Explanatory Power of Selected Proxies in Predicting Stock Returns of Large U . K . Companies

Predicting stock returns has been instrumental in our understanding of capital market structure. The validity of models, like the Capital Asset Pricing Model or the Gordon Growth Model, has influenced and contributed to building mathematical representations in predicting required return. Several studies attempted to explore different variables to determine the explanatory power of proxies in predicting stock return. For example, it is reported that dividends can explain up to 25% of the variance in returns. The explanatory power of dividends in the regression analysis showed a significant variation when the analysis follows time-series methodology. This study aims at examining the predicting power in the U.K. equity market by plugging into the regression model some of the variables conventionally measured in the Structural Equation Modeling. The study is quantitative and uses secondary data. The findings of this study suggest that the selected proxies, dividend growth, earnings per share, and beta exhibit weak explanatory power in predicting returns of large U.K. companies.


Introduction
The paper contributes to on-going debate on the possibility of predicting stock returns.The research area is rich and there exists a voluminous literature on it.The issue, however, is far from settled and continues to attract new researchers who strive to develop models and techniques to outperform the market.The motivation of this research comes from the understanding developed on existing literature evidence that it would be highly useful and relevant to examine the returns predictability in the U.K. equity market by plugging into the regression some of the variables conventionally measured in the Structural Equation Modeling (SEM).The study is the first attempt to examine this for large UK companies by not performing the Structural Equation Modelling but plugging into simple and multiple regression analysis some the latent variables conventionally used in the SEM.The research framework and findings are likely to be of interest and will encourage further investigation into plugging together isolated indicators to determine proxy power of predicting stock returns.
The analysis of Structural Equation Modelling (SEM) is used to establish a more integrated view of the relationship of variables, in which the correlation of latent variables and indicators can be measured.In the analysis of SEM, the predictability of stock return is built upon three factors that resolve the explanatory power.According to Anhar (2015), these factors can be used to predict stock return in the analysis of SEM.The first factor is company performance and its indicators are: earnings per share (EPS), price-earnings ratio (PER), book value (BV), price-book value ratio (PBV), debt-equity ratio (DER), return on assets (ROA), return on equity (ROE), and net profit margin (NPM).The second factor is investor expectations, and its indicators are: price trend, latest return, average return, return trend, latest return percentage, average return percentage, and return trend percentage (PT, LR, AR, RT, LR%, AR% and RT%).The third factor is the investment risk and its indicators are: standard deviation of return, coefficient of variation, and coefficient beta of stock (SD, CV and Beta).
It is not intended to perform Structural Equation Modeling analysis, we rather examine some of the indicators selected and to evaluate the explanatory power using simple and multiple regression analysis.The factors are assumed as latent variables used in the analysis of Structural Equation Modelling (SEM).The indicators subject to the model in this paper are earnings per share (PER), beta value () and dividend growth (DG).

The Classical Approach to Efficiency
There is a growing body of literature that recognizes the importance of market efficiency theory in testing the ability to find abnormal returns.According to Fama (1991), there are three forms of efficient market hypothesis (EMH): weak, semi-strong, and strong.Empirical tests have focused on the weak form of efficiency, concluding that it is not possible to predict future stock prices based on past information.Most of these studies implemented the stochastic approach, meaning that they focused on the use of random probability distribution (Lean & Smyth, 2015).
For investment opportunities, many strands of literature focused on company performance ratios, such as the market-to-book ratio.In general, the market-to-book ratio has been a significant proxy in stock returns.According to Detzel and Strauss (2017), this ratio provides an indication of future cash flows in present value.Their findings showed that a cross-section of the industry book-to-market values has mere explanatory power using a combination of quarterly forecast returns.
Another proposition to examine future investment opportunities is related to the price-earnings ratio (PER), indicating the ratio of market value of equity and present earnings.As stated by Pietrovito (2016), the PER ratio does add value to the investment rates when it is included in the Tobin's q model.It is incorporated in a model of regression to determine the explanatory power of investment rate, giving a positive relation for the predictive model.
Tobin's q model equation:  =  ( ) +  +  +  +  +  In Tobin's q model the  is the average for market to book ratio explained by its replacement cost, the X it are the independent variables , e it is the error term in the regression model, and  ,  ,  values are dummy variables to control exogenous variables as industry effects.

