# Expected rates of equity returns: evidence from Indian stock market.

Abstract

This purpose of this paper is to present the expected equity returns for the Indian stock market for the benefit of investors, who may then compare such returns with actual market returns to evaluate whether the Indian stock market provides returns in excess of expectations. Both the capital asset pricing model (CAPM) which is based on systematic risk and the risk premium approach which is based on unsystematic risk, have been used to compute expected returns.

The CAPM appears to be an appropriate model to calculate expected returns emanating from the Indian stock market. The average expected returns are 13.47 per cent and the average market index returns are 16.46 per cent, indicative of the market being able to perform better than the expected returns by the technical investors. The average cost of equity (ke) for the sample companies based on the risk premium approach is also around 14 per cent (13.75 per cent). The Indian equity market continues to be an attractive investment destination for both fundamental (long-term) and technical (short-term traders) investors. However, in the presence of volatility in the short-run which increases the risk, it would perhaps be prudent to invest in the long-run.

As is evident from the literature reviewed, this is perhaps the first time expected Indian stock market returns are presented and computed through both the CAPM and the risk premium approach.

Keywords : CAPM; Risk premium approach; Expected equity returns; DOL, DFL, NSE 500 Index

JEL Classification : C42; C52; C82; E27; G11; N25

Introduction

Before embarking on the estimation of market returns earned on equity shares in India, it would be useful to have an estimate of the expected returns in the Indian stock market. Only after arriving at this required return, it would be useful/ insightful first to ascertain whether the rate of return earned by equity investors is adequate or not and secondly to compare the two sets of returns--expected and actual. Amongst the measures available in literature to estimate the required return, the capital asset pricing model (CAPM) remains, perhaps, the most utilized. This paper is devoted to the computation of the estimated required rate of return for the sample companies (NSE 500 constituent companies) based on the CAPM. The estimated returns are then compared with the actual market returns posted by the market index (NSE 500 index), to provide a better understanding of returns, from both the expectations and the actual market index returns' perspectives. Expected returns are conditional on the fundamental strength and financial performance of the underlying company whose shares the investors purchase. Further, it is also dependent on the company's relative performance vis-a-vis the underlying market. The measure that finds mention in literature is the firm's beta ([beta]), which is the covariance of the security's returns with the market returns divided by the variance of the market returns. Beta, being a market measure, captures only the systematic or market risk associated with company returns, and, is an important part of the CAPM, determining expected ROE.

Prelude

The literature review focuses on the risk factors/ determinants affecting the CAPM in particular, and expected returns, in general.

Sharpe (1), Lintner (2) and Mossin (3) developed the capital asset pricing model (CAPM) which measured the performance of assets in terms of returns. They proposed that an asset's risk could be measured by the covariance of the asset's return with the market portfolio return. Hamada (4) also analytically proved that if a firm increased its leverage, it directly affected its beta. The study of individual firms' risk as related to their underlying characteristics began with the seminal work of Beaver, et al. (5) who examined the relationship of certain accounting ratios (payout, liquidity and earning variability) to the firm's systematic risk (beta), and reported a strong and significant association between them. Rubinstein (6) developed a model which included two components of operating risk of a firm--the amount of fixed and variable costs employed in the production technology, and the co-variability of firm's output with market return. Lev (7) reported that a negative relationship existed between the level of unit variable cost and systematic risk.

Robichek and Cohn (8) tested the influence of real economic growth and inflation on the systematic risk (beta) of individual firms. They reported that these macro variables shed no light on the determinants of the systematic risk, and that only for a small number of firms can variations in beta be explained by real growth and inflation. In contrast, however, Hamada (9) reported that, conditional on the validity of Modigliani and Miller's model, leverage accounted for a substantial portion (21-24 per cent) of the systematic risk. Logue and Merville (10), based on a multiple regression technique, attempted to relate financial variables and estimated beta. Assets size, return on assets and financial leverage were found to be significant variables. Along similar lines, Rosenberg and McKibben (11) analyzed the joint influence of the firm's accounting data and its historical stock returns on the systematic and specific risks of its common stocks.

Breen and Lerner (12) tested the beta variance through independent variables such as the ratio of debt to equity, growth of earnings, stability of earnings growth, size of company, dividend payout ratio and number of shares traded. Melicher (13) divided risk into systematic or market risk and specific or diversified risk. Black and Scholes (14) suggested that it was not possible to demonstrate, using CAPM that the expected returns on high-yield common stocks differed from the expected returns on low-yield common stocks. Galai and Masulis (15) linked the firm's equity beta with factors like level of financial leverage, debt maturity, variation in income, cyclicality, operating leverage and dividends.

Hill and Stone (16) empirically confirmed that a positive relationship existed between co-variability of firm's profitability and market return. Gordon and Bradford (17) measured the relative valuation of dividends and capital gains in the stock market, using a variant of the CAPM. Hawawini and Michael (18) presented an empirical examination of the relationship between the average return and the risk of a comprehensive sample of 200 securities which traded continuously from 1966-1980 on the Brussels stock exchange. Based on their findings, they could not reject the hypothesis that the pricing of common stocks on the Brussels stock exchange conformed to the CAPM. Cohen, et al. (19) developed an analytical model that indicated how estimates of the market model beta parameter could be biased by friction in the trading process (information, decision and transaction costs) which led to a distinction between observed and 'true' returns.

Mandelker and Rhee (20) reported a positive relationship between systematic risk and degree of operating leverage. Moreover, a positive relationship was also observed between the degree of financial leverage and systematic risk. Ang, et al. (21) included the degree of operating leverage as an independent variable in the regression model to explain systematic risk but they failed to produce conclusive results. Handa, et al (22) examined the behavior of beta as a function of the return measurement interval and whether the size-effect tests were sensitive to beta estimation. Greig (23) reexamined the Ou and Penman (24) conclusion that fundamental analysis identified equity values not currently reflected in stock prices, and thus systematically predicted abnormal returns.

Koutmos, et al. (25) investigated the degree of volatility persistence and the time-varying behavior of systematic risk (beta) for ten international stock markets, using the GARCH model. The findings suggested that small capitalization markets exhibited considerably higher volatility persistence than large capitalization markets. Ismail, et al. (26) focused on beta prediction in the extreme risk categories and considered the predictive contribution of accounting information across the risk spectrum. Their results provided evidence that inclusion of accounting risk measures, alone or in combination with market beta, substantially improved beta prediction for high risk securities, but not for low and medium risk securities. Fletcher (27) examined the conditional relationship between beta and returns in U.K. from 1975-1994. His results supported the findings of Fama and French (28) and Strong and Xu (29) as there was no evidence of a significant risk premium on beta, when the unconditional relationship between beta and returns was examined. Brooks, et al. (30) explored the issue of beta instability in the Singaporean stock market over the period 1986-1993. Analysis of the eight-year interval revealed a very high incidence of beta instability, namely, at about 40 per cent of the individual stocks tested. However, CAPM continues to be deployed for measuring expected returns as it appears to be the most appropriate model as it captures the effect of volatility on market returns.

Allen and Cleary (31) studied the returns on the Malaysian stock market for the duration 1977-1992 and concluded an inverse relationship between beta and expected returns. They observed that the accounting variables like ratio of book-to-market equity and value of outstanding securities could help in explaining increments in non-systematic risk. Sheu, et al. (32) analyzed the cross-sectional relationships among market beta, trading volume and stock returns, on the Taiwan stock exchange from 1976-1996. They reported that market beta and trading volume could be combined to explain the cross-section of average returns. Reyes (33) analyzed the relationship between firm size and time-varying betas of U.K. stocks and demonstrated that the time-varying coefficient was not statistically significant for both the small and large firm stock indices. Gangemi, et al. (34) analyzed Australia's country risk using a country beta market model on the lines of Harvey and Zhou (35) and Erb, et al. (36). They observed that exchange rates were the only macroeconomic factor that had significant impact on Australia's country beta.

Lau, et al. (37) examined the relationship of stock returns with beta, size, the earnings-to-price (E/P) ratio, the cash flow-to-price ratio, the book-to-market equity ratio, and sales growth (SG) by studying the data of the Singapore and Malaysian stock markets for the period 1988-1996. The analysis revealed a negative relationship between size and stock returns and between weighted average annual sales growth and stock returns for the Singapore stock market. For the Malaysian stock market, they noted a negative size effect and a positive E/P effect on stock returns. Elsas, et al. (38) compared the unconditional and conditional test procedure using Monte Carlo simulations and reported that the conditional test significantly supported the relation between beta and return. Turner and Morrell (39) documented the calculation of the cost of equity capital in a sample of airlines, in comparison to industry-calculated values. They applied the CAPM to airlines stock prices and market indices. Tang and Shum (40) investigated the conditional relationship between beta and returns in 13 international stock markets for the period 1991-2000. They reported a significant positive relationship between beta and returns in up-market periods (positive market excess returns) but a significant negative relationship in down-market periods (negative market excess returns).

