Modeling volatility of size, value and financial leverage‐sorted portfolios: Evidence from Egyptian stock exchange

• Published date: 01 May 2022
• Author: Mahmoud Otaify
• Date: 01 May 2022
• DOI: http://doi.org/10.1002/pa.2369

ACADEMIC PAPER

Modeling volatility of size, value and financial leverage-sorted

portfolios: Evidence from Egyptian stock exchange

Mahmoud Otaify

Faculty of Business Department, Economics

and Political Science, The British University in

Egypt, Egypt

Correspondence

Mahmoud Otaify, The British University in

Egypt Egypt.

Email: mahmoud.otaify@bue.edu.eg

This paper aims at examining the volatility properties of equity portfolios sorted

according to three firm characteristics: size, value and financial leverage. Using daily

share prices of the most active stocks listed in the Egyptian stock exchange, we

adopt the GJR-GARCH (1, 1)-M model to investigate volatility properties of the daily

portfolio returns. The findings indicate that the characteristics-sorted portfolios

(CSPs) have different degrees of both volatility clustering and persistence. Moreover,

they document the presence of the asymmetric effect, reflecting that bad news have

a larger impact on the volatility of the CSPs than the good news, of the same magni-

tude. However, the conditional variance has insignificant effect on the conditional

mean returns across the CSPs. Volatility of most portfolios increases significantly dur-

ing period of the 2008 financial crisis as well as in the period of the precautionary

procedures post the Egyptian revolution in 2011. The findings of the study have

important implications to asset pricing modeling and active portfolio strategies.

JEL CLASSIFICATION

G11; G12

1|INTRODUCTION

The stock market plays a vital role in the modern economy since it

acts as a mediator between lenders and borrowers. That is, a well-

functioning stock market assists the development process in the econ-

omy through two important channels: boosting savings and allowing

for a more efficient allocation of resources. However, excessive vola-

tility could prevent the smooth functioning of financial markets and

adversely affect the performance of the economy. Volatility of stock

return is widely considered as a measure of risk. Moreover, volatility

is a priced factor in the asset pricing models (e.g., Connor, 1995;

French, Schwert, & Stambaugh, 1987). Specifically, high volatility is

responsible for increasing the cost of capital (Choe, Masulis, &

Nanda, 1993), depressing market liquidity (Engle, 1993), discouraging

current consumption (Raunig & Scharler, 2011) and investment

(Hu, 1995). Therefore, market participants, regulators, academicians

and even media are interested in monitoring the level of stock market

volatility in the home country.

In the investment community, portfolio managers compete in

designing strategies able to derive above the risk-adjusted returns.

Many practitioners used fundamental characteristics such as firm size,

book-to-market (BM) ratio and others to construct stock portfolios.

Success of such strategies attracted the academic community to doc-

ument and explain such evidence that could contradict the efficient

market hypothesis (EMH). Banz (1981) investigated the relation

between the firm size and the return on NYSE stocks. Interestingly,

he found that smaller firms experienced higher returns than larger

firms. Moreover, Basu (1977) documented that forming a portfolio of

stocks with low price-earnings (PE) ratio is more likely to earn higher

risk-adjusted return than high PE ratio stocks. Rosenberg, Reid, and

Lastein (1985) argued that abnormal returns could be derived when

investors follow a “BM”strategy –buy high BM ratio stocks and sell

low BM ratio stocks.

A growing body of research has provided strong evidence of such

strategies but the pioneer evidence in this regard provided by Fama

and French (1993) when they documented the ability of size premium

(the difference between returns on small and large capitalization

stocks, SMB) and value premium (the difference between returns on

high and low BM ratio stocks; HML) in addition to the market risk pre-

mium to explain the cross-sectional variation of stock returns. Their

Received: 7 July 2020 Revised: 3 August 2020 Accepted: 8 August 2020

DOI: 10.1002/pa.2369

J Public Affairs. 2022;22:e2369. wileyonlinelibrary.com/journal/pa © 2020 John Wiley & Sons Ltd 1of16

https://doi.org/10.1002/pa.2369

model is known as three factors Fama–French (3FF) model. An exces-

sive number of subsequent researches had examined this model, and

others scholars added other variables to the 3FF model. Carhart (1997)

added the price momentum as a fourth factor to the 3FF model, while

Chan and Faff (2005) investigated the role of share turnover (as a

proxy of liquidity) in pricing Australian stocks. More recently, Mirza,

Saeed, and Rizvi (2013) used financial leverage mimicking portfolios

to derive financial leverage premium and documented its role in

explaining the cross-sectional expected returns.

On micro level, stock prices are assumed to be random variables,

not deterministic variables. Hence, the stock prices should not be pre-

dictable. Since volatility of asset prices should reflect the randomness

of asset prices, it also should not be predictable (Schwert, 1990).

