How Reliable is Leverage as a Predictor of Excess Returns?

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How Reliable is Leverage as a Predictor of Excess Returns?

Abstract:

This paper investigates whether leverage can be used to predict excess returns of individual assets. The predictive capabilities of a market-based leverage ratio are compared with three well-known predictors: the dividend yield, book-to-market and earnings-price ratios. The sample used includes over 18,000 observations and focuses on the FTSE 100 for the period 1985-2015. This study finds that the leverage ratio performs relatively well as a predictor compared to the earnings-price ratio. However, more reliable predictors are the dividend yield and book-to-market ratios. This study argues that the book-to-market ratio is the most reliable predictor, as it performs better compared to the dividend yield ratio over a longer prediction horizon. 1

Björn E. Trouerbach S2569639

Program: MSc Finance (University of Groningen) Thesis supervisor: Dr. L. Dam

Date: 26-06-2015

Number of words: 11,400

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I. Introduction

The use of financial ratios to improve return predictability is a widely accepted practice (Lettau and Ludvigson, 2005). However, Goyal and Welch (2008) contend that it remains unclear exactly which ratio yields the most accurate results. Dividend yield is considered the most reliable predictor, however, various scholars find that in more recent years the predictive capability of this ratio has been limited. As Lewellen (2004) observes: ‘Dividend yield reached a new low in May 1995, predicting that returns going forward should be far below average. In reality, the NYSE index more than doubled over the subsequent six years.’

The main findings of Goyal and Welch (2008) are a starting point for this paper. The aim is to investigate if their results for predicting the excess returns of an index can also be applied to individual assets. They estimate using all well-known predictors, but find only marginally significant results for some of the predictors. Therefore, they acknowledge that a healthy skepticism towards the prediction of returns is appropriate. This study predicts excess returns with predictors that yield the most reliable results for them: the dividend yield, the book-to-market and the earnings-price ratios. However, the main focus of this study is on a new model developed by Dam and Heijnen (2014). Their model explains variation in returns with variation in the leverage of a firm. Their leverage model is employed in this paper to predict returns of individual firms, and to compare the results with those of the other well-known predictors used to obtain estimations in this paper.

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The dataset of this paper focuses on the FTSE 100 index, which celebrated its 30th

birthday in 2014. The FTSE 100 started in January 1984 with 100 constituents and a base level of 1,000 points. Recently, the FTSE 100 set a new all-time high of over 7,000 points. However, of the initial 100 companies only 29 are still listed today, with the remainder either acquired or bankrupt. These 29 companies are included in the sample (subsample 1). To improve the size of the sample, current constituents of the FTSE 100 that were added to the index before the year 2000, are also included (subsample 2). In total, this renders a dataset of 59 companies, with over 18.000 monthly observations.

All predictors are considered to have a degree of predictability, however, there is considerable variation in their reliability. The leverage ratio is more reliable than a well-known predictor like the earnings-price ratio. However, it is less reliable than the dividend yield and the book-to-market ratios. The book-to-market and dividend yield ratios work equally well regarding monthly predictions, but the book-to-market is the most reliable with a longer prediction horizon. The contribution of this thesis to the literature is two-fold: 1. This study compares the performance of leverage as a predictor to the most reliable predictors according to Goyal and Welch (2008), and 2. This research further adds to the scarce literature that investigates predictability for individual assets, rather than for indexes.

This thesis is organized into six sections. Following the introduction, the existing literature and past empirical findings on return predictions are reviewed in section II. Next, I introduce my methodology and elaborate how the different models are tested. Section IV includes the data used and a selection of descriptive statistics, and the analysis is conducted and the results are presented in Section V. Finally, section VI offers a detailed discussion of the results and a conclusion to this study.

II. Literature Review

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most used predictor, is discussed in further detail. Next, I elaborate on the methodological issues regarding return predictability and discuss the following:

• the prediction horizon;

• the magnitude of the R-squared statistic;

• the scarce literature regarding individual asset studies;

• and the lack of a clear test to assess the reliability of a predictor.

The last part of the literature review focuses on more details of the four predictors in this study.

Goyal and Welch (2008) comprehensively re-examine the predictive capabilities of different ratios using the same methods for all ratios assessed. Goyal and Welch (2003) define the equity premium (market premium) as the return on the stock market minus the return on a short-term risk-free treasury bill. They regress an independent lagged predictor on the equity premium of the market; this is the most used prediction method. Goyal and Welch (2008) examine the most explored variables including: the dividend yield, dividend price, earnings-price, book-to-market, and the investment-capital ratio, along with various interest rates. They question results from articles that were written several years prior to their own study as the results may change with more recent data.

Goyal and Welch (2003) use S&P 500 index returns from 1926 to 2005 and subtract US Treasury bill rates to determine the equity premium. They find that dividend ratios have weak forecasting abilities and are not able to accurately predict this equity premium. This is in contradiction with the findings of Fama and French (1988). The latter found that the dividend yield can predict market returns, as the dividend yield correctly predicted monthly NYSE returns between 1941 and 1986. By way of an explanation for these differences, Goyal and Welch (2003) point to a different horizon and estimation period as a possible cause. The dividend price ratio, for example, offers a good performance for the 1930s to the mid-1980s, but it underperforms with regard to other periods. The dividend yield ratio is also not consistent and even more volatile than the dividend price ratio2, however, in relatively volatile times it performs better than the latter. Examples of volatile periods are the 1973-1975 Oil Shock and the market decline of 2000-2002.

2_{Goyal
and
Welch
(2008)
define
the
dividend
price
ratio
as
the
log
of
the
dividends
to
the
log
of
prices,}

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Moreover, the earnings-price ratio had superior performance from 1945 up until the late 1970s. Like the other ratios, the earnings-price’s performance was negative over the most recent 30 years, while its best sample period was from 1943 to 2002. For all other ratios, Goyal and Welch (2003, 2008) report insignificant results for at least a part of the estimation period, although some yielded no significant results during the entire out-of-sample (OOS) period. One of the more reliable ratios is the book-to-market ratio, which is statistically significant at the 6% level for the full period (Goyal and Welch, 2008). A further look at the results shows that the predictive performance until the Oil Shock was very good. However, following this, the performance of the book-to-market ratio decreased significantly, and during the most recent 30 years, it has demonstrated a negative performance.

Similarly to Goyal and Welch (2003, 2008), Cochrane (2008) focuses on predicting (excess) returns with dividend ratios. He introduces his study by observing that if both returns and dividend growth cannot be predicted, present value logic implies that the dividend price ratio is constant. However, it is in fact clear that this ratio is not constant. Cochrane (2008) also argues that the dividend yield is stationary, which implies that either dividend growth or price growth can be predicted. Moreover, Cochrane (2008) finds estimates that are,

economically, highly significant. He finds R-squared statistics of 4-7%, but the R-squared rises with a longer horizon to values between 30 and 60%.