Fernandez (41) estimated the CAPM at different time scales for the Chilean stock market, by resorting to wavelet analysis. He reported evidence in support of the CAPM at a medium-term horizon. Ho, et al. (42) examined empirically the pricing effects of beta, firm size, and book-to-market equity, but conditional on market situations, i.e., whether the market was up or down, using Hong Kong equity stock data for cross-sectional regression method. On similar lines, Morelli (43) examined the role of beta, size and book-to-market equity as competing risk measurements in explaining the cross-sectional returns of U.K. securities for the period 1980- 2000. Cai, et al. (44) focused on the effects of event risk on asset price and modeled investors' optimal portfolio policy in the case of potential event risk in the Chinese stock market, and derived a liquidity-based asset pricing model. Iqbal and Brook (45) investigated the ordinary least square (OLS) beta estimates and different alternative estimators designed to correct the downward bias in the OLS beta, on a sample of 89 stocks from the Karachi stock exchange. They compared the applicability of the two asset pricing models, namely, the CAPM and the Fama-French model.

Hooper, et al, (46) compared a series of competing models to forecast beta in order to reduce forecast error. It was reported that an autoregressive model with two lags produced the lowest or close to the lowest error for quarterly stock beta forecasts. Lally and Swidler (47) investigated the relationship between the market weight of a single stock and the betas of that stock as well as of the residual portfolio. Adrian and Franzoni (48) modelled conditional betas using the Kalman filter as it focused on low-frequency variation inbetas. Manjunatha and Mallikarjunappa (49) attempted to test the validity of the combination effect of the two-parameter CAPM to determine the security/portfolio returns. Hearn (50) contrasted the performance of the CAPM, augmented by size and liquidity factors, with its time varying coefficient counterpart, using a unique market universe compiled from constituent stocks of blue chip indices BSE-100 (India), KSE-30 (Pakistan), DSE-20 (Bangladesh) and Dow Jones Titans (Sri Lanka).

Ray (51) analyzed the stability of beta for the Indian stock market for a ten year period, 1999-2009. The monthly returns data of 30 selected stocks were considered for examining the stability of beta in different market phases. Masih, et al. (52) estimated the systematic risk 'beta' at different time scales in the context of the emerging Gulf Cooperation Council (GCC) equity markets by applying a relatively new approach (known as wavelet analysis). They reported that VaR (value at risk) measured at different time scales suggested that risk tended to be concentrated more at the higher frequencies (lower time scales) of the data. Durand and Ng (53) applied the methodology proposed by Pettengil, et al. (54) on eleven Pacific Basin emerging markets. Their study supported the beta based tests. Morelli (55) examined the role of beta in explaining security returns in the U.K. stock market over the period of 1980-2006 by applying a joint conditionality, and incorporating various versions of ARCH models to estimate time varying betas. Majumder (56) developed a model which incorporated market sentiments in the domain of the standard rational model of asset pricing.

Da, et al. (57) evaluated the empirical evidence against the standard CAPM from the perspective that it could nevertheless provide a reasonable estimate of a project's cost of capital. Hasan, et al. (58) investigated the risk-return trade off within the CAPM structure for the Dhaka stock exchange. Manjunatha and Mallikarjunappa (59) examined the validity of the five parameter model (the combination of five variables, viz., beta ([beta]), size, E/P, book value/market value (BV/MV) and market risk premium ([R.sub.m]-[R.sub.f])) on the Indian stock returns using cross sectional regression.

Even though there are recent measures like the Fama-French 3 factor and 5 factor models available to measure expected returns, the CAPM remains more popular and more utilized. Further, the CAPM remains the model that captures the effect volatility has on market returns. These are the rationales for using the CAPM for calculating expected returns in this paper. Further, as the CAPM is based on the market risk, the authors felt it useful to compute expected returns through a model that is based on the unique risk of the company, viz., the operating and financial leverage. This, then, forms the rationale for using the risk premium approach.

Methodology Used

The research methodology adopted in the paper to compute the estimated returns (using the CAPM) and its comparison with market returns (for corresponding periods) has been delineated hereunder. Further, the cost of equity so computed would reflect the expected rates of return on equity shares. The NSE 500 index of India comprises of the top 500 companies listed on the NSE based on their market capitalization and is the chosen sample for this paper. The total traded value for the last six months ending December 2013, of all Index constituents was approximately 97.01 per cent of the traded value of all stocks on NSE. Hence, virtually, the chosen sample presents a census on equity market returns in India.

The date of sample selection was March 11, 2013. The study period for this paper is 2001-2014. This universe was chosen for the convenience of access to the data required and also on the assumption that it would be an accurate representation of the equity returns in India. It is important to state here that the constituent companies are amongst the most stable companies in the country due to their large market capitalizations and asset bases. As a result of this there were very minimal changes in the companies constituting the index, over the period of the study. Further, the index returns for the NSE 500 index ** were taken as the proxy for market returns in the CAPM.

Similarities/Differences Among S&P, CRISIL and NSE-Based Indices

The collaboration between S&P and CNX on the top 500 stocks traded at the National Stock Exchange gave rise to the S&P CNX NSE 500 index. It is different from other indices as it is based upon solid economic research. A trillion calculations were expended to evolve the rules inside the S&P CNX NSE 500 index. The results of this work are remarkably simple: (a) the correct size to use is 500, (b) stocks considered for the S&P CNX NSE 500 must be liquid by the 'impact cost' criterion, (c) the largest 500 stocks that meet the criterion go into the index. S&P CNX NSE 500 is a contrast to the ad-hoc methods that have gone into index construction in the preceding years, where indices were made out of intuition and lacked a scientific basis. The research that led up to S&P CNX NSE 500 is well-respected internationally as a pioneering effort in better understanding how to make a stock market index.

Further, S&P CNX NSE 500 is a more diversified index, accurately reflecting overall market conditions. The reward-to-risk ratio of S&P CNX NSE 500 is higher than other leading indices, making it a more attractive portfolio hence offering similar returns, but at lesser risk. S&P CNX NSE 500, is managed by a professional team at IISL, a company setup by NSE and CRISIL. There is a three-tier governance structure comprising the board of directors of IISL, the Index Policy Committee, and the Index Maintenance Sub-committee. S&P CNX NSE 500 has fully articulated and professionally implemented rules governing index revision, corporate actions, etc.

The CAPM Model ***

The CAPM model uses the following computation: E ([R.sub.i]) = [R.sub.f] + [[beta].sub.l] (E([R.sub.m]) - [R.sub.f]) (1)

where,

* E ([R.sub.i]) is the expected return on the security i;

* [R.sub.f] is the risk-free rate of interest, such as interest arising from government bonds;

* [[beta].sub.1], (the beta) is the sensitivity of the expected excess asset returns to the expected excess market returns, or also

[[beta].sub.1] = Cov ([R.sub.1], [R.sub.m])

Var([R.sub.m]) (2)

* E([R.sub.m]) is the expected return of the market.

In deploying the CAPM, the following methodology has been adopted:

* The risk-free return for the 364-day treasury bills has been taken as the proxy for risk-free return as the actual returns have also been computed annually, hence the corresponding periods,

* The annual NSE index returns have been taken as the proxy for market returns, and

* The weighted beta for the sample has been taken as the beta for the model. The market capitalization of the constituent companies in the sample has been taken as the weight.

Cost of Equity (ke) or Expected Rates of Return on Equity Shares

The cost of equity has been computed for the sample companies, as a measure of the return expected for the risk undertaken. The formula derived through the theory proposed by Ross (1976) and used for the same is:

[k.sub.e] = [r.sub.f] + b + f (3.3)

where [r.sub.f] = Risk free rate of return

b = Business risk premium

f = Financial risk premium

while the degree of operating leverage (DOL) measures the operating risk, the degree of financial leverage (DFL) measures the financial risk. Therefore, in an attempt to compute the cost of equity through the above stated equation, the DOL and DFL of the sample companies were computed for the period, 2001-2014.

DOL and DFL

Degree of operating leverage is calculated as percentage change in earnings before interest and taxes (EBIT) divided by percentage change in net sales. Degree of financial leverage is calculated as percentage change in earnings per share (EPS) divided by percentage change in EBIT. Further, it may be noted that the negative values have been excluded from analysis as they do not serve the intended purpose of measuring risk on the one hand and would have caused distortion in determination of average values on the other. To have better and more representative data on the subject, we have also excluded extreme values (exceeding 5) of DOL/DFL.

Expected Rates of Return Based on C APM

The model, CAPM, has been used to compute expected returns on an annual basis, in order to facilitate comparison with annual market index returns for the corresponding periods.

The non-availability of corporate financial data prior to 2001 is the reason for the non-computation of expected returns for the years prior to 2001. Hence, comparison between the market index returns and the expected returns would be made for the period 2001-2014.

Table 1 presents the expected returns for the years 2001-2014 and the corresponding market index returns. To enable better comparison, Table 2 (A & B) presents the computed mean, standard deviation, variance, coefficient of variation, minimum, maximum, skewness and kurtosis, and quartile values of both the expected and the market index returns on the basis of size (market capitalization) of sample companies (2001-2014) for the period.

As is evident from Table 1, the expected returns and the actual market index returns appear to follow the same pattern. Both the expected actual returns dropped drastically in 2009 and became negative, perhaps as a result of the recession that originated in the U.S.A. in 2008. Hence, the CAPM model appears to be an appropriate model to estimate expected returns in the Indian stock market, represented through the sample companies. Table 2 (A & B), in this regard, is perhaps more revealing. The average expected returns for the period are 13.47 per cent compared to average market index returns of 16.46 per cent. The standard deviations, coefficient of variation and variance figures are also similar, indicating that expected returns mirror the volatility present in the market. However, expectedly, the market index presents a volatility that is substantially higher than the expectations. The skewness and kurtosis figures are low indicating returns lying closer to the previous and subsequent return values. A paired t-test (Table 3) was administered to analyze whether the average expected returns were statistically different from market returns. As is evident from the t-statistic, there is no statistically significant difference between the expected and the market index returns.

