

Secondly, the contrarian model, which assumes that investors undervalue value stocks whereas they overvalue glamour stocks (e.g. Lakonishok, Shleifer, and Vishny, 1994; Gregory, Harris, and Michou, 2001; and Bulky and Harris, 1997).

Thirdly, the superiority of value stocks is attributed to the bias induced by research design such as survivorship bias and data mining in the selection of the sample (e.g. Lo and Mackinlay, 1990; Kothari, Shanken, and Sloan, 1995). Finally, the superiority of value stocks can be interpreted by the bid-ask spread and infrequent trading (e.g. Conrad and Kaul, 1993).

1 For example, see Saleh and Tucker (2007) in which they constructed portfolios based on intrinsic value to price ratio. Where intrinsic value was estimated using different specifications of the residual income model. 2 Value (glamour) stocks refer to those stocks that have low (high) price relative to some measure of their fundamental value.



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Fama and French (1998) undertook a comprehensive study in which they investigated the value strategy for 13 developed markets as well as for 16 emerging markets. They found that value stocks outperform glamour stocks in twelve out of thirteen developed markets over the period 1975-1995. However, they were unable to conclude that value premium in emerging markets is reliably positive for two reasons3. Firstly, the nine year sample period (1987-1995) was too short. Secondly, they argued that emerging market returns suffer from high stock volatility. Amman Stock Exchange (ASE) had been one among those emerging markets that were investigated by Fama and French (1998). Their results for ASE showed that high (low) book-to-market stocks earn 0.0146 (-0.029) and that small stocks outperform large stocks by 0.0125; 0.0237 against 0.0113.

This paper investigates the ability of book-to-market equity and size to explain the cross-sectional stock returns using data from ASE over the period 1980-2000. In particular, this study aims to explore the superiority of value stocks. Furthermore, this study seeks to solve the main two problems raised by Fama and French (1998) concerning emerging market returns, the sample period and stock volatility.

Thus, this paper contributes to the extant literature by introducing stock volatility as a potential explanation of value premium, especially for emerging market returns.

It is found that the value-glamour strategy does not work in ASE and that small stocks deliver higher returns than large stocks but the difference is not significant. Consistent with Fama and French’s (1998) prediction, stock volatility helps in explaining the difference in returns between value stocks and glamour stocks. Furthermore, evidence is provided to suggest that the underperformance of the value-glamour strategy is mainly related to stock volatility. Therefore, it is concluded that small and high book-to-market stocks outperform small and low book-to-market stocks because returns of the first are more volatile than those of the latter, whilst large and high book-to-market under-perform large and low book-to-market stocks because returns of the first are more volatile than those of the latter. Thus, large and low book-to-market stocks deliver higher returns. Moreover, the results assert that stock 3 Note that Chen and Zhang (1998) documented that value stocks deliver reliably higher returns in the US, Japan, Malaysia, and Hong Kong, their results for Taiwan and Thailand did not assert the value premium.



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volatility should be modeled as a risk factor over the one-year period. For example, it is found that high volatility stocks deliver higher returns than low volatility stocks over a one-year period, and this difference is significant at less than 10% level, on an average. Splitting the sample into different market conditions shows that stock volatility has no effect on small stocks in up market states, whilst it has a significant effect on large stocks, particularly on the low book-to-market stocks. In down market conditions, the results show that stock volatility has a significant effect on small and high book-to-market stocks as well as on large and low book-to-market stocks.

This paper is organized as follows: Section 2 introduces the related literature whilst Section 3 describes the data and methodology. Section 4 examines the difference in returns between value and glamour stocks. Section 5 summarizes and concludes. 2 - Literature Review

Fama and French (1993, 1995, and 1996) argued in favour of “rational investment” behaviour in the explaination of the value premium. They argued that value stocks outperform glamour stocks because value stocks are fundamentally riskier in some aspects than glamour stocks. Fama and French (1992) found that size (market value of equity) and the ratio of book equity to market equity capture much of the cross-section of average stock returns. They argued that if stocks are priced rationally, systematic differences in average return are due to differences in risk, then size and the book-to-market ratio must proxy for sensitivity to common risk factors in returns.

However, Lakonishok, Shleifer, and Vishny (1994) argued in favour of “irrational explanation”. Under this strategy, investors invest disproportionately (over-invest) in stocks that are under-priced and under-invest in stocks that are overpriced. For instance, investors assume that stocks that have done very well in the recent past will continue to do so, thus they buy them up. Consequently, these stocks become overpriced. Likewise, investors assume that stocks that have done poorly in the recent past will continue to do so, thus, they oversell them. As a result, these “out-of-favour” stocks become under-priced. Thus, value stocks refer to stocks that have a low price relative to some measure of their fundamental value, while growth or glamour stocks refer to stocks that have high price relative to some measure of their fundamental values.



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Fama and French (1998) found that value stocks outperform glamour (growth) stocks in twelve out of thirteen developed markets. Cai (1997) documented the same result for the Tokyo stock market. While recent research shows that “out-of-favour” (value) stocks earn higher returns than glamour stocks in most international markets (e.g. the U.S., the UK, Japan, Germany, Italy, the Netherlands, Belgium, Australia, Hong Kong, Singapore, among others, and some emerging markets), the underlying reasons for this superiority remain debatable.

Overall, most empirical studies documented a robust value premium that is both economically and statistically significant for most developed markets. However, Spyrou and Kassimatis (2006) argued that previous studies drew their conclusions based on long-term averages and overlooked the year-by-year stability of the effect. Therefore, they examined the year-by-year return performance and stability of value-glamour investment strategy for twelve European markets. Overall, they provided evidence suggesting that the value premium is driven by few years where HML returns are high and significant. Furthermore, they found that historical betas for value and glamour portfolios vary significantly over time and that value portfolio betas are not always smaller than glamour portfolio betas.

Ang and Chen (2005) examined the value premium over the period 1926-1963. They provided evidence suggesting that the value premium is captured by the CAPM. Furthermore, they argued that even the post-1963 period produces no reliable evidence against a CAPM story for the value premium, when the tests allow for time-varying market betas. Loughran (1997) showed that the value premium of 1963-1995 is restricted to small stocks.

Fama and French (2006) showed that Loughran’s (1997) evidence is special to 1963-1995, U.S. stocks, and the book-to-market value-glamour indicator. Further, they showed that Agn and Chen’s (2005) evidence is special to 1926-1963. Thus, the CAPM’s problem is that variation in beta unrelated to size and value-glamour goes unrewarded throughout 1926-2004. This produces rejections of the model for 1926-1963 and 1963-2004.



95

In another series of studies, extant research investigates whether the profitability of HML, SMB and WML4 can be linked to future GDP growth (e.g. Liew and Vassalou, 2000; Vassalou, 2000; and Gregory, Harris and Michou, 2003). In general, Liew and Vassalou (2000) and Vassalou (2000) indicated that news related to future GDP growth explains the cross-section of equity returns. However, Gregory, Harris and Michou (2003) provided evidence suggesting that there is no correlation between value strategy returns and future GDP growth once HML and SMB are included as risk factors.

Liew and Vassalou (2000) aimed to investigate whether the profitability of HML, SMB, and WML can be linked to future GDP growth. They used data from ten developed countries to conduct their analysis5. Their results confirmed those in Fama and French (1998) that the value premium is pervasive. They found that the returns of HML are higher when the portfolios are rebalanced more frequently. SMB produces positive returns in all countries except Switzerland. Furthermore, they examined the returns on HML, SMB, and WML at different states of future economic growth. Their results showed that the returns on HML and SMB are positively related to future growth in the macro economy. High portfolio returns precede periods of high GDP growth. Likewise, low portfolio returns are associated with low future GDP growth.

