1
The Implied Equity Risk Premium at the Nederlandse
Gasunie N.V.
Abstract
This master thesis applies the model of Goedhart et al. (2002) to estimate the Equity Risk Premium for the Nederlandse Gasunie. The combination of different estimates for growth in earnings and return on equity result in different models to estimate the ERP. Almost all models show that that the implied ERP was low during the 1990 and higher after the financial crisis of 2008. The results of statistical test show that ERP models based on GDP growth are generally more stable than their earnings based equivalent. The different estimates for the return on equity do not have a significant different effect on the volatility of the ERP estimate. The models in this paper may better estimate the ERP for the Gasunie but cannot be directly implemented within their WACC calculations.
J.S. Piksen*
Master thesis Finance, University of Groningen
JEL Codes: G12, G30, G32
Key Words: Equity Risk Premium (ERP), Market Risk Premium (MRP), Market cost of Equity, Weighted Average Cost of Capital (WACC), Dividend Growth Model, P/E ratio, Market Earnings Growth, Return on Equity and Reinvestment Rate.
*Jelle Sybren Piksen is a MSc. Finance student at the University of Groningen, student number: S2073080, email:
2
I.
Introduction
The equity risk premium (ERP) represents the access of the expected return on the market portfolio of stocks over the risk free rate and is a highly debated in finance. The ERP is commonly used to price risk and therefore plays a central role in portfolio allocation decisions, valuations and cost of (equity) capital estimations. Different approaches have been used to estimate the ERP. The most common method uses a long term average of the difference between historical annual returns of stocks over the yield on long term government bonds. ERP estimates based on historical returns highly differ but are generally in the range of 4% to 6%.
At the N.V. Nederlandse Gasunie (hereafter Gasunie) finance practitioners periodically update their estimate of the Weighted Average Cost of Capital (WACC). To estimate the cost of equity (used in the WACC), Gasunie practitioners use the CAPM model and hence the ERP. The Gasunie uses the WACC for different purposes. The largest business unit of the Gasunie, Gas Transport Services, operates in a regulated market where tariffs are partly based on WACC determined by the regulator, the Authority Consumer Markets. Another business unit of Gasunie uses the WACC to value investment opportunities. Further, in the near future, the Ministry of Finance will set a cost of equity requirement primary based on the CAPM model.
At the moment, the Gasunie, bases its ERP on a long term historical average from 1900 onwards. But evidence exist that the ERP varies over the business cycle (e.g. Ilmanen, 2011; Damodaran, 2014) and thus ERPs based on historical returns may not be a good estimate for expected ERPs. For that reason, the historical average ERP does not entirely satisfies their ERP preference. Gasunie’ ERP preference are as follows: First, the ERP estimate should reflect current market circumstances (conditional). An ERP estimate that reflects current market circumstances reflects both the risk of investments, seen by stock market investors and the collective risk aversion of those same investors (Duff and Phelps, 2014). Second, the ERP estimate should be generally in line with historical ERPs and reasonable stable to prevent that their WACC estimate constantly changes. Third, the ERP estimate should justify current stock market prices.
3 Goedhart et al. (2002) assume that market real earnings growth and return on (book value of) equity (ROE) are entirely stable over time, but this may bias ERP estimates as in reality, both variables do change over time. Based on either GDP or S&P500 data, this paper uses six estimates of earnings growth and four different estimates of ROE. These different growth and ROE estimates potentially lead to better ERP estimates than the assumptions made in Goedhart et al. These estimates however, also affect the stability of the ERP estimate. As Gasunie prefers an ERP that is both, conditional on the market and reasonable stable, the main question (and focus of the statistical tests) in this paper is how the estimates of market earnings growth and ROE affect the stability of the ERP, generated by the Goedhart et al. (2002) model.
Combining the six growth estimates and four ROE estimates results 24 different ERP models. All 24 models estimate the ERP on a quarterly basis between the period 1995 to 2014. Based on the different estimates of growth and ROE, the 24 ERPs are separated in independent groups. The independent groups allow statistical tests to analyze the effect of the estimates for growth and ROE on the volatility of the ERP estimate. A same methodology is used to analyze the economic consequences of the different estimates of variables for the Gasunie. Further, Gasunie practitioners suspect that there exist correlation between the ERP and the risk free rate. Therefore, this paper also performs a correlation test between the ERP and the risk free rate. Based on economic relevant arguments the outcomes of the statistical tests and Gasunie preferences, recommendations whether and how (meaning which estimates of variables) the Gasunie can apply the Goedhart et al. (2002) model in their WACC calculations.
This master thesis proceeds as follows. The first section presents an overview of the Gasunie, their WACC model, and preference regarding the ERP. The second section presents a short overview of existing literature regarding the ERP and discusses the model of Goedhart et al. (2002). Thereafter the research methodology and descriptive statistics are presented. Subsequently, the results of the statistical tests and recommendations regarding ERP estimates are put forward. The final section concludes.
4
II.
Gasunie, WACC and ERP preference
Within Europe, the Gasunie is one of the largest gas infrastructure companies. The Dutch government is the only shareholder as it considers this infrastructure to be vital for consumers and the Dutch economy. The largest business unit of Gasunie is Gas Transport services (GTS). Per annum, GTS and Gasunie Deutschland convey almost one fourth of gas consumption within the European Union. Further the company participates in the LNG terminal in Rotterdam, pipelines such as North Stream, BBL and the NEL and is full owner of the Gas storage in Zuidwending.
To estimate cost of equity, the Gasunie uses different scenarios based on the CAPM model. Scenarios differ in different inputs for the risk free rate and beta. Depending on the scenario, the risk free rate is either based on the two year weekly average or five year monthly average yield to maturity of (10-year) government bonds. The estimate for the beta is based on either two year weekly or five year monthly stock returns. Gasunie practitioners monitor the scenarios on an annual basis and if necessary, the WACC is updated. As the estimates for the risk free rate and beta are not only based on the most recent data (for instance, the risk free rate is not the spot yield), they do not represent current market circumstances but do represent (two to five year) trends in financial markets. Gasunie currently uses an ERP of 5% which is based on an ERP analysis of Dimson, Marsh and Staunton (2006, 2011), who estimate the ERP by comparing historical market returns with the return on government bonds.
5
III. Literature Review
This literature review starts with an overview of historical and survey ERPs and why Gasunie does not prefer these methodologies. Thereafter the implied ERP method is discussed. The end of this literature review introduces the model of Goedhart et al. (2002)
The most common method to estimate the ERP uses historical returns of common stocks. The ERP is calculated as the difference between return on stocks and the yield on government bonds. Ibbotson Associates ‘ annual reviews (classic yearbooks) are the most cited articles in literature. They examine various returns on stock- and bond portfolios since 1926. The use of Ibbotson’ ERP is widespread under practitioners, Welch (2000). The Duff and Phelps valuation handbook (2014) finds the arithmetic ERP for the U.S market, using the Ibbotson annual data from 1926 to 2013, to be 6.94%. The standard deviation of this estimate is 20.29%, which shows that annual stock market returns differ sharply trough years. Historical premiums for the U.S. generally range from 4% to 6% after correction for survivorship bias (For instance, Koller et al. 2010 find the U.S. historical ERP to range between 4.6% and 5.3%) The estimates differ due to the use of different time periods, mean calculation and data.
