# Leverage With High And Low Debt Equity Ratios

The theme of the study is to inspect the effect of the leverage with high and low debt to equity ratios on identified portfolios required rate of returns listed in Karachi Stock Exchange (KSE). The multivariate regression has been used to identify the relationship among market premium, debt – to – equity premium and portfolio returns. The sample has been selected from 21 sectors consisting 100 listed- Pakistani firms for the period of January 2001 to December 2007. The P-value at 95% confidence level shows the relationship with CAPM is positive and significant related to portfolio returns (P1 to P10), while the leverage premium (DER premium) is positively insignificant. The proposed multi-factor model explains that the value of R2 indicated that there is no contribution by adding the identified variable (Leverage premium). Therefore the security analyst's, institutional investors, fund managers and other stakeholders should not consider the leverage premium as an important factor for determinant of required rate of returns.

## INTRODUCTION

Leverage refers to the use of fixed cost in attempt to increase profitability. The two principles of leverage are Operating leverage and financial leverage. The former is due to the fixed operating costs associated with the production of goods or services, whereas the latter is due to the existence of fixed financing cost. Both type of leverage affect the level and variability of firm's stock return. These studies fall out that several of the CAPM average returns anomalies are interrelated. The CAPM has been one of the most frequently used, but today many empirical studies have pointed out some deficiencies in the model, as an explanation of the link between risk and return. CAPM is weak as it based on Efficient Market Hypothesis, which means: transparency; no transaction costs; no significant restriction to investment; investor's rational behavior and expectations. These assumptions imply that the market is not affected by imperfections. There is mixed support for a positive linear association between required rates of return and systematic risk for portfolios of stock. Some recent evidence indicated the need to consider the additional risk variables or different risk proxies. That's why several studies criticize the tests of the model and usefulness of the model in portfolio evaluation because of its dependence on a market portfolio of risky assets. Empirical studies have shown the accessibility of extra required rate of returns by using active investment strategies base on a number of firm variables such as leverage (Bhandari, 1988), size (Banz, 1981), price earnings ratio (Basu, 1977), book to market ratio (Stattman, 1980); Rosenberg, Reid and Lanstein, (1985), etc. These evidences, since inconsistent with the CAPM, are popularly known as CAPM anomalies. The asset-pricing model of Sharpe (1964), Linter (1965) and Black (1972) has long formed the mode academics and practitioners thought about average required rate of returns and risk. There are various observed contradictions of the Sharpe-Linter-Black (SLB) model. One of the contradictions of the Sharpe-Linter-Black (SLB) model is inverse relation between leverage and return acknowledged by Bhandari (1988). It has been brought into the account that the leverage is related with risk and expected return. The most leading work of Fama-French (1992) three factor model in which they attach two variables in addition to the market return, the returns on small minus big stocks (SMB) and the returns of high book to market value minus low book to market value stocks (HML). This particular study discussed the two-factors that included one variable other than market premium i-e the returns with high leverage stocks minus the low leverage stocks (Debt/equity ratio premium). Leverage effect is the most important assets pricing anomalies. The recognition of the leverage effect leads the researchers to investigate its possible causes, as its presence implies that either the CAPM is miss-specified or that market is inefficient. The leverage ratio of the firm in this study was high and it has been argued that the small firms usually do not have almost as much collateral as big firms and would not have the similar capability to increase outdoor finances. Consequently, small firms would be more negatively affected by lower liquidity and higher short-term interest rates. This study tests the leverage effect in Pakistan stock market over a long period of seven years. The leverage is the most important factor that determines the leveraged. There are various sources of corporate financing, financial leverage is one of among it and is supposed to have both positive and negative features as a debt- financing tool. The issuance of debt makes a firm liable to pay cash as interest and principal. Bhandari (1988) concluded in his study that the expected returns on common stocks are inversely linked to the debt to equity ratio. This particular study examines how the stock price of a firm reacts to the overall change of its leverage ratio. It is a significant subject since the option of capital structure is possibly one of the mainly important decisions managers face, and a change in the leverage ratio can affect a firm's financing capability, risk, cost of capital, investment and planned decisions, and eventually shareholder wealth. The descriptive statistical trend of the calculated portfolios on the base of leverage follow the abnormal behavior as the general theoretical phenomena is that the firms with high debt to equity ratios have high risk adjusted high return, but this particular study has reported the high volatility in low debt to equity ratio in compare to the high debt to equity ratio. The required rate of return of the firms with low debt to equity ratio (P1 to P5) is high and there is an increasing trend, while there is decreasing trend in the firms with high debt to equity ratio. The findings reveal a positive and insignificant relationship between leverage premium and expected returns. The same result supported by Ho et al (2006) in Singapore. The study is aim to;