The Pearson correlation coefficient between expected and actual market index returns was 0.98, further substantiating that the CAPM is an appropriate tool to forecast actual market index returns. It appears safe to postulate that the Indian stock market provides volatility and returns to the technical (short-term) investors and also allows returns over the long-run to the fundamental (long-term) investors. Buy-and-hold strategy returns over the long-term mirror the ROEF (return on equity funds). However, in the presence of volatility in the short-run which increases the risk, it would perhaps be wiser to invest in the long-run in the Indian stock market. Such a strategy should result in relatively less risky and more stable returns vis-a-vis the short-run returns.

It is important to emphasize that expected returns which are computed, based on the CAPM Model, take into consideration only the systematic risk of the security under consideration. Since systematic risk is a function of the covariance of the security's returns with the variance in market returns, the returns may be negative in response to the market (as is evident from Table 1). However, the cost of equity (returns expected by the equity providers) for a company can never be negative. Hence, simply basing our analysis on expected returns based on the CAPM model would be incomplete. There is a requirement to compute the returns expected by the equity providers based on the risk undertaken by investing in that particular security.

Expected Rates Of Return--Cost Of Equity

Would an investor in India, be satisfied with 8-10 per cent return on equity investment? The answer is likely to be in the negative; this rate of return can be easily earned by investing in safe instruments like the public provident fund (PPF), the Indira Vikas Patra (IVP), long-term deposit with commercial banks and so on (with virtually full safety of investments). Obviously, the investors would like to be compensated for the extra risk they are assuming by investing in the equity shares of a corporate enterprise. A corporate firm is subject to business risk (b). This apart, there is a variability in the rates of return available to equity-holders (as they are the last claimants on dividends as well as repayment of capital in the event of liquidation of a company), known as financial risk (f). As a compensation to the higher risk exposure, equity-holders expect a higher return and, therefore, higher cost is associated with them. In brief, the cost of equity ([k.sub.e]) is:

[k.sub.e] = [r.sub.f] + b + f (3)

The business risk is measured through a ratio called the degree of operating leverage (DOL) and the financial risk is measured through the degree of financial leverage (DFL). Therefore, in an attempt to compute the cost of equity through the above stated equation, the DOL and DFL of the constituent companies have been computed for the period, 2001-2014. Relevant data pertaining to mean, standard deviation, coefficient of variation, skewness, kurtosis, median, and quartiles values of DOL and DFL of the sample companies are contained in Table 4. Frequency distribution pertaining to DOL and DFL of the sample companies is presented in Table 5 for the period under study.

The average DOL for the sample companies is 1.46 and has remained stable through phases 1 and 2. The paired t-test (Table 6) does not indicate any statistically significant changes in mean values over the two phases indicating stable operating risk conditions. Similarly, average financial leverage in the sample companies has been 1.32. Thus, the sample companies have managed their combined risk within controllable limits, an indication of sound risk management practices. The skewness and kurtosis figures indicate that only few companies reported large values of the two measures of risk indicating low risk statistics (for sizeable corporates). As per the frequency distribution, nearly sixty per cent of sample companies have low DOL of less than 1.5 (Table 5) in 2014 compared to the reverse in 2001. Hence, the risk in the sample companies appears to have reduced through the period of the study (2001-2014). DFL also presents similar properties. The lowering of risk is further emphasized through the values of both DOL and DFL being above 5 in 2001 for more than 30 per cent of the sample companies, and which has reduced substantially over the period of the study. These findings are similar to the findings on public sector enterprises over a period of 1991-2003, reporting a DOL of 1.18 and a DFL of 1.09 respectively.

In order to arrive at an approximation of the cost of equity, the values of DOL and DFL were assigned a probable risk premium rate, in percentage terms, as provided in Table 7. For example, a rate of 1 per cent was assigned to a DOL/DFL of even less than 0, as the investment in the shares of a corporate enterprise is by nature more risky than a government debt security; business and financial risk not withstanding, a shareholder only has residual claim over the net earnings of a company, and even that can be retained by the company.

Based on the average DOL and DFL values for each year, the following risk premia (in percentage terms) provided in Table 7, have been assigned to the corresponding periods, in order to arrive at the cost of equity (Table 8).

Thus, the cost of equity is likely to be less than/ nearlytwice the risk-free rate prevalent in the market for a typical corporate firm. The average cost of equity over the period of the study (2001-2014) for the sample companies, has been nearly 14 per cent, assuming the average risk free rate to be 7.75 per cent. The same is substantiated by the average expected returns of 13.47 per cent computed via the CAPM. Obviously, the individual company's cost of equity would be dependent on its relative risk complexion, vis-a-vis the other securities available in the market.

Conclusions

This paper presents the expected equity returns, measured through the CAPM and the risk premium approach, for the Indian stock market, represented by the NSE 500 companies. The CAPM appears to be an appropriate model to calculate expected returns emanating from the Indian stock market. The average expected returns are 13.47 per cent and the average market index returns are 16.46 per cent, indicative of the market being able to perform better than the expected returns by the technical investors. The average cost of equity (ke) for the sample companies based on the risk premium approach, over the period of the study, is also around 14 per cent (13.75 per cent). The average ROE is 19.20 per cent, indicative of the fundamental strength of the sample companies in earning returns which are above the expectations. The 'small' and 'medium' size companies fare better (at robust returns of 40 per cent) than their 'large' counterparts by 10 percentage points. In other words, the small and medium capitalization (cap) companies lead the returns compared to large cap companies. This may be attributed to the aspect that they are growth companies with increasing market share, whilst the large companies are mature companies with low further growth or expansion opportunities. As is perhaps expected, volatility remains evident in these segments as well. Tata Elxsi recorded high returns in the 'small' segment whilst Aurobindo Pharma recorded high returns in the 'medium' size segment, as well. Amongst the 'large' companies, Reliance Communications recorded high returns.

Hence, prima-facie, the sample companies, constituting 96.27 per cent of the total market capitalization at NSE, continues to be an attractive investment destination for both fundamental (long-term) and technical (short-term traders) investors. However, in the presence of volatility in the short-run which increases the risk, it would perhaps be prudent to invest in the long-run in the Indian stock market. Such a strategy should result in relatively less risky and more stable returns vis-a-vis the short-run returns.

SHVETA SINGH, Ph D.

Associate Professor

email: shvetasingh@dms.iitd.ernet.in

Professor P. K. JAIN, Ph.D.

email: pkjain@dms.iitd.ac.in

Professor SURENDRA S. YADAV, Ph.D.

email: ssyadav@dms.iitd.ac.in

Department of Management Studies

Indian Institute of Technology, Delhi

New Delhi, INDIA

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(60.) i) Investopedia website, http://www.investopedia.eom/terms/s/sp_cnx_nifty.asp, Accessed on December 31, 2013, (2013)

ii) Wikipedia website, http://en.wikipedia.org/wiki/S%26P_CNX_500, Accessed on March 10, 2014.

ii) Price Waterhouse Coopers website, https://www.pwc.in/en_IN/in/assets/pdfs/publications/2013/dissecting-indias-risk-equity-premium.pdf

(61.) i) National Stock Exchange website, http://www.nseindia.com/products/content/equities/indices/ cnx_500.htm, Accessed on March 10, 2014

ii) Ross S. A., The Arbitrage Theory of Capital Asset Pricing, Journal of Economic Theory, Vol 13, Issue 3, pp. 341-360, (1976).

* The paper, revised based on Journal JFMA referees comments, is primarily based on the research monograph titled "Equity Markets in India: Returns, Risk and Price Multiples" published by Springer. The study covers virtually all the major aspects of the Indian equity returns and risk for the past two decades : 1993-2014.

The authors own full responsibility for the contents of paper.

** The company Standard & Poor's (S&P) introduced its first stock based index in 1923 in the U.S.A. The index had traditionally been market-value weighted, that is, the movements in the prices of the stocks with higher market capitalizations (the share price times the number of shares outstanding) had a greater effect on the index than the companies with smaller market capitalizations. However, the index is now float weighted (Source: Wikipedia website. http://en.wikipedia.org/wiki/S%26P_CNX_500).

The CNX 500 is the Indian counterpart (hereby referred to as NSE 500). CNX stands for the Credit Rating Information Services of India Limited (CRISIL) and the NSE. These two bodies own and manage the index through a joint venture called the India Index Services and Products Limited (IISL) (Investopedia60). The NSE 500 companies are disaggregated into 72 industry indices. Industry weightages in the index reflect the industry weightages in the market (Source: National Stock Exchange (NSE) website, http://www.nseindia.com/products/content/equities/indices/cnx_500.htm).61

*** The relevant data (secondary) were collected from the Bloomberg[R] database, for fourteen years (2001-2014) and from the website of the Reserve Bank of India (RBI). Descriptive statistical values/positional values, i.e., mean, standard deviation, variance, coefficient of variation, minimum, maximum, skewness, kurtosis and quartile values have been computed for each year. The entire set of data has been analyzed using Microsoft Excel[R] spreadsheets and the statistics software SPSS[R], namely, Statistical Package for Social Sciences.

This purpose of this paper is to present the expected equity returns for the Indian stock market for the benefit of investors, who may then compare such returns with actual market returns to evaluate whether the Indian stock market provides returns in excess of expectations. Both the capital asset pricing model (CAPM) which is based on systematic risk and the risk premium approach which is based on unsystematic risk, have been used to compute expected returns.