Historical stock returns are widely used to estimate the ERP and is based on the assumption that information surprises are cancelled out over a longer period and that the average return is therefore a good estimate for expected returns, Elton (1999). The main benefit of the use of historical returns is that it shows the actual return of stock markets over the yield on government bonds. Long term historical ERPs often include dramatic historical events (and corresponding effect on the ERP) which may happen again in the future. For that reason historical ERPs may be a good proxy for future ERPs (Duff and Phelps, 2014). Another benefit is the fact that data on both historical stock markets returns and government bonds are widely available, especially for the U.S. This increases the number of potential observations and results in a more accurate estimation of the historical ERP. The use of historical returns in estimating the ERP has benefits but is also broadly criticized in academic literature.
6 stable ERPs which is in line with Gasunie’ stability preferences. But the ERP seems to vary over time due to changes in both risk aversion and underling risk (operating risk and financial leverage) and these changes in ERP are not reflected in long term average ERPs based on annual stock returns. This is an argument to use more short term averages but this increases volatility of the ERP estimate, which is not preferred by the Gasunie.
ERPs can be calculated using arithmetic means. The arithmetic mean ERP is based on series of annual return of stock markets. Geometric mean ERPs use the compound returns of stock markets. If the assumption is made that annual returns are uncorrelated over time, the arithmetic ERP would be the best and most unbiased estimate of the ERP in the following year (Damodaran 2014). However, some research shows that long run market returns have significant negative correlations over time. (e.g. Ray and Kothari 1989). If positive stock returns are followed negative stock returns (and vice versa), than the average (arithmetic) return in this period is an upwards biased estimate of the actual return (Koller et al. 2010). Therefore, if the ERP is used for expected returns over a longer period, geometric averages generate better estimates (Koller et al. 2010). For that reason Koller et al. uses a mix of the arithmetic and geometric mean to estimate the ERP. If the period of forecast increases, more weight is put on the geometric mean.
Average stock markets return may also overstate the cost of equity, as Dichev (2007) shows that there exists a difference between stock markets return and the returns investors make in these stock markets. This is possibly caused by the fact that managers successfully time the market meaning that they raise capital in times when stock prices are temporary high and rebuy shares when prices are temporary low. The difference in return may show that historical ERPs are upwards biased. Historical ERPs also be biased due to survivorship bias. Survivorship bias refer to the fact that historical ERPs are not a good forecast for future ERP as these are largely based on stock market returns with strong historical returns (Koller et al.2010). Other stock markets with less strong returns are often not included in the sample. Therefore the survival of certain markets upwards bias the ERP estimate. Koller et al. therefore correct historical premiums with 0.8% to correct for survivorship bias. It seems difficult to estimate the exact ERP for the U.S. market. But estimating historical ERPs for European market can be even more difficult as in the past, many businesses were private, trading on stock markets was thin, and the same markets were often dominated by a few companies with a large market capitalization (Damodaran, 2014).
7 changes in expected ERPs as a result of changes in market circumstances. Gasunie therefore investigates the option to introduce another method to estimate the ERP.
A second method to estimate the ERP is the survey approach. This method estimates the ERP by surveying investors, academics or practitioners. Fernandez et al. (2013) survey thousands of academics, investors and practitioners in several countries and ask what they use as ERP in calculating the required return on equity for certain countries. The average (mean of observations) U.S. ERP used by academics, investors and practitioners is 5.6%, 5.0% and 5.5%, respectively. The standard deviation of these estimates range from 1.1% to 1.6%. Fernandez et al. (2013) do not explicitly mention an ERP for Europe but for Germany the ERPs are 5.7%, 5.5% 5.1%, respectively. Graham and Harvey (2014) periodically survey U.S. CFO’s of large corporations. They ask what these CFOs expect to be the 10 year S&P 500 return relative to a 10-year U.S. Treasury bond yield. Based on their results, they estimate the ERP to be 3.73% .
The ERP is an estimate for the level of risk compensation that investors ask to invest in the market portfolio. Surveying investors seems to be the right way to estimate the ERP. But according to Damodaran (2014) practitioners are reluctant to use these survey ERP estimates and mentions several reasons for this reluctance. First, sometimes ERP questions are clear but sometimes they are not and this can bias the estimate for the ERP.1 Second, outcomes are dependent on the kind of
investors surveyed. Surveying individual investors result in different ERPs when surveying institutional investors. It is unclear which group generates the most unbiased ERP estimate. Third, the outcomes of survey ERP seems to be dependent on stock price movements. ERP estimates peak after a bull market and are low after a bear market. Duff and Phelps (2014) state that this is contradictive as when an economy is in recession, reflected by an increase of economic uncertainty and relative lower stock returns, the ERP is more likely to be higher (for instance in December 2008). When there is a peak in the economy, reflected by increased economic certainty and relative high returns on stocks, the ERP is likely to be lower. For the same reason Ilmanen (2003) state that due to behavior biases, survey ERPs may be a better proxy for hoped returns than required returns. It seems that if survey ERPs have any predictive power, it is in the wrong direction (Damodaran, 2014). Survey ERPs are increasingly available but seem behavioral biased and therefore may not be a good proxy for required returns. As survey ERPs are potentially biased, Gasunie is reluctant to use survey ERPs. Additionally, on the advice of a consultancy firm, the Dutch regulator does not use the survey approach to determine the level of the ERP (see Brattle Group, 2012).
1 Damodaran (2014) for instance state that asking ‘’What will stocks do next year?’’ result in different ERPs
8 Implied ERP models are forward looking and are conceptually preferred as investors expected return should be reflected in the cost of equity. These models link current stock prices to expected dividends, earnings or equity cash flows. The typical starting point of an implied model is the Gordon (1962) dividend growth model. The discount rate that equals the present value of expected dividends to current share price is the estimated cost of equity. The past decades firms have moved from paying dividends towards share repurchases and therefore the Gordon model (1962) has been modified by many different authors. Implied models now focus on free cash flows to common equity (‘potential’ dividends). These free cash flows can either be paid out as dividends, used for share repurchases or be held as cash at the corporate level.
Damodaran (2014) discounts expected dividends and share repurchases of the S&P500, matches the present value with stock prices and subsequently derives an implied ERP on an annual basis. Damodaran’ implied ERPs range from 2% (1999) to 6.4% (2008) and has a value of 4.9% on January 1, 2014. Damoradan uses the total cash returned to stockholders in the past twelve months as a starting point and subsequently uses an expected earnings growth rate, based on analyst forecasts, to estimate cash returns in the following five years. Thereafter growth stabilizes at the risk free rate. Damodaran (2014) also examines various determinants of the implied ERPs. He finds that during period 1960 to 2014, interest rates have a slightly positive effect on the implied ERP. But Damodaran (2014) state that between 2008 and 2013 a strong opposite effect is visible. Authors such as Claus and Thomas (2001) and Gebhardt et al. (2001) use residual income models which links current share price with the book value of equity and the expected stream of abnormal earnings. Claus and Thomas(2001) and Gebhardt et al. (2001) both proxy expected abnormal earnings by taking analyst expected earnings and subsequently subtract a percentage of estimated (future) book value. The percentage is derived from the model and is a proxy for the cost of equity.Gebhardt et al. (2001) use their model to estimate implied cost of capital of individual U.S. firms but Claus and Thomas (2001) use their model to estimate annual U.S. ERPs. The estimates of Claus and Thomas (2001) range from 2.5% to 4% but is on average 3% for the period 1985 to 1998.