1. To evaluate the effect of leverage on stock return through CAPM.

2. To determine the direction of relationship between leverage and required rate of return.

## LITERATURE REVIEW

Bhandari (1988) proposed to use Debt/ Equity ratio as an additional variable to explain the stock returns. He argued in his paper that an increase in debt/ equity ratio of a firm increases the risk of common equity. He concluded that the debt/ equity ratio has a significant positive effect on the expected common stock returns though in the month of January is much larger. Empirical studies have shown the accessibility of extra normal required rate of returns by using active investment strategies based on a number of firm variables such as size (Banz, 1981), leverage (Bhandari, 1988), price earnings ratio (Basu, 1977). These evidences, since inconsistent with the CAPM, are popularly known as CAPM anomalies. Fama and French (1992) reported that average returns on small stocks are too high with given estimated beta, while average returns on large stocks are too low. This study reported that the relationship between beta and average return disappeared during the period 1963–1990 and weak relation between beta and average return during (1941 –1990). Their study reported that size & beta of size portfolios were highly correlated (- 0.988, in their data) so problem arose to separate the effect of size and beta on average return. When portfolio was formed alone on size, there is strong negative relationship between size and average return. Fama & French (1992) concluded that for the period 1963 – 1990 French (1996) argued in their study that the small stocks tend to have higher returns than big stocks and high-book-to-market stocks have high returns than low BE/ME stocks. Moreover, stocks with low long-term past returns revealed a significant relationship between the fundamental financial variables (earnings yield, size, book to market ratio, and cash flow yield) and expected returns in the Japanese market. The book to market ratio and cash flow yield has the most significant positive impact on expected returns. Another variable, cash flow yield, also has a positive and in general highly significant impact on expected returns. Their findings confirmed the existence of a "size effect"; small firms tend to outperform larger firms, after adjusting for market risk and the other fundamental variables but the statistical significance of the market capitalization variable is sensitive to the specification of the model; indeed, in some cases it is not significant. Choi, J. (2009) reported that the large positive alpha from the high book to market portfolios came from financial leverage. When the risk premium was high, book to market firm's equity beta tends to increase more than those of low book to market firms. Their study showed that the book to market changes driven by changes in market leverage. The result suggested that the firms become high book to market firms because their equity value falls after negative shocks. Nishat (2000) concluded in his study that in Pakistan, industry leverage is high, hence there were negative and significant relationships between return and volatility change. Kane, Marcus and McDonald (1985) concluded that benefit to debt finance is the difference in the rate of return (premium return) earned by optimally levered and un-levered firms. Odit, Chittoo (2008) conducted empirical study in Stock Exchange of Mauritius and found relationship between leverage and investment. There study has investigated the two kinds of firms, that is: (1) high-growth firms; and (2) low- statistically significant both for the firms with low growth and as well as the firm with high growths. Maroney, Naka and Wans (2004) conducted a study in the context of 1997 Asian financial crisis; it included 6 Asian countries (Malaysia, South Korea, Taiwan, Indonesia Thailand and Philippines). Their study considers leverage as a key feature for financial crisis that the firms were highly levered with dollar denominated debt. The devaluation in currency resulted in increase in leverage and interest payments. Leverage increased with exchange rate depreciation caused equity betas to rise; investors suffered capital losses because the equity they hold became more risky. The positive correlation between exchange rates and local returns were consistent with leverage linked to exchange rate. The local returns have positive correlation with exchange rate changes because they were associated with capital gains and losses in local market. The increased leverage contributes to the rise in equity beta and raises expected returns. Cai, Zhang (2008) examined the extensively inverse cause of the change in leverage ratio on the portfolio returns. There was a significant, inverse result of the change in long-term debt leverage on stock returns, but a weaker cause for the change in short-term debt leverage. Their study reported straight indications that rise in leverage proportion lead to lower investment in future, which is an inverse cause of leverage change on future investment. Hull (1999) analyzed whether the stock value was influenced by how a firm changed its leverage ratio in relationship to its industry leverage ratio norm. He found out in his study that the stock returns for firms moving "away from" debt-to- equity norms were significantly more negative than return for firms moving "closer capital structure theory if industry debt-to- equity norms were reasonable approximations of wealth-maximizing leverage ratios. Ho, Tjahjapranata, and Yap (2006) conducted a study in Singapore which investigated that a firm's ability to arise the growth opportunities from R&D investments depend on its size, leverage, and the industry concentration. The analysis of the firm size, financial leverage, and industry concentration interactions showed that the levels of financial leverage moderate the firm size benefits. The R&D investments were positively associated with growth opportunities as firm size increases when financial leverage is high. The study concluded the effectiveness of R&D investment in generating growth opportunities has a significant positive effect for firm size and a significant negative effect for industry concentration, whereas non-significant ambiguous results for the independent effect of financial leverage. The current study conducted is to find the multifactor model, to test the application of CAPM, to express the relationship between leverage premium and equity returns in Pakistan equity market. These finding suggest fund managers, analysts, institutional investors and individual investors to consider the identified variables to obtain optimal expected average returns.

## III. RESEARCH METHODOLOGY

Stephen Ross in 1976, create the theory by which to predict the association between the returns of a single asset and the returns of a portfolio through a linear combination of many independent macro-economic variables.

The asset pricing model is frequently viewed as substitute to the capital asset pricing model (CAPM), since the arbitrage pricing theory (APT) has more elastic supposition requirements, while the CAPM require the market's predictable return.