However, Boudoukh, Richardson and Whitelaw (2006) stress to be cautious making inferences that can only be made using the horizon of predictability. For one-month

regression predictions they find R-squared statistics that never exceed 2%, yet this increases to 14% with a two-year horizon and even further with a four-year horizon. They find a high correlation between multiple-horizon estimations, which is mainly caused by the degree of overlap across horizons. They stress the necessity to account for the degree of overlap, however, econometrists disagree about the exact method to do this. This is why Goyal and Welch (2008) have expressed uncertainty regarding the reliability of their long-horizon predictions. They use overlapping periods, but are hesitant about how to interpret the results. Furthermore, Boudoukh, Richardson and Whitelaw (2006) conclude that there are no other clear advantages of long-horizon regressions. Cochrane (2008) confirms their assertion by stating that long-horizon regressions have very little additional power at best, since

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In addition, Ang and Bekaert (2007) only find significant results for the dividend yield ratio and the short rate when estimating for a short horizon. They suggest that predictability is mainly a short horizon phenomenon, while most recent studies in finance focus on a long horizon. They use a sample of four countries: the United States (US), United Kingdom (UK), France and Germany. Their findings yield very different outcomes for the UK compared to the US. The coefficients in the UK are positive and more than twice as large as their US counterparts when predicting with the dividend yield ratio. This paper focuses on the FTSE 100 (UK), in contrast to most other prediction studies that are based on US data.

The R-squared statistics found by Boudoukh, Richardson and Whitelaw (2006), seem very small. Yet as Campbell and Thompson (2008) show, even very small R-squared statistics can generate large improvements in portfolio performance. They analyze the correct way to judge the magnitude of R-squared and show that it should be compared with the squared Sharpe ratio (S-squared). If the R-squared is larger than the S-squared, then the investor can use the information of the predictive regression to obtain a proportional increase in portfolio return. Campbell and Thompson (2008) conclude by saying that even small R-squared statistics can generate large profits. Regressions with high R-squared statistics would be too profitable to believe, as the predictive regressions have only modest explanatory capabilities.

Although Campbell and Thompson (2005) find a degree of predictability, they argue that a reasonable investor would not use a model to predict a negative equity premium. Goyal and Welch (2008) agree with Campbell and Thompson (2005) and their suggestion to truncate such predictions to zero. Campbell and Thompson (2008) use at least 20 years of data to obtain initial coefficient estimates and show that many predictive regressions beat the

historical average in predicting excess returns. They argue that the outcomes are economically meaningful for mean-variance investors.

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The previously discussed literature is based on return predictability of indexes. There is scarce literature that investigates predictability at the individual asset level. Some additional issues arise when predicting at the individual asset level, however, using panel data can also help to improve the assessment of a predictor. Goyal and Welch (2003, 2008) argue that small sample bias decreases the reliability of their sample. This is less likely to be an issue with multiple individual assets compared to the use of a single index. An additional issue with individual assets is the availability of data; Stambaugh (1990) argues that data series that span over a long period of time are a necessity in return predictability studies. And while for most indexes long time series are available, this is often not the case for multiple individual assets. The use of only short horizon estimation, for example, on a monthly basis, partly overcomes this issue.

Another issue in this area of research is the lack of a clear test, and the disagreement between academics about the correct methods, to determine the reliability of a predictor. Kapetanios (2003) and Smeekes (2014) propose an approach to investigate individual assets in a time series panel. The main advantage that Kapetanios (2003) and Smeekes (2014) identify is that with sequential testing, a cross-sectional comparison is possible. On the other hand, multiple testing does not allow for an effective cross-sectional comparison. However, Smeekes (2014) stresses that it remains important to keep using conventional panel unit root tests. The methods for sequential testing he proposes are not substitutes, but they can provide more information than just a rejection or no rejection of the full panel.

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unusual and does not attach much value to the results. In his study, Lewellen (2004)

concludes that the dividend yield predicts returns more strongly than other studies show. For the book-to-market ratio and earnings price ratio he finds less reliable evidence than for the dividend yield. The results of the book-to-market are similar to those of the earnings-price ratio. Yet up until now, there has been little evidence that these ratios can predict returns.

Some ratios turn out to be good predictors for a period of time, yet the results are not consistent. Consequently, Dam and Heijnen (2014) have developed a new general asset-pricing model that uses the leverage ratio to predict returns. Dam and Qiao (2015) show that variation in expected excess returns is caused by four sources: variation in leverage, variation in the price of risk, variation in the variance of the market portfolio, and variance in unlevered betas. The leverage effect captures most of the variation from these sources, as it is only weakly linked to the real economy. All the other sources of time variation are directly linked to the real economy and thus, these sources of variation are set constant over time in the asset-pricing model. This implies that expected excess returns are only driven by variation in the leverage ratio.

Although there is some consensus amongst academics that a degree of return

predictability exists, there is disagreement with regard to which variable works and what the correct method is to predict these returns. Most academics agree that long horizon predictions have little additional power and that research should focus on a short horizon. The literature on individual asset predictions is scarce, since most studies focus on an index. The lack of a clear test further adds to the methodological issues of individual asset prediction, although statistics as the R-squared can be used to determine the reliability of a predictor.

III. Methodology

This section describes the research methods for obtaining predictions according to the ratio used and for each prediction period. The general predictive regression and the different predictors are discussed first. Next, I discuss the assessment of the predictors and some methodological choices.

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different variables (predictors) are regressed on the excess return of individual assets. All regressions are run separately, between assets and ratios, to prevent multicollinearity.

Predictive regressions for all variables only differ with regard to the variable itself and not in the estimation method, yielding the following general equation:

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𝑅

_!,!!!

− 𝑅

_!!!

= 𝑎

_!

+ 𝑥 ∗ 𝛽

_!

+ 𝜖

_!,!!!

,

Here

𝑅

_!,!!!

− 𝑅

_!!! represents the excess return in period t+1.

𝑅

_!,!!! defines the return of asset i in period t+1 and

𝑅

_!!! is the risk-free rate in period t+1. The coefficient

𝛽

_! is

estimated per asset and measures how significant variable

𝑥

is in predicting the excess return of the asset. The four prediction variables used in this study are described in detail in table 1.

Table 1 – Overview of predictors of the excess returns of the FTSE 100 companies

Variable (𝑥) Description

Leverage (K/E) !!,!

!!,! is the leverage ratio of asset i in period t. This is a market-based leverage

ratio, with total assets K over equity E. The market value of equity is calculated by multiplying the number of outstanding shares with the stock price at the end of the month. The market value of total assets consists of the market value of equity and the notional value of debt.

Dividend yield (d/y) !!,!

!!,! is the dividend yield ratio of asset i in period t. d represents the log of the

dividends and y the log of the lagged prices. The dividend is based on an anticipated annual dividend and excludes special or once-off dividends.

Book-to-market (b/m) !!,!