9
Implied models are very sensitive to assumptions. Analyst earnings growth is commonly used as proxy for ‘potential dividend’ growth in the first five years and thereafter growth is generally assumed to stabilize at either analyst forecast of long term growth (Gebhardt et al. 2001), risk free rate (Damodaran, 2014), GDP growth (Pastor et al. 2008) or long term average earnings growth (Fama and French, 2002). Easton (2007) discusses limitations of the use of book values and earnings forecast based on analyst expectations. First, analyst expectations are often upwards biased, especially for forecasts with a longer horizon. Too optimistic earnings forecasts results in a higher implied cost of capital and corresponding upwards biased ERPs. Claus and Thomas (2001) do not correct for this bias and therefore state that their ERP is estimate of 3% during the period 1985 to 1998 is probably too high. Second, book values are not always known at the valuation date. These are often estimated using earnings forecasts but these do not include one-time items. Book value is affected by these items and therefore can seriously bias the ERP estimate. Further, residual income models always assume market capitalizations to be higher than book value of equity. If this is not the case, residual income models generate confusing results.
Implementation of a residual income model at the Gasunie may be problematic as the company does not have full access to analyst earnings forecast (only for one year ahead). Even if Gasunie has full access, residual income models are complex to regular update as much data (earnings and book values) from many individual companies should be collected and aggregated.
Goedhart et al. (2002) use a relative simple methodology to estimate the implied ERP. Starting point of the model is the investment opportunity approach introduced by Miller and Modigliani (1961). Goedhart et al. (2002) also discount expected cash flows and link the presents value to stock prices. Subsequently, the cost of equity is derived. The derived cost of equity is therefore a function of known current share values and estimates of future cash flows. Goedhart et al. (2002) introduce the following formula.
𝑃
𝑡=
𝐸𝑡+1∗(1− 𝑔𝑡 𝑅𝑂𝐸𝑡) 𝑘𝑒,𝑡−𝑔𝑡 (1) Where,𝑃𝑡 = Price per share at time 𝑡
10 The nominator on the right hand side of the equation is used as proxy for annual ´dividendable cash flow´. It is the earnings minus the required investment to sustain long term growth rate. Equation (1) can be rewritten for the implied cost of equity :
𝑘
𝑒,𝑡=
(1− 𝑔𝑡 𝑅𝑂𝐸𝑡) 𝑃𝑡 𝐸𝑡+1+ 𝑔
𝑡 (2)Equation (2) shows that the implied cost of equity becomes a function of the P/E ratio of the company, long term earnings growth rate and long term ROE. All other things equal, an increase in the P/E ratio lowers the implied cost of capital and an increase in either long term growth or long term ROE results in a higher implied cost of capital. Goedhart et al. (2002) use equation (2) to estimate the market cost of equity and therefore estimate the variables on a market level.
To estimate market level P/E ratios, (index) aggregate P/E ratios2 can be used. Goedhart et al. (2002) state that some large companies (in terms of market capitalization) heavily weight on the S&P500 index and therefore the aggregate S&P500 P/E ratio is not representative for the U.S. economy as a whole. Goedhart et al. find that the aggregate P/E ratio and the median P/E ratio of the companies in the S&P500 index diverge sharply during the 1990s. (In 1999 almost 70% of the firms in the S&P500 had a lower P/E ratio than the index aggregate P/E ratio.) To prevent companies with a large market capitalizations bias the estimate of the implied ERP, Goedhart et al. (2002) use the median P/E ratio in the index as estimate for the U.S. market P/E ratio. Koller et al. (2010) discuss the use of both backward-looking P/E ratios and forward looking P/E ratios and suggests to use forward looking multiples (using forecast of profits) as this consistent with principles of valuation : the present value of future cash flows should match stock price valuations.
Equation (2) shows that the long term growth rate is a major driver of the market cost of equity. As stated, much evidence exist that analyst forecast, are upwards biased, especially forecast with a long term horizon. To prevent that long term analyst earnings forecast upwards bias the estimate for ERP, Goedhart et al. (2002) use a fixed real GDP growth of 3.5% plus an average inflation of the past five years prior to the year of analysis as proxy for expected earnings growth. GDP growth seems to be a good proxy as in the long term, the investor expected rate of return is dependent on the productivity of corporations in the real economy (Ibbotson and Chen, 2003). For that reason Pastor et al. (2008) use an average historical annual GDP growth up to the year of analysis as proxy for expected growth
2 In this paper aggregate P/E refer to the sum of market capitalization of all companies in an index to the sum
11 rate. Bernstein and Arnott (2003) investigate earnings growth in the past century and show that the ratio of U.S. corporate earnings to U.S. GDP has been remarkable stable. But question is whether this also holds for U.S. most successful companies. Claus and Thomas (2001) criticize the use of macro-economic growth such as GDP as it includes growth which is not generated by public traded companies (such as private companies). Further, public traded companies often generate overseas profits which are not included in domestic GDP. For that reason, the ERP estimates in Goedhart et al. (2002) may be biased.
The return on (book value) of equity (ROE) measures the ability of firms to generate earnings with the invested equity capital. It is calculated by taking the ratio of earnings per share to book value (of equity) per share. As with the P/E ratio, ROE can be calculated both on an (index) aggregate level and company level. But as with the aggregate P/E ratio, aggregate ROE can be distorted by some large companies that are able to make extraordinary high or low returns. Goedhart et al. (2002) use a fixed ROE of 13% per year. Koller et al. (2010) sets ROE at a fixed rate of 13.5% per year. Gebhardt et al. (2001) another forecast for the ROE. This ROE forecast is constructed by taking the ratio of expected earnings per share to current book value per share.
IV.
Research Methodology
Goedhart et al. (2002) use a fixed rate for both real GDP growth (3.5%) and the ROE (13%). As in reality both, growth and ROE vary over time, fixed estimates potentially bias the implied ERP estimate. This paper extents the model of Goedhart et al. (2002) by introducing other estimates for long term growth and ROE. GDP growth is often used as proxy for long term earnings growth but is also criticized (see above for a discussion). For that reason, besides using GDP growth, this paper uses growth rates based on historical earnings growth. (As suggested in Fama and French, 2002).
First, in line with Pastor et al. (2008) the average annual nominal GDP growth rate (from 1950 onwards) up to the quarter of analysis is taken as proxy for earnings growth. In this paper, this growth rate is referred as Long term GDP. Fama and French (2002) state that the best forecast for earnings growth is the historical average growth rate. Therefore, the second proxy for long term growth is the average annual earnings growth rate (from 1955 onwards) up to the quarter of analysis. 3 This growth rate is referred as Long term Earnings. A same growth rate is constructed for the ROE and is referred as Long term ROE.
3
12
The long term averages of both growth in GDP and earnings are used in literature but may overstate the expected values for several reasons. Long term average nominal GDP, for example, also includes the high inflation rates during the 1970’s and early 1980’s, which are not representative for inflation rates in the following decades. Additionally, the average real GDP growth rate before 1990 was substantially higher than in years thereafter. (Table A.1 shows that average growth rates between the period 1950-1990 and 1990-2014 significantly differ). Further, the average growth in earnings may overstate expected growth due to survival ship bias (Brown, Goetzman and Ross, 1995). A same argument can be used for long term ROE. A too high estimate for either growth or ROE results in an upwards biased estimate for the ERP. Averages based on more recent data may better reflect market expectations. Therefore, the second way of estimating growth and ROE is based on a five year4 moving averages of quarterly observations. The use of moving averages for both growth and ROE may generate less biased estimate, but, all other things equal, increases volatility of the ERP estimate. These estimates are referred as Recent GDP, Recent Earnings and Recent ROE respectively.