The basis of arbitrage pricing theory is the initiative that the price of an asset is determined by a number of factors. These numbers of factors can be divided into two groups: micro factors and macro factors. The name of the theory comes from the fact that this division, together with Arbitrage can be used to derive the following formula: r = rf + β1f1 + β2f2 + β3f3 +….. βnfn. r = rf + β1f1 + β2f2 8Where r is the expected return on the security, rf is the risk free rate, each "f" is a separate factor, f1 denote market premium while f2 represent the difference of high and low leverage stocks portfolio and each coefficients are the risk sensitivities of returns for market risk (β1) and leverage (β2). The two-factor model is an addition of a sole factor CAPM; lot of literature today supports other additional factors beside the traditional beta. Fama & French (1992) have done wide investigate in this region and initiate factors describing "value" and "size" to be the most considerable factors, other than the market risk, they value risk. The word SMB means small minus big, i–e, the firm with low market capitalization and the firm with high market capitalization. HMB stands for high minus low, has been designed to determine the value premium. The two factors model allows the investors to weight their portfolios in such a way that they have larger or lesser coverage to each of the particular risk factors and there fore can mark more accurately various levels of expected return. To test the two factor model this particular study follow the traditional multivariate regression framework and convert the above equation into a simple time series model represented as follows:

Rί = R?+βί (Rm-R?) + hί (DER Premium). This study constructs two factors; (Rm-R?) address market premium and (DER Premium) address debt to equity ratio premium. (DER Premium) stands for the leverage premium that is the differentiation of the high and low debt to equity ratio. As regression analysis is used to predict dependent variable by using one or more independent variables. Where Rί present the return on portfolios, it is the dependent variable that is to be predicted, (Rm-R?) and (DER Premium) are the independent variables that is use to predict it, βί and hί are the coefficients or multipliers that describe the level of the effect, the independent variables has on dependent variable.

Population The study has been conducted in Karachi Stock Exchange (KSE) that is Pakistan equity market. There are three markets in Pakistan where stocks are traded that is Islamabad Stock Exchange (ISE), Lahore Stock Exchange (LSE) and Karachi more active stock market in Pakistan. According to accounting information 65 to 70% value of total transaction of the country recorded at KSE on 1st October 2004. It was stated the "Best performing stock market of the world for 2002" Suliaman et al (2009). In 1991, KSE was declared as an open market and it is considered as an emerging stock market and is therefore consider different from the developed markets. There are 34 sectors that have been traded, and each sector consist bundle of companies. As for the particular study is concerned, the population to be studied includes 34 sectors from Karachi Stock Exchange (KSE). It contains a large number of listed firms.

## Sample

The secondary data has being used for this particular study. The data collected from the financial data available in the Karachi stock exchange web site (www. kse .com. Pk), cover a phase from 2001 to 2007. The sample include 100 listed- Pakistani firms at Karachi Stock Exchange among the identified sample i–e 21 sectors which is almost equal to 60%, from 2001 to 2007, the monthly data on closing price of stocks and Karachi Stock Exchange index gathered from the www.brecorder.com and Ready Board Quotations issued by Karachi Stock Exchange at the closing of trading day, that is also accessible in the documents of Security and Exchange Commission of Pakistan (SECP). The procedure to create a sample size from the identified population is to select those 100 companies that are traded eight (8) months a year at least, while as the companies that has been traded less than eight months a year has been excluded, the analysis of the relationship between stock returns and the identified variables is conducted at the portfolio level. To find out the leverage ratio (debt – to – equity ratio) of the sorted companies the value of debt divided by the value of equity. These values of debt and equity of the sorted company are obtained from the annual report of companies. The companies with low leverage ratio have been placed in small and those with high leverage ratio have been placed in large. The treasury-bill rate is used as risk free rate and KSE Index as the return rate of market. The data on treasury-bill rates are taken from Monthly Billiton of State Bank of Pakistan. The financial sector including banks, insurance and leasing etc; are excluded from the total selected sample, as the majority of the studies exclude the financial sectors while conducting the study because of highly differentiated risk profiles, Fama and French (1992).

The industries to be studied listed at Karachi Stock Exchange

1. Textile Spinning.

2. Transport.

3. Technology and Communication.

4. Woolen.

5. Jute.

6. Sugar and Allied Industries.

7. Cement.

8. Tobacco.

9. Refinery.

10. Power Generation and Distribution.

12. Oil and Gas Exploration Companies.

13. Automobile Assembler.

14. Automobile Parts and Accessories.

15. Cable and Electronic Goods.

16. Fertilizer.

17. Pharmaceuticals.

18. Chemical.

19. Leather and Tanneries.

20. Food and Personal Care Products.

21. Miscellaneous.

## IV. ANALYSIS AND EMPIICAL RESULT

The empirical estimation is based on a cross-sectional regression analysis of the relationship between stock prices in form of portfolios and the firm debt to equity ratio. It actually test the relationship of portfolio return as dependent variable and two independent variables i.e. market premium (Rm-Rf) and leverage premium.

Dependent Variable

PORTFOLIO RETURNS

The average returns of the firms included in sample of all stocks by creating portfolios, represented by P1 to P10 is to be cosidered as dependent variable for the two factor model. Stock returns are calculated as;

Rit = Ln (Pit-1/ Pit)

Where Pit is the stock price of the i- th firm in time period t and the average return of this stock is the return of portfolios that has been regressed as dependent variable on two factors namely market premium premium and leverage premium. The independent variables include market premium and leverage premium.