!!,! is the book-to-market ratio of asset i in period t. The book value of equity is

the balance sheet value of the common equity of the company, denoted by b. This value is divided by the market value of common equity, denoted by m.

Earnings price ratio (e/p) !!,!

!!,! is the earnings price ratio of asset i in period t. Earnings 𝑒 are divided by

price 𝑝 . The earnings are based on published accounts of the respective asset, while price is the official closing price at time t.

Note: This table presents the different predictive variables, that are inserted at the x in the predictive regression:

𝑅!,!!!− 𝑅!!!= 𝑎!+ 𝑥 ∗ 𝛽!+ 𝜖!,!!! The x is replaced by: !!,!

!!,! (leverage), !!,! !!,! (dividend yield), !!,! !!,! (book-to-market ratio), !!,!

!!,! (earnings-price ratio). Data sources:

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As no test exists that can achieve an accurate assessment of individual asset predictions, this study employs two diagnostics. First, the number of significant individual asset predictions is compared with the different predictors. Second, I take the R-squared statistics of the individual assets to construct an average R-squared statistic per predictor and compare these. The coefficients of all assets are then tested for joint significance with an adjusted Gibbons-Ross-Shanken (GRS) statistic3. This GRS test assesses whether the beta is significantly different from zero, whereas the standard GRS test does the same for the alpha. The test requires a balanced panel; therefore, some firms are excluded from the sample (see Appendix E).

Furthermore, this paper focuses on making predictions with a short horizon. As the studies by Boudoukh, Richardson and Whitelaw (2006), and Cochrane (2008) demonstrate, long horizon predictions have very little additional power at best. Ang and Bekaert (2007) find no results for longer horizon predictions and argue that prediction studies should solely focus on the short horizon. Therefore, in this study, the predictions for excess returns are made only on a monthly and yearly basis. This also helps to prevent the issue of overlap.

With regard to overlap, different academics, among them Goyal and Welch (2008), find this to be a problem. They are uncertain about how to solve this issue and how to interpret the results. To prevent overlap from biasing the results, this study aims to reduce overlapping as much as possible. This means that returns for the year are only predicted once a year (in February), instead of a year forward every month. This method reduces the number of observations when the horizon is increased, however, it also prevents high correlation between multiple-horizon estimations (Boudoukh, Richardson and Whitelaw, 2006).

Moreover, a longer horizon would further reduce the number of observations too much. This would give no additional explanatory power to the predictability of excess returns, since the time series are not long enough (Stambaugh, 1999).

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IV. Data

This section describes the data used in this study. Following the introduction of the sample and subsamples, the dependent variable (excess return) is discussed. Next the

independent variables are described and finally I give descriptive statistics. This analysis uses three different data sources: Worldscope, Datastream and the Treasury bill rates from the United Kingdom Debt Management Office.

Only 31 of the initial constituents of 1984 are still on the FTSE 100 index – the others are acquired, relegated, dissolved or bankrupt. The dataset used in this study thus consists of companies that were on the FTSE 100 before the year 2000 and are still listed there today. Four subsamples are formed, one with the initial constituents from 1984 and the second with only the current FTSE 100 companies (added before the year 2000). These subsamples act as a robustness check. The third and the fourth subsample include all companies, but only with observations of the last 20 and 10 years, respectively. Financials are excluded from the sample, as these have a very different leverage structure and are therefore not appropriate for the application of the leverage model.

The dependent variable in this study is the excess return. This excess return is

obtained by subtracting the risk-free rate from the rate of return of the asset. The source of the return of the asset is Datastream. This analysis employs stock returns on a monthly basis, based on the month-end values. Most stocks returns from 1984, when the FTSE 100 was formed, are publicly available. For companies that are formed after 1984, for example, through mergers, the earliest available returns are used in this paper.

Furthermore, I follow Koller’s (2010) recommendation to use government default-free bonds in the same currency with a similar maturity to estimate the risk-free rate. Returns are estimated on a monthly basis, thus short-term bonds are preferred over long-term bonds. The three-month UK treasury bills (UKGBILL3) are deemed the most appropriate4. The interest rates from the UK Treasury bills are annual rates from the United Kingdom Debt

Management Office and are based on the midpoint between the bid and offered rates. Because the provided rates are based on a midpoint between the bid and offered rate at the beginning of a period, these are moved one month forward to match them with the month-end values of

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the return of the asset. In this paper, the annual rates are converted into monthly risk-free rates for the months in question5_.

The first predictor used in this study is a market-based monthly leverage ratio. The book value of equity is subtracted from the book value of total assets to calculate the notional value of debt. The book value of total assets is obtained from Worldscope and represents the sum of total current assets, long-term receivables, investments, net property plant and equipment, and other assets. The book value from equity is also from Worldscope and

represents the common shareholders' equity. However, data on book values of total assets and equity are not available on a monthly basis for every company. In those cases, it is assumed that the debt level is constant over a year. This is not completely accurate, however, the implications for the model are limited. The leverage ratio is most influenced by variation in the value of equity (Dam & Qiao, 2015). The monthly market value of equity is then

calculated by multiplying the number of outstanding common shares and the month-end stock price. The source of this data is Datastream. The calculated debt and market value of equity are then added together to compute the month-end market value of total assets. I define the ratio between the market value of equity and the market value of total assets as the market-based leverage ratio.

The second predictor is the dividend yield, which is obtained from Datastream. The dividend yield expresses the gross dividend per share as a percentage of the lagged share price. It is based on an anticipated net annual dividend over the following 12 months.

The third predictor is the book-to-market ratio. This ratio is converted from a market-to-book ratio using Datastream. The ratio is defined as the market value of common equity, calculated by multiplying the share price with the number of outstanding shares, divided by the balance sheet value of common equity in the company. The book value of common equity is calculated by subtracting the total liabilities of the book value of total assets.

The fourth and final predictor is the earnings-price ratio. The data for this ratio is also obtained from Datastream and converted from a price-earnings ratio. The ratio is defined as the earnings, which are based on published accounts, divided by the official closing price of the asset on the respective date. The sample includes only companies listed on the FTSE 100, thus differences in accounting practices between the companies are limited.

5_{The
annual
rates
of
the
United
Kingdom
Debt
Management
Office
are
adjusted
to
a
monthly
risk-‐free
rate}

in month t+1 by: 𝑙𝑛((1 + !!

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Table 2 - Descriptive statistics FTSE 100 companies based on monthly data, 1985-2015

Obs. Mean Median St. D. Min. Max.

Excess return (%) 19,417 0.56 0.95 9.22 -48.58 35.66 Return (%) 19,417 0.95 1.37 9.10 -47.92 34.91 Leverage (%) 18,303 56.05 56.97 10.38 28.99 75.70 Dividend yield (%) 19,308 3.62 3.34 1.97 1.05 16.17 Book-to-market (%) 18,591 58.03 52.54 30.52 15.56 229.06 Earnings price (%) 19,035 7.31 6.62 3.69 2.53 29.95 Growth: Equity (%) 965 8.73 9.80 33.22 -66.04 75.72

Note: This table presents descriptive statistics of the full dataset, which consists of initial FTSE 100 companies from 1984

and additions to the index before the year 2000. All companies are still listed today; acquired or bankrupt companies are excluded. Leverage is measured as the market value of equity divided by the market value of total assets. In this paper, the inverse ratio of leverage (assets over equity) is used to predict excess returns, however, for the purpose of comparison, this study presents the more common ratio here as well. The growth rate of the market value of equity is an annualized percentage.