In the UK, Gregory, Harris and Michou (2003) examined the relationship between the returns to value investment strategies and various macroeconomic state variables that in a multi-factor asset pricing model could be taken as proxies for risk. Further, they investigated whether the returns to value strategies predict future GDP, consumption and investment growth over and above the contribution of the Fama and French’s three factors. They found little evidence suggesting that value stocks are riskier than glamour stocks. Moreover, they found no evidence of a correlation between value

4 HML is the return to a portfolio strategy that is long on high book-to-market stocks and short on low book-to-market stocks, holding the other two attributes (size and momentum) constant. Likewise, SMB is the return on a portfolio that is long on small MV stocks and short on big MV stocks, holding the B/M and momentum characteristics of the portfolio constant. WML is the return on a portfolio that is long on the best performance stocks (winners) and short on the worst performance stocks (losers), holding the B/M and size effects of the portfolio constant. 5 These countries were Australia, Canada, France, Germany, Italy, Japan, the Netherlands, Switzerland, the UK and the US.



96

strategy returns and future GDP growth once HML and SMB are included as risk factors. Specifically, they found that the Fama and French’s three factors have explanatory power to explain future GDP growth on an individual basis, with SMB having the greatest explanatory power (0.37 for SMB versus 0.19 and 0.18 for excess market returns and HML factors, respectively). However, when the three factors are combined, the HML marginally loses its significance as an explanatory variable at the 10% level. Further, when the three factors are combined with factors that are known to predict stock returns, the explanatory power of HML completely disappears and the Treasury bill rate, the lagged dividend yield, and the term structure of interest rate play significant role.

Prior research used the time-variation in the relation between firm characteristics and returns to investigate whether the mis-pricing or risk compensation view provides a more plausible explanation for realized excess returns. Lucas, Dijk and Klock (2002) examined whether size and the book-to-market ratio generate excess returns. In contrast to prior studies that focused on models that imply fixed investment styles (e.g. small size and/or high book-to-market ratio), they employed a model that allows the investment style to vary over time. Specifically, they investigated whether the impact of size and the book-to-market ratio varies with macroeconomic conditions. They used two macroeconomic variables: the term-spread of interest rates and a composite of leading indicators of the business cycle6. They argued that the former variable can be considered as an indicator of economic activity. For example, the term-spread of interest rates decreases when the economy is expanded because short-term rates generally rise more than long rates. Likewise, during recession, it generally increases. The above example suggests that some stocks, likely to be small and rapidly growing firms, show higher returns in periods of a small term spread. This excess return results from higher and better quality earnings expectations. Furthermore, they argued that the term-spread affects the sensitivity of stock prices to changes in interest rates. For instance, an increase in the term-spread causes short-term earnings to play a relatively more important role in a dividends or free-cash

6 They constructed an index to proxy the business cycle. The index was constructed by taking the weighted average of ten series: average working hours by production workers, initial claims for unemployment insurance, new orders for consumer goods, new orders for capital goods, vendor performance, residential building permits, S&P 500 price movements, money supply M2, interest rate spread, and an index of consumer expectations.



97

flow discount model, whilst the long-run earnings are relatively less significant.

Their results revealed that the impact of size and the book-to-market ratio on future excess returns varies considerably over time, that is, the impact can be either positive or negative at different times. Finally, they concluded that the excess returns are not consistent with the risk compensation view using the Fama and French (1993) three- factor model. 3 - Data and Methodology

The sample data consisted of monthly stock returns for all non-financial firms; dead and alive, 3-month Treasury bill rates, and monthly returns on ASE value-weighted index over the period 1980-2000. Further, the empirical analysis used annual accounting data such as book-to-market equity, market capitalization, trading volume, and total assets. To explain the returns of value and glamour stocks, the paper employed the Fama and French (1993) three-factor model using the following formula:

,( )f i m f i i i tRp R a R R s SMB h HML e (1) Where, p fR R is the excess returns for individual portfolios

7, mR is the monthly return of the ASE value-weighted index, fR is the monthly 3-month Treasury bill rate. Following Fama and French (1993) the mimicking portfolios for the size (SMB) and book-to-market (HML) factors were constructed as follows. At the end of April of each year t stocks were allocated to two groups (big and small) based on whether their market value is above or below the median of the market. Moreover, stocks were allocated in an independent sort to three book-to-market groups (high, medium, and low) based on the breakpoints for the top 30 percent, middle 40 percent, and bottom 30 percent of the book-to-market values. Thus, SMB (small minus big) is the monthly difference between the average of the returns on the three small-stock portfolios (S/L, S/M, and S/H) and the average of the returns on the three big-stock portfolios (B/L, B/M, and B/H). HML is the monthly difference between the average of the returns on the two high-book-to-market

7 For the hedge portfolios, p fR R was replaced by monthly portfolio returns for VMG portfolios.



98

portfolios (S/H and B/H) and the average of the returns on the two low-book-to-market portfolios (S/L and B/L).

In general, emerging market returns have higher stock volatility than developed market returns (Fama and French, 1998, P. 1993). That is, Fama and French (1998) seemed to suggest that controlling for stock volatility is an important issue when investigating value premium in emerging markets. Therefore, the paper constructed high-stock-volatility- minus-low-stock-volatility (HSVMLSV) factor, then added it to the Fama-French three-factor model, that is,

,( )f i m f i i i i tRp R a R R s SMB h HML v HSVMLSV e (2) HSVMLSV factor was constructed as follows: At the end of April of each year t stocks were allocated to two groups (big and small, B & S) based on whether their market value is above or below the median of the market. Further, stocks were allocated in an independent sort to three stock volatility groups (high, medium, and low, H, M, & L) based on the breakpoints for the top 30 percent, middle 40 percent, and bottom 30 percent of the standard deviation of the past 12-month returns. From the intersection of the two size groups (S and B) and the three standard deviation groups (L, M, H), six size-volatility portfolios were constructed. These portfolios are, SL, SM, SH, BL, BM, and BH. Thus, the HSVMLSV is the monthly difference between the average of the returns on the two high-stock-volatility portfolios (SH and BH) and the average of the returns on the two low-stock-volatility portfolios (SL and BL). 4 - Results 4.1 - Descriptive Statistics Table 1 presents statistics for some variable of interest as well as other variables that could help in explaining the results8. The results show that low book-to-market stocks achieve higher earnings than high book-to-market

8 Note that the number of companies over the sample period (1980-2000) ranged from 59 to 232.



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Table 1: Descriptive Statistics

Small Big LBM MBM HBM p-

value LBM MBM HBM p-

value EPS 0.302 0.192 0.178 0.00 0.426 0.379 0.315 0.02 P/E 31.49 45.26 44.18 0.31 20.29 29.17 20.53 0.89 BM 0.563 0.938 2.919 0.06 0.486 0.730 1.107 0.00 DY 23.60 19.51 16.567 0.00 22.71 21.75 18.10 0.00

TL/TA 0.407 0.349 0.319 0.02 0.461 0.333 0.314 0.00 Past 12-month return

-0.001

0.025 0.060 0.14 0.042 0.024 0.027 0.26

MV 3.286 1.91 1.42 0.00 5.562 4.261 2.835 0.00 STD 0.085 0.093 0.105 0.25 0.092 0.095 0.076 0.00

VT/MV 0.697 1.561 3.286 0.00 1.349 1.629 1.940 0.03 This Table presents mean annual statistics for the sample over the period 1980-2000. At the end of April of each year t stocks were sorted into two groups (small and big) based on whether their market capitalization is above or below the median of the market. Moreover, stocks were allocated in an independent sort to three book-to-market groups (high, medium, and low) based on the breakpoints for the top 30 per cent, middle 40 per cent, and bottom 30 per cent of the book-to-market values. From the intersection of the two size groups (S and B) and the three book-to-market groups (H, M, and L) six size-book-to-market portfolios were constructed. Further, note that EPS is earnings per share, P/E is the price to earnings ratio, BM is the book-to-market equity ratio. DY is the dividend yields, TL/TA is total liabilities to total assets, past 12-month returns is the return during the past 12 months, MV is the market value of equity at the end of the year. STD is the standard deviation of past 12-month returns, and VT/MV is the average trading volume to market value of equity in the past five year. P-value is calculated with standard errors using White (1980). stocks and the difference is statistically significant, p-value of 0.00. They also show that large stocks achieve higher earnings than those of small stocks. Furthermore, they show that the difference in PE ratios between high and low book-to-market stocks is not significant.