The use of time series regression models to make forecast is widely used in finance literature. According to Brooks (2008) time series forecasting is using a given value to predict its future value. O’brien (1988) for instance uses an auto-regressive model to investigate whether analyst earnings forecast have predictive power. Though analyst earnings forecast outperform the regression model on the short term (one to three quarters), O’Brien (1988) finds that for one year and onwards, the auto-regressive model outperforms analysts in forecasting earnings. Fama and French (2002) use auto-regressive models to forecast earnings growth and find that lagged growth have some predictive power for growth in the short term. Autoregressive models are widely used to forecast values and therefore this paper uses an AR(1) process to forecasts both growth and ROE.
Table A.2 presents the regression results based on annual observations5 for the year 2014. Nominal GDP and earnings growth in previous year, seem to be poor proxy for growth in the following year. To increase power of the regression models, both GDP and earnings growth are split in real growth and inflation. Inflation in the previous year seems to be a reasonable proxy for inflation in the subsequent year. As investors take into account both expected short- and long term growth rates, the AR(1) regressions are used to forecast growth up to three years ahead. (See Appendix B for the full derivation of this estimate). For each year the estimated values for real growth (either GDP or
4 A 5 year average is an arbitrary length, but is short enough to cancel out survivorship bias and not long
enough to be fully stable .
5
13 earnings) are add up to the forecast for inflation to arrive at the nominal expected growth.6 Forecasts based on regressions are referred as Forecast GDP, Forecast Earnings, Forecast ROE.
The final estimate for the ROE is in line with Gebhardt et al. (2001) who construct a forward looking ROE by taking the ratio of expected earnings in the next year to current book value per share. For each quarter in the analysis I construct this forward looking estimate. Subsequently the median value of these estimates serves as expected ROE for the market. Analyst earnings forecast serve as expected earnings in the following year, but notable is that these may somewhat upwards bias the ERP estimate. This ROE is referred as Analyst expected ROE. In line with Goedhart et al. (2002) the median (forward) P/E ratio in the index serves as proxy for the market P/E ratio.
This paper applies the six estimates for growth in earnings and the four estimates for the ROE in the model of Goedhart et al. (2002). Combining these variable estimates result in 6*4 = 24 different models to calculate the ERP. These models calculate the ERP on a quarterly basis between January 1995 and October 2014, which leads to 80 observations per model. The best models satisfy one requirement and meets preferences of the Gasunie.
The requirement is made that inputs of the implied ERP model should make sense economically. For instance, negative long term growth or negative return on equities do not make sense economically
requirement. The first preference of the Gasunie is that the estimate of the ERP it reflects current market circumstances. Second, the estimate of the ERP is reasonable stable for both management and accounting purposes (see section 2). Third, the preferred ERP model is a model which is consistent in the estimations methods of variables. For instance, Long term GDP is preferred to be combined with the Long term ROE and not with the Recent ROE. Fourth, the Gasunie prefers an ERP which is generally in line with historical averages. Pratt and Grabowski (2008) state that long term historical ERP generally lie in the range of 3.5% to 6%. Koller et al. (2010) state that 4.5% to 5.5% is an appropriate range for the ERP. Literature is not clear but seems to agree that 4% to 6% is an appropriate range for the ERP.
6 The regression models use data up to the year of forecast. For instance, to estimate GDP growth in 2002, the
14 Table 4.1
Overview models to calculate ERP.
This table presents an overview of the different ERP models. The 24 models all generate 80 ERPs. Those models which are consistent in the way variables are estimated are preferred.
Variable estimate Long term ROE Recent ROE Analyst expected ROE Forecast ROE
Long term GDP 1 2 3 4
Recent GDP 5 6 7 8
Forecast GDP 9 10 11 12
Long term Earnings 13 14 15 16
Recent Earnings 17 18 19 20
Forecast Earnings 21 22 23 24
The statistical testing focuses on the impact of different estimates of variables on the ERP. The main focus is the impact on volatility. But besides testing the effect on the volatility, other statistical test analyse whether the estimates of variable have significant different economic consequences for the Gasunie. To test for differences (in terms of volatility and economic consequences), a top-down method is used. The first statistical tests analyse whether GDP based models (models based on GDP growth) generate significant different ERPs than earnings based models (models based on earnings growth), irrespective whether these models are based on a long term, recent or forecast growth. Then differences between the long term, recent and forecast growth models, irrespective of GDP and earnings growth is the center of attention. Thereupon, a more detailed analysis on the lowest level is performed. These tests focus on the effect of the long term, recent and forecast method between GDP and Earnings based models (for instance differences between the Long term GDP and Long term earnings). Thereafter, the same statistical tests analyse the effect of the four different ROEs on the ERP.
To analyse differences, the twenty-four models are split into independent ERP groups. For instance, to test whether growth based on GDP generates significant different ERPs than using growth based on historical earnings, the twenty-four models are split up in two groups consisting of twelve models7 and corresponding 960 observations. These groups are referred as GDP group and earnings group. To test whether the use of long term, recent or forecast growth generates significant different ERPs, the twenty-four models are divided in three groups consisting out of eight models per group and corresponding 640 observations etc..8 The independent groups allow statistical tests to analyse the effect of different estimates of variables on the ERP. A same procedure is followed to
7 In this case, models one till twelve form one group and models thirteen till twenty-four will form one group 8 In this case, group one consist out of models one till four and thirteen till sixteen, group two consist out of
15 test the effect of the four different ROEs on the ERP. Table A.3 presents the composition per group regarding the underlying models.
Then based on the ERP groups, four different statistical tests are performed. First, the Bartlett and Brown-Forsythe tests test for equality of variances between two or more groups. The Bartlett test is a parametric test and therefore assumes that the ERP groups have a normal distribution. To prevent that non-normality cause to bias the results and corresponding interpretation and recommendation, the non-parametric Brown-Forsyth tests is performed. This is a non-parametric test and thus does not require a specific distribution of the ERP groups. The Anova F-test and the Kruskall-Wallis test are used to test whether the different estimates of variables have significant different economic consequences for the Gasunie. As with the Bartlett test, the Anova F-test assumes ERP groups to be normal distributed but also requires equal variances of the different ERP groups. The Anova is a statistical method to test for differences in mean between two or more groups. Again, to prevent that non-normality causes to bias the results, the non-parametric Kruskall-Wallis method tests whether the ERP groups originate from a same distribution. The Anova F-test and Kruskall-Wallis test are based on Moore et al. (2008) The Bartlett and Brown-Forsythe tests are used as in Agung (2011)
On request of the Gasunie, the Pearson’s correlation test is used to test whether the twenty-four ERP models have a significant correlation with the proxy for the risk free rate. (10-year yield on U.S. government bonds) The Bartlett test and Brown-Forsythe tests, presented above, test the following (most important) hypothesis:
Variance hypotheses: 𝐇0: 𝜎21= 𝜎22= . . . = 𝜎2𝐼 𝐇1: not all of the 𝜎2𝑖 are equal Where
𝜎2
𝑖 = Variance of ERP model 𝑖
Rejecting the variances null hypothesis, using both the Bartlett and Brown-Forsyth tests, means that at least one group has significant more volatile ERPs. The Anova F-test, Kruskall-Wallis test, and Pearson’s correlation tests, test the following three hypotheses:
16 Where,
𝜇𝑖 = Mean ERP of model 𝑖 𝑑𝑖 = Distribution of ERP model 𝑖
𝜎2
𝑖 = Variance of ERP model 𝑖
𝜌𝑖,𝑗 = Correlation coefficient between ERP model 𝑖 and the risk free rate 𝑗
Rejecting the mean null hypothesis, using the Anova F-test, means that at least one of the ERP groups has a significant different mean ERP over time. Rejecting the distribution null hypothesis, using the Kruskall-Wallis test, means that at least one of the groups has a significant different distribution implying that ERPs in one or more groups are systemically higher than in other a group(s). Differences in mean or distribution indicate that the use of variables underlying the groups has different economic consequences for the Gasunie. The correlation null hypothesis is rejected when there exists significant correlation between the ERP model and risk free rate. The results of the statistical tests are used in the recommendations regarding the estimation methods of variables.