Independent Variables

1. Market premium (Rm-Rf)

2. Leverage premium (DER PREMIUM)

1. MARKET PREMIUM (Rm-Rf) Market premium, it is calculated as the differentiation among risk free rate and return on market, that presents the excess return that investor could receive if he invests in market both CAPM and three factor model, but today the empirical studies have shown the accessibility of extra normal returns by adding other factors that has the affect on the returns of the stocks. In this particular paper other two independent variables are; Return of market is calculated as; Rm = Ln (KSE Indexit -1/ KSE Indexit) Market premium (Rm-Rf) is calculated as, the difference between the return on KSE index and T-bill yield. This factor is enough to found the CAPM, however there is another risk factors to be studied in this study that is leverage.

2. LEVERAGE PREMIUM (DER PREMIUM) Leverage premium, is measured as the difference between the firms with high debt to equity ratios and the firms the low debt to equity ratios. Leverage premium (DER premium) is computed as; There are two ways to measure the capital structure supported by literature: book leverage and market leverage. This paper use the book leverage, which equates the historical (book) value of total liabilities, divided by the book value of total assets. As for this study is concern the market leverage inappropriate, as its change is automatically linked with stock price. Therefore, the particular studies use the 3book leverage to determine the debt ratio. The book value of the assets is stable as compare to the market value.