The difference between high and low book-to-market values is statistically significant, p-values of 0.06 and 0.00 for small and large stocks, respectively. The difference in DY between high and low book-to-market stocks is significant, p-value of 0.00. The difference in TL/TA between high and low book-to-market stocks is significant. The difference in market values between high and low book-to-market stocks is significant, p-value of 0.00.



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The above results assert that low book-to-market portfolio consists of large stocks, whilst high book-to-market portfolio consists of small stocks. The difference in STD between high and low book-to-market stocks is significant only for large stocks. Finally, the difference in VT/MV between high and low book-to-market stocks is significant, p-values of 0.00 and 0.03 for small and large stocks, respectively. 4.2 - Equally and Value Weighted Returns for Portfolios Formed on Book-to-Market Equity

Panel A of Table 2 presents the equally weighted returns for portfolios formed based on their book-to-market equity. For each portfolio, I computed the return for 3-month (M3), 6-month (M6), one-year (R1), two-year (R2), three-year (R3), four-year (R4), five-year (R5), the average annual return over the five-year period (AR5), and the cumulative three year return (CR3) as well as the cumulative five year return (CR5). The results show that high book-to-market stocks (“value” stocks) have higher returns than low book-to-market stocks (“glamour” stocks), except for 6-month period. On an average, value stocks outperform glamour stocks by 0.0595. Over the three (five) year period, the cumulative return difference between value and glamour stocks is 0.1446 (0.3162). However, the difference in returns between high and low book-to-market stocks is not significant for 3-month, 6-month, one-year, two-year, three-year, and four-year period. Over the five-year period, the difference is marginally significant, p-value of 0.08. The cumulative return difference between high and low book-to-market stocks over the three-year and five-year period is significant at less than 5% level. Panel B of Table 2 reports the results based on value weighted returns. It is obvious that value strategy has no longer profitable. For example, in the first, second, third and a fourth year period of portfolio formation, value stocks under-perform glamour stocks by 0.0831, 0.0950, 0.0460, and 0.0725, respectively. However, in the fifth year of portfolio formation, value stocks outperform glamour stocks by 0.0926. The average difference in returns between value and glamour stocks is –0.0397. Over three and five-year period, the cumulative difference in returns between value stocks and glamour stocks is –0.2266 and –0.3025, respectively. However, the difference in returns between high and low book-to-market stocks is not significant in most cases. The p-values are 0.81, 0.96, 0.09, 0.14, 0.50, 0.28, and 0.11 for 3-month, 6-month, one-year, two-year, three-year, four-year, and five-year

101

Tab

le 2

: Ret

urns

For

Por

tfolio

s For

med

Bas

ed o

n Bo

ok-to

-Mar

ket R

atio

s

Pa

nel A

: Equ

ally

Wei

ghte

d

Pane

l B: V

alue

Wei

ghte

d

E

qual

ly

wei

ghte

d V

alue

w

eigh

ted

LB

M

MB

M

HB

M

LBM

M

BM

H

BM

V

MG

V

MG

M

3

0.02

42

0.

0538

0.03

80

0.

0394

0.08

97

0.

0345

0.01

38

(0.5

8)

-0.0

049

(0.8

1)

M6

0.02

68

0.

0247

0.02

31

0.

0208

0.01

11

0.

0192

-0.0

037

(0.8

5)

-0.0

016

(0.9

6)

R1

0.21

59

0.

2220

0.28

06

0.

2370

0.18

07

0.

1539

0.06

46

(0.1

8)

-0.0

831

(0.0

9)

R2

0.14

19

0.

2183

0.17

21

0.

1814

0.21

13

0.

0865

0.03

02

(0.3

9)

-0.0

950

(0.1

4)

R3

0.17

30

0.

1648

0.22

02

0.

1789

0.13

81

0.

1382

0.04

72

(0.3

0)

-0.0

406

(0.5

0)

R4

0.18

72

0.

1706

0.22

54

0.

1969

0.15

56

0.

1244

0.03

81

(0.4

2)

-0.0

725

(0.2

8)

R5

0.16

41

0.

2074

0.28

16

0.

1275

0.13

12

0.

2200

0.11

74

(0.0

8)

0.09

26

(0.1

1)

AR

5 0.

1765

0.

1966

0.

2360

0.

1843

0.

1634

0.

1446

0.

0595

-0

.039

7 C

R3

0.43

70

0.

5210

0.58

17

0.

5180

0.46

92

0.

3015

0.14

46

(0.0

4)

-0.2

166

(0.0

5)

CR

5 0.

7666

0.92

88

1.

0828

0.86

33

0.

7327

0.56

09

0.

3162

(0

.04)

-0

.302

5 (0

.11)

N

ote:

Tab

le-2

val

ues

repr

esen

t mea

n 3-

mon

th, 6

-mon

th, o

ne-to

-five

-yea

r buy

and

hol

d re

turn

s fo

r por

tfolio

s fo

rmed

in A

pril

each

yea

r, ba

sed

on

book

-to-m

arke

t rat

ios.

The

sam

ple

perio

d is

1980

-200

0. A

t the

end

of A

pril

of ea

ch y

ear t

stoc

ks w

ere s

orte

d in

to th

ree b

ook-

to-m

arke

t gro

ups (

high

, m

ediu

m, a

nd lo

w) b

ased

on

the

brea

kpoi

nts f

or th

e to

p 30

per

cent

, mid

dle

40 p

er ce

nt, a

nd b

otto

m 3

0 pe

r cen

t of t

he b

ook-

to-m

arke

t val

ues.

AR5

is

the

aver

age

retu

rn fo

r R1

to R

5. C

R3 a

nd C

R5 a

re th

e th

ree-

year

and

five

-yea

r cum

ulat

ive

retu

rns.

VM

G re

pres

ents

the

diffe

renc

e be

twee

n hi

gh

book

-to-m

arke

t sto

cks (

HBM

) and

low

boo

k-to

-mar

ket s

tock

s (LB

M).

P-va

lues

are i

n pa

rent

hese

s, ca

lcul

ated

sing

Whi

te (1

980)

.

Wal

id S

aleh

- Si

ze, B

ook-

to-M

arke

t, Vo

latil

ity a

nd S

tock

Ret

urns

: Evi

denc

e fr

om A

mm

an

Stoc

k Ex

chan

ge (A

SE)-

Fron

tiers

in F

inan

ce a

nd E

cono

mic

s – V

ol. 7

No.

2 –

Oct

ober

201

0, 9

0 –

124

FFE

is h

oste

d an

d m

anag

ed b

y SK

EMA

Busi

ness

Sch

ool

102

period, respectively. The cumulative return difference over three (five)-year period is significant (insignificant) at 5% level. 4.3 - Equally and Value Weighted Returns for Portfolios Formed on Market Capitalization.

Panel A of Table 3 reports the equally weighted returns for portfolios formed on market capitalization. The results show that the difference in returns between small and large firms is 0.0842, 0.0654, 0.0626, 0.0377, and 0.0348 in the first, second, third, fourth, and fifth year period after portfolio formation, respectively. The difference in returns between small and large stocks averaged over the five-year period is 0.0569. The cumulative return difference is 0.1648 and 0.2594 over the three and five year period, respectively. The p-values are 0.99, 0.66, 0.23, 0.03, 0.04, 0.33, and 0.43 for 3-month, 6-month, one-year, two-year, three-year, four-year, and five-year period, respectively. The cumulative difference in returns between small and large stocks over three-year and five-year period is significant, p-values of 0.05 and 0.00 for small and large stocks, respectively. Panel B of Table 3 displays the value-weighted returns for portfolios formed on market capitalization. The results confirm that small stocks outperform large stocks over 6-month up to five-year period. In the first, second, third, fourth, and fifth year period, small stocks outperform large stocks by 0.0756, 0.0341, 0.0656, 0.0530, and 0.0735, respectively. On average small stocks outperform large stocks by 0.0604. Over the three and five-year period, the difference in returns between small and large stocks is 0.1413 and 0.2801, respectively. The p-values show that the difference in returns between small and large stocks is not significant, 0.50, 0.63, 0.44, 0.55, 0.13, 0.23, and 0.17 for 3-month, 6-month, one-year, two-year, three-year, four-year, and five-year period, respectively. 4.4 - Equally and Value Weighted Returns for Portfolios Formed on Market Capitalization and Book-to-Market Equity.