The CAPM appears to be an appropriate model to calculate expected returns emanating from the Indian stock market. The average expected returns are 13.47 per cent and the average market index returns are 16.46 per cent, indicative of the market being able to perform better than the expected returns by the technical investors. The average cost of equity (ke) for the sample companies based on the risk premium approach is also around 14 per cent (13.75 per cent). The Indian equity market continues to be an attractive investment destination for both fundamental (long-term) and technical (short-term traders) investors. However, in the presence of volatility in the short-run which increases the risk, it would perhaps be prudent to invest in the long-run.

As is evident from the literature reviewed, this is perhaps the first time expected Indian stock market returns are presented and computed through both the CAPM and the risk premium approach.

Keywords : CAPM; Risk premium approach; Expected equity returns; DOL, DFL, NSE 500 Index

JEL Classification : C42; C52; C82; E27; G11; N25

Introduction

Before embarking on the estimation of market returns earned on equity shares in India, it would be useful to have an estimate of the expected returns in the Indian stock market. Only after arriving at this required return, it would be useful/ insightful first to ascertain whether the rate of return earned by equity investors is adequate or not and secondly to compare the two sets of returns--expected and actual. Amongst the measures available in literature to estimate the required return, the capital asset pricing model (CAPM) remains, perhaps, the most utilized. This paper is devoted to the computation of the estimated required rate of return for the sample companies (NSE 500 constituent companies) based on the CAPM. The estimated returns are then compared with the actual market returns posted by the market index (NSE 500 index), to provide a better understanding of returns, from both the expectations and the actual market index returns' perspectives. Expected returns are conditional on the fundamental strength and financial performance of the underlying company whose shares the investors purchase. Further, it is also dependent on the company's relative performance vis-a-vis the underlying market. The measure that finds mention in literature is the firm's beta ([beta]), which is the covariance of the security's returns with the market returns divided by the variance of the market returns. Beta, being a market measure, captures only the systematic or market risk associated with company returns, and, is an important part of the CAPM, determining expected ROE.

Prelude

The literature review focuses on the risk factors/ determinants affecting the CAPM in particular, and expected returns, in general.

Sharpe (1), Lintner (2) and Mossin (3) developed the capital asset pricing model (CAPM) which measured the performance of assets in terms of returns. They proposed that an asset's risk could be measured by the covariance of the asset's return with the market portfolio return. Hamada (4) also analytically proved that if a firm increased its leverage, it directly affected its beta. The study of individual firms' risk as related to their underlying characteristics began with the seminal work of Beaver, et al. (5) who examined the relationship of certain accounting ratios (payout, liquidity and earning variability) to the firm's systematic risk (beta), and reported a strong and significant association between them. Rubinstein (6) developed a model which included two components of operating risk of a firm--the amount of fixed and variable costs employed in the production technology, and the co-variability of firm's output with market return. Lev (7) reported that a negative relationship existed between the level of unit variable cost and systematic risk.

Robichek and Cohn (8) tested the influence of real economic growth and inflation on the systematic risk (beta) of individual firms. They reported that these macro variables shed no light on the determinants of the systematic risk, and that only for a small number of firms can variations in beta be explained by real growth and inflation. In contrast, however, Hamada (9) reported that, conditional on the validity of Modigliani and Miller's model, leverage accounted for a substantial portion (21-24 per cent) of the systematic risk. Logue and Merville (10), based on a multiple regression technique, attempted to relate financial variables and estimated beta. Assets size, return on assets and financial leverage were found to be significant variables. Along similar lines, Rosenberg and McKibben (11) analyzed the joint influence of the firm's accounting data and its historical stock returns on the systematic and specific risks of its common stocks.

Breen and Lerner (12) tested the beta variance through independent variables such as the ratio of debt to equity, growth of earnings, stability of earnings growth, size of company, dividend payout ratio and number of shares traded. Melicher (13) divided risk into systematic or market risk and specific or diversified risk. Black and Scholes (14) suggested that it was not possible to demonstrate, using CAPM that the expected returns on high-yield common stocks differed from the expected returns on low-yield common stocks. Galai and Masulis (15) linked the firm's equity beta with factors like level of financial leverage, debt maturity, variation in income, cyclicality, operating leverage and dividends.

Hill and Stone (16) empirically confirmed that a positive relationship existed between co-variability of firm's profitability and market return. Gordon and Bradford (17) measured the relative valuation of dividends and capital gains in the stock market, using a variant of the CAPM. Hawawini and Michael (18) presented an empirical examination of the relationship between the average return and the risk of a comprehensive sample of 200 securities which traded continuously from 1966-1980 on the Brussels stock exchange. Based on their findings, they could not reject the hypothesis that the pricing of common stocks on the Brussels stock exchange conformed to the CAPM. Cohen, et al. (19) developed an analytical model that indicated how estimates of the market model beta parameter could be biased by friction in the trading process (information, decision and transaction costs) which led to a distinction between observed and 'true' returns.

Mandelker and Rhee (20) reported a positive relationship between systematic risk and degree of operating leverage. Moreover, a positive relationship was also observed between the degree of financial leverage and systematic risk. Ang, et al. (21) included the degree of operating leverage as an independent variable in the regression model to explain systematic risk but they failed to produce conclusive results. Handa, et al (22) examined the behavior of beta as a function of the return measurement interval and whether the size-effect tests were sensitive to beta estimation. Greig (23) reexamined the Ou and Penman (24) conclusion that fundamental analysis identified equity values not currently reflected in stock prices, and thus systematically predicted abnormal returns.

Koutmos, et al. (25) investigated the degree of volatility persistence and the time-varying behavior of systematic risk (beta) for ten international stock markets, using the GARCH model. The findings suggested that small capitalization markets exhibited considerably higher volatility persistence than large capitalization markets. Ismail, et al. (26) focused on beta prediction in the extreme risk categories and considered the predictive contribution of accounting information across the risk spectrum. Their results provided evidence that inclusion of accounting risk measures, alone or in combination with market beta, substantially improved beta prediction for high risk securities, but not for low and medium risk securities. Fletcher (27) examined the conditional relationship between beta and returns in U.K. from 1975-1994. His results supported the findings of Fama and French (28) and Strong and Xu (29) as there was no evidence of a significant risk premium on beta, when the unconditional relationship between beta and returns was examined. Brooks, et al. (30) explored the issue of beta instability in the Singaporean stock market over the period 1986-1993. Analysis of the eight-year interval revealed a very high incidence of beta instability, namely, at about 40 per cent of the individual stocks tested. However, CAPM continues to be deployed for measuring expected returns as it appears to be the most appropriate model as it captures the effect of volatility on market returns.

Allen and Cleary (31) studied the returns on the Malaysian stock market for the duration 1977-1992 and concluded an inverse relationship between beta and expected returns. They observed that the accounting variables like ratio of book-to-market equity and value of outstanding securities could help in explaining increments in non-systematic risk. Sheu, et al. (32) analyzed the cross-sectional relationships among market beta, trading volume and stock returns, on the Taiwan stock exchange from 1976-1996. They reported that market beta and trading volume could be combined to explain the cross-section of average returns. Reyes (33) analyzed the relationship between firm size and time-varying betas of U.K. stocks and demonstrated that the time-varying coefficient was not statistically significant for both the small and large firm stock indices. Gangemi, et al. (34) analyzed Australia's country risk using a country beta market model on the lines of Harvey and Zhou (35) and Erb, et al. (36). They observed that exchange rates were the only macroeconomic factor that had significant impact on Australia's country beta.

Lau, et al. (37) examined the relationship of stock returns with beta, size, the earnings-to-price (E/P) ratio, the cash flow-to-price ratio, the book-to-market equity ratio, and sales growth (SG) by studying the data of the Singapore and Malaysian stock markets for the period 1988-1996. The analysis revealed a negative relationship between size and stock returns and between weighted average annual sales growth and stock returns for the Singapore stock market. For the Malaysian stock market, they noted a negative size effect and a positive E/P effect on stock returns. Elsas, et al. (38) compared the unconditional and conditional test procedure using Monte Carlo simulations and reported that the conditional test significantly supported the relation between beta and return. Turner and Morrell (39) documented the calculation of the cost of equity capital in a sample of airlines, in comparison to industry-calculated values. They applied the CAPM to airlines stock prices and market indices. Tang and Shum (40) investigated the conditional relationship between beta and returns in 13 international stock markets for the period 1991-2000. They reported a significant positive relationship between beta and returns in up-market periods (positive market excess returns) but a significant negative relationship in down-market periods (negative market excess returns).

Fernandez (41) estimated the CAPM at different time scales for the Chilean stock market, by resorting to wavelet analysis. He reported evidence in support of the CAPM at a medium-term horizon. Ho, et al. (42) examined empirically the pricing effects of beta, firm size, and book-to-market equity, but conditional on market situations, i.e., whether the market was up or down, using Hong Kong equity stock data for cross-sectional regression method. On similar lines, Morelli (43) examined the role of beta, size and book-to-market equity as competing risk measurements in explaining the cross-sectional returns of U.K. securities for the period 1980- 2000. Cai, et al. (44) focused on the effects of event risk on asset price and modeled investors' optimal portfolio policy in the case of potential event risk in the Chinese stock market, and derived a liquidity-based asset pricing model. Iqbal and Brook (45) investigated the ordinary least square (OLS) beta estimates and different alternative estimators designed to correct the downward bias in the OLS beta, on a sample of 89 stocks from the Karachi stock exchange. They compared the applicability of the two asset pricing models, namely, the CAPM and the Fama-French model.