Investment Risk
In functional markets, all managers and investors are rewarded when welcoming the high risks associated with investing in assets.Risk is also referred to as 'risk factors' (Besley and Brigham, 2006).Systematic risk is measured by evaluating the movement of the return trend of a company stock to follow the movement of the stock market return, and its size is the beta coefficient (β) of stock (Besley and Brigham, 2006, p. 34) Some analysts, like Setiono and Strong (1998), attempted to draw fine distinctions between markets in many countries, which are semi-strong form, efficient finding, and predicting abnormal stock returns with publicly available financial statements.Some earlier observed reports indicated that, to some degree, future earnings can be predicted from current and past incomes and that current stock prices reflect inexperienced expectations of earnings.
Linear predictive regression is an increasingly important area in applied market studies.Some earlier studies used the techniques of time-series or cross section analysis to explain market beta in expected returns (Fama and French, 2004).Such techniques can also be applied, as proposed by Bekiros and Gupta (2015), using a linear predictive regression model with different indicators to predict stock market returns in monthly sequences.Difficulties arose, however, when attempts were made to implement this model to predict volatility.This encouraged more focused studies, such as mixes of other tests to examine real returns and their link to investor sentiment indexes.
According to Choudhary and Choudhary (2010), testing the Capital Asset Pricing Model (CAPM) should be performed by modifying the conventional formula.CAPM is tested with a regression of security return for beta value where the intercept is the difference between estimate of the expected return and the actual CAPM return.
The model of regression analysis for CAPM is: where Rf is risk-free return, rⱼ is required return on investment, rₘ is expected market value of return, β is beta (risk), εⱼ is the disturbance term or error, and ∝ is the intercept.
There is evidence of a positive relation between beta and stock return in the case where the difference between market value of the stock and the risk-free return is greater than zero.
The validity of CAPM has been repeatedly tested.To some extent, the earlier studies are responsible for simplifying the model of the analysis.Researchers, such as Sharpe (1964) and Lintner (1965), suggested that the risk-free rate of return is the intercept of the equation, and the difference between expected market return and risk-free rate will always be the slope.These assumptions result in a flat outcome when measuring the relationship between return and beta (Miller & Scholes, 1972).
Conventionally, dividend yield has a strong predictive power on stock return; however, Ang and Bekaert (2007) reported that dividend yield has explanatory power only for short time horizons.Campbell and Yogo (2006) found a strong predictive power for short rates rather than long periods.All the components from the dividend growth model are generally seen as indicators strongly related to return prediction.Some of the literature has focused on the relationship between dividend yield and earnings growth.As stated by Kothari and Shanken (1992), since the empirical argument shows that dividend constrains funds for future investments, it tends to have a negative impact on earnings growth.This argument contradicts Zhou and Ruland (2006), who found a strong relationship between the two variables.
The model developed by Kothari and Shanken (1992) to predict Swedish stock return from dividend yield and dividend growth showed a rather weak explanatory power.It measured the natural log of the continuous compounded ratio from the dividend D t in year t and the dividend in year t -1.DG = Ln(D t /D (t -1) ), FGD = Ln(D t /D (t + k -1) ), for the year t + k.where DG is the dividend growth, FDG is the dividend growth at the time T + K -1.The model also included a dividend to price ratio (D/P), Nordic 40 index (RNAS), and the productivity growth index (PGI).After all the proxies are established the model takes the form: Where the dependent variable R i is the return on equal weighted portfolio from the NASDAQ OMX index from Stockholm.
The result of the study showed a weak relationship between dividend yield and dividend growth when measured only with the dividend proxies shown in the equation.However, the explanatory power of the model increases its R 2 when using the U.S. equity market (NYSE), indicating strong aggregate stock returns in the case of Swedish stocks.

Investors' Expectation
The expectation of an investment is related to the evaluation of a certain trading security and its future trend.
Most of the indicators associated with investor expectations are defined by technical analyses that focus on the history of stock actions in order to predict future movements.Investor expectation can be outlined by price trend, latest return, average return, return trend, latest return percentage, average return percentage, and return trend percentage (Anhar, 2015).
In technical analysis, the research leads to decisions on using linear and nonlinear methods.Enders and Pascalau (2015) tested the linearity of real exchange rates using the smooth transition autoregressive (STAR) model and found that, when rejecting the null hypothesis of a linear model, the forecast will result in low mean square prediction errors.By not rejecting the linearity, the nonlinear model also produces low mean square prediction errors and will beat the random walk forecast.It seems that, according to Enders and Pascalau (2015), the nonlinear methods in technical analysis produce a superior predictive forecast.
Sheela and Murugesan (2017) stated that daily return predictability for nonlinear models provide better captured information of the behavior on daily stocks' returns.It then improves the accuracy of forecasting for short term horizons, even more so than linear models.
Whereas fundamental analysis focuses on the influence of other proxies, such as dividend yield, earnings, and insider trading, technical analysis relies on the premise that stocks already have all this information and absorb new data automatically (Gong and Sun, 2009).The factor that explains trading movements is the sentiment of the investor responses to changes, showing enough patterns and historical trends to provide prediction power (Murphy and Murphy, 1999).It is not the intention of this research to explore technical analysis; however, this could be part of the recommendations for further studies, considering some of these indicators as part of further methodologies of fundamental analysis.Although, even when measuring a wide range of information, stock returns are not well explained and predicted even in the most recent and complex tests.Hou et al. (2017) found 450 anomalies in stock returns not yet clarified, even when classic approaches were used to relate these anomalies with the relative size of the investor.