However, empirical evidence in the literature documented that volatil-

ity tends to cluster, that is, large (small) changes in stock prices tend

to be followed by large (small) changes in prices. Moreover, for sim-

plicity, volatility of different asset classes was assumed to be constant

over time, for example, the mean–variance optimization of Markowitz

involved known and constant volatility over the holding period. How-

ever, empirical studies on financial time series found strong evidence

on the time-varying of volatility and its relationship with expected

return. Moreover, volatility of asset returns responds asymmetrically

to good and bad news. In turn, ignoring such properties could result in

excess allocation to risky assets, implying suboptimal portfolio and risk

management strategies.

Since volatility patterns vary across individual assets, sectors and

indices, they could vary significantly across portfolios contained indi-

vidual stocks common in certain characteristic such as size, BM, lever-

age, etc. Typically, constructed portfolios based on different

fundamental characteristics are expected to have different returns

and associated risk levels and also different degrees of volatility prop-

erties including clustering, persistence and asymmetric effect. Thus,

style investing

1

managers should care with these features of volatility

of the interest characteristics-sorted portfolio (CSP) to achieve opti-

mal portfolio and risk management.

The rest of the paper is organized as follows: Section 2presents

the literature review, while section 3describes the data and tech-

niques used to construct the CSPs. Section 4shows empirical model

used, and section 5presents results of the empirical analysis. Implica-

tions and Directions for Future Research are given in Section 6.

2|LITERATURE REVIEW

Cohen, Ness Jr., Okuda, Schwartz, and Whitcomb (1976) asserted an

international evidence on financial economies of scale as firms

became larger. Authors suggested that small firm with few number of

outstanding shares and/or low share price was more likely to be less

liquid, have higher cost of capital and have greater share price vari-

ance. So, as firms became larger, their volatility of stock prices would

be lower. Moreover, Ross (1989) attributed asset price volatility to

the flow rate of new information to the market. Accordingly, if the

negative return shocks are followed by much information flow for the

large firms, the volatility of large stocks would respond asymmetrically

to good and bad news. Wanga and Ma (2014) observed that stocks of

the large firms experienced excess volatility and idiosyncratic volatility

less than stocks of the small firms. They attributed this lower excess

volatility to the presence of more rational investors in large firms.

With respect to the differences in the conditional volatility pro-

cess among value stocks and growth stocks, the main motivations had

been argued in the literature related to the irreversibility of invest-

ment decisions (Kogan, 2004) and the time-varying of risk premium

(Zhang, 2005). Kogan (2004) examined the effect of irreversibility of

real investment on the behavior of stock prices through using the

M/B ratio as proxy of the state of the economy. He observed that

High (low) M/B ratio was positively (negatively) related to the condi-

tional volatility of stock returns because the irreversibility of invest-

ment decisions would make the conditional volatility of growth firms

less countercyclical than that of the value firms.

Zhang (2005) assumed that the costly reversibility and countercy-

clical price of risk weaken the flexibility of value firms in reducing capi-

tal which make them much riskier than growth firms. Zhang argued

that asymmetry in the ability of value and growth firms to reverse capi-

tal stocks in bad times or to expand that capital in good times was the

source of high (low) risk dispersion between value and growth stocks

in bad (good) times. In bad times, value firms have more unproductive

capital and face high costs to reverse that capital than growth firms

and hence returns on the value stocks tend to change more with eco-

nomic depressions. In good times, although growth firms could face

higher adjustment costs to exploit the favorable investment opportu-

nities, they could easily expand capital and hence the returns on their

stocks did not covary much with favorable economic conditions. On

the other hand, the value firms already have unproductive capital

stocks which become productive in good times.

Li, Brooks, and Miffre (2009) estimated volatility properties of

value, growth and HML portfolios in the context of GARCH model

and conveyed interesting results. Firstly, volatility of value portfolio

was more (less) sensitive to recent (older) information than that of

growth portfolio. Secondly, volatilities of both the value portfolio and

the HML portfolio were indifferent for good or bad news, but volatil-

ity of the growth portfolio increased after announcement of bad news.

Finally, using GJR-GARCH(1, 1)-M model, the authors documented

positive, significant relation between the excess return of the value

portfolio and the time-varying volatility, while the excess return of the

growth portfolio was negatively related to volatility, and therefore the

expected return of the value premium (HML portfolio) was positively

associated with its time-varying volatility. Thereby, the authors argued

that return on the value portfolio was more sensitive to its volatility

than the growth portfolio.

According to financial leverage theory, when a firm raises its

financial leverage by issuing more debts in order to recapitalize its

capital structure (by buying back some of outstanding equity), firm's

financial risk will increase and in turn volatility of share price would

increase (Schwert, 1990). This relation was documented by

Schwert (1989) who found positive correlation between market vola-

tility and corporate leverage. The main motivation to analyze the

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