Table 2 presents some summary statistics, yet more are provided in Appendix B. It is clearly observable that the panel is unbalanced, since the number of observations for any variable is below 21,240 (59 assets* 360 months). The leverage is with a mean and median of 56% close to the leverage of 59% that Dam & Qiao (2015) find in the US. On average, the returns are around 1%, where the excess return has a mean of 0.56%.

As stated earlier, many ratios have proven to be less reliable predictors in recent times. A possible explanation lies in the changing economic environment. Therefore, the subsamples used in this study consist of the most recent 20 and 10 years. The predictive capabilities of all ratios in these periods can thus be found, which might be very relevant in the near future of return predictability. Because of the non-overlapping estimation method in this study, the subsamples are only estimated on a monthly basis, as a yearly frequency would reduce the observations per asset too much. Table 3 presents some descriptive statistics for the

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Table 3 - Descriptive statistics for FTSE 100 companies based on monthly data, 2005-2015

Subs. 2005-2015 Obs. Mean Median St. D. Min. Max.

Excess return (%) 6,519 0.67 1.15 8.74 -39.10 26.72 Return (%) 6,519 0.81 1.32 8.57 -38.45 25.67 Leverage (%) 6,434 54.67 55.00 7.69 36.37 68.21 Dividend yield (%) 6,962 3.50 3.16 1.91 1.53 12.97 Book-to-market (%) 6,939 55.55 51.92 26.84 23.80 183.50 Earnings price (%) 6,867 8.11 7.26 3.97 3.78 24.98

Note: This table presents descriptive statistics of FTSE 100 companies in the period 2005 to 2015, used as the subsample of

the last 10 years. The subsample includes the initial FTSE 100 companies and additions to the index before the year 2000. All companies are still listed today; acquired or bankrupt companies are excluded. Leverage is measured as the market value of equity divided by the market value of total assets. The inverse ratio of leverage (assets over equity) is used to predict excess returns, however, for comparison, the more usual ratio is displayed here.

V. Results

This section presents the results of the four models. I compare the performance of the models for the full dataset, the last 20 years, the last 10 years, the initial FTSE 100

companies, and the current FTSE 100 companies. The focus is on monthly data, however, the models are also predicted for a longer horizon with yearly predictions. The different

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Table 4 – Coefficients of monthly individual asset predictions of the FTSE 100 companies per asset and for all ratios, 1985 - 2015

Company Name Leverage (𝛽!) DY (𝛽!) BTMV (𝛽!) EP (𝛽!) 1. Ass. British Foods 0.045* 0.002 0.011 0.109 2. Barratt Developments 0.010** 0.000 0.013** 0.037 3. Br. American Tobacco 0.000 0.007** 0.015 0.069 4. British Aerospace 0.003 -0.004** 0.002 -0.175 5. BP 0.011 0.000 0.035 0.061 6. Diageo 0.005 0.023*** 0.032* 0.757*** 7. Aviva 0.001** 0.010*** 0.068*** 0.188** 8. GlaxoSmithKline 0.059** 0.006* 0.267** 0.330* 9. GKN 0.010 -0.002 0.033* 0.066 10. Imperial Tobacco 0.000* 0.011** -0.011 1.055*** 11. Johnson Matthey 0.024** 0.006* 0.074*** 0.841*** 12. Land Securities -0.004 0.002 0.054*** 0.132 13. Marks & Spencer 0.018 0.004 0.034 0.170 14. Pearson 0.091*** 0.013*** 0.027 0.494** 15. Reckitt Benckiser 0.004 0.013** 0.050 0.532* 16. Reed Elsevier 0.023 0.013** 0.033* 0.615*** 17. Rio Tinto 0.002 0.009** 0.166*** 0.234* 18. Sainsbury (J) 0.010 0.003 0.023 0.219 19. Smith & Nephew 0.023 0.002 0.111** 0.336 20. Royal Dutch Shell 0.024*** 0.009*** 0.032* 0.040 21. Taylor Wimpey 0.007*** 0.002*** 0.020*** 0.167*** 22. Tesco 0.004 0.003 0.070** 0.148 23. Unilever 0.013** 0.019*** 0.069*** 0.443** 24. Whitbread 0.029 0.002 0.007 0.449** 25. Balfour Beatty 0.019*** 0.005** 0.019 0.602*** 26. Cable & Wireless 0.016* 0.002 0.001 0.285 27. Elementis 0.029** 0.001 0.019 0.200 28. Ladbrokes 0.044** 0.007** 0.028** 0.023 29. Rexam 0.016** 0.007** 0.047*** 0.607*** 30. Bunzl 0.016 0.001 0.045 0.267 31. Dixons Carphone 0.018 0.100** 0.359 32. Intu Properties -0.003 0.010*** 0.046*** 1.030*** 33. ITV 0.022 -0.003 -0.036 0.017 34. Next -0.004 -0.005** 0.004 -0.041 35. Rolls Royce 0.026*** 0.002 0.049** 0.071 36. Vodafone 0.004 0.003 -0.001 0.155 37. Anglo American 0.022 0.002 0.068*** 0.252 38. ARM Holdings 0.354 0.010 0.007 0.204 39. Astrazeneca 0.039 0.006** 0.070 0.127 40. BHP Billiton 0.030 0.015** 0.089 0.416 41. British Gas 0.022 0.001 0.001 0.175 42. British Land 0.009 0.004 0.052*** 0.339 43. Centrica 0.021 -0.001 0.038 -0.002 44. Compass 0.073 0.267** 1.628** 45. National Grid -0.005 0.008*** 0.026 0.385** 46. Old Mutual 0.002** -0.001 0.032** 0.082 47. Sage Group 0.042 0.003 -0.038 0.367 48. Schroders 0.003* 0.015** 0.087*** 0.142 49. Severn Trent 0.005 0.007** 0.007 0.098 50. Wolseley 0.013 0.004 0.043** 0.147 51. WPP 0.000 0.002 0.003 0.047 52. Vesuvius 0.006 0.001 0.025 0.163* 53. Daily Mail 0.009 0.011** 0.022 0.144 54. De La Rue 0.068** 0.003 0.016 0.621** 55. Hays 0.052 0.003 -0.008 0.009 56. Inchcape 0.002 0.002 0.008 0.180 57. Pennon 0.026** 0.004* -0.039 -0.156 58. Rentokil 0.006 -0.003 0.012 0.298 59. Segro 0.007 0.003 -0.009 -0.258

Note: This table reports the individual assets prediction with the predictive regression:

𝑅!,!!!− 𝑅!!!= 𝑎!+ 𝑥 ∗ 𝛽!+ 𝜖!,!!!