To shed further light on the intersection between size and the book-to-market equity, I constructed 6-portfolios formed on size and book-to-market equity. Panel A of Table 4 reports the equally weighted returns for those portfolios. The results for small stocks show that value stocks outperform glamour stocks. For example, the difference in returns between value and glamour stocks is 0.0605, 0.0184, 0.0573, 0.1051, and 0.1631 in the first, second, third, fourth, and fifth year period after portfolio formation,



103

Tab

le 3

: Ret

urns

For

Por

tfolio

s For

med

Bas

ed o

n M

arke

t Cap

italiz

atio

n

Pane

l A: E

qual

ly W

eigh

ted

Pa

nel B

: Val

ue W

eigh

ted

Smal

l m

ediu

m

Big

SM

B Sm

all

med

ium

B

ig

SMB

M3

0.

0404

0.04

49

0.

0406

-0.0

002

(0.9

9)

0.03

69

0.

0408

0.06

44

-0

.027

5 (0

.50)

M

6 0.

0246

0.01

01

0.

0363

-0.0

117

(0.6

6)

0.02

91

0.

0067

0.01

29

0.

0162

(0

.63)

R

1 0.

3031

0.21

11

0.

2190

0.08

42

(0.2

3)

0.28

08

0.

1960

0.20

51

0.

0756

(0

.44)

R

2 0.

1944

0.20

57

0.

1290

0.06

54

(0.0

3)

0.19

57

0.

2072

0.16

16

0.

0341

(0

.55)

R

3 0.

2057

0.21

26

0.

1430

0.06

26

(0.0

4)

0.19

87

0.

2175

0.13

31

0.

0656

(0

.13)

R

4 0.

2007

0.23

01

0.

1631

0.03

77

(0.3

3)

0.19

43

0.

2334

0.14

13

0.

0530

(0

.23)

R

5 0.

2260

0.23

05

0.

1912

0.03

48

(0.4

3)

0.22

41

0.

2232

0.15

05

0.

0735

(0

.17)

A

R5

0.22

60

0.21

80

0.16

90

0.05

69

0.21

87

0.21

55

0.15

83

0.06

04

CR

3 0.

5921

0.53

91

0.

4273

0.16

48

(0.0

5)

0.56

02

0.

5312

0.41

89

0.

1413

(0

.25)

C

R5

0.99

43

1.

0595

0.73

49

0.

2594

(0

.00)

0.

9353

1.05

99

0.

6552

0.28

01

(0.0

8)

Not

e: T

able

-3 v

alue

s re

pres

ent m

ean

3-m

onth

, 6-m

onth

, one

-to-f

ive-

year

buy

and

hol

d re

turn

s fo

r po

rtfol

ios

form

ed i

n A

pril

each

yea

r, ba

sed

on m

arke

t cap

italiz

atio

n. T

he s

ampl

e pe

riod

is 1

980-

2000

. At t

he e

nd o

f A

pril

of e

ach

year

t st

ocks

wer

e so

rted

into

thre

e gr

oups

(sm

all,

med

ium

, and

big

) ba

sed

on th

e br

eakp

oint

s for

the

top

30 p

er c

ent,

mid

dle

40 p

er c

ent,

and

botto

m 3

0 pe

r cen

t of

the

mar

ket c

apita

lizat

ion

valu

es. A

R5

is th

e av

erag

e re

turn

for R

1 to

R5.

CR

3 an

d C

R5

are

the

thre

e-ye

ar a

nd fi

ve-y

ear c

umul

ativ

e re

turn

s. SM

B re

pres

ents

the

diff

eren

ce b

etw

een

smal

l sto

cks a

nd b

ig st

ocks

. P-v

alue

s are

in p

aren

thes

es, c

alcu

late

d si

ng W

hite

(198

0).

Wal

id S

aleh

- Si

ze, B

ook-

to-M

arke

t, Vo

latil

ity a

nd S

tock

Ret

urns

: Evi

denc

e fr

om A

mm

an

Stoc

k Ex

chan

ge (A

SE)-

Fron

tiers

in F

inan

ce a

nd E

cono

mic

s – V

ol. 7

No.

2 –

Oct

ober

201

0, 9

0 –

124

FFE

is h

oste

d an

d m

anag

ed b

y SK

EMA

Busi

ness

Sch

ool

104

respectively. The average difference in returns between value and glamour stocks is 0.0809 over the five-year period. Over the three (five) year period, the cumulative difference in returns between value and glamour stocks is 0.1876 (0.4795). The p-values are 0.88, 0.65, 0.53, 0.74, 0.45, 0.10, and 0.08 for 3-month, 6-month, one-year, two-year, three-year, four-year, and five-year period, respectively. Over the three-year and five-year period, the cumulative difference in returns is significant, p-values of 0.10 and 0.02, respectively. For large stocks the value-glamour strategy seems to be weaker than that in small stocks. For example, in the first, second, third, fourth, and fifth year period of portfolio formation, the difference in returns between value and glamour stocks is 0.0625, -0.0314, -0.0166, -0.0252, and 0.0625, respectively. On average, value stocks outperform glamour stocks by 0.0104 over the five-year period. The cumulative difference in returns is 0.0370 and 0.0876 over the three and five-year period, respectively. The p-values confirm that the difference in returns between high and low book-to-market stocks is not significant, 0.66, 0.97, 0.14, 0.59, 0.69, 0.69, and 0.24 for 3-month, 6-month, one-year, two-year, three-year, four-year, and five-year period, respectively. Panel B of Table 4 presents the value-weighted returns for portfolios formed on size and book-to-market equity. For small stocks, the difference in returns between value and glamour stocks (VMG portfolio) is 0.0263, 0.0204, 0.0768, 0.0946, and 0.1573 in the first, second, third, fourth and fifth year period of portfolio formation, respectively. On average, this difference over the five-year period is 0.0751, whilst the cumulative difference over the three and five year period is 0.1848 and 0.4757, respectively. The p-values assert that the difference in returns between high and low book-to-market stocks is not significant, except for the five-year period (0.89, 0.65, 0.81, 0.68, 0.33, 0.19, and 0.05 for 3-month, 6-month, one-year, two-year, three-year, four-year, and five-year period, respectively). For large stocks the results assert that the value-glamour strategy does not work. For example, value stocks under-perform glamour stocks in the first four periods. The average difference in returns between value and glamour stocks is –0.0380. Over the three and five-year period, the cumulative difference in returns is –0.1707 and –0.2666, respectively. The p-values for 3-month, 6-month, one-year, two-year, three-year, four-year, and five-year period are 0.66, 0.97, 0.37, 0.64, 0.31, 0.30, and 0.47, respectively, which confirm that the difference in returns between high and low book-to-market stocks is not significant. To sum up, the above results show that the value-glamour strategy does not appear on Amman Stock Exchange (ASE).



105

Tab

le 4

: Ret

urns

For

Por

tfolio

s For

med

Bas

ed o

n Si

ze a

nd B

ook-

to-M

arke

t

Pane

l A: E

qual

ly W

eigh

ted

Sm

all

Big

Sm

all

Big

LBM

M

BM

H

BM

LB

M

MB

M

HB

M

VM

G

VM

G

M3

0.

0343

0.04

97

0.

0366

0.01

00

0.

0445

0.05

72

0.

0023

(0

.88)

0.

0472

(0

.66)

M

6 0.

0273

0.03

49

0.

0141

0.02

05

0.

0047

0.03

89

-0

.013

1 (0

.65)

0.

0184

(0

.97)

R

1 0.

2443

0.28

89

0.

3048

0.17

67

0.

1777

0.23

92

0.

0605

(0

.53)

0.

0625

(0

.14)

R

2 0.

2003

0.24

33

0.

2187

0.18

47

0.

1380

0.15

33

0.

0184

(0

.74)

-0

.031

4 (0

.59)

R

3 0.

1698

0.23

79

0.

2271

0.18

22

0.