V.
Data and Descriptive Statistics
All the data used in this master thesis is retrieved from the Bloomberg terminal at the Gasunie. The S&P500 index serves as representative for the market portfolio. The S&P500 (ticker SPX INDEX) consist out of 500 companies which are listed on the NYSE or the NASDAQ and have both, a large market capitalization and high stock liquidity. As companies enter and leave the S&P500, each quarter, the most recent constituents list of S&P500 is used to prevent bias in the ERP estimate. The use of the S&P500 index as proxy for the market portfolio is in line with, Goedhart et al. (2002), Damodaran (2014) and Fama and French (2002).
Bloomberg provides S&P500 data on both the aggregate9 and company level. To construct the growth estimates, aggregate S&P500 realized earnings are used. I further use realized and expected earnings, book values per share and forward P/E ratios on the company level. The data regarding the expected earnings requires some additional explanation. Bloomberg collects earnings forecast provided by analyst. These analysts commonly provide earnings forecast for full fiscal years. In my analysis I take into account expected earnings for the coming 12 months, not for calendar or fiscal years. Unfortunately expected earnings for the coming 12 months are not provided by analyst forecasts. To solve this problem Bloomberg provides so-called 12 month blended earnings forecast. These blended earnings forecasts are calculated using a weighted average of earnings forecast for current and next fiscal year. The days left in current fiscal year determine the weights on both fiscal
9
17 years. Therefore, as the fiscal years moves forward, more weight is put on next fiscal year. Bloomberg also uses these 12 month blended earnings forecast to calculate the forward P/E ratios. The forward P/E ratios used in the analysis are directly downloaded from Bloomberg.
Bloomberg provides company level data of the S&P500, such as book values, realized/expected earnings (on a per share level) and forward P/E ratios from 1990 onwards. Therefore the ROE estimates are based on quarterly observations from 1990 onwards. S&P500 aggregate book value per share is also available from 1990 but data regarding aggregate S&P500 realized earnings is available from 1955 onwards. As most data about the S&P500 is available from 1990 onwards and the fact that I take into account five year averages, the performed analysis starts in 1995. Table 5.1 presents an overview of the S&P500 data.
Table 5.1
Overview of S&P500 data
This table provides an overview of the data used in estimating the different variables. Bloomberg provides company data from 1990 onwards. Aggregate data regarding earnings per share is available from 1955 onwards. The ticker to retrieve aggregate level data is: SPX INDEX. All variables are downloaded on a quarterly basis. Mnemonics- or field code can be used to find the exact variable. The field code refers to the variable code in Bloomberg. Period refers to the period for which the data is downloaded.
Level of
observation Variable mnemonic Field code period
Aggregate Earnings per share TRAIL_12_EPS RR906 1955-2014 Company Earnings per share TRAIL_12_EPS RR906 1990-2014 Company Expected earnings per share BEST_EPS BE008 1995-2014 Company Book value per share BOOK_VAL_PER_SHARE RR020 1990-2014 Company Forward P/E ratio BEST_PE_RATIO BE051 1995-2014
Data regarding GDP and inflation is gathered for the period 1950-2014. In line with studies such as Goedhart et al. (2002) and Claus and Thomas (2001), the spot (most recent) yield to maturity on 10-year U.S. government bonds serves as proxy for risk free rate. The use of bonds with a maturity of 10 years is in line with current practice of Gasunie. Table 5.2 provides an overview of the more broad economic data.
18 Table 5.2
Overview of U.S. (Macro) Economic data
This table provides an overview of macro-economic data. Data regarding annual GDP and the CPI inflation rate is retrieved for the period 1950-2014. Data regarding the YTM on U.S. government bonds is retrieved on a quarterly basis between 1995 and 2014. For all variables the same mnemonics and field code is used as this provides the latest value available for a certain moment in time in Bloomberg.
Ticker variable mnemonics field code period
GDP CUR$ Index Nominal GDP PX_LAST PR005 1950-2014
CPURNSA Index CPI inflation PX_LAST PR005 1950-2014
GTDEM10Y Govt YTM 10-year
government bond PX_LAST PR005 1995-2014
Table 5.3 presents the descriptive statistics regarding the estimates of variables. The means growth estimates range from 4.54% to 7.35%. Most of the estimates are reasonable stable except for the Recent earnings growth. This growth estimate is highly volatile with a maximum value of 18.32% and a minimum value of -2.57%. Such long term growth rates are unrealistic and are not supported by long term historical data. Problems arise when plugging these high or low growth rate in the formula presented by Goedhart et al. (2002). Using such high or low growth rates would generate negative payout ratios or payout ratios that are larger than one. Both are in economic terms unrealistic, especially in the long run. The minimum payout ratio of those models not using the Recent earnings growth is 0.5910 (results not presented). The mean ROE estimates range from 13% to 17%.
Table 5.3
Descriptive statistics per variable estimate.
This table presents the descriptive statistics per variable estimate. The descriptive statistics are based on 80 quarterly observations between January 1995 and October 2014.
Variable Estimate Mean Median Max Min Std.Dev.
YTM 10-year government bonds 4.38% 4.36% 7.82% 1.62% 1.48%
median forward P/E ratio 15.39 15.30 19.45 11.40 1.75
Average Long term GDP 6.85% 6.87% 7.25% 6.37% 0.26%
Recent GDP 4.54% 4.97% 5.89% 2.20% 1.20%
Forecast GDP 6.18% 6.20% 6.94% 4.91% 0.58%
Long term Earnings 6.17% 6.20% 6.60% 5.44% 0.27%
Recent Earnings 7.35% 6.18% 18.32% -2.57% 5.55%
Forecast Earnings 4.95% 4.90% 5.89% 1.39% 1.03%
Long term ROE 13.64% 13.78% 14.13% 12.34% 0.44%
recent ROE 14.13% 14.16% 15.80% 12.22% 0.94%
Analyst expected ROE 17.78% 17.99% 21.00% 13.82% 1.47%
Forecast ROE 13.75% 13.76% 15.33% 12.10% 0.94%
10 Goedhart et al.(2002) cap the reinvestment rate at 70%. The minimum payout ratio thus has a maximum
19 Figure 5.1 to 5.3 show the different variable estimates through time. Figure 5.1 presents the three growth estimates based on U.S. GDP data. As expected, the Recent GDP growth is lower than the Long term GDP Growth. At most recent data points, Long term GDP, Recent GDP and Forecast GDP have values of 6.4%, 3.6% and 5.4%, respectively. Figure 5.2 presents the three growth estimates based on the S&P500 earnings. The Recent earnings growth is highly volatile and has high peaks and valleys. At most recent data point the Long term Earnings, Recent earnings and Forecast earnings have values of 6.2%, 14.4% and 4.8%, respectively. Figure 5.3 presents the four estimates for the ROE. The Analyst expected estimate is, except for the period 2009-2010 higher than the other three estimates. At the most recent data point, Long term, Recent, Forecast, and Analyst expected ROE have values 13.9%, 13.6%, 13.9 and 18.8%, respectively.