DER = Total Liabilities /Total Equity

Total Liabilities = Total Asset – Total Equity

Leverage Premium = High DER last 30% – Low DER top30% liabilities on the book value of total equity at the ending period of each year of the sample. The identified sample then ranked and grouped into 3 different groups based on the bottom 30% classified as low debt to equity ratios, middle 40% classified as Medium and top 30% classified as high debt to equity ratios. The firms were sorted into ten portfolios, with portfolio one (P1) having the lowest leverage ratio and portfolio ten (P10) having the highest leverage ratio. The firms in Pakistan are highly levered; the average equity is 35% while the average debt is 65% of the identified population that contain approximately 400 companies. The Table 4.1 shows the descriptive statistical trend of the calculated portfolios on the base of leverage. The 1st portfolio (P1) present the firms with low debt to equity ratio and the last portfolio (P10) present the firms with high debt to equity ratio. It follow the abnormal behavior as the general theoretical phenomena is that the firms with high debt to equity ratios have high risk adjusted high return, but this particular study report the high volatility in low debt to equity in compare to the high debt to equity ratio (Fig. 4.1.A). At extreme level the expected return of the firm with high debt to equity ratio is high than the firm with low debt to equity ratios but overall the expected return of the firms with low debt to equity ratio (P1 to P5) is high and there is an increasing trend, while there is decreasing trend in the firms with high debt to equity ratio (Fig. 4.1.B). The reason for such behavior may be the industry effect that the firms in these portfolios mostly belong to textile spinning, sugar and chemical industry. The trading volume in these industries is low in this particular period that may miss priced the securities. The 6 th portfolio (P6) reported in Fig. 4.1. B also affected by the industry factor that is textile spinning and sugar. MEAN P 1 P 2 P 3 P 4 P 5 P 6 P 7 P 8 P 9 P 1030Mean 0. 0028 0. 0116 0.0151 0. 0145 0. 0182 0. 0059 0. 0140 0.10139 0. 0107 0. 0053 Standard Error 0. 0095 0. 0096 0. 0080 0. 0083 0. 0074 0. 0079 0. 0080 0. 0066 0. 0077 0. 0089 Median -0. 0001 0. 0084 0. 0113 0. 0028 0. 0161 -0. 0004 0. 0096 0. 0182 -0. 0017 -0. 0007 18Mode #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A Standard Deviation 0. 0870 0. 0875 0. 0729 0. 0760 0. 0680 0. 0725 0. 0736 0. 0605 0. 0702 0.0819 Sample Variance 0. 0076 0. 0077 0. 0053 0. 0058 0. 0046 0. 0053 0. 0054 0. 0037 0. 0049 0.0067 Kurtosis 0.7974 1.5235 1.1644 0.3897 0.0609 0.5231 0.9866 -0.2800 0.3757 1.3534 5Skewness 0. 0467 0. 7305 0. 2540 0. 2827 0. 1311 0. 2868 0. 7281 0. 0441 0. 3698 0. 4540 1Range 0. 4565 0. 4933 0. 4404 0. 4160 0. 3548 0. 3761 0. 3909 0. 2908 0. 3741 0. 5089 Minimum -0. 2179 -0. 2033 -0. 1781 -0. 1780 -0. 1507 -0. 1512 -0. 1487 -0. 1196 -0. 1362 -0. 2186Maximum 0. 2385 0. 2900 0. 2623 0. 2379 0. 2042 0. 2248 0. 2422 0. 1712 0. 2379 0. 2903 Sum 0.2372 0.9723 1.2656 1.2151 1.5262 0.4959 1.1793 1.1674 0.8960 0.4432 Count 84.0000 84.0000 84.0000 84.0000 84.0000 84.0000 84.0000 84.0000 84.0000 84.0000 Confidence Level (95%) 0.0189 0.0190 0.0158 0.0165 0.0148 0.0157 0.0160 0.0131 0.0152 0.0178 Fig. 4.1.A. Graph of Leverage sorted portfolio returns (2001 to 2007) 2001 to 2007 0.0200 0.0150 0.0100 0.0050 0.0000 R.P 1 R.P 2 R.P 3 R.P 4 R.P 5 R.P 6 R.P 7 R.P 8 R.P 9 R.P 10 Portfolios Standard Deviation Fig. 4.1.B. Graph of Leverage sorted portfolio of standard deviation (2001 to 2007) 2001 to 2007 0.1000 0.0800 0.0600 0.0400 0.0200 0.0000 R.P 1 R.P 2 R.P 3 R.P 4 R.P 5 R.P 6 R.P 7 R.P 8 R.P 9 R.P 10 Portfolios The data is further classified into two- sub group for more precise examination. The table 4.2 presents the statistical behavior of 1 st sub group that is from January 2001 to December 2003. The 1 st sub group follows almost the same behavior. The effect of industry is found in both P6 and P10. The P10 present the most high leverage ratios because of the textile spinning industry. Most of the firms belong to textile sector has negative equity that result in low trading and that also result in low returns. Mean P 1 P 2 P 3 P 4 P 5 P 6 P 7 P 8 P 9 P 1054Mean 0. 0092 0. 0166 0. 0270 0. 0201 0. 0249 0. 0176 0. 0201 0. 0302 0.0238 0. 0168 Standard Error 0. 0176 0. 0177 0. 0138 0. 0141 0. 0133 0. 0135 0. 0133 0. 0102 0.0123 0. 0161 Median -0. 0013 0. 0240 0. 0266 0. 0178 0. 0195 0. 0088 0. 0135 0. 0312 0. 0253 0. 0094 Mode 16#N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A Standard Deviation Sample Variance 0. 1053 0. 1062 0. 0829 0. 0849 0. 0795 0. 0807 0. 0796 0. 0611 0. 0735 0. 0967 0. 0111 0.0113 0.0069 0.0072 0.0063 0.0065 0.0063 0.0037 0.0054 0.0094 ]Kurtosis 0. 1066 0. 8914 0. 6407 -0. 1493 -0. 1222 0. 5813 0. 9614 -0. 2317 -0. 4227 1.3774 Skewness 0. 