Hooper, et al, (46) compared a series of competing models to forecast beta in order to reduce forecast error. It was reported that an autoregressive model with two lags produced the lowest or close to the lowest error for quarterly stock beta forecasts. Lally and Swidler (47) investigated the relationship between the market weight of a single stock and the betas of that stock as well as of the residual portfolio. Adrian and Franzoni (48) modelled conditional betas using the Kalman filter as it focused on low-frequency variation inbetas. Manjunatha and Mallikarjunappa (49) attempted to test the validity of the combination effect of the two-parameter CAPM to determine the security/portfolio returns. Hearn (50) contrasted the performance of the CAPM, augmented by size and liquidity factors, with its time varying coefficient counterpart, using a unique market universe compiled from constituent stocks of blue chip indices BSE-100 (India), KSE-30 (Pakistan), DSE-20 (Bangladesh) and Dow Jones Titans (Sri Lanka).

Ray (51) analyzed the stability of beta for the Indian stock market for a ten year period, 1999-2009. The monthly returns data of 30 selected stocks were considered for examining the stability of beta in different market phases. Masih, et al. (52) estimated the systematic risk 'beta' at different time scales in the context of the emerging Gulf Cooperation Council (GCC) equity markets by applying a relatively new approach (known as wavelet analysis). They reported that VaR (value at risk) measured at different time scales suggested that risk tended to be concentrated more at the higher frequencies (lower time scales) of the data. Durand and Ng (53) applied the methodology proposed by Pettengil, et al. (54) on eleven Pacific Basin emerging markets. Their study supported the beta based tests. Morelli (55) examined the role of beta in explaining security returns in the U.K. stock market over the period of 1980-2006 by applying a joint conditionality, and incorporating various versions of ARCH models to estimate time varying betas. Majumder (56) developed a model which incorporated market sentiments in the domain of the standard rational model of asset pricing.

Da, et al. (57) evaluated the empirical evidence against the standard CAPM from the perspective that it could nevertheless provide a reasonable estimate of a project's cost of capital. Hasan, et al. (58) investigated the risk-return trade off within the CAPM structure for the Dhaka stock exchange. Manjunatha and Mallikarjunappa (59) examined the validity of the five parameter model (the combination of five variables, viz., beta ([beta]), size, E/P, book value/market value (BV/MV) and market risk premium ([R.sub.m]-[R.sub.f])) on the Indian stock returns using cross sectional regression.

Even though there are recent measures like the Fama-French 3 factor and 5 factor models available to measure expected returns, the CAPM remains more popular and more utilized. Further, the CAPM remains the model that captures the effect volatility has on market returns. These are the rationales for using the CAPM for calculating expected returns in this paper. Further, as the CAPM is based on the market risk, the authors felt it useful to compute expected returns through a model that is based on the unique risk of the company, viz., the operating and financial leverage. This, then, forms the rationale for using the risk premium approach.

There appears to be no study estimating expected returns for the Indian stock market based on the CAPM. There appears to be no study estimating expected returns for the Indian stock market based or the risk premium approach (operating leverage and financial leverage). This paper is a modest attempt to fill these gaps.

Methodology Used

The research methodology adopted in the paper to compute the estimated returns (using the CAPM) and its comparison with market returns (for corresponding periods) has been delineated hereunder. Further, the cost of equity so computed would reflect the expected rates of return on equity shares. The NSE 500 index of India comprises of the top 500 companies listed on the NSE based on their market capitalization and is the chosen sample for this paper. The total traded value for the last six months ending December 2013, of all Index constituents was approximately 97.01 per cent of the traded value of all stocks on NSE. Hence, virtually, the chosen sample presents a census on equity market returns in India.

The date of sample selection was March 11, 2013. The study period for this paper is 2001-2014. This universe was chosen for the convenience of access to the data required and also on the assumption that it would be an accurate representation of the equity returns in India. It is important to state here that the constituent companies are amongst the most stable companies in the country due to their large market capitalizations and asset bases. As a result of this there were very minimal changes in the companies constituting the index, over the period of the study. Further, the index returns for the NSE 500 index ** were taken as the proxy for market returns in the CAPM.

Similarities/Differences Among S&P, CRISIL and NSE-Based Indices

The collaboration between S&P and CNX on the top 500 stocks traded at the National Stock Exchange gave rise to the S&P CNX NSE 500 index. It is different from other indices as it is based upon solid economic research. A trillion calculations were expended to evolve the rules inside the S&P CNX NSE 500 index. The results of this work are remarkably simple: (a) the correct size to use is 500, (b) stocks considered for the S&P CNX NSE 500 must be liquid by the 'impact cost' criterion, (c) the largest 500 stocks that meet the criterion go into the index. S&P CNX NSE 500 is a contrast to the ad-hoc methods that have gone into index construction in the preceding years, where indices were made out of intuition and lacked a scientific basis. The research that led up to S&P CNX NSE 500 is well-respected internationally as a pioneering effort in better understanding how to make a stock market index.

Further, S&P CNX NSE 500 is a more diversified index, accurately reflecting overall market conditions. The reward-to-risk ratio of S&P CNX NSE 500 is higher than other leading indices, making it a more attractive portfolio hence offering similar returns, but at lesser risk. S&P CNX NSE 500, is managed by a professional team at IISL, a company setup by NSE and CRISIL. There is a three-tier governance structure comprising the board of directors of IISL, the Index Policy Committee, and the Index Maintenance Sub-committee. S&P CNX NSE 500 has fully articulated and professionally implemented rules governing index revision, corporate actions, etc.

The CAPM Model ***

The CAPM model uses the following computation: E ([R.sub.i]) = [R.sub.f] + [[beta].sub.l] (E([R.sub.m]) - [R.sub.f]) (1)

where,

* E ([R.sub.i]) is the expected return on the security i;

* [R.sub.f] is the risk-free rate of interest, such as interest arising from government bonds;

* [[beta].sub.1], (the beta) is the sensitivity of the expected excess asset returns to the expected excess market returns, or also

[[beta].sub.1] = Cov ([R.sub.1], [R.sub.m])

Var([R.sub.m]) (2)

* E([R.sub.m]) is the expected return of the market.

In deploying the CAPM, the following methodology has been adopted:

* The risk-free return for the 364-day treasury bills has been taken as the proxy for risk-free return as the actual returns have also been computed annually, hence the corresponding periods,

* The annual NSE index returns have been taken as the proxy for market returns, and

* The weighted beta for the sample has been taken as the beta for the model. The market capitalization of the constituent companies in the sample has been taken as the weight.

Cost of Equity (ke) or Expected Rates of Return on Equity Shares

The cost of equity has been computed for the sample companies, as a measure of the return expected for the risk undertaken. The formula derived through the theory proposed by Ross (1976) and used for the same is:

[k.sub.e] = [r.sub.f] + b + f (3.3)

where [r.sub.f] = Risk free rate of return

b = Business risk premium

f = Financial risk premium

while the degree of operating leverage (DOL) measures the operating risk, the degree of financial leverage (DFL) measures the financial risk. Therefore, in an attempt to compute the cost of equity through the above stated equation, the DOL and DFL of the sample companies were computed for the period, 2001-2014.

DOL and DFL

Degree of operating leverage is calculated as percentage change in earnings before interest and taxes (EBIT) divided by percentage change in net sales. Degree of financial leverage is calculated as percentage change in earnings per share (EPS) divided by percentage change in EBIT. Further, it may be noted that the negative values have been excluded from analysis as they do not serve the intended purpose of measuring risk on the one hand and would have caused distortion in determination of average values on the other. To have better and more representative data on the subject, we have also excluded extreme values (exceeding 5) of DOL/DFL.

Expected Rates of Return Based on C APM

The model, CAPM, has been used to compute expected returns on an annual basis, in order to facilitate comparison with annual market index returns for the corresponding periods.

The non-availability of corporate financial data prior to 2001 is the reason for the non-computation of expected returns for the years prior to 2001. Hence, comparison between the market index returns and the expected returns would be made for the period 2001-2014.

Table 1 presents the expected returns for the years 2001-2014 and the corresponding market index returns. To enable better comparison, Table 2 (A & B) presents the computed mean, standard deviation, variance, coefficient of variation, minimum, maximum, skewness and kurtosis, and quartile values of both the expected and the market index returns on the basis of size (market capitalization) of sample companies (2001-2014) for the period.

As is evident from Table 1, the expected returns and the actual market index returns appear to follow the same pattern. Both the expected actual returns dropped drastically in 2009 and became negative, perhaps as a result of the recession that originated in the U.S.A. in 2008. Hence, the CAPM model appears to be an appropriate model to estimate expected returns in the Indian stock market, represented through the sample companies. Table 2 (A & B), in this regard, is perhaps more revealing. The average expected returns for the period are 13.47 per cent compared to average market index returns of 16.46 per cent. The standard deviations, coefficient of variation and variance figures are also similar, indicating that expected returns mirror the volatility present in the market. However, expectedly, the market index presents a volatility that is substantially higher than the expectations. The skewness and kurtosis figures are low indicating returns lying closer to the previous and subsequent return values. A paired t-test (Table 3) was administered to analyze whether the average expected returns were statistically different from market returns. As is evident from the t-statistic, there is no statistically significant difference between the expected and the market index returns.