Figure 5.1
GDP growth estimates through time.
This figure presents the three growth rates based on U.S GDP data. The vertical axis presents the level of estimated growth, the horizontal axis denotes the time period.
Figure 5.2
S&P500 Earnings growth estimates through time
This figure presents the three growth rates based on S&P500 earnings. The vertical axis presents the level of estimated growth, the horizontal axis denotes the time period.
2% 3% 4% 5% 6% 7% 8% 19 95 19 96 19 97 19 98 19 99 20 00 20 01 20 02 20 03 20 04 20 05 20 06 20 07 20 08 20 09 20 10 20 11 20 12 20 13 20 14
Long term GDP Recent GDP Forecast GDP
-3% 1% 5% 9% 13% 17% 19 95 19 96 19 97 19 98 19 99 20 00 20 01 20 02 20 03 20 04 20 05 20 06 20 07 20 08 20 09 20 10 20 11 20 12 20 13 20 14
20 Figure 5.3
Return on Equity estimates through time
This figure presents the four estimates for the Return on Equity. The vertical axis presents the estimated Return on Equity, the horizontal axis denotes the time period.
VI.
Results and Recommendations
This section first presents the ERP outcomes for the different ERP groups. Thereafter, the results of the statistical tests are presented and recommendations regarding estimates of variable are discussed.
Table 6.1 presents the descriptive statistics regarding the different ERP growth groups. The groups all generate mean and median ERPs in the range of 4% to 6%. However, the minimum and maximum ERP for all groups are outside this range. The minimum and maximum ERP are 0.57% and 13.51%, respectively. Jarque-Bera values11 indicate that implied ERPs are not normally distributed and therefore results regarding the Bartlett and Anova F-tests tests should be interpret with caution. Descriptive statistics regarding the groups based on the six growth and four ROE estimates can be found in table A.4. Table A.5 presents the descriptive statistics for the 24 ERP models.
11
Jarque Bera tests the null hypothesis whether the sample has a normal distribution. 11% 13% 15% 17% 19% 21% 23% 19 95 19 96 19 97 19 98 19 99 20 00 20 01 20 02 20 03 20 04 20 05 20 06 20 07 20 08 20 09 20 10 20 11 20 12 20 13 20 14
21 Table 6.1
Descriptive statistics ERP groups.
This table presents the descriptive statistics for the ERP groups. The different ERP groups consist out of several ERP models. Descriptive statistics are based on all the observations within the specific group.
ERP Group Mean Median Max Min Std.
Dev. Skewness Kurtosis
Jarque-Bera GDP 5.43% 5.28% 10.13% 2.04% 1.60% 0.41 2.69 30.55** Earnings 5.65% 5.30% 13.51% 0.57% 2.21% 0.6 3.25 59.24** Long term 5.79% 5.57% 10.13% 2.19% 1.67% 0.29 2.44 17.46** Recent 5.57% 5.00% 13.51% 0.57% 2.32% 0.83 3.55 82.35** Forecast 5.28% 5.19% 9.64% 1.92% 1.70% 0.28 2.54 13.94**
*Rejected at the 5% level; **Rejected at the 1% level
Figure 6.1 presents the mean ERP over time regarding the GDP and earnings groups. The ERPs generated by both groups have an upwards trend implying risk compensation for investing in the market portfolio increased over time. During the period from 1995 to 2000 the ERP ranges from 3% to 4% for the GDP group, which is in line with Goedhart et al. (2002) who find the ERP to be 3.6% in this period. Claus and Thomas find an average ERP of 3.3% in the period 1995 to 1998. During the period 2002 to 2007, the implied ERP for both GDP- and earnings group is stable and ranging between 4% and 6%. As suggested by KPMG NL, the implied ERP rises in 2008, reaching values of more than 8% as a result of the financial crisis. On January 1, 2014, the mean ERP for the GDP- and earnings groups are 5.8% and 6.8%, respectively. On the same date, Damodaran (2014) finds the ERP to be lower at 5.0%. At most recent data point the mean ERP for the GDP- and Earnings groups are 6.8% and 8.6% respectively. Figure 6.2 presents the mean ERP per quarter regarding the long term, recent and forecast groups. In line with the results found in table 6.1, the recent group is more volatile than both the long term and forecast group. At the most recent data point, the ERPs for the long term, recent and forecast groups are 7.5%, 6.8%, 9.0%, respectively.
Figure 6.1
Mean ERPs for the GDP and Earnings groups
This figure presents the mean ERP (per quarter) for the GDP and Earnings groups. Per quarter, the average of twelve ERP models is taken. The vertical axis presents level ERP, the horizontal axis denotes the time period.
0% 2% 4% 6% 8% 10% 12% 19 95 19 96 19 97 19 98 19 99 20 00 20 01 20 02 20 03 20 04 20 05 20 06 20 07 20 08 20 09 20 10 20 11 20 12 20 13 20 14
22 Figure 6.2
Mean ERPs for the Long term, Recent and Forecast groups
This figure presents the mean ERP (per quarter) for the Long term, Recent and Forecast group. Per quarter, the average of eight models is taken. The vertical axis presents the height of the ERP, the horizontal axis denotes the time period.
Table 6.2 presents the outcomes of the statistical tests performed on the GDP and Earnings groups, and the Long term, Recent and Forecast groups. As the ERP groups do not have a normal distribution, I focus on the non-parametric tests. Regarding differences in variance between the GDP and Earnings group, results are clear. Both variance tests show significant differences at the 1% level and therefore the variance null hypothesis is rejected. This implies that ERPs based on GDP growth are on average more stable than ERPs based on earnings growth. The Kruskall-Wallis test shows no significant results and therefore the distribution null hypothesis cannot be rejected.
Table 6.2
ERP Performance of the growth groups.
This table presents the outcomes of the statistical tests between different ERP growth groups. The X-square, F-value and H-value represent the test statistics of the Bartlett test, Brown-Forsythe- or Anova F test and Kruskall-Wallis test. The ‘Mean Abs. Median Diff.’’ reflects the mean absolute deviation from the median ERP in the specific group. Regarding the Kruskall-Wallis test, the number and percentage of observations above overall median are presented in table A.7.
Bartlett test Brown-Forsythe test Anova test Kruskall-Wallis test
Std.Dev X2 value Mean Abs.
Median Diff. F-value Mean F-value
Media n H-value GDP 1.60% 98.08** 1.28% 65.28** 5.43% 6.24* 5.28% 1.52 Earnings 2.21% 1.73% 5.65% 5.30% Long term 1.67% 32.22** 1.35% 20.59** 5.79% 11.42** 5.57% 28.41** Recent 2.32% 1.75% 5.57% 5.00% Forecast 1.70% 1.37% 5.28% 5.19%
*Rejected at the 5% level; **Rejected at the 1% level
Statistical tests regarding differences between the Long term, Recent and Forecast group show that at least one group has a higher variance, mean and distribution, implying that all three
0% 2% 4% 6% 8% 10% 12% 19 95 19 96 19 97 19 98 19 99 20 00 20 01 20 02 20 03 20 04 20 05 20 06 20 07 20 08 20 09 20 10 20 11 20 12 20 13 20 14
23
accompanying null hypotheses are rejected. The Recent group generates the ERPs with the highest variance and thus is the least stable. No statistical differences in variance exist between the Long term and Forecast group (see table A.6).