1319

0.16

56

0.

0573

(0

.45)

-0

.016

6 (0

.69)

R

4 0.

1388

0.20

59

0.

2438

0.21

00

0.

1705

0.18

48

0.

1051

(0

.10)

-0

.025

2 (0

.69)

R

5 0.

1632

0.22

26

0.

3263

0.17

45

0.

1878

0.23

70

0.

1631

(0

.08)

0.

0625

(0

.24)

A

R5

0.18

33

0.23

97

0.26

42

0.18

56

0.16

12

0.19

60

0.08

09

0.01

04

CR

3 0.

4809

0.64

61

0.

6686

0.45

73

0.

4182

0.49

43

0.

1876

(0

.10)

0.

0370

(0

.66)

C

R5

0.

7639

1.12

82

1.

2434

0.83

53

0.

7769

0.92

29

0.

4795

(0

.02)

0.

0876

(0

.44)

Wal

id S

aleh

- Si

ze, B

ook-

to-M

arke

t, Vo

latil

ity a

nd S

tock

Ret

urns

: Evi

denc

e fr

om A

mm

an

Stoc

k Ex

chan

ge (A

SE)-

Fron

tiers

in F

inan

ce a

nd E

cono

mic

s – V

ol. 7

No.

2 –

Oct

ober

201

0, 9

0 –

124

FFE

is h

oste

d an

d m

anag

ed b

y SK

EMA

Busi

ness

Sch

ool

Wal

id S

aleh

- Si

ze, B

ook-

to-M

arke

t, Vo

latil

ity a

nd S

tock

Ret

urns

: Evi

denc

e fr

om A

mm

an

Stoc

k Ex

chan

ge (A

SE)-

Fron

tiers

in F

inan

ce a

nd E

cono

mic

s – V

ol. 7

No.

2 –

Oct

ober

201

0, 9

0 –

124

FFE

is h

oste

d an

d m

anag

ed b

y SK

EMA

Busi

ness

Sch

ool

106

Pane

l B: V

alue

Wei

ghte

d

Sm

all

Big

Sm

all

Big

LBM

M

BM

H

BM

LB

M

MB

M

HB

M

VM

G

VM

G

M3

0.

0477

0.04

57

0.

0406

0.04

42

0.

0642

0.06

06

-0

.007

1 (0

.89)

0.

0164

(0

.66)

M

6 0.

0316

0.03

32

0.

0197

0.02

04

0.

0036

0.02

17

-0

.011

9 (0

.65)

0.

0013

(0

.97)

R

1 0.

2538

0.27

74

0.

2801

0.23

15

0.

1616

0.16

51

0.

0263

(0

.81)

-0

.066

3 (0

.37)

R

2 0.

2057

0.25

26

0.

2261

0.19

53

0.

1229

0.15

60

0.

0204

(0

.68)

-0

.039

2 (0

.64)

R

3 0.

1638

0.23

70

0.

2406

0.19

75

0.

0684

0.12

96

0.

0768

(0

.33)

-0

.067

9 (0

.31)

R

4 0.

1597

0.20

44

0.

2543

0.19

02

0.

1389

0.12

46

0.

0946

(0

.19)

-0

.065

5 (0

.30)

R

5 0.

1826

0.26

44

0.

3399

0.13

21

0.

1160

0.18

09

0.

1573

(0

.05)

0.

0488

(0

.47)

A

R5

0.19

31

0.24

72

0.26

82

0.18

93

0.12

16

0.15

13

0.07

51

-0.0

380

CR

3 0.

4920

0.64

71

0.

6768

0.54

26

0.

3307

0.37

19

0.

1848

(0

.18)

-0

.170

7 (0

.28)

C

R5

0.80

55

1.

1328

1.28

12

0.

8883

0.51

20

0.

6217

0.47

57

(0.0

4)

-0.2

666

(0.2

5)

Note:

Tab

le-4 v

alues

repres

ent m

ean 3

-mon

th, 6-

mon

th, on

e-to-f

ive-ye

ar bu

y and

hold

return

s for

portfo

lios f

ormed

in A

pril e

ach y

ear, b

ased o

n size

and b

ook-t

o-mark

et rat

ios. T

he

sample

perio

d is 1

980-2

000.

At th

e end

of A

pril o

f eac

h yea

r t sto

cks w

ere so

rted i

nto tw

o grou

ps (s

mall

and b

ig) ba

sed on

whe

ther th

eir m

arket

capit

aliza

tion i

s abo

ve or

below

the

med

ian of

the m

arket.

More

over,

stock

s were

alloc

ated i

n an i

ndep

ende

nt so

rt to t

hree b

ook-t

o-mark

et gro

ups (

high,

med

ium, a

nd lo

w) ba

sed on

the b

reakp

oints f

or the

top 3

0 per

cent,

m

iddle

40 pe

r cen

t, and

botto

m 30

per c

ent o

f the b

ook-t

o-mark

et va

lues. F

rom th

e inte

rsecti

on of

the t

wo siz

e grou

ps (S

and B

) and

the t

hree b

ook-t

o-mark

et gro

ups (

H, M

, and

L) s

ix siz

e-boo

k-to-m

arket

portfo

lios w

ere co

nstru

cted.

AR5

is the

avera

ge re

turn

for R

1 to

R5. C

R3 an

d CR

5 are

the t

hree-y

ear a

nd fi

ve-ye

ar cu

mula

tive r

eturns

. VM

G rep

resen

ts the

dif

feren

ce be

twee

n high

book

-to-m

arket

stock

s (HB

M) a

nd lo

w bo

ok-to

-mark

et sto

cks (

LBM

). P-

value

s are

in pa

renthe

ses, ca

lculat

ed sin

g Whit

e (19

80).

107

4.5 - Is Stock Volatility a Cross-Sectional Risk Factor?

Fama and French (1998) investigated the value premium in 13 developed markets as well as for 16 emerging markets. They provided evidence suggesting that value stocks outperform glamour stocks in 12 developed markets. However, in their investigation for the emerging market, they said that (P. 1996) “the short nine-year sample period and the volatility of emerging market returns have prevented us from concluding that the value premium in these markets is reliably positive”.

The evidence from the above results yields that value premium is not pervasive since it does not appear on ASE. Therefore, this section aims to investigate whether the reason behind these results is driven by high volatility of ASE returns and whether it is sensible to think of stock volatility as a risk factor.

Panel A of Table 5 reports the equally weighted returns for portfolios formed on size and stock volatility. For small stocks, the results show that the difference in returns between high and low stock volatility is 0.0565, -0.0066, 0.1080, 0.0407, 0.0048, 0.0440, and –0.0144 with p-values of 0.13, 0.74, 0.10, 0.44, 0.92, 0.46, and 0.81 for 3-month, 6-month, one-year, two-year, three-year, four-year, and five-year period, respectively. On an average, this difference is 0.0366. The cumulative difference in returns over three-year and five-year period is 0.1606 and 0.2750 with p-values of 0.13 and 0.05, respectively. For large stocks, the difference in returns between high and low stock volatility is 0.0500, 0.0217, 0.0964, 0.0517, 0.0726, 0.0107, and –0.0345 with p-values of 0.00, 0.38, 0.09, 0.14, 0.06, 0.84, and 0.70 for 3-month, 6-month, one-year, two-year, three-year, four-year, and five-year period, respectively. On an average, the difference in returns between high and low stock volatility is 0.0394. Over the three (five)-year period, the cumulative difference in returns is 0.2035 (0.2619) with p-values of 0.02 (0.05). The last column in Panel A of Table 5 presents the difference between the average of the returns on the two high stocks-volatility (SHV and BHV) and the average of the returns on the two low stocks-volatility (SLV and BLV). The results show that the difference in the average of returns between high and low stock volatility is 0.0532, 0.0075, 0.1022, 0.0462, 0.0387, 0.0274, and –0.0244 with p-values of 0.13, 0.62, 0.06, 0.19, 0.34, 0.53, and 0.69 for 3-month, 6-month, one-year, two-year, three-year, four-year, and five-year period, respectively. On an average this difference is 0.038, whilst the cumulative difference in returns over three-year and five-year period is



108

Tabl

e-5:

Ret

urns

For

Por

tfolio

s For

med

Bas

ed o

n Si

ze a

nd S

tock

Vol

atili

ty

Pa

nel A

: Equ

ally

wei

ghte

d re

turn

s

Smal

l (S)

La

rge

(B)

S B

Ave

rage

(S,B

)

Low

stoc

k vo

latil

ity

(LV

)

Hig

h st

ock

vola

tility

(H

V)

Low

stoc

k vo

latil

ity

(LV

)

Hig

h st

ock

vola

tility

(H

V)

SHV

- SL

V

BH

V -

BLV

A

vg(S

HV

, BH

V)

– A

vg(S

LV, B

LV)

3M

0.01

39

0.