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An interesting and unexpected observation is that some companies seem more predictable, regarding all ratios, than others. For six companies, the coefficients of all four ratios are significant; for Taylor Wimpey (a house building company) this is even at the 1% level. Sixteen companies are predictable with at least three out of four predictors. This cross-sectional comparison is made possible with the sequential estimation method (Smeekes, 2014), however, there is no indication why some companies are generally more predictable than others. The excess returns, other statistics and industry of the more predictable

companies are not consistent and show no clear differences to other companies in the sample. The results further prove that leverage correctly predicts the excess return for 27.12% of the assets. As such, it performs slightly less accurately than the dividend yield and book-to-market (which is correct for 38.98% and 35.59% of the assets, respectively). However, it is more reliable than a well-known predictor such as the earnings-price ratio. Lewellen (2004) argues that a positive relationship between the predictors and returns is to be expected. This holds for the results of this study, as a significantly negative relationship is only incidentally found. The leverage has almost no negative coefficients, only four, to be precise, and with a minimum coefficient of -0.005. None of the four negative observations are significant. This is not true for the dividend yield, which has two coefficients that are negative and significant. The reliability of these results can be questioned: a higher dividend yield should lead to an increase and not a decrease in the excess return, thus reducing the reliable predictions for the dividend yield to 35.59% of the assets.

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Table 5 – Individual asset test results for all predictors on the FTSE 100 companies, including all subsamples

Leverage Full dataset Last 20y Last 10y Initial Current

Significant at 0.10 (%) 33.90 33.90 23.73 51.72 28.26 Significant at 0.05 (%) 27.12 25.42 6.78 41.38 21.74 Significant at 0.01 (%) 8.47 10.17 3.39 13.79 8.70 Significant and positive (%) 27.12 25.42 6.78 41.38 21.74 Average R-Squared 0.0092 0.0120 0.0157 0.0116 0.0088

Dividend yield Full dataset Last 20y Last 10y Initial Current

Book-to-market Full dataset Last 20y Last 10y Initial Current

Earnings price Full dataset Last 20y Last 10y Initial Current

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Table 5 provides an overview of the test results for all predictors for the full dataset and all subsamples. Restricting the data to more recent years clearly does not lead to an improvement in predicting excess returns with the leverage ratio. The last 10 years include several crises, among them the financial crisis of 2007-2008. In this period, only 6.78% of the assets where predicted correctly at the 5% significance level, decreasing from 27.12% in the full sample period. This deterioration is worse than the three other predictors, which lose only 50%, approximately, of the significant observations. The reduced reliability is in line with results described in the literature, where in almost all studies of recent years the predictive capabilities decrease as well. However, the results of the full dataset and for the last 20 years do not differ significantly, indicating that leverage does not predict well in the changed market conditions of the last 10 years.

The subsample with the initial FTSE 100 companies is also displayed in table 5. This subsample consists of 29 companies, almost half of the full sample of 59 companies (see Appendix A). Interestingly, the leverage ratio predicts 51.72% of these 29 initial FTSE 100 companies correctly at the 10% level, and 41.38% at the 5% level. This is considerably more than the 33.90% and 27.12% that are found for the full sample. The other predictors show comparable characteristics: the initial companies are more predictable than the later additions to the index. This can potentially be explained by the difference in growth: the initial

companies show less growth than the additions to the index (see Appendix B).

Moreover, the average R-squared for all the predictors and all the samples, is between 0.9% and 2%. Dividend yield and book-to-market excel in this as well, with an R-squared statistic of more than 1% for the full dataset. For the last 10 years, this increases to 1.94% for both ratios. The leverage and earnings-price ratios perform less and have a lower R-squared statistic for both the full dataset and all subsamples. These results are in line with Boudoukh, Richardson and Whitelaw (2006), whose findings demonstrate that R-squared statistics never exceed 2% for one-month regression predictions. These percentages seem very small,

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Figure 2 – Histogram of the coefficients for all predictors of the FTSE 100 companies

Note: This figure presents a histogram of the predictions of the excess return of the FTSE 100 companies with the four predictive variables. The predictive variables include the leverage, dividend yield, book-to-market, and the earnings-price ratios. The coefficient represents the beta, which measures the magnitude of a change in the predictive variable to a change in the excess return. The sources of the data are Datastream, Worldscope and the United Kingdom Debt Management Office.

Table 6 – Summary test results of monthly data for all predictors of companies on the FTSE 100, 1985-2015

Leverage Dividend Yield Book-to-market Earnings-Price % significant at 0.10 33.90 44.07 44.07 32.20 % significant at 0.05 27.12 38.98 35.59 25.42 % significant at 0.01 8.47 13.56 18.64 13.56

% Significant (+)* 27.12 35.59 35.59 25.42

Average R-Squared 0.0092 0.0107 0.0130 0.0089 Joint sign. χ2_-stat _94.92 _155.48 _111.88 _87.36

Joint sign. p-value 0.00 0.00 0.00 0.00

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In figure 2, a histogram of all significant individual coefficients is displayed. An increase in the predictor of one unit leads to a change in the excess return with the magnitude of the coefficient. Most coefficients are slightly above zero, which appears to be realistic. Table 6 provides a summary of the results for all predictors, including the joint significance for all ratios (see Appendix D for more details). As Smeekes (2014) explains, sequential testing is not a substitute for the conventional unit root test. This analysis employs an adjusted GRS test to test the joint significance of all coefficients of the estimated regressions. Assets with missing observations are excluded, since a balanced panel is required for the test. This procedure is extensively elaborated in Appendix E, where the excluded companies are specified as well. All ratios are jointly significant at any significance level for the full sample period. Restricting the data to more recent periods changes this, demonstrating that only the book-to-market ratio is significant at any significance level in the last 10 years. The dividend yield and leverage ratios also remain highly significant in the subsamples of recent years, while the earnings-price ratio fails to maintain high significance. The earnings-price ratio is therefore confirmed as the least reliable predictor – individually and jointly, it performs less well than all other ratios. A table with joint significance test results is added in Appendix E.

Boudoukh, Richardson and Whitelaw (2006) describe no clear advantages of longer horizon predictions. However, to ensure thorough testing in this analysis, predictions for excess returns are made with all models on a yearly basis and are briefly assessed here. The tables with individual coefficients and the summary test results are provided in Appendix C. According to Brooks (2014), less significant predictions should be expected because of the reduced number of observations in the explanatory variables. Indeed, less significant assets at any significance level are found for all ratios. This means that less variation in the excess return is explained by the leverage, dividend yield, book-to-market or earnings-price ratios.