Based on the results found in table 6.2, one would expect that the Long term GDP and Forecast GDP generate the most stable ERPs. However, results in table 6.3 show that results in table 6.2 should be interpret with caution. In this table, The Long term, Recent and Forecasts groups are all split up in a GDP and an Earnings group. The results of the statistical tests show that the high volatile ERPs in the Recent group (table 6.2) are a result of high volatile ERPs generated by the Recent earnings estimate. The Recent GDP however generates the most stable ERPs which contradicts the expectations from table 6.2.
The Recent GDP generate more stable ERPs than the Recent earnings, but also the Forecast GDP seems to generate more stable ERPs than its earnings based equivalent. Regarding the Forecast method, the Brown-Forsythe test does not significant results (though its test-statistic is high12) but the Bartlett test does. No statistical evidence exist that the Long term GDP generate more stable ERPs than the Long term earnings but it does have a lower standard deviation and lower absolute deviation from its median value. Overall, the GDP estimates seem to generate more stable ERPs and therefore, from a stability perspective, Gasunie should use a growth rate based on GDP to estimate the ERP (either Long term, Recent or Forecast).
Kruskall-Wallis and Anova F test show significant results for all the three estimation methods of variables and therefore reject the distribution and mean hypotheses. The use of a Long term earnings or Forecast earnings result in significant lower ERPs than the use of their GDP based equivalent. The Recent earnings growth however generates higher ERPs than the Recent GDP growth. The use of either GDP or earnings based growth thus has significant different economic consequences for the Gasunie.
12
24
Table 6.3
ERP performance within timing groups
This table presents the outcomes of different statistical tests within the different timing groups. The X-square, F-value and H-value represent the test statistics of the Bartlett test, Brown-Forsythe- and Anova F test and Kruskall-Wallis test. The ‘Mean Abs. Median Diff.’’ reflects the mean absolute deviation from the median value. Regarding the Kruskall-Wallis test, the number and percentage of observations above overall median are presented in table A.9
Table 6.4 presents the results regarding differences between the ROE groups. Both the Brown-Forsythe and the Bartlett test do not show a significant difference in variance between the four ROE estimates. Therefore, there is not statistical evidence that one of the four ROEs generate more stable ERPs. The Kruskall-Wallis and Anova F tests shows that at least one of the four ROE estimate generate significantly higher ERPs and therefore reject the accompanying distribution and mean hypotheses . Table 6.4 also shows that there exist no differences in mean or distribution between the groups based on Long term, Recent of Forecast ROE. For that reason the conclusion is made that the Analyst expected ROE generate significant higher ERPs. These higher ERPs are in line with economic arguments, the ROE based on Analyst forecast is substantial higher and therefore generate a higher payout ratio, implying that more money is returned to shareholders. This increases compensation for risk and thus results in a higher ERP.
Std.Dev X2 value Median Diff.Mean Abs. F-value Mean F-value Median H-value
Long term GDP 1.61% 1.31% 5.97% 179
Long term Earnings 1.71% 1.38% 5.61% 141
Recent GDP 1.35% 1.04% 4.73% 119
Recent Earnings 2.75% 2.25% 6.41% 201
Forecast GDP 1.57% 1.26% 5.61% 192
Forecast Earnings 1.76% 1.40% 4.94% 128
Barlett test Brown-Forsythe test Anova test Kruskall-Wallis test
*Rejected at the 5% level; **Rejected at the 1% level
25
Table 6.4
ERP performance ROE groups
This table presents the outcomes of the statistical tests between different ROE groups. The X-square, F-value and H-value represent the test statistics of the Bartlett test, Brown-Forsythe- and Anova F test and Kruskall-Wallis test. The ‘Mean Abs. Median Diff.’’ reflects the mean absolute deviation from the median value. Regarding the Kruskall-Wallis test, the number and percentage of observations above overall median are presented in table A.10.
The results in table 6.4 show that variances in ERP do not significantly differ due to the use of different ROE estimates. Therefore, none of the ROE estimates is preferred above the other three. Based on the stability preference, the models based on GDP growth are preferred above earnings based models. As the preferred ERP models are consistent in the way variables are estimated, the preferred Long term, Recent and Forecast GDP growth estimates should match their ROE equivalent. (Long term GDP with Long term ROE etc...) This implies that based models one, six and twelve are preferred (see table 4.1).
The Gasunie requested to examine whether there exist significant correlation between the implied ERP and the risk free rate. Table 6.5 presents the outcomes of the Pearson correlations test. The results are striking. Except for models using Recent earnings growth, all ERP models based show significant negative correlations with the risk free rate and thus the Pearson correlation test rejects the correlation null hypothesis for most models. Figure A.1 shows that the market cost of equity has been remarkable stable over the time period 1995 to 2014. This is in line with the results of Koller et al. (2010). How is a stable market cost of equity possible when the risk free rate declines from 7.1% to 2.3% in this time period? As the risk free rate has a strong negative correlation with the ERP, a decrease (increase) in the risk free rate is compensated by an increase (decrease) in ERP.
Group
Std.Dev X2- value Median Diff.Mean Abs. F-value Mean F-value Median H-value
Long term 1.87% 1.48% 5.34% 5.07% Recent 1.91% 1.51% 5.43% 5.16% Analyst expected 1.98% 1.49% 6.03% 5.72% Forecast 1.89% 1.48% 5.37% 5.12% Long term 1.87% 1.48% 5.34% 5.07% Recent 1.91% 1.51% 5.43% 5.16% Forecast 1.89% 1.48% 5.37% 5.12% 0.25 0.12 0.28 0.5
*Rejected at the 5% level; **Rejected at the 1% level
Barlett test Brown-Forsythe test Anova test Kruskall-Wallis test
26 Table 6.5
Pearson correlation coefficients regarding of Equity Risk Premium and risk free rate.
This presents the Pearson correlation coefficients regarding the 24 models used to generate ERPs. The models correspond with the models presented in table 4.1. The value between the brackets represents the test-statistic of the test-statistical test.
Variable estimate Long term ROE Recent ROE Analyst expected ROE Forecast ROE
Long term GDP -0.98 -0.96 -0.95 -0.97 (39.17)** (32.11)** (26.23)** (32.75)** Recent GDP -0.91 -0.89 -0.85 -0.89 (19.21)** (17.26)** (14.17)** (17.31)** Forecast GDP -0.96 -0.95 -0.91 -0.95 (30.50)** (27.76)** (19.99)** (25.95)** Long term Earnings -0.98 -0.97 -0.95 -0.97 (40.60)** (25.29)** (27.47)** (32.96)** Recent Earnings -0.14 -0.12 0.01 -0.13 -1.29 -1.09 -0.12 -1.19 Forecast earnings -0.94 -0.93 -0.89 -0.93 (23.47)** (22.69)** (17.24)** (21.70)**
*Rejected at the 5% level; **Rejected at the 1% level
Recommendations regarding the estimate of variables are based on the selection criteria presented in section 4. The implied ERP model of Goedhart et al. (2002) reflects current market circumstances and therefore satisfies the first preference of the Gasunie. The other requirement and preferences are as follows, first, the requirement is made that the variable inputs make sense economically. Second, the Gasunie prefers a model that generates reasonable stable ERPs. Third, the preferred model is consistent in the estimation method of input variables. Fourth, Gasunie further prefers an ERP that is generally in line with historical averages ERPs, which are assumed to be in the range of 4% to 6%. This requirement and preferences are discussed in order.