0704

0.00

42

0.

0542

0.05

65

(0.1

3)

0.05

00

(0.0

0)

0.05

32

(0.1

3)

6M

0.03

58

0.

0292

0.01

09

0.

0325

-0.0

066

(0.7

4)

0.02

17

(0.3

8)

0.00

75

(0.6

2)

R1

0.22

92

0.

3372

0.13

49

0.

2313

0.10

80

(0.1

0)

0.09

64

(0.0

9)

0.10

22

(0.0

6)

R2

0.14

68

0.

1875

0.09

39

0.

1456

0.04

07

(0.4

4)

0.05

17

(0.1

4)

0.04

62

(0.1

9)

R3

0.14

07

0.

1454

0.11

42

0.

1867

0.00

48

(0.9

2)

0.07

26

(0.0

6)

0.03

87

(0.3

4)

R4

0.13

23

0.

1764

0.15

52

0.

1659

0.04

40

(0.4

6)

0.01

07

(0.8

4)

0.02

74

(0.5

3)

R5

0.18

06

0.

1661

0.22

08

0.

1863

-0.0

144

(0.8

1)

-0.0

345

(0.7

0)

-0.0

244

(0.6

9)

AV

G

0.16

59

0.20

25

0.14

38

0.18

32

0.03

66

0.03

94

0.03

80

CR

3 0.

4357

0.59

63

0.

2662

0.46

97

0.

1606

(0

.13)

0.

2035

(0

.02)

0.

1820

(0

.03)

CR

5 0.

6638

0.93

88

0.

5252

0.78

71

0.

2750

(0

.05)

0.

2619

(0

.05)

0.

2685

(0

.02)

Wal

id S

aleh

- Si

ze, B

ook-

to-M

arke

t, Vo

latil

ity a

nd S

tock

Ret

urns

: Evi

denc

e fr

om A

mm

an

Stoc

k Ex

chan

ge (A

SE)-

Fron

tiers

in F

inan

ce a

nd E

cono

mic

s – V

ol. 7

No.

2 –

Oct

ober

201

0, 9

0 –

124

FFE

is h

oste

d an

d m

anag

ed b

y SK

EMA

Busi

ness

Sch

ool

Wal

id S

aleh

- Si

ze, B

ook-

to-M

arke

t, Vo

latil

ity a

nd S

tock

Ret

urns

: Evi

denc

e fr

om A

mm

an

Stoc

k Ex

chan

ge (A

SE)-

Fron

tiers

in F

inan

ce a

nd E

cono

mic

s – V

ol. 7

No.

2 –

Oct

ober

201

0, 9

0 –

124

FFE

is h

oste

d an

d m

anag

ed b

y SK

EMA

Busi

ness

Sch

ool

109

Pane

l B: V

alue

wei

ghte

d re

turn

s

Sm

all (

S)

Larg

e (B

) S

B A

vera

ge (S

,B)

Low

stoc

k vo

latil

ity

(LV

)

Hig

h st

ock

vola

tility

(H

V)

Low

stoc

k vo

latil

ity

(LV

)

Hig

h st

ock

vola

tility

(H

V)

SHV

- SL

V

BH

V -

BLV

A

vg(S

HV

, BH

V)

– A

vg(S

LV, B

LV)

3M

0.00

69

0.

0795

0.02

25

0.

0469

0.07

27

(0.0

6)

0.02

44

(0.4

1)

0.04

85

(0.9

6)

6M

0.03

06

0.

0253

0.02

36

0.

0274

-0.0

054

(0.8

6)

0.00

39

(0.8

9)

-0.0

008

(0.9

6)

R1

0.20

78

0.

3355

0.13

01

0.

1758

0.12

78

(0.0

3)

0.04

57

(0.5

2)

0.08

68

(0.1

0)

R2

0.14

18

0.

1727

0.07

40

0.

0948

0.03

09

(0.5

9)

0.02

08

(0.7

3)

0.02

58

(0.4

5)

R3

0.15

44

0.

1358

0.12

73

0.

1136

-0.0

185

(0.6

3)

-0.0

137

(0.7

6)

-0.0

161

(0.6

3)

R4

0.13

87

0.

1621

0.14

15

0.

1923

0.02

34

(0.6

9)

0.05

08

(0.3

6)

0.03

71

(0.3

4)

R5

0.19

82

0.

1542

0.23

19

0.

1576

-0.0

441

(0.4

2)

-0.0

742

(0.3

8)

-0.0

591

(0.2

7)

AV

G

0.16

82

0.19

21

0.14

10

0.14

68

0.02

39

0.00

59

0.01

49

CR

3 0.

4074

0.57

63

0.

2577

0.31

63

0.

1689

(0

.03)

0.

0586

(0

.63)

0.

1137

(0

.13)

CR

5 0.

6772

0.88

74

0.

4849

0.55

16

0.

2102

(0

.05)

0.

0667

(0

.65)

0.

1384

(0

.10)

Wal

id S

aleh

- Si

ze, B

ook-

to-M

arke

t, Vo

latil

ity a

nd S

tock

Ret

urns

: Evi

denc

e fr

om A

mm

an

Stoc

k Ex

chan

ge (A

SE)-

Fron

tiers

in F

inan

ce a

nd E

cono

mic

s – V

ol. 7

No.

2 –

Oct

ober

201

0, 9

0 –

124

FFE

is h

oste

d an

d m

anag

ed b

y SK

EMA

Busi

ness

Sch

ool

110

Pan

el C

: Tes

t of t

he S

tatis

tical

Sig

nific

ance

of V

alue

-Wei

ghte

d M

onth

ly R

etur

ns’ V

olat

ility

:

HSV

MLS

VH

SVLS

VH

RR

R

t-t

est

p-va

lue

0.

006

1.67

0.

10

Not

e th

at A

t the

end

of A

pril

of e

ach

year

t st

ocks

wer

e al

loca

ted

to tw

o gr

oups

(big

and

smal

l, B

& S

) bas

ed o

n w

heth

er th

eir

mar

ket v

alue

is a

bove

or b

elow

the

med

ian

of th

e m

arke

t. Fu

rther

, sto

cks

wer

e al

loca

ted

in a

n in

depe

nden

t sor

t to

two

stoc

k vo

latil

ity g

roup

s (hi

gh a

nd lo

w, H

& L

) bas

ed o

n th

e w

heth

er th

eir s

tand

ard

devi

atio

n of

the

past

12-

mon

th re

turn

s is b

elow

or

abov

e th

e m

edia

n of

the

stan

dard

dev

iatio

n of

the

past

12-

mon

th m

arke

t ret

urns

. Fro

m th

e in

ters

ectio

n of

the

two

size

gro

ups

(S a

nd B

) and

the

two

stan

dard

dev

iatio

n gr

oups

(L, M

, H),

four

siz

e-vo

latil

ity p

ortfo

lios

are

cons

truct

ed (S

LV, S

HV

, BLV

, an

d B

HV

). H

SVM

LSV

R i

s th

e di

ffer

ence

, eac

h m

onth

, bet

wee

n th

e av

erag

e of

the

ret

urns

on

the

two

high

-sto

ck-v

olat

ility

po

rtfol

ios (

SHV

and

BH

V) a

nd th

e av

erag

e of

the

retu

rns o

n th

e tw

o lo

w-s

tock

-vol

atili

ty p

ortfo

lios (

SLV

and

BLV

). t-s

tatis

tic

with

stan

dard

err

ors i

s cal

cula

ted

usin

g W

hite

(198

0).