1930 0. 6009 0. 5844 -0. 0209 0. 1658 0. 5579 0. 4964 0. 0643 -0. 1648 0. 4486 Range 0. 4565 0. 4933 0. 3946 0. 3758 0. 3548 0. 3459 0. 3907 0. 2535 0. 2843 0. 5089 Minimum -0. 2179 -0. 2033 -0. 1323 -0. 1780 -0. 1507 -0. 1211 -0. 1487 -0. 0823 -0. 1362 -0. 2186 Maximum 0. 2385 0. 2900 0. 2623 0. 1977 0. 2042 0. 2248 0. 2420 0. 1712 0. 1481 0. 2903 Sum 0.3298 0.5977 0.9710 0.7221 0.8968 0.6328 0.7243 1.0862 0.8585 0.6035 Count 36.0000 36.0000 36.0000 36.0000 36.0000 36.0000 36.0000 36.0000 36.0000 36.0000 Confidence Level(95%) 0.0356 0.0359 0.0280 0.0287 0.0269 0.0273 0.0269 0.0207 0.0249 0.0327 Fig. 4.2.A. Graph of Leverage sorted portfolio returns (2001 to 2003) 2001 to 2003 0.0350 0.0300 0.0250 0.0200 0.0150 0.0100 0.0050 0.0000 R.P 1 R.P 2 R.P 3 R.P 4 R.P 5 R.P 6 R.P 7 R.P 8 R.P 9 R.P 10 Portfolios Mean Standard Deviatio 2001 to 2003 0.1200 0.1000 0.0800 0.0600 0.0400 0.0200 0.0000 R.P 1 R.P 2 R.P 3 R.P 4 R.P 5 R.P 6 R.P 7 R.P 8 R.P 9 R.P 10 Portfolios Standard Deviation The table 4.3 presents the 2 nd sub group that contains the data from January 2004 to December 2007. In this particular duration there is a high variation in mean of the firms with high debt to equity ratio in portfolios as compare to other identified periods, even in some cases their trend is negative (P6 and P10 see Fig 4.3.A) which indicate the industry factor followed by P6 in each period. In 2 nd sub group period the negative trend of P10 is because of industry factor. In which most of the companies belong to textile spinning and sugar. In this particular time large numbers of textile companies were de listed from KSE. There may some macro economic indicator also involve in this particular period that is the interest rate, exchange rate and inflation rate increase at increasing rate. P 1 P 2 P 3 P 4 P 5 P 6 P 7 P 8 P 9 P 10Mean -0. 0019 0. 0078 0.0061 0. 0103 0. 0131 -0. 0029 0. 0095 0. 0017 0. 0008 -0. 0033 Standard Error 0. 0103 0. 0103 0. 0092 0. 0100 0. 0084 0. 0094 0. 0100 0. 0083 0. 0096 0. 0099 Median -0.0001 0. 0047 0. 0012 -0. 0101 0. 0148 -0. 0093 0. 0014 -0. 0063 -0. 0110 -0. 0098 Mode 16#N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A Standard Deviation Sample Variance 0. 0711 0. 0714 0. 0639 0. 0693 0. 0582 0. 0653 0. 0693 0. 0577 0. 0667 0. 0685 0. 0051 0.0051 0.0041 0.0048 0.0034 0.0043 0.0048 0.0033 0.0044 0.0047 Kurtosis 1.0956 1.4548 0.8971 1.3503 -0.4150 -0.4151 1.2643 -0.4202 2.0809 -0.4177 5Skewness -0. 5540 0. 7717 -0. 5549 0. 6067 -0. 1664 -0. 2848 0. 9538 -0. 0488 0. 8397 0. 0785 Range 0. 3622 0. 3809 0. 3134 0. 3722 0. 2381 0. 2581 0. 3412 0. 2423 0. 3657 0. 2953 Minimum -0. 1948 -0. 1456 -0. 1781 -0. 1343 -0. 1091 -0. 1512 -0. 0990 -0. 1196 -0. 1277 -0. 1505 Maximum 0. 1674 0. 2353 0. 1353 0. 2379 0. 1291 0. 1068 0. 2422 0. 1227 0. 2379 0. 1448 Sum -0.0926 0.3746 0.2945 0.4930 0.6294 -0.1368 0.4550 0.0812 0.0375 -0.1603 Count 48.0000 48.0000 48.0000 48.0000 48.0000 48.0000 48.0000 48.0000 48.0000 48.0000 Confidence Level (95.0%) 0. 0206 0. 0207 0. 0185 0. 0201 0. 0169 0. 0190 0.0201 0. 0167 0. 0194 0. 0199 Standaiationrd De Mean 2004 to 2007 0.0150 0.0100 0.0050 Mean 0.0000 -0.0050 R.P 1 R.P 2 R.P 3 R.P 4 R.P 5 R.P 6 R.P 7 R.P 8 R.P 9 R.P 10 Portfolios Fig. 4.3.B. Graph of leverage sorted portfolio of standard deviation (2004 to 2007) 2004 to 2007 0.0800 0.0700 0.0600 0.0500 0.0400 0.0300 0.0200 0.0100 0.0000 R.P 1 R.P 2 R.P 3 R.P 4 R.P 5 R.P 6 R.P 7 R.P 8 R.P 9 R.P 10 Portfolios Standard Deviation Table 4.4: CAPM P1 to P10 (2001 to 2007) 2001 to 2007 P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 Rm-Rf 0. 6139 0. 5538 0. 4958 0. 4584 0. 4897 0. 5342 0. 6992 0. 7182 0. 9143 0. 9301 T-statistics 4.4118 4.6371 4.8907 5.6019 5.9395 7.1472 8.4852 10.1047 13.9437 22.1909 P- value 713.09E-05 1. 32E -05 4.93E -06 2. 76E-07 6. 63E-08 3.32E-10 7.61E-13 4.64E-16 2.4E-23 2.06E-36 35R2 0. 1918 0. 2077 0. 2258 0. 2767 0. 3008 0. 3838 0. 4675 0. 5546 0. 7033 0. 8572 The regression use the natural logs to found out the empirical link between the risk and return of portfolios that is the market premium, in other word to test the CAPM that is most frequently used. The P-value at 95% confidence level shows the relationship is highly significant at each portfolio (P1 to P10). A higher value of R 2 is associated with more explanatory power of a model but the table 4.4 suggests space for other variable, as the value of R 2 is not high. Table 4.5: Regression Market Premiums and Leverage P1 to P10 (2001 to 2007) P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 Rm-Rf 0. 6402 0. 5813 0. 6110 0. 6382 0. 5959 0. 7007 0. 5539 0. 4837 0. 5451 0. 6437 T- statistics 6.8075 5.6327 7.8876 8.1968 8.6013 11.4118 6.6843 7.3051 7.0040 7.3814 4P- value 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 DER (PREMIUM) -0. 6282 -0. 3881 0. 0729 -0. 3754 -0. 1046 0. 5139 0. 2662 -0. 0996 0. 2246 0. 