Furthermore, with regard to yearly estimations, the book-to-market ratio is superior to all other ratios. It has the most significant individual coefficients and also the highest average R-squared statistic. With 8.59% this statistic is far higher than the average R-squared of the other ratios. Interestingly, as a predictor on a yearly basis, the dividend yield is less reliable than as a predictor with monthly predictions. The number of significant assets with a positive sign drops to 8.47% (from 35.59% with monthly predictions). On a yearly basis, the dividend yield performs less than the leverage ratio, as the leverage has a higher R-squared statistic and more significant assets with a positive sign. Ang and Bekaert (2007) argue that return

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confirmed by the results of this study. Indeed, less significant results with a longer horizon are found here, while Ang and Bekaert (2007) find no significant results at all. As such, it would be premature to doubt the value of longer horizon predictions.

VI. Conclusion

This study endeavoured to predict excess returns using known predictors including the dividend yield, book-to-market and the earnings-price ratios. Their performances were

compared with the predictive capabilities of a market-based leverage ratio. The predictors were then compared with the initial companies on the FTSE 100 as well as with additions to the index before the year 2000, which are still listed today. Monthly data from the last 30 years was employed, while for longer horizon predictions the excess returns were estimated on a yearly basis. In recent times, the prediction of excess returns has been even more difficult, as academics have shown that the predictive performance plummets in later years. Therefore subsamples of the last 20 and the last 10 years were constructed, and all the models of these recent periods were tested for this analysis.

Based on the findings of the analysis, this paper finds that the market-based leverage is more reliable than a known predictor like the earnings-price ratio. However, it

underperforms in comparison to the dividend yield and book-to-market ratios. On the other hand, the performance of the leverage ratio is mediocre for the whole sample period and the last 20 years, however, its performance lapses further for the last 10 years.

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These results are partially in line with existing literature on this subject, as most studies find the dividend yield ratio to be the most reliable predictor and not the book-to-market ratio. In the literature, the dividend yield is described as inconsistent; this is confirmed since the performance of dividend yield drops for yearly predictions. Consequently, this study confirms that longer horizon predictions have little additional power. Sequential testing provides more information about the predictive capabilities of the predictors.

For future research, it might be interesting to estimate for a greater sample, both in numbers and years, though the availability of long time series for individual assets may pose a problem. However, the main issue is the lack of a clear test to assess the reliability of an individual asset predictor, as econometrists disagree about the exact testing method. Thus, the development of a clear test would mean a significant improvement for research on individual asset predictability. A clear test would also help to investigate the very relevant

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References

Ang, A., Bekaert, G., 2007. Return predictability: Is it there?, Review of Financial Studies 20, 651-707. Boudoukh, J., Richardson, M., Whitelaw R., 2006. The Myth of Long-Horizon Predictability. Review of Financial Studies 21, 1577-1605.

Brooks, C., 2014. Introductory Econometrics for Finance. Cambridge University Press, Cambridge. Campbell, J., Thompson, B., 2005. Predicting the Equity Premium Out of Sample: Can Anything Beat the Historical Average. Unpublished working paper. National Bureau of Economic Research, Cambridge. Campbell, J., Thompson, B., 2008. Predicting Excess Stock Returns Out of Sample: Can Anything Beat the Historical Average. Review of Financial Studies 21, 1509-1531.

Cochrane, J., 2008. The Dog That Did Not Bark: A defense of return predictability. Review of Financial Studies 21, 1533-1575.

Dam, L., Heijnen, P., 2014. Market Clearing and Stock Returns of Levered Firms when Equity Supply is Fixed. Unpublished working paper. University of Groningen, Groningen.

Dam, L., Qiao, K., 2015. Reconsidering the Capital Asset Pricing Model: Unlevered Betas and the Cross-section of Unlevered Stock Returns. Unpublished working paper. University of Groningen, Groningen.

Fama, E., French, K., 1998. Dividend Yields and Expected Stock Returns. Journal of Financial Economics 22, 3-25.

Fama, E., French, K., 2002. The Equity Premium. Journal of Finance 57, 637-659.

Goyal, A., Welch, I., 2003. Predicting the Equity Premium with Dividend Ratios. Management Science 49, 639-654.

Goyal, A., Welch, I., 2008. A Comprehensive Look at The Empirical Performance of Equity Premium Prediction. Review of Financial Studies 21, 1455-1508.

Keim, D., Stambaugh, R., 1986. Predicting returns in the stock and bond markets. Journal of Financial Economics 17, 357-390.

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Koller, T., Goedhart, M., Wessels, D., 2010. Valuation, Measuring and Managing the Value of Companies. McKinsey & Company, New York.

Lettau, M., Ludvigson, S., 2005. Expected returns and expected dividend growth. Journal of Financial Economics 73, 583-626.

Lewellen, J., 2004. Predicting Returns with Financial Ratios. Journal of Financial Economics 74, 209-235. Smeekes, S., 2014. Bootstrap Sequential Test to Determine the Order of Integration of Individual Units in a Time Series Panel. Unpublished working paper. Maastricht University, Maastricht.

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Appendix A - 'Company lists'

FULL DATASET

Original constituents currently on FTSE 100:

1. Associated British Foods 2. Barratt Developments 3. British American Tobacco 4. British Aerospace (BAE systems) 5. BP

6. Diageo (Distillers Company and Grand Metropolitan became part of Diageo)

7. Aviva (General Accident Fire & Life and Commercial Union Assurance part of Aviva) 8. GlaxoSmithKline (Glaxo merged in 2000 with Smithkline Beecham plc).

9. GKN (formerly known as Guest, Keen & Nettlefolds) 10. Imperial Tobacco Group (formerly known as Imperial) 11. Johnson Matthey

12. Land Securities Group 13. Marks & Spencer Group

14. Pearson (formerly known as Pearson & Son)

15. Reckitt Benckiser Group (formerly known as Reckett & Colman) 16. Reed Elsevier (formerly known as Reed International)

17. Rio Tinto 18. Sainsbury (J) 19. Smith & Nephew

20. Royal Dutch Shell (formerly known as Shell Transport & Trading). 21. Taylor Wimpey (formerly known as George Wimpey)

22. Tesco 23. Unilever 24. Whitbread

Relegated original constituents:

25. Balfour Beatty (Formerly known as British Insulated Callender's Cables) 26. Cable & Wireless Communications

27. Elementis (formerly known as Harrison's & Crosfield) 28. Ladbrokes

29. Rexam (formerly known as Bowater)

Added to FTSE 100 before the year 2000:

30. Bunzl (1986)

31. Dixons Carphone (1985 formerly known as Dixons Group) 32. Intu Properties (1984 formerly known as Libery International) 33. ITV (1984 multiple mergers)

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35. Rolls Royce (1987) 36. Vodafone Group (1991) 37. Anglo American (1999) 38. ARM Holdings (1999) 39. Astrazeneca (1999) 40. BHP Billiton (1997)