Data and Methodology
This study was designed to explore some of the indicators used to predict stock returns.Relevant results on previous studies have led to the conclusion that there is no complete and certain technique to predict returns without any biases or concerns about statistical methods, such as data mining, spurious results, or correlations between evidence and real time performance (Avramov & Chordia, 2006).This means that there is no best-fit strategy and it is possible to find techniques better than others.
The most obvious outcome to emerge from this study is that building a critical framework to predict stock return will benefit investors who must allocate funds, but must consider many difficulties in current academic stages and mathematical techniques when considering uncertainty.
We employed 95% level of certainty and the data required to address the topic were largely the secondary data.Also, this study was designed as associative, time-series, and quantitative research to study the predictability of stock returns and create a model with different variables using the methodology of Fama and French (1992).The paper examines the stock returns of 36 large U.K. companies over the period from 2013 to 2016 in order to analyze the performance explained by means of three proxies: beta value, dividend growth, and earnings per share.
The variables in this paper consist of: (1) Risk free rate and beta () The risk-free rate of return is estimated most of the times as the government bond yield.The monthly data from U.K. for the 10 years yield were retrieved from the Bloomberg database and then the risk-free rate of return was used as one of the components of beta value.Fama and MacBeth (1973) stated that beta value is estimated by monthly returns of each stock by the following formula: (2) Stock and market return (R) The return of stock is the continuously compounded return on equal-weighted portfolio and is calculated as the natural log of (P/P -1).
Ri = Ln(P/P -1) (2 where P is the monthly closing price.
The portfolio return is built equally weighted with the following formula: The market value is continuously compounded return for the FTSE 100 index, where the closing monthly price t is divided by the closing price in month t -1 (3) Dividend growth Dividend growth is calculated by  / where D is the dividend and is defined as the natural log of the ratio of quarterly paid dividends in month t -1 to quarterly paid dividends for month t.
(4) Earnings per share EPS is defined as the natural log of the ratio of quarterly paid EPS in month t -1 to quarterly paid EPS for month t.

The Regression Model
For this paper, the independent variables Xi were beta value, dividend growth, and earnings per share (EPS).The regression model takes the general form: For observations Tⱼ, the coefficient  is the unknown parameter of interest.When testing in a regression model, the variable  has the ability to forecast  if  ≠0.The parameter  is the stock return or the dependent variable for the modelling.
It is assumed that variables are independently and identically distributed.

Step 1
Based on Equation (1), the values for beta are calculated from the stock returns of each security and the market return for the period of 2013 to2016.Secondly, the return value for the 36 largest U.K. companies from the FTSE 100 were ranked from the largest to the lowest stock return values and were divided into 6 portfolios.Previous studies based their criteria for selection on portfolios.Fama and MacBeth (1973) agreed that diversification of portfolios can minimize the effect of firm-specific risk, improving the estimation of beta values and future returns.
A total of 100 firms were screened from the FTSE 100 index, from which a total of 36 companies met the sample requirement and provided weekly data of stock closing price over the study period.This produced a total of 7488 closing prices.
The first formula of the regression model was built with the parameter taken from investment risk factor, which is beta value.
It was our intention to estimate parameters using fundamental analysis with regression analysis and time-series tool techniques.The primary source of the data was FTSE 100, giving us access to the dataset for large U.K. companies from a variety of industries.
A total of 100 firms were screened from the FTSE 100 index, from which a total of 36 companies were selected that provided quarterly information of dividends.This represented a total of 576 continuously-compounded dividend growth values for month t.In the cases where no data were found for the dividends and earnings, we used the extrapolation technique following Fama's methodology (Fama, 1990).
The second formula for the regression model is similar to that of earlier literature on dividends explanation power on return, such as Fama and French (1998), Campbell (1991), and Kothari and Shanken (1992).
EPS are the profits for a certain period of time divided by the number of outstanding shares.In this paper, the proxy used to build the model was the EPS when the companies announce the financial information every three months.
A total of 36 companies in the years 2013-2016 with quarterly earnings and dividends information qualified for the sample requirements.This represented a total of 576 quarterly earnings announcements.
EPS is defined as the natural log of the ratio of quarterly paid EPS in month t -1 to quarterly paid earnings per share EPS for month t.
Regression analysis was applied to test the effect of explanatory factors and to assess the correlation of the independent variables.
After including all proxies, the model was formed as follows: The proportion of variance due to the dependent variable was explained by  or the coefficient of determination. indicates the squared correlation between an independent variable and predictions made by the regression of the dependent variables (Kothari and Shanken, 1992).

Hypothesis
The result of the test was used to interpret the relationship between beta and return.
In order to test if coefficient  is significantly different from zero, the following hypothesis was formulated: The joint hypothesis was considered to summarize the variation in the total independent variables, and the ANOVA f test assesses the fitness of the regression model as a group.Here, the adjusted  statistic was used to explain the relationship of this group of independent variables with return.

Result
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