5054 T- statistics -3.2207 -1.8134 0.4537 -2.3252 -0.7281 4.0355 1.5490 -0.7255 1.3914 2.7944 4P- value 0. 0018 0. 0735 0. 6513 0. 0226 0. 4686 0. 0001 0. 1253 0. 4702 0. 1679 0. 0065 R2 0. 4153 0. 3041 0. 4348 0. 4751 0. 4800 0. 6414 0. 3658 0. 4004 0. 3848 0. 4319 By adding other factor the regression predict that the dependent variable is not more effected by leverage premium (DER premium), the P-value at 95% confidence level is highly significant at market premium but almost insignificant at leverage premium. The R 2 increase highly in small firms (P1 to P5), this makes R 2 sensitive to number of explanatory variables including in model. The difference between the values of R 2 is almost equal to zero by adding 2 nd factor (DER premium) that predict no contribution towards the equity returns. Conclusive result of all the two tables in the period of 2001 to 2007 clearly suggest that the market premium does exit contribution towards the stock returns, while the leverage ratio dose not affect the stock returns in identified period and time. 2001 to 12003 P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 Rm-Rf 0. 6097 0. 4567 0. 4208 0. 4734 0. 4875 0. 5643 0. 7017 0. 7997 1.0423 1.0005 T-statistics 3.5320 2.4908 3.1141 5.6393 4.2490 6.5681 6.3983 8.8634 11.5965 22.2875 20P-value 0. 0012 0. 0178 0. 0037 0.0000 0. 0002 0.0000 0.0000 0.0000 0.0000 0.0000 R2 0. 2684 0. 1543 0. 2219 0. 4833 0. 3468 0. 5592 0. 5463 0. 6979 0. 7982 0. 9359 The table 4.6 regresses the sub period from 2001 to 2003 to predict the linear relationship between the portfolio returns and risk. The P-value at 95% confidence level is highly significant at each portfolio, as reported in table 4.6. The value of R 2 is high with same factor (market premium) and same model (CAPM) in sub period. The higher value of R 2 indicates more explanatory power of model in sub period. Table 4. 7: Regression Market Premium and Leverage P1 to P10 (2001 to 12003) P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 Rm-Rf 0. 6290 0. 6884 0. 7096 0. 6444 0. 6691 0. 7033 0. 6065 0. 4875 0. 5616 0. 7450 T- statistics 4.5695 4.5780 7.7303 6.5886 7.2923 8.6674 5.8244 6.5908 5.8158 5.9996 4P- value 0. 0001 0. 0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 DER (PREMIUM) -1.1500 -0.7034 0.0954 -0.7578 -0.2427 0.2865 -0.2597 -0.3164 -0.1302 0.1314 T- statistics -4.0704 -2.2791 0.5065 -3.7753 -1.2890 1.7201 -1.2153 -2.0840 -0.6570 0.5156 4P- value 0. 0003 0. 0293 0. 6159 0. 0006 0. 2064 0. 0948 0. 2329 0. 0450 0. 5158 0. 6096 R2 0. 5117 0. 4269 0. 6493 0. 6202 0. 6191 0. 7109 0. 5108 0. 5812 0. 5064 0. 5288 Almost same behavior is followed in table 4.7 by regressing two factors for 1st sub period that is the market premium is highly significant at 95% confidence level, while the leverage is insignificant. 1P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 Rm-Rf 0. 6156 0. 6892 0. 5999 0. 4327 0. 4940 0. 4898 0. 6923 0. 5907 0. 7156 0. 8234 T-statistics 2.6730 4.3240 3.8005 2.9263 3.9416 3.8017 5.3308 5.2482 7.8105 11.4892 43P 0. 0104 0. 0001 0. 0004 0. 0053 0. 0003 0. 0004 0.0000 0.0000 0.0000 0.000020R2 0. 1344 0. 2890 0. 2390 0. 1569 0. 2525 0. 2391 0. 3819 0. 3745 0. 5701 0.7416 The CAPM in 2nd sub period that is from 2004 to 2007 predict that it is highly significant at 95% confidence level; the P -value of 1st portfolio is significant at 90% confidence level. The value of R 2 is low as compare to the CAPM applied in 1st sub group (see table 4.6). The 2nd period that is 2004 to 2007 Pakistan stock market suffers due to macro factors. Table 4. 9: Regression Market Premium and Leverage P1 to P10 (2004 to 12007) P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 Rm-Rf 0. 7533 0. 4714 0. 4358 0. 6988 0. 5015 0. 7318 0. 5765 0. 4951 0. 5745 0. 5517 T- statistics 6.4090 3.2099 3.3728 5.8465 4.5757 7.7722 4.8593 4.5264 4.7426 4.5422 4P- value 0.0000 0. 0025 0. 0015 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 DER (Premium) 0. 2092 0. 0121 -0. 1219 0. 2262 0. 0257 0. 8464 1.0852 0. 1508 0. 7328 0. 9958 T- statistics 0. 8331 0. 0387 -0. 4416 0. 8861 0. 1099 4.2085 4.2820 0.6455 2.8320 3.8384 4P- value 0. 4092 0. 9693 0. 6609 0. 3803 0. 9130 0. 0001 0. 0001 0. 5219 0. 0069 0.0004 R2 0. 4780 0. 1911 0. 2183 0. 4320 0. 3235 0. 6027 0. 4403 0. 3133 0. 3698 0. 3991 In 2 nd sub period lot of variation has been experienced (see mean value, table 4.3), the same impact is found in table 4.9 by regressing the 2 nd factors, the P-value of market premium is highly significant at 95% confidence level at each portfolios, while the same consistency is not followed by leverage (DER premium). The another independent variable that is the leverage, is highly significant in few portfolios (P6, P7, P9 and p10) at 95% confidence level that predict the contribution of last identified factor. The value of R 2 is also high as compare to previous periods that indicate the high contribution by 3 rd factor in this particular period.