41. British Gas (BG Group) (1986) 42. British Land (1997)

43. Centrica (1997) 44. Compass Group (1998) 45. National Grid Group (1995) 46. Old Mutual (1999) 47. Sage Group (1999) 48. Schroders (1984) 49. Severn Trent (1999) 50. Wolseley (1993) 51. WPP (1998)

52. Vesuvius plc (formerly known as Cookson Group) (1986) 53. Daily Mail and General Trust (1999)

54. De La Rue (1985) 55. Hays (1996) 56. Inchcape (1991) 57. Pennon Group (1984) 58. Rentokil (1991) 59. Segro (1984)

SUBSAMPLE - INITIAL CONSTITUENTS Currently on FTSE 100:

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17. Rio Tinto 18. Sainsbury (J) 19. Smith & Nephew

Relegated from FTSE 100:

25. Balfour Beatty (Formerly known as British Insulated Callender's Cables) 26. Cable & Wireless Communications

27. Elementis (formerly known as Harrison's & Crosfield) 28. Ladbrokes

29. Rexam (formerly known as Bowater)

SUBSAMPLE - CURRENT CONSTITUENTS Initial constituents:

9. GKN (formerly known as Guest, Keen & Nettlefolds) 10. Imperial Tobacco Group (formerly known as Imperial) 11. Johnson Matthey

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19. Smith & Nephew

Added to FTSE 100 before 2000:

25. Bunzl (1986)

26. Dixons Carphone (1985 formerly known as Dixons Group) 27. Intu Properties (1984 formerly known as Libery International) 28. ITV (1984 multiple mergers)

29. Next plc (1987) 30. Rolls Royce (1987) 31. Vodafone Group (1991) 32. Anglo American (1999) 33. ARM Holdings (1999) 34. Astrazeneca (1999) 35. BHP Billiton (1997)

36. British Gas (BG Group) (1986) 37. British Land (1997)

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Appendix B 'Descriptive Statistics'

Table - Descriptive Statistics of the FTSE 100 companies, based on monthly data

1985-2015 Obs. Mean Median St. D. Min. Max. Excess return 19,417 0.56% 0.95% 9.22% -48.58% 35.66% Return 19,417 0.95% 1.37% 9.10% -47.92% 34.91% Leverage (E/K) 18,303 56.05% 56.97% 10.38% 28.99% 75.70% Dividend yield (d/y) 19,308 3.62 3.34 1.97 1.05 16.17 Book-to-market (b/m) 18,591 0.58 0.53 0.31 0.16 2.29 Earnings price (e/p) 19,035 0.07 0.07 0.04 0.03 0.30

Growth:

Equity (mv) 965 8.73% 9.80% 33.22% -66.04% 75.72%

Subs. 1995-2015 Obs. Mean Median St. D. Min. Max. Excess return 12,825 0.56% 1.04% 9.28% -45.68% 32.45% Return 12,825 0.82% 1.34% 9.15% -45.08% 31.58% Leverage (E/K) 12,882 56.34% 56.92% 9.26% 32.87% 73.49% Dividend yield (d/y) 13,731 3.43 3.08 1.90 1.13 14.42 Book-to-market (b/m) 13,463 0.55 0.50 0.28 0.17 2.10 Earnings price (e/p) 13,479 0.07 0.07 0.04 0.03 0.26

Subs. 2005-2015 Obs. Mean Median St. D. Min. Max. Excess return 6,519 0.67% 1.15% 8.74% -39.10% 26.72% Return 6,519 0.81% 1.32% 8.57% -38.45% 25.67% Leverage (E/K) 6,434 54.67% 55.00% 7.69% 36.37% 68.21% Dividend yield (d/y) 6,962 3.50 3.16 1.91 1.53 12.97 Book-to-market (b/m) 6,939 0.56 0.52 0.27 0.24 1.83 Earnings price (e/p) 6,867 0.08 0.07 0.04 0.04 0.25

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Table - Descriptive Statistics of FTSE 100 companies, based on yearly data

1985-2015 Obs. Mean Median St. D. Min. Max. Excess return 1,680 1.68% 2.13% 40.95% -75.72% 101.14% Leverage (K/E) 1,480 2.58 2.25 1.11 1.60 6.38 Dividend yield (d/y) 1,568 3.56 3.35 1.69 1.16 8.40 Book-to-market (b/m) 1,514 0.55 0.51 0.31 0.06 1.38 Earnings price (e/p) 1,553 0.07 0.07 0.03 0.03 0.17

Note: This tables presents descriptive statistics of the FTSE 100 companies from 1984 and additions to the index before the year 2000. All companies are still listed today; acquired or bankrupt companies are excluded.

Leverage is measured as the market value of equity divided by the market value of total assets. I use the inverse ratio of leverage (assets over equity) to predict excess returns, however for comparison I display the more usual ratio here.

Table - Descriptive statistics initial FTSE 100 companies 1985-2015

Average Median St. D. Min. Max. Leverage (E/K) 54.91% 56.10% 9.84% 27.75% 72.95% Return 0.91% 1.28% 8.58% -46.50% 33.62% Excess return 0.45% 0.82% 8.58% -46.94% 33.17% Growth: Leverage (E/K) 0.60% 0.98% 17.36% -42.54% 41.76% Equity (mv) 8.03% 9.13% 28.46% -60.29% 66.17% Debt (bv) 7.02% 6.03% 31.44% -78.67% 88.17%

Table - Descriptive statistics current FTSE 100 companies 1985-2015

Average Median St. D. Min. Max. Leverage (E/K) 56.09% 56.91% 10.01% 30.65% 74.66% Return 1.00% 1.39% 8.78% -44.87% 33.57% Excess return 0.59% 0.98% 8.79% -45.32% 33.10% Growth*: Leverage (E/K) 0.00% 1.05% 18.53% -42.29% 41.31% Equity (mv) 9.63% 10.42% 31.85% -61.56% 72.96% Debt (bv) 8.41% 6.71% 29.44% -61.10% 85.88%

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Appendix C ‘Yearly Predictions’

Table – Coefficients of yearly predictions per asset on the FTSE 100 for all ratios, 1985 - 2015