The Pearson correlation coefficient between expected and actual market index returns was 0.98, further substantiating that the CAPM is an appropriate tool to forecast actual market index returns. It appears safe to postulate that the Indian stock market provides volatility and returns to the technical (short-term) investors and also allows returns over the long-run to the fundamental (long-term) investors. Buy-and-hold strategy returns over the long-term mirror the ROEF (return on equity funds). However, in the presence of volatility in the short-run which increases the risk, it would perhaps be wiser to invest in the long-run in the Indian stock market. Such a strategy should result in relatively less risky and more stable returns vis-a-vis the short-run returns.

It is important to emphasize that expected returns which are computed, based on the CAPM Model, take into consideration only the systematic risk of the security under consideration. Since systematic risk is a function of the covariance of the security's returns with the variance in market returns, the returns may be negative in response to the market (as is evident from Table 1). However, the cost of equity (returns expected by the equity providers) for a company can never be negative. Hence, simply basing our analysis on expected returns based on the CAPM model would be incomplete. There is a requirement to compute the returns expected by the equity providers based on the risk undertaken by investing in that particular security.

Expected Rates Of Return--Cost Of Equity

Would an investor in India, be satisfied with 8-10 per cent return on equity investment? The answer is likely to be in the negative; this rate of return can be easily earned by investing in safe instruments like the public provident fund (PPF), the Indira Vikas Patra (IVP), long-term deposit with commercial banks and so on (with virtually full safety of investments). Obviously, the investors would like to be compensated for the extra risk they are assuming by investing in the equity shares of a corporate enterprise. A corporate firm is subject to business risk (b). This apart, there is a variability in the rates of return available to equity-holders (as they are the last claimants on dividends as well as repayment of capital in the event of liquidation of a company), known as financial risk (f). As a compensation to the higher risk exposure, equity-holders expect a higher return and, therefore, higher cost is associated with them. In brief, the cost of equity ([k.sub.e]) is:

[k.sub.e] = [r.sub.f] + b + f (3)

The business risk is measured through a ratio called the degree of operating leverage (DOL) and the financial risk is measured through the degree of financial leverage (DFL). Therefore, in an attempt to compute the cost of equity through the above stated equation, the DOL and DFL of the constituent companies have been computed for the period, 2001-2014. Relevant data pertaining to mean, standard deviation, coefficient of variation, skewness, kurtosis, median, and quartiles values of DOL and DFL of the sample companies are contained in Table 4. Frequency distribution pertaining to DOL and DFL of the sample companies is presented in Table 5 for the period under study.

The average DOL for the sample companies is 1.46 and has remained stable through phases 1 and 2. The paired t-test (Table 6) does not indicate any statistically significant changes in mean values over the two phases indicating stable operating risk conditions. Similarly, average financial leverage in the sample companies has been 1.32. Thus, the sample companies have managed their combined risk within controllable limits, an indication of sound risk management practices. The skewness and kurtosis figures indicate that only few companies reported large values of the two measures of risk indicating low risk statistics (for sizeable corporates). As per the frequency distribution, nearly sixty per cent of sample companies have low DOL of less than 1.5 (Table 5) in 2014 compared to the reverse in 2001. Hence, the risk in the sample companies appears to have reduced through the period of the study (2001-2014). DFL also presents similar properties. The lowering of risk is further emphasized through the values of both DOL and DFL being above 5 in 2001 for more than 30 per cent of the sample companies, and which has reduced substantially over the period of the study. These findings are similar to the findings on public sector enterprises over a period of 1991-2003, reporting a DOL of 1.18 and a DFL of 1.09 respectively.

In order to arrive at an approximation of the cost of equity, the values of DOL and DFL were assigned a probable risk premium rate, in percentage terms, as provided in Table 7. For example, a rate of 1 per cent was assigned to a DOL/DFL of even less than 0, as the investment in the shares of a corporate enterprise is by nature more risky than a government debt security; business and financial risk not withstanding, a shareholder only has residual claim over the net earnings of a company, and even that can be retained by the company.

Based on the average DOL and DFL values for each year, the following risk premia (in percentage terms) provided in Table 7, have been assigned to the corresponding periods, in order to arrive at the cost of equity (Table 8).

Thus, the cost of equity is likely to be less than/ nearlytwice the risk-free rate prevalent in the market for a typical corporate firm. The average cost of equity over the period of the study (2001-2014) for the sample companies, has been nearly 14 per cent, assuming the average risk free rate to be 7.75 per cent. The same is substantiated by the average expected returns of 13.47 per cent computed via the CAPM. Obviously, the individual company's cost of equity would be dependent on its relative risk complexion, vis-a-vis the other securities available in the market.

Conclusions

This paper presents the expected equity returns, measured through the CAPM and the risk premium approach, for the Indian stock market, represented by the NSE 500 companies. The CAPM appears to be an appropriate model to calculate expected returns emanating from the Indian stock market. The average expected returns are 13.47 per cent and the average market index returns are 16.46 per cent, indicative of the market being able to perform better than the expected returns by the technical investors. The average cost of equity (ke) for the sample companies based on the risk premium approach, over the period of the study, is also around 14 per cent (13.75 per cent). The average ROE is 19.20 per cent, indicative of the fundamental strength of the sample companies in earning returns which are above the expectations. The 'small' and 'medium' size companies fare better (at robust returns of 40 per cent) than their 'large' counterparts by 10 percentage points. In other words, the small and medium capitalization (cap) companies lead the returns compared to large cap companies. This may be attributed to the aspect that they are growth companies with increasing market share, whilst the large companies are mature companies with low further growth or expansion opportunities. As is perhaps expected, volatility remains evident in these segments as well. Tata Elxsi recorded high returns in the 'small' segment whilst Aurobindo Pharma recorded high returns in the 'medium' size segment, as well. Amongst the 'large' companies, Reliance Communications recorded high returns.

Hence, prima-facie, the sample companies, constituting 96.27 per cent of the total market capitalization at NSE, continues to be an attractive investment destination for both fundamental (long-term) and technical (short-term traders) investors. However, in the presence of volatility in the short-run which increases the risk, it would perhaps be prudent to invest in the long-run in the Indian stock market. Such a strategy should result in relatively less risky and more stable returns vis-a-vis the short-run returns.

SHVETA SINGH, Ph D.

Associate Professor

email: shvetasingh@dms.iitd.ernet.in

Professor P. K. JAIN, Ph.D.

email: pkjain@dms.iitd.ac.in

Professor SURENDRA S. YADAV, Ph.D.

email: ssyadav@dms.iitd.ac.in

Department of Management Studies

Indian Institute of Technology, Delhi

New Delhi, INDIA

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* The paper, revised based on Journal JFMA referees comments, is primarily based on the research monograph titled "Equity Markets in India: Returns, Risk and Price Multiples" published by Springer. The study covers virtually all the major aspects of the Indian equity returns and risk for the past two decades : 1993-2014.

The authors own full responsibility for the contents of paper.

** The company Standard & Poor's (S&P) introduced its first stock based index in 1923 in the U.S.A. The index had traditionally been market-value weighted, that is, the movements in the prices of the stocks with higher market capitalizations (the share price times the number of shares outstanding) had a greater effect on the index than the companies with smaller market capitalizations. However, the index is now float weighted (Source: Wikipedia website. http://en.wikipedia.org/wiki/S%26P_CNX_500).

The CNX 500 is the Indian counterpart (hereby referred to as NSE 500). CNX stands for the Credit Rating Information Services of India Limited (CRISIL) and the NSE. These two bodies own and manage the index through a joint venture called the India Index Services and Products Limited (IISL) (Investopedia60). The NSE 500 companies are disaggregated into 72 industry indices. Industry weightages in the index reflect the industry weightages in the market (Source: National Stock Exchange (NSE) website, http://www.nseindia.com/products/content/equities/indices/cnx_500.htm).61

*** The relevant data (secondary) were collected from the Bloomberg[R] database, for fourteen years (2001-2014) and from the website of the Reserve Bank of India (RBI). Descriptive statistical values/positional values, i.e., mean, standard deviation, variance, coefficient of variation, minimum, maximum, skewness, kurtosis and quartile values have been computed for each year. The entire set of data has been analyzed using Microsoft Excel[R] spreadsheets and the statistics software SPSS[R], namely, Statistical Package for Social Sciences.