27 One of the main preferences of Gasunie is a reasonable stable ERP. Models based on GDP growth (Long term, Recent and Forecast GDP) generate more stable ERPs than then S&P500 earnings based equivalent and are therefore preferred. The Bartlett and Brown-Forsythe show that the difference in variance is (partly) significant for both the Recent and Forecast method. The Long term GDP generates more stable ERPs than the Long term Earnings but this difference in variance is not significant. The statistical tests show that the four ROE estimates do not have a significantly different effect on the stability of the ERP and therefore, none of the ROEs is preferred above the others.
The preferred model is consistent in the estimations method of input variables. As none of the ROE estimates result in more stable ERPs, the Long term, Recent and Forecast GDP should match their corresponding ROE estimate. This implies that the Long term GDP is combined with the Long term ROE, the Recent GDP is combined with the Recent ROE and the Forecast GDP is combined with the Forecast ROE. Therefore models one, six and twelve are preferred.
Figure 6.3 presents the minimum and maximum ERP between 1995 and 2014 generated by model one, six or twelve. The average ERP of all three models between 1995 and 2000 is 3.6% which is exactly in line with the estimate of Goedhart et al. (2002) for the period 1990 to 2000. In comparison to Damodaran (2014) models one, six and twelve generate higher implied ERPs. Figure 6 shows that until 2009 the difference between the minimum and maximum ERP is generally 1%. After 2009 this increases up to 2%. At most recent observation, the minimum and maximum of these models is 5.8% and 7.4%, respectively.
Figure 6.3 Minimum and maximum ERP of models one, six and twelve
This table presents the minimum and maximum observations of the models one, six and twelve. The figure shows that the gap between the minimum and maximum observations increases over time.
Model six generates the most stable ERPs. This model uses the Recent GDP and Recent ROE estimates. However, an average of five year is in literature not commonly accepted as estimate for
28 long term growth or ROE. Due to business cycles, the recent GDP estimate may understate (overstate) the expected growth and thus understate (overstate) the ERP. The use of a long term average GDP growth is more accepted and is in line with Pastor et al. (2008). However a long term average GDP growth rate may overstate the expected growth rate as a result of both high real growth and inflations rates. This may upwards bias the ERP estimate. The Forecast GDP estimate may be the most accurate estimate as it uses both short and long term GDP growth rates which may be the best reflection of stock market expected growth. But the regression model possibly generates poor proxy for growth as it does not have much power. For these reasons the recommendations is made to use all three models.
The Gasunie prefers an ERP estimate between 4% and 6% which are common estimates based on long term historical average ERPs. Though the models one, six and twelve all have a mean and median ERP within this range, many of the observations are outside this range. The model with the most ERP observations within this range is model six with 41 of the 80 observations. (See table A.11). Therefore the conclusion is made that none of the three models complies with this final preference.
Though implied models do reflect current market conditions, they are more volatile than historical ERPs. The recommended models do not comply with Gasunie preference to generate ERPs which are in line historical ERPs. Therefore the conclusion is made that the Implied ERP model of Goedhart et al. (2002) cannot be directly implemented within Gasunie WACC calculations. However this does not imply that the implied ERP method is useless.
Duff and Phelps (2014) suggest using both the historical and implied method to estimate the ERP. First, a reasonable range for historical ERP should be established (for instance 4% to 6%). Thereafter, Duff and Phelps suggest using the implied method to estimate where the ‘true’ ERP is likely at. In case when the implied ERP is at higher levels, the top of the historical range is used as proxy for the ERP. If the ERP is in lower levels, the bottom of the historical range is used as proxy for the ERP. As models one, six and twelve suggest that the implied ERP is higher than the top of the historical ERP range, Gasunie should currently use an ERP of 6%. The use of an ERP of 6% is in line with KPMG NL.
VII.
Conclusion
29 at the Gasunie. As it is an implied model, the model is able to reflect current market conditions and to justify stock market prices. Based on U.S. GDP and S&P500 data, six different estimates for market earnings growth and four different estimates for market return on equity are introduced. Combining these estimates result in 24 different ERPs models. Using a top down methodology, this paper uses parametric and non-parametric tests to examine whether the use of these different estimates of variables result in ERPs with different variances. Other statistical tests examine whether the use of these estimates have different economic consequences for the Gasunie. Based on the outcomes of these statistical tests, economic arguments and Gasunie preferences, recommendations are made whether and how the Gasunie should use the Goedhart et al. (2002) model.
The results show that for all three estimations methods of growth (Long term average, a five-year average, AR(1) regression), GDP growth generally generate more stable ERP than their earnings based equivalent. For the five-year average and AR(1) regression method this difference in volatility is (partly) significant. Though the long term average GDP growth has a lower variance than the long term average earnings growth, this difference in volatility is not significant. The most stable ERPs are generated by the five-year average GDP growth. The five-year average earnings growth generates the most volatile ERPs. The statistical tests show that the four ROE estimates do not have a significantly different effect on the stability of the ERP. Further do both, parametric and non-parametric tests show that GDP based growth generate significant different ERPs than their earnings based equivalent. The use of either GDP or earnings based growth thus has different economic consequences for the Gasunie. Further has the use of an analyst expected ROE an upwards effect on the estimate for the ERP.
30 Unfortunately, these models do not meet the preference of the Gasunie to be generally in line with the historical ERP. The three models often generate ERPs outside the preferred range of 4% to 6%. For that reason Gasunie cannot implement these models directly in their WACC methodology. This paper therefore recommends using both the historical and implied method to estimate the ERP. Gasunie can use the three recommended models to estimate whether the ERP is in the upper or lower range of the historical ERP estimate. At most recent observations, the recommended models estimate the implied ERP to be in the range of 5.8% to 7.4%. This implies that ERP is currently in the upper side of the historical range and thus Gasunie should currently use an ERP of 6%.
This paper has also some limitations. First, this paper estimates the implied ERP for the S&P500 index. Though the S&P500 is a common proxy for the market portfolio, ERP estimates of other indexes may be different. However, this leads possibilities for further research. Second, the implied model of Goedhart et al. (2002) is sensitive for assumptions. Though the growth and ROE are estimated in several ways, other parties can confront the Gasunie with different estimates for these variables. The use of different market variables might result in different ERP estimates.
References
Agung, I. Gusti Ngurah. Cross Section and Experimental Data Analysis Using EViews. John Wiley & Sons, 2011.
Baker, Malcolm, and Jeffrey Wurgler. "Investor sentiment and the cross‐section of stock returns." The
Journal of Finance 61.4 (2006): 1645-1680.
Ball, Ray, and S. P. Kothari. "Nonstationary expected returns: Implications for tests of market efficiency and serial correlation in returns." Journal of Financial Economics 25.1 (1989): 51-74.
Bernstein, William J., and Robert D. Arnott. "Earnings growth: The two percent dilution." Financial
Analysts Journal (2003): 47-55.
Brattle Group, The. Calculating the Equity Risk Premium and the Risk-free Rate. (2012)
Brooks, Chris. Introductory econometrics for finance. Cambridge university press, 2008.
Brown, Stephen J., William N. Goetzmann, and Stephen A. Ross. "Survival."The Journal of
Finance 50.3 (1995): 853-873.
Claus, James, and Jacob Thomas. "Equity premia as low as three percent? Evidence from analysts' earnings forecasts for domestic and international stock markets." The Journal of Finance 56.5 (2001): 1629-1666.