V. SUMMARY, CONCLUSION AND RECOMMENDATIONS

5 .1 Summary This study was conducted to determine the affect of market premium and one of CAPM anomaly in Pakistan equity market. The anomaly that has been studied is the leverage premium. The study uses the secondary data of the firms that has been traded in Karachi stock exchange (KSE). The data has been collected from the financial data published in the Karachi stock exchange web site (www. kse .com. Pk), covering a phase from 2001 to 2007. The sample includes 100 listed- Pakistani firms at Karachi Stock Exchange among 21 sectors, the monthly data on ending price and Karachi Stock Exchange index collected from the www.brecorder and Ready Board Quotations that is issued by Karachi Stock Exchange at the closing of trading day, which are also presented in the records of Security and Exchange Commission of Pakistan (SECP). The multivariate regression model has been used to identify the relationship among market premium, debt – to – equity premium and portfolio returns. The P-value at 95% confidence level shows the relationship with CAPM is positive and is significant related to portfolio returns (P1 to P10), while the leverage premium (DER premium) is positively insignificant. The proposed multi-factor model explains that the value of R2 indicated that there is no contribution by adding the identified variable (Leverage premium).

5.2 Conclusion

This study relates cross-sectional differences in returns on Pakistan stocks to the underlying behavior of two identified variables i-e market premium (Rm-Rf) and DER (Premium). It has been experienced that there exist lot of variation in Pakistan and the multivariate regression model. It includes 21 sectors consisting of 100 listed- Pakistani firms for the period of January 2001 to December 2007. The data has been classified into there different time periods. First time period follows the abnormal behavior as the general theoretical phenomena is that the firms with high debt to equity ratios have high risk adjusted high return. But this particular study report the high volatility in low debt to equity in compare to the high debt to equity ratio (Fig. 4.1.A) by using descriptive statistics (Table 4.1). At extreme level the expected return of the firm with high debt to equity ratio is high than the firm with low debt to equity ratios but overall the expected return of the firms with low debt to equity ratio (P1 to P5) is high and there is an increasing trend, while there is decreasing trend in the firms with high debt to equity ratio (Fig. 4.1.B). The reason for such behavior may be the industry effect that the firms in these portfolios mostly belong to textile spinning, sugar and chemical industry. The trading volume in these industries is low in this particular period that may miss priced the securities. The 6 th portfolio (P6) reported in Fig. 4.1.B also affected by the industry factor that is textile spinning and sugar. The data is further classified into two- sub group for more precise examination. The 1 st sub group consists of three years from January 2001 to December 2003. The 1st sub group follows almost the same behavior. The effect of industry is found in both P6 and P10. The table 4.3 presents the 2nd sub group that contains the data from January 2004 to December 2007. In this particular duration there is a high variation in mean of the firms with high debt to equity ratio in portfolios as compare to other identified periods, even in some cases their trend is negative (P6 and P10 see Fig 4.3.A) which indicate the industry factor followed by P6 in each period. In 2 nd sub group period belong to textile spinning and sugar. The regression uses the natural logs to found out the empirical link between the identified variables and portfolios return. Conclusive result of all the two tables (Table 4.4 and 4.5) in the period of 2001 to 2007 clearly suggest that the market premium does exit contribution towards the stock returns, while the leverage ratio dose not affect the stock returns in identified period and time. The first sub period (Table 4.6) from 2001 to 2003 predict that the P-value at 95% confidence level is highly significant at each portfolio. The value of R 2 is high with same factor (market premium) and same model (CAPM) in sub period. Almost same behavior is followed in table 4.7 by regressing two factors for 1st sub period that is the market premium is highly significant at 95% confidence level, while the leverage is insignificant. In 2nd sub period Pakistan stock market suffers due to macro factors. In 2nd sub period lot of variation has been experienced (see mean value, table 4.3), the same impact is found in table 4.9 by regressing the 2nd factors, the P-value of market premium is highly significant at 95% confidence level at each portfolios, while the same consistency is not followed by leverage (DER premium). 5.3 Recommendation As conclusive result suggest that the market premium does exit contribution towards the stock returns, while the leverage ratio dose not affect the stock returns in identified period. This particular study recommends that there might many other independent macro-economic or micro-economic variables that predict a relationship between the returns of a portfolio. Today lot of literature support other company price earnings ratio and book to market ratio etc.

ABSTRACT CAPM anomalies. The asset-pricing model of Sharpe (1964), Linter (1965) and firms risk premium. The company by more debt finance than equity finance is to be considered highly Chan et al. (1991) conducted a study in Tokyo stock market; their findings growth firms. The association between leverage and corporate value is negative and to" these norms. He also mentioned that there finding was consistent with optimal constructed two factors; SMB to address size risk and book -to- market to address34Stock Exchange (KSE). The Karachi Stock Exchange (KSE) is the highly liquid and To find out the leverage ratio (debt – to – equity ratio) of the sorted 11. Oil and Gas Marketing Companies. portfolio instead of investing in a risk free asset. The market premium is the same in Debt to equity ratio (DER) ratio is calculated by dividing book value of total Table 4 .1: Descriptive Statistics of portfolios sorted on leverage (2001 to 2007) Table 4.2: Descriptive Statistics of portfolios sorted on leverage (2001to 2003) Fig. 4.2.B. Graph of leverage sorted portfolio of standard deviation (2001 to 2003) Table 4.3. Descriptive Statistics of portfolios sorted on leverage (2004 to 2007) Fig. 4.3.A. Graph of leverage sorted portfolio returns (2004 to 2007). Table 4.6: CAPM P1 to P10 (2001 TO 2003) Table 4.8: CAPM P1 TO P10 (2004 to 2007) in relation to portfolio returns the particular study use the descriptive statistical trend the negative trend of P10 is due to industry factor that is most of the companies specific (micro) factors to determine the required rate of return i-e size premium, 1 2 3 4 tend to have positive SMB & HML slopes and higher future average return. 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 equity returns as in other developing countries. To determine the identified variables 26 27 28 29