TABLE 1 EXPECTED RETURNS FOR THE SAMPLE COMPANIES AND THEIR COMPARISON WITH MARKET INDEX RETURNS FOR THE PERIOD : 2001-2014 Year Average Expected Index Return (%) Returns (%) 2001 -14.26 -42.99 2002 5.29 2.82 2003 -2.72 -10.78 2004 59.86 106.39 2005 13.14 18.89 2006 35.56 61.21 2007 8.09 8.07 2008 17.77 21.64 2009 -22.55 -39.89 2010 66.29 85.54 2011 6.89 6.47 2012 -5.53 -9.01 2013 5.64 5.13 2014 15.09 17.00 TABLE 2 (A) MEAN, STANDARD DEVIATION, VARIANCE, COEFFICIENT OF VARIATION, MINIMUM, MAXIMUM, SKEWNESS, KURTOSIS AND QUARTILE VALUES OF EXPECTED AND MARKET INDEX RETURNS: 2001-2014 Statistic Expected Index Returns (%) Returns (%) Mean Returns 13.47 16.46 Standard Deviation 25.33 42.50 Variance 641.63 1806.16 Coefficient of Variation 188.05 258.20 Minimum Returns -22.55 42.99 Maximum Returns 66.29 106.39 Skewness 0.98 0.84 Kurtosis 0.66 0.50 Lower Quartile -3.42 -9.45 Upper Quartile 22.22 31.53 TABLE 2 (B) WEIGHTED ANNUAL AVERAGE RETURNS AND STATISTICS OF MEAN, STANDARD DEVIATION, VARIATION, COEFFICIENT OF VARIATION, SKEWNESS, KURTOSIS AND QUARTILE VALUES OF RETURNS ON THE BASIS OF SIZE OF SAMPLE COMPANIES, 2001-2014 Year Weighted Average Mean Standard Variance Annual Returns Returns Deviation Small 2001 -19.55 -8.97 23.53 553.81 2002 41.03 10.58 56.11 3148.71 2003 15.67 8.15 29.39 864.04 2004 87.95 51.59 99.75 9949.35 2005 99.94 47.05 93.13 8672.96 2006 75.75 39.57 71.22 5072.17 2007 8.6 -0.08 36.72 1348.45 2008 26.16 12.81 51.93 2696.37 2009 -43.23 -39.03 27.81 773.24 2010 165.86 137.86 13027 16969.38 2011 14.92 6.08 41.89 1754.60 2012 1.51 0.01 34.88 1216.88 2013 22.69 12.69 47.58 2264.11 2014 66.23 45.73 78.79 6208.09 Average 40.25 23.15 58.79 4392.30 Medium 2001 -20.04 -1.51 65.93 4346.65 2002 32.07 16.49 39.11 1529.95 2003 12.28 7.82 35.98 1294.60 2004 165.86 106.96 147.35 21710.57 2005 75.57 49.05 74.77 5590.14 2006 84.89 61.73 88.76 7877.99 2007 15.8 19.50 150.36 22609.51 2008 40.71 26.52 55.42 3070.87 2009 -41.82 -37.00 27.80 773.08 2010 156.74 136.59 100.34 10068.80 2011 11.31 11.57 42.49 1805.07 2012 3.39 -2.29 36.99 1368.33 2013 8.04 -4.36 36.21 1311.40 2014 27.75 18.13 49.74 2474.21 Average 40.90 29.23 67.95 6130.80 Large 2001 -23.67 -7.99 33.00 1089.19 2002 27.95 20.25 43.26 1871.03 2003 -0.96 4.30 28.65 820.99 2004 141.92 116.28 125.60 15775.06 2005 36.87 67.46 364.41 132793.12 2006 70.34 63.82 84.23 7094.36 2007 29.38 14.36 77.33 5979.26 2008 35.67 31.87 53.39 2850.74 2009 -25.52 -29.28 27.66 765.08 2010 100.76 121.27 88.26 7789.87 2011 12.22 11.59 31.79 1010.83 2012 -3.63 -3.77 23.51 552.73 2013 11.22 5.11 38.40 1474.53 2014 20.77 14.75 30.07 904.21 Average 30.95 30.72 74.97 12912.21 Year Coefficient Minimum Maximum Skewness of Variation Returns Returns Small 2001 -262.32 -91.44 42.84 -1.24 2002 530.34 -50.06 560.33 7.84 2003 360.61 -54.72 148.00 2.12 2004 193.35 -14.56 660.08 3.21 2005 197.94 -43.79 629.20 3.67 2006 179.98 -40.69 344.48 2.17 2007 -45900.00 -77.70 240.79 2.67 2008 405.39 -76.38 252.94 2.32 2009 -71.25 -82.49 14.68 0.34 2010 94.49 0.00 642.00 1.32 2011 688.98 -55.88 229.38 1.94 2012 348800.00 -53.03 150.24 1.65 2013 374.94 -59.14 200.31 1.96 2014 172.29 -53.23 51324 3.04 Average 21840.34 -53.79 330.61 2.36 Medium 2001 -4366.23 -85.93 616.14 6.96 2002 237.17 -52.44 176.17 1.80 2003 460.10 -81.46 203.50 2.43 2004 137.76 0.00 732.43 1.99 2005 152.44 -25.93 312.90 1.81 2006 143.79 -22.49 435.43 1.76 2007 771.08 -68.81 1639.70 10.19 2008 208.97 -55.95 385.93 3.30 2009 -75.14 -85.83 30.01 0.09 2010 73.46 -1.39 493.06 0.74 2011 367.24 -73.98 195.63 1.17 2012 -1615.28 -73.49 160.91 1.25 2013 -830.50 -75.80 142.88 0.95 2014 274.35 -55.37 237.21 1.71 Average -290.06 -54.21 411.56 2.58 Large 2001 -413.02 -89.22 143.00 0.96 2002 213.63 45.35 161.93 1.74 2003 666.28 -61.65 121.42 1.45 2004 108.02 0.00 671.38 1.57 2005 540.19 -36.97 4068.89 10.55 2006 131.98 -23.41 747.58 4.43 2007 538.51 45.36 802.61 8.64 2008 167.52 -68.62 335.53 2.00 2009 -94.47 -87.03 54.01 0.26 2010 72.78 46.03 412.63 1.02 2011 274.29 45.85 149.37 1.04 2012 -623.61 -53.55 83.41 0.40 2013 751.47 -74.66 235.22 2.89 2014 203.86 -75.21 125.94 0.55 Average 181.25 -53.78 579.49 2.68 Year Kurtosis Lower Upper Quartile Quartile Small 2001 1.57 -21.66 0.00 2002 75.28 0.00 8.52 2003 7.67 0.00 10.19 2004 13.17 0.00 66.09 2005 18.02 0.00 70.41 2006 4.86 0.00 67.98 2007 14.65 -20.70 1.73 2008 7.47 -7.64 20.07 2009 -1.25 -62.30 -12.84 2010 2.19 33.57 191.39 2011 6.91 -2021 23.03 2012 4.55 -22.36 14.73 2013 4.54 -16.22 25.71 2014 13.85 -1.03 73.33 Average 12.39 -9.90 40.02 Medium 2001 62.92 -20.12 0.00 2002 3.54 0.00 27.25 2003 1127 0.00 12.69 2004 4.59 0.00 155.68 2005 2.92 0.00 83.99 2006 3.42 0.00 100.36 2007 110.11 -6.58 1026 2008 16.46 0.00 41.87 2009 -1.01 -63.27 -12.95 2010 0.49 66.33 198.63 2011 2.73 -17.74 32.60 2012 2.90 -27.51 14.56 2013 2.21 -28.15 15.24 2014 4.42 -11.86 40.21 Average 1621 -7.78 51.46 Large 2001 5.50 -24.51 0.00 2002 2.45 0.00 27.61 2003 4.10 -6.24 9.23 2004 3.49 0.00 180.83 2005 116.04 0.00 46.32 2006 33.22 0.25 95.35 2007 86.10 -10.32 20.07 2008 7.80 0.00 60.99 2009 -0.23 -52.43 -6.21 2010 1.39 64.42 168.65 2011 2.97 -10.68 29.63 2012 0.47 -20.81 12.70 2013 15.36 -16.03 19.21 2014 2.56 -0.22 27.26 Average 20.09 -5.47 49.40 TABLE 3 PAIRED SAMPLES TEST Paired Differences 95% Confidence Interval of the Mean Standard Standard Difference Deviation Error Mean Lower Upper Expected Returns 2.99 18.25 4.88 -13.53 7.54 - Index Returns Significance t df (2-tailed) Expected Returns -0.61 13 0.55 - Index Returns TABLE 4 MEAN, STANDARD DEVIATION, COEFFICIENT OF VARIATION, SKEWNESS, KURTOSIS, MEDIAN AND QUARTILE VALUES OF DEGREE OF OPERATING LEVERAGE (DOL) AND DEGREE OF FINANCIAL LEVERAGE (DFL) OF SAMPLE COMPANIES: 2001-2014 Year Ending Leverage Number Mean Standard Deviation 2001 DOL 237 1.53 1.08 DFL 255 1.53 1.10 2002 DOL 237 1.53 1.08 DFL 256 1.52 1.10 2003 DOL 257 1.43 1.16 DFL 256 1.56 1.07 2004 DOL 285 1.46 1.08 DFL 310 1.49 0.99 2005 DOL 312 1.49 1.08 DFL 341 1.30 0.87 2006 DOL 329 1.63 1.15 