111

0.1820 and 0.2685 with p-values of 0.03 and 0.02, respectively. The above results suggest that the difference in returns over one-year period (R1) between high and low stock volatility is significant at 10% level or less. This result motivates us to think of stock volatility as a risk factor9. That is, this result suggests that stock volatility could be modeled as a cross-sectional risk factor and compensated by higher stock returns. The results also provide an evidence of returns reversal. For example, the last column in Panel A of Table 5 shows that the difference in returns declines from 0.1022 over one-year period to 0.0462, 0.0387, 0.0274, and –0.0244 over two-year, three-year, four-year, and five-year period, respectively. Panel B of Table 5 reports the value-weighted returns for portfolios formed on size and stock volatility. The results, for small stocks, show that the difference in returns between high and low stock volatility is 0.0727, -0.0054, 0.1278, 0.0309, -0.0185, 0.0234, and –0.0441 with p-values of 0.06, 0.85, 0.03, 0.59, 0.63, 0.69, and 0.42 for 3-month, 6-month, one-year, two-year, three-year, four-year, and five-year period, respectively. The cumulative difference in returns between high and low stock volatility over three-year and five-year period is 0.1689 and 0.2102 with p-values of 0.03 and 0.05, respectively. For large stocks, the difference in returns between high and low stock volatility is 0.0244, 0.0039, 0.0457, 0.0208, -0.0137, 0.0508, and –0.0742 with p-values of 0.41, 0.89, 0.52, 0.73, 0.76, 0.36, and 0.38 for 3-month, 6-month, one-year, two-year, three-year, four-year, and five-year period, respectively. Over three (five)-year period, the cumulative difference in returns between high and low stock volatility is 0.0586 (0.0667) with p-values of 0.63 (0.65). The last column in Panel B of Table 5 shows that the difference in returns between the average of returns of the two high stocks-volatility (SHV and BHV) and the average of the returns on the two low stocks-volatility (SLV and BLV) is 0.0485, -0.0008, 0.0868, 0.0258, -0.0161, 0.0371, and –0.0591 with p-values of 0.96, 0.96, 0.10, 0.45, 0.63, 0.34, and 0.27 for 3-month, 6-month, one-year, two-year, three-year, four-year, and five-year period, respectively. The cumulative difference in returns over three-year and five-year period is 0.1137 and 0.1384 with p-values of 0.13 and 0.10, respectively. The value weighted results from Panel B of Table 5 assert that the difference in returns between high and low stock volatility over one-year period (R1) is significant at 10% level or less, except for large stocks. Further, the paper 9 Note that we were interested in one-year horizon returns since portfolios were constructed annually.





112

examined the significance of one-year value weighted returns based on monthly data. Panel C of Table 5 shows that the difference in the average returns between the two high stocks-volatility and the two low stocks-volatility is significant at 10% level. Thus, this motivates us to think of modeling stock volatility as a cross-sectional risk factor compensated for higher returns. 4.6 - The Fama and French (1993) Three-Factor Model

In this section, the paper checked for a potential risk differences between value and glamour portfolios. Therefore, the Fama and French (1993) three-factor model was employed to test whether this model can explain the difference in returns between value and glamour stocks. If the Fama-French three-factor model describes expected returns, the regression intercepts from such a model should be close to zero using a conventional t-statistics. Panel A of Table 6 reports the results of a one-year period for portfolios formed on size and book-to-market equity.

The results show that the values of the estimated intercepts are positive and significant in 5 cases out of 6. These results suggest that the Fama-French three-factor model does not fully explain the portfolio returns. In other words, the model leaves a large positive unexplained return for 5 portfolios out of 6. For the arbitrage portfolios (VMG), the intercept values are 0.008 and 0.000 with t-statistics of 2.03 and 0.14 for small and large stocks, respectively. Thus, the Fama-French three-factor model does capture the variation in the average returns on large stocks, but does not explain most of the variations in the average returns on small stocks.

The values of the beta coefficient for VMG portfolios are not significant. Thus, the difference in returns between value and glamour portfolios cannot be attributed to risk differences.

The loading of SMB factor for small stocks is positive and significant, however, for large stocks, the coefficient values load negative and significant only for high book-to-market stocks. Thus, the SMB factor loads positive and significant (negative and not significant) for glamour small stocks (glamour large stocks), whilst it loads positive and significant (negative and significant) for value small stocks (value large stocks). As expected, the loading of the SMB factor for VMG portfolios is not significant since the paper considered the size-effect when calculating the VMG

113

Tabl

e 6:

Con

trol

ling

for

Risk

Fac

tors

- Por

tfolio

s For

med

on

Size

and

Boo

k-to

-Mar

ket E

quity

Pane

l A: F

ama

and

Fren

ch T

hree

-Fac

tor

Mod

el

Sm

all

Big

Sm

all

Big

LBM

M

BM

H

BM

LB

M

MB

M

HB

M

VM

G

VM

G

a 0.

008

0.01

1 0.

016

0.01

1 0.

004

0.01

1 0.

008

0.00

0 t(a

) 2.

23

3.15

4.

52

2.12

1.

33

2.77

2.

03

0.14

0.92

0.

86

0.91

0.

82

0.79

0.

86

-0.0

1 0.

04

t()

6.57

8.

01

8.43

4.

27

7.35

6.

09

-0.0

9 0.

16

S 0.

39

0.39

0.

38

-0.3

8 0.

06

-0.3

1 -0

.01

0.07

t(s

) 4.

29

4.48

4.

21

-1.3

9 1.

02

-2.8

8 -0

.14

0.25

H

-0

.15

-0.0

7 0.

14

-0.4

8 -0

.08

0.18

0.

29

0.66

t(h

) -2

.13

-1.1

5 1.

71

-1.7

3 -1

.61

2.31

2.

80

2.28

2 R

0.

371

0.34

6 0.

360

0.27

3 0.

305

0.36

4 0.

06

0.18

9 Pa

nel B

: Fam

a an

d Fr

ench

Thr

ee-F

acto

r M

odel

- inc

ludi

ng H

SVM

LSV

Smal

l Bi

g Sm

all

Big

LB

M

MB

M

HB

M

LBM

M

BM

H

BM

V

MG

V

MG

a

0.00

7 0.

010

0.01

5 0.

007

0.00

3 0.

012

0.00

8 0.

005

t(a)

2.21

2.

89

4.27

1.

48

1.14

2.

76

1.87

0.

63

0.

90

0.80

0.

81

0.60

0.

75

0.87

-0

.09

0.27

t(

) 6.

44

7.33

7.

43

2.78

7.

13

5.78

-0

.65

1.06

S

0.40

0.

39

0.38

-0

.37

0.06

-0

.31

-0.0

2 0.

06

t(s)

4.26

4.

78

5.06

-1

.78

1.03

-2

.89

-0.1

2 0.

29

H

-0.1

4 -0

.03

0.19

-0

.36

-0.0

6 0.

18

0.33

0.

54

t(h)

-1.8

6 -0

.57

2.76

-2

.13

-1.1

0 2.

10

3.17

2.

89

Wal

id S

aleh

- Si

ze, B

ook-

to-M

arke

t, Vo

latil

ity a

nd S

tock

Ret

urns

: Evi

denc

e fr

om A

mm

an

Stoc

k Ex

chan

ge (A

SE)-

Fron

tiers

in F

inan

ce a

nd E

cono

mic

s – V

ol. 7

No.

2 –

Oct

ober

201

0, 9

0 –

124

FFE

is h

oste

d an

d m

anag

ed b

y SK

EMA

Busi

ness

Sch

ool

Wal

id S

aleh

- Si

ze, B

ook-

to-M

arke

t, Vo

latil

ity a

nd S

tock

Ret

urns

: Evi

denc

e fr

om A

mm

an

Stoc

k Ex

chan

ge (A

SE)-

Fron

tiers

in F

inan

ce a

nd E

cono

mic

s – V

ol. 7

No.