Company Name Leverage DY BTMV EP

1. Ass. British Foods 0.191 -0.050 -0.087 -1.480 2. Barratt Developments 0.114 -0.058** 0.152* -0.403 3. Br. American Tobacco -0.028 0.062 -0.032 -0.010 4. British Aerospace 0.021 -0.012 -0.053 -1.492 5. BP 0.042 0.002 0.110 0.062 6. Diageo -0.022 0.058 0.229 3.945 7. Aviva 0.009* 0.055** 0.288 1.560* 8. GlaxoSmithKline 0.496 0.028 2.056* 1.275 9. GKN 0.184*** 0.009 0.481*** 2.999*** 10. Imperial Tobacco 0.000 0.070 -0.158 11. Johnson Matthey 0.255*** 0.082** 0.680*** 9.328*** 12. Land Securities 0.067 0.019 -0.138 1.805 13. Marks & Spencer 0.203 0.034 0.237 2.274 14. Pearson 0.655 0.083 0.054 3.047 15. Reckitt Benckiser -0.269* -0.014 -0.165 -1.335 16. Reed Elsevier 0.199 0.083 0.234 3.570 17. Rio Tinto 0.071 0.041 1.634*** 3.724** 18. Sainsbury (J) 0.143 0.003 0.106 0.615 19. Smith & Nephew -0.104 0.001 0.757 2.455 20. Royal Dutch Shell 0.127 0.078** 0.164 -0.422 21. Taylor Wimpey 0.113** 0.025** 0.247*** 1.596*** 22. Tesco -0.079 -0.012 0.279 -1.831 23. Unilever 0.100** 0.079 0.759*** 2.455 24. Whitbread 0.247 -0.034 0.131 2.475 25. Balfour Beatty 0.098 -0.022 -0.086 2.838 26. Cable & Wireless 0.161* 0.013 -0.311 2.068 27. Elementis 0.083 0.017 -0.057 -1.069 28. Ladbrokes 0.161 0.041 0.191 -0.169 29. Rexam 0.070 0.028 0.257 2.793 30. Bunzl -0.011 -0.003 0.167 -1.371 31. Dixons Carphone -0.061 0.742 29.026** 32. Intu Properties -0.054 0.082 0.453** 3.680 33. ITV 0.165 -0.031 -0.682 -1.573 34. Next 0.188 -0.122** 0.753** -4.692 35. Rolls Royce 0.204** -0.002 0.391* 0.118 36. Vodafone 0.019 0.022 -0.229* 0.848 37. Anglo American 0.306 0.062 0.993*** 3.983 38. ARM Holdings 2.023 -0.133 -0.455 2.853 39. Astrazeneca 0.293 0.042 0.457 0.779 40. BHP Billiton 0.073 0.206 -0.773 -0.199 41. British Gas 0.251 0.011 -0.015 0.073 42. British Land 0.083 0.051 0.004 3.976 43. Centrica -0.097 0.084** -1.357* -1.272 44. Compass 0.135 0.801 6.729 45. National Grid -0.082 0.063 -0.342 3.850 46. Old Mutual 0.019** -0.013 0.345** 1.317 47. Sage Group -0.281 -0.016 -0.965 -0.596 48. Schroders 0.022 0.173 0.686* -1.318 49. Severn Trent 0.024 0.020 0.034 0.364 50. Wolseley -0.080 -0.028 -0.063 -2.965* 51. WPP -0.018 0.077 0.181* -1.350 52. Vesuvius 0.238* -0.022 0.833*** 2.102 53. Daily Mail 0.103 0.133** -0.108 1.128 54. De La Rue -0.009 -0.059 0.141 6.538* 55. Hays 0.723 0.042 -0.517 2.164 56. Inchcape 0.304*** 0.046 0.272 4.705 57. Pennon 0.176 0.019 -0.370 -0.992 58. Rentokil 0.202 -0.105** 0.426 6.742 59. Segro -0.009 -0.006 -0.266 -2.263

Note: This table reports the individual assets prediction with the predictive regression:

𝑅!,!!!− 𝑅!!!= 𝑎!+ 𝑥 ∗ 𝛽!+ 𝜖!,!!!

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Table – Summary test results yearly data for all predictors of assets on the FTSE 100, 1985 - 2015

Leverage Dividend Yield Book-to-market Earnings-Price

% significant at 0.10 20.34 22.03 28.81 15.25 % significant at 0.05 11.86 13.56 16.95 8.47

% significant at 0.01 5.08 3.39 11.86 5.08

% Significant (+)* 11.86 8.47 16.95 8.47

Average R-Squared 0.0634 0.0557 0.0859 0.0567

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Appendix D ‘Test results for all predictors’

Table – Test results with leverage as predictor (monthly)

Full dataset Last 20y Last 10y Initial Current

% significant at 0.10 33.90 33.90 23.73 51.72 28.26 % significant at 0.05 27.12 25.42 6.78 41.38 21.74 % significant at 0.01 8.47 10.17 3.39 13.79 8.70 % Significant (+)* 27.12 25.42 6.78 41.38 21.74 Average R-Squared 0.0092 0.0120 0.0157 0.0116 0.0088 Joint sign. χ2_-stat _94.92 _94.16 _82.58

Joint sign. p-value 0.00 0.00 0.02

Table – Test results with dividend yield as predictor (monthly)

Table – Test results with book-to-market as predictor (monthly)

Full dataset Last 20y Last 10y Initial Current % significant at 0.10 44.07 38.98 33.90 58.62 52.17 % significant at 0.05 35.59 32.20 18.64 41.38 41.30 % significant at 0.01 18.64 13.56 6.78 24.14 21.74 % Significant (+)* 35.59 32.20 18.64 41.38 41.30 Average R-Squared 0.0130 0.0142 0.0194 0.0143 0.0152 Joint sign. χ2_-stat _111.88 _110.60 _103.88

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Table – Test results with earnings-price as predictor (monthly)

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Appendix E ‘Joint significance testing’

The GRS test for joint significance needs a balanced panel. Therefore the analysis excludes some companies from the sample. The full sample contains companies from at least 300 months, the subsample for the last 20 years contains companies from at least 150 months, and the subsample for the last 10 years contains companies from at least 100 months. Specifically, this means that the following companies are excluded:

Leverage – Full sample: 8, 20, 31, 32, 33, 37, 38, 39, 40, 43, 44, 45, 46, 49, 55, 57. Leverage – Last 20 years: 31, 33.

Leverage – Last 10 years: 31.

Dividend yield – Full sample: 27, 31, 35, 37, 38, 39, 40, 43, 44, 45, 46, 52. Dividend yield – Last 20 years: 31, 35, 38.

Dividend yield – Last 10 years: 2, 21, 33, 35, 50, 52, 58.

Book-to-market – Full sample: 8, 17, 20, 24, 31, 32, 33, 37, 38, 39, 40, 43, 44, 45, 46. Book-to-market – Last 20 years: 31, 33.

Book-to-market – Last 10 years: 31.

Earnings-price – Full sample: 31, 32, 37, 38, 39, 40, 43, 44, 45, 46. Earnings-price – Last 20 years: none.

Earnings-price – Last 10 years: 21.

Note that the other subsamples (initial and current FTSE 100 companies) are not tested for joint significance. The balanced panel requirement would reduce the sample observations for these subsamples too much.

Table – Joint significance test results

Leverage Dividend yield Book-to-market Earnings-price χ2_{-stat p-value χ}2_-stat _{p-value χ}2_-stat _{p-value χ}2_{-stat p-value}

Full sample 94.92 0.00 155.48 0.00 111.88 0.00 87.36 0.00 Last 20 years 94.16 0.00 176.04 0.00 110.60 0.00 72.35 0.10 Last 10 years 82.58 0.02 80.18 0.01 103.88 0.00 57.20 0.47