DFL 373 1.18 0.81 2007 DOL 367 1.50 1.00 DFL 414 1.08 0.72 2008 DOL 368 1.45 0.92 DFL 425 1.13 0.76 2009 DOL 310 1.34 0.96 DFL 410 1.25 0.82 2010 DOL 311 1.63 1.12 DFL 382 1.37 0.94 2011 DOL 351 1.27 0.94 DFL 417 1.28 0.78 2012 DOL 329 1.19 0.84 DFL 396 1.15 0.83 2013 DOL 310 1.37 0.95 DFL 390 1.32 0.86 2014 DOL 305 1.64 1.10 DFL 379 1.31 0.87 2001-2014 DOL 308 1.46 1.03 DFL 356 1.32 0.90 Phase 1 DOL 299 1.50 1.07 (2000-2001 DFL 329 1.35 0.93 to 2007-2008) Phase 2 DOL 319 1.41 0.99 (2008-2009 DFL 396 1.28 0.85 to 2013-2014) Year Ending Leverage Coefficient of Skewness Kurtosis Variation (%) 2001 DOL 70.59 1.14 0.87 DFL 71.90 0.15 0.82 2002 DOL 70.59 1.14 0.87 DFL 72.37 0.15 6.81 2003 DOL 81.12 1.18 0.77 DFL 68.59 6.15 1.35 2004 DOL 73.97 1.12 0.75 DFL 66.44 0.14 1.34 2005 DOL 72.48 1.14 0.87 DFL 66.92 0.13 4.85 2006 DOL 70.55 1.12 0.48 DFL 68.64 6.13 4.91 2007 DOL 66.67 1.33 1.51 DFL 66.67 0.12 4.62 2008 DOL 63.45 1.30 1.67 DFL 67.26 0.12 5.41 2009 DOL 71.64 1.27 1.29 DFL 65.60 0.12 3.75 2010 DOL 68.71 0.87 -0.03 DFL 68.61 6.13 2.64 2011 DOL 74.02 1.51 2.34 DFL 60.94 0.12 3.79 2012 DOL 70.59 1.49 2.88 DFL 72.17 6.12 4.54 2013 DOL 69.34 1.41 2.00 DFL 65.15 6.12 3.06 2014 DOL 67.07 0.98 0.40 DFL 66.41 0.13 2.64 2001-2014 DOL 70.77 1.21 1.19 DFL 67.79 0.13 3.22 Phase 1 DOL 71.18 1.18 0.97 (2000-2001 DFL 68.60 0.14 3.01 to 2007-2008) Phase 2 DOL 70.23 1.26 1.48 (2008-2009 DFL 66.48 0.12 3.40 to 2013-2014) Year Ending Leverage Median Quartile 1 Quartile 3 2001 DOL 1.26 0.78 2.03 DFL 1.18 6.81 2.oi 2002 DOL 1.26 0.78 2.03 DFL 1.18 0.80 2.01 2003 DOL 1.07 0.60 1.98 DFL 1.23 6.91 2.oi 2004 DOL 1.21 0.69 1.96 DFL 1.23 0.86 1.84 2005 DOL 1.18 0.71 1.96 DFL 1.10 0.81 1.53 2006 DOL 1.25 0.82 2.17 DFL 1.04 0.73 1.34 2007 DOL 1.21 0.85 1.92 DFL 0.98 0.65 1.28 2008 DOL 1.20 0.88 1.77 DFL 1.00 0.72 1.23 2009 DOL 1.07 0.69 1.69 DFL 1.08 6.84 1.43 2010 DOL 1.26 0.79 2.31 DFL 1.11 0.82 1.75 2011 DOL 1.00 0.70 1.63 DFL 1.09 0.83 1.54 2012 DOL 1.03 0.66 1.43 DFL 1.01 0.69 1.39 2013 DOL 1.11 0.78 1.68 DFL 1.11 0.85 1.56 2014 DOL 1.34 0.90 2.22 DFL 1.09 0.82 1.54 2001-2014 DOL 1.18 0.76 1.91 DFL 1.10 0.79 1.61 Phase 1 DOL 1.21 0.76 1.98 (2000-2001 DFL 1.12 0.79 1.66 to 2007-2008) Phase 2 DOL 1.14 0.75 1.83 (2008-2009 DFL 1.08 0.81 1.54 to 2013-2014) TABLE 5 FREQUENCY DISTRIBUTION PERTAINING TO DEGREE OF OPERATING LEVERAGE (DOL) AND DEGREE OF FINANCIAL LEVERAGE (DFL) OF SAMPLE COMPANIES: 2001-2014 (Figures are in percentages) Leverage Range 2001 2002 2003 2004 2005 DOL Less than 19.60 20.00 18.40 18.80 19.20 DFL 0 15.20 15.00 17.80 14.80 17.60 DOL 0.0-0.5 7.00 7.00 11.60 9.40 9.00 DFL 8.40 8.00 6.40 7.80 7.40 DOL 0.5-1.0 10.40 10.00 12.00 14.00 15.60 DFL 10.20 10.00 9.40 13.60 21.20 DOL 1.0-1.5 11.60 11.00 9.40 12.80 13.60 DFL 13.40 13.00 14.60 17.40 22.60 DOL 1.5-2.0 6.60 6.00 6.00 7.20 9.80 DFL 720 7.00 8.80 9.40 8.60 DOL 2.0-5.0 12.40 13.00 12.80 14.40 14.40 DFL 13.00 13.00 13.00 13.60 9.00 DOL Above 32.80 32.80 30.00 24.00 1820 DFL 5.0 33.40 33.40 30.80 23.00 14.00 Total (%) 100 100 100 100 100 Leverage Range 2006 2007 2008 2009 2010 DOL Less than 17.40 12.60 17.00 27.80 22.60 DFL 0 14.40 8.40 11.60 13.40 15.80 DOL 0.0-0.5 7.00 6.40 7.40 8.40 8.00 DFL 10.60 13.80 12.40 10.80 8.20 DOL 0.5-1.0 16.00 21.00 18.60 18.80 14.00 DFL 22.80 29.60 29.80 23.60 20.20 DOL 1.0-1.5 14.80 19.60 21.40 16.00 13.40 DFL 27.00 26.00 28.80 28.60 23.80 DOL 1.5-2.0 9.60 10.40 12.40 7.00 8.60 DFL 6.80 520 4.60 8.00 9.80 DOL 2.0-5.0 18.80 16.40 14.60 11.80 19.00 DFL 8.60 8.80 9.60 10.80 14.60 DOL Above 16.60 13.80 920 10.00 15.00 DFL 5.0 10.80 8.60 320 4.40 7.60 Total (%) 100 100 100 100 100 Leverage Range 2011 2012 2013 2014 DOL Less than 23.00 2720 26.00 27.60 DFL 0 12.60 17.60 16.60 17.60 DOL 0.0-0.5 8.80 10.80 8.80 7.60 DFL 8.40 14.00 8.00 8.20 DOL 0.5-1.0 26.40 20.80 15.20 12.20 DFL 24.60 24.40 23.00 23.80 DOL 1.0-1.5 16.00 19.00 19.40 14.80 DFL 29.20 24.80 26.60 24.60 DOL 1.5-2.0 620 520 7.00 9.20 DFL 9.80 8.00 9.40 720 DOL 2.0-5.0 12.80 1020 11.80 18.00 DFL 11.20 820 11.40 12.40 DOL Above 6.60 6.80 11.80 11.20 DFL 5.0 3.80 3.00 520 6.40 Total (%) 100 100 100 100 TABLE 6 PAIRED SAMPLES T-TEST Paired Differences 95% Confidence Interval of the Mean Standard Standard Difference Deviation Error Mean Lower Upper DOL Phase 1 - Phase 2 0.11 0.14 0.06 -0.04 0.25 DFL Phase 1 - Phase 2 0.15 0.19 0.78 -0.05 0.35 Significance t df (2-tailed) DOL Phase 1 - Phase 2 1.19 5 0.12 DFL Phase 1 - Phase 2 2.00 5 0.11 TABLE 7 ASSIGNMENT OF RISK PREMIUM RATE FOR DOL AND DFL Leverage Range Risk Premium Assigned (rate per cent) DOL Less than 0 1.00 DFL 1.00 DOL 0.0-0.5 1.50 DFL 1.50 DOL 0.0-1.0 2.00 DFL 2.00 DOL 1.0-1.5 3.00 DFL 3.00 DOL 1.5-2.0 4.00 DFL 4.00 DOL 2.0-5.0 5.00 DFL 5.00 DOL Above 5.0 10.00 DFL 10.00 TABLE 8 COST OF EQUITY BASED ON THE RISK PREMIUM APPROACH Year Ending Risk Free Rate Business Business Risk (in per cent) Risk (DOL) Premium (in rate per cent) 2001 9.44 1.53 4.00 2002 7.34 1.53 4.00 2003 5.71 1.43 3.00 2004 6.11 1.46 3.00 2005 7.34 1.49 3.00 2006 7.89 1.63 4.00 2007 8.12 1.50 4.00 2008 7.69 1.45 3.00 2009 7.23 1.34 3.00 2010 7.92 1.63 4.00 2011 8.52 1.27 3.00 2012 8.40 1.19 3.00 2013 8.36 1.37 3.00 2014 8.41 1.64 2.50 2001-2014 7.75 1.46 3.00 Year Ending Financial Financial Cost of Risk Risk Premium Equity (in (DFL) (in rate rate per cent) per cent) 2001 1.53 4.00 17.44 2002 1.52 4.00 15.34 2003 1.56 4.00 12.71 2004 1.49 3.00 12.11 2005 1.30 3.00 13.34 2006 1.18 3.00 14.89 2007 1.08 3.00 15.12 2008 1.13 3.00 13.69 2009 1.25 3.00 13.23 2010 1.37 3.00 14.92 2011 1.28 3.00 14.52 2012 1.15 3.00 14.40 2013 1.32 3.00 14.36 2014 1.31 3.00 13.91 2001-2014 1.32 3.00 13.75

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Author: | Singh, Shveta; Jain, P.K.; Yadav, Surendra S. |
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Publication: | Journal of Financial Management & Analysis |

Article Type: | Report |

Geographic Code: | 9INDI |

Date: | Jan 1, 2016 |

Words: | 10598 |

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