2 –

Oct

ober

201

0, 9

0 –

124

FFE

is h

oste

d an

d m

anag

ed b

y SK

EMA

Busi

ness

Sch

ool

114

HSV

MLS

V

0.06

0.

23

0.35

0.

78

0.15

-0

.03

0.29

-0

.81

t(HSV

MLS

V)

0.65

2.

59

3.50

2.

58

1.85

-0

.33

2.05

-2

.55

2 R

0.37

1 0.

374

0.42

1 0.

406

0.32

1 0.

362

0.09

3 0.

323

Not

e: A

t the

end

of

Apr

il of

eac

h ye

ar t

stoc

ks w

ere

sorte

d in

to tw

o gr

oups

(sm

all a

nd b

ig)

base

d on

whe

ther

thei

r m

arke

t ca

pita

lizat

ion

is a

bove

or

belo

w th

e m

edia

n of

the

mar

ket.

Mor

eove

r, sto

cks

wer

e al

loca

ted

in a

n in

depe

nden

t sor

t to

thre

e bo

ok-to

-mar

ket g

roup

s (h

igh,

med

ium

, and

low

) ba

sed

on th

e br

eakp

oint

s fo

r th

e to

p 30

per

cen

t, m

iddl

e 40

per

cen

t, an

d bo

ttom

30

per c

ent o

f the

boo

k-to

-mar

ket v

alue

s. Fr

om th

e in

ters

ectio

n of

the

two

size

gro

ups (

S an

d B

) and

the

thre

e bo

ok-to

-m

arke

t gro

ups (

H, M

, and

L) s

ix si

ze-b

ook-

to-m

arke

t por

tfolio

s wer

e co

nstru

cted

.

,(

)f

im

fi

ii

tR

pR

aR

Rs

SMB

hH

ML

e

,(

)f

im

fi

ii

it

Rp

Ra

RR

sSM

Bh

HM

Ll

HSV

MLS

Ve

Whe

re,

fR

pR

is

the

indi

vidu

al p

ortfo

lios

retu

rn m

inus

Tre

asur

y bi

ll ra

te o

r the

VM

G p

ortfo

lio re

turn

. SM

B (s

mal

l min

us

big)

is th

e di

ffer

ence

, eac

h m

onth

, bet

wee

n th

e av

erag

e of

the

retu

rns

on th

e th

ree

smal

l-sto

ck p

ortfo

lios

(S/L

, S/M

, and

S/H

) an

d th

e av

erag

e of

the

retu

rns

on th

e th

ree

big-

stoc

k po

rtfol

ios

(B/L

, B/M

, and

B/H

). H

ML

is th

e di

ffer

ence

, eac

h m

onth

, be

twee

n th

e av

erag

e of

the

retu

rns

of th

e tw

o hi

gh-b

ook-

to-m

arke

t por

tfolio

s (S

/H a

nd B

/H) a

nd th

e av

erag

e of

the

retu

rns

on

the

two

low

-boo

k-to

-mar

ket p

ortfo

lios

(S/L

and

B/L

). H

SVM

LSV

is th

e di

ffer

ence

, eac

h m

onth

, bet

wee

n th

e av

erag

e of

the

retu

rns

on th

e tw

o hi

gh-s

tock

-vol

atili

ty p

ortfo

lios

(SH

and

BH

) and

the

aver

age

of th

e re

turn

s on

the

two

low

-sto

ck-v

olat

ility

po

rtfol

ios

(SL

and

BL)

. VM

G r

epre

sent

s th

e di

ffer

ence

bet

wee

n hi

gh b

ook-

to-m

arke

t st

ocks

(H

BM

) an

d lo

w b

ook-

to-m

arke

t st

ocks

(LB

M).

t( )

is th

e t-s

tatis

tic w

ith st

anda

rd e

rror

s cal

cula

ted

usin

g W

hite

(198

0).

2 Ris

adj

uste

d fo

r deg

ree

of fr

eedo

m.

115

returns10. The HML factor is significant only in 2 out of 6 cases at the conventional 5% level. As expected, lower book-to-market portfolios (glamour) tend to produce a negative loading factor for the book-to-market factor, whilst higher book-to-market portfolios (value) tend to produce a positive loading factor for book-to-market factor. That is, the HML slopes increase always monotonically from negative values for the lowest book-to-market stocks. Moreover, the loading of HML factor in the arbitrage portfolios (VMG) is always significant and positive. Thus, the HML factor captures some variation in stock returns that is missed by the market and by the SMB factor. 4.7 - The Four-Factor Model

The results from section 4.5 suggest that it is sensible to think of volatility as a cross-sectional risk factor and compensated by higher stock returns. Since this factor is not captured by the Fama and French (1993) three-factor model, the paper constructed a new factor called high stock volatility minus low stock volatility (HSVMLSV), then added it to the Fama-French three-factor model. Panel B of Table 6 presents the results of the four-factor model. The values of the intercept coefficient for small stocks are positive and significant. This suggests that the four-factor model leaves a large positive unexplained return for small stocks. For large stocks, the values of the intercept coefficient are positive but significant only for high book-to-market stocks. Thus, for large stocks the four-factor model does capture the variation in the average returns on low and medium book-to-market stocks, but does not fully capture the variation in the average returns on high book-to-market stocks. For the arbitrage portfolios (VMG), the values of the intercept coefficient are positive but not significant at the conventional 5% level. In comparison with the three-factor model (Panel A of Table 6), it seems that the four-factor model does a better job in explaining the variation in the average stock returns for the VMG portfolios, especially for small stocks.

10 Note that I have done the analysis excluding the SMB factor; the final conclusion does not change.





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The values of beta coefficient for VMG portfolios are –0.09 and 0.27 with t-statistics of –0.65 and 1.06 for small and large stocks. This result confirms that there is no difference in risk between high and low book-to-market stocks as measured by the four-factor model. The loading of SMB factor for small stocks is positive and significant, however, for large stocks; it is significant only for high book-to-market stocks. Since the paper considered the size-effect when calculating the VMG returns, the loading of the SMB factor for VMG portfolios is not significant.

The loading of HML factor is significant for the extreme value and glamour portfolios, but not for the medium book-to-market stocks. As expected, the loading on the HML factor is much higher for value portfolio than that for glamour portfolio. Thus, the HML slopes increase always monotonically from negative values for the lowest book-to-market stocks to strong positive values for the highest book-to-market stocks. The significant role of HML factor for the extreme value and glamour portfolios is highlighted in the VMG regression which shows significant loading on HML factor. The loading of stock volatility factor (HSVMLSV) for small stocks is positive and significant for value stocks whereas it loads positive but not significant for glamour stocks. The slopes of the HSVMLSV factor for small stocks increase always monotonically from weak positive values for the lowest book-to-market stocks to strong positive values for the highest book-to-market stocks. However, for large stocks, the HSVMLSV factor loads positive and significant for low book-to-market stocks (glamour portfolio), whereas it loads negative but not significant for high book-to-market stocks (value portfolio). Thus, for large stocks the HSVMLSV slopes decrease always monotonically from strong positive value for glamour stocks to a negative value for value stocks. The above results suggest that there is a positive relationship between stock volatility and small book-to-market stocks, whereas there is a negative relationship between stock volatility and large book-to-market stocks. Recall that small and high book-to-market portfolio contains the smallest stocks whereas large and low book-to-market portfolio contains the largest stocks (Table 1). For the arbitrage portfolios (VMG), the loading of the HSVMLSV is positive (negative) and significant for small (large) stocks. Thus, the HSVMLSV factor captures some variation in stock returns that is missed by the market, SMB, and by HML.



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The coefficients of determination of the four-factor model average generally higher than those of the three-factor model, particularly, small and high book-to-market stocks as well as large and low book-to-market stocks. For example, Panel B of Table 6 shows the values of adjusted 2R for small stocks (0.371, 0.374, and 0.421 compared to 0.371, 0.346, and 0.360 for low, medium, and high book-to-market stocks, respectively), and for large stocks (0.406, 0.321, and 0.362 compared to 0.273, 0.305, and 0.364 for low, medium, and high boo

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Size, Book-to-Market, Volatility and Stock Returns: Evidence from Amman Stock Exchange ... · 2016....

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