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Diversification Benefits in Portfolios Using the Discounted Free Cash
Flow Model, Intrinsic Value and Value Investing Principles an
Empirical Research
Abstract
This paper uses multiple portfolios with different criteria for stocks and tries to find whether diversification has benefits in value investing. The results of this study suggests that using the intrinsic value to select stocks reduces risks on small portfolios. However, these benefits diminish when diversifying the portfolios. Furthermore, using the intrinsic value and the quality factor of ten consecutive years of positive free cash flow to select stocks for portfolio reduces the risk of that portfolio at the expense of return.
Supervisor: dr. J.J. Bosma Author: Joost Boschman Student number: S2407515 Rijksuniversiteit Groningen
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1. Introduction
Value investing is a popular investing method pioneered by Benjamin Graham and with many success stories such as Warren Buffett. Although some research is done about value investing methods there is little research about the free cash flow as the main component of the model. Furthermore, the possible benefits of diversification in value investing is also a subject that is not much researched. Classic financial theory suggests that diversification is always beneficial. However, value investors claim that the risk of their portfolios are reduced by carefully selecting stocks. This study aims to compare and evaluate the principles and methods of value investing in light of methodologies closer related to the free cash flow model. Furthermore, this study compares and evaluates the impact of portfolio sizes on portfolios when using stock criteria for portfolios using value investing principles. Value investing in its core is to buy cheap or reasonable priced stocks of high quality firms. It capitalizes on mispriced stocks in order to make reliable profits. There are two different views on stock prices on the market. One take on stock prices is that there are no mispriced stocks and that value investors are getting premiums on the risk they take for investing in value stocks. This is in accordance with the efficient market theory and capital asset pricing model (CAPM). The other take on stock prices is that the efficient market theory does not hold up for all stocks and there are indeed mispriced stocks. In this study we will try to find further evidence regarding the topic of efficient market theory versus the mispricing theory. Furthermore, this paper aims to give value investors more insight about the impact of free cash flows and diversification of their portfolios.
3 Free cash flows is an underrated indicator for quality and cheapness of firms in the current value investing models. The advantages of incorporating a free cash flow model in
calculating the value of a stock can be significant. The most important benefit is eliminating differences in accounting biases in the income statements. Since the main inputs of value investing comes from the accounting data of the firm it is important to neutralize the differences in accounting practices. Some studies take accrual accounting into account in their models but I have seen none so far which take it as far as calculating free cash flows and incorporating it into the model. Furthermore, free cash flows are a more comprehensive estimate of cash flows flowing to the owners of a firm during the accounting period
compared to reported earnings.
The most controversial topic of value investing is the explanation for consistently
outperforming the market, is it compensation for risk or are there firms mispriced on the market. Prominent researchers like Fama and French (1992) argue value investors are compensated for the risk exposure of their portfolios. Griffin and Lemmon (2002) find that there is no evidence supporting the statement that the excess returns made by value investing is explained due to risk exposure. Many more researchers have tried to explain why value investors tend to make exceptional returns, some supporting the efficient market theory and some supporting the mispricing theory. Therefore, this study tries to find
additional evidence regarding this controversial topic by comparing returns and risks of portfolios created with different stock criteria.
Another unexplained concept in value investing is the possible benefits of diversification. The basic rule in finance is in order to reduce risks one has to diversify, this contradicts value investing principles that encourages to focus on a limited amount of firms that meet certain criteria. No prior research is done about diversification in value investing. Since the risks of value investing is the soundness of the criteria diversification should have no impact. However, no definitive answer has been found in research.
Furthermore, this study will be based on yearly financial accounting data ranging from 2000 to 2018. The data gains results of portfolios in the years 2009 to 2016. No portfolios are created before 2009 since the free cash flow model needs 10 years of data to calculate intrinsic values and portfolio returns needs data one year after the portfolio construction. So there are two main research question of this paper is as follows:
4 - Does diversification impact the risks of portfolios consisting of stocks picked with
value investing principles in mind?
This contribution of this paper to existing literature will be the possible significance of adding intrinsic value to value investing concepts. Intrinsic value is not closely related to value investing in previous literature. Furthermore, this paper gives a better understanding about the risks associated with value investing and the possible diversification benefits for value investors.
2. Literature review
The capital asset pricing model (CAPM) is one of the more prominent theories in finance and often used in portfolio selection and determining asset prices. One of the early developers of the CAPM suggested that asset returns can be divided into two components, the price of time and the price of risk (Sharpe, 1964). The price of time is referred to in his paper as the pure interest rate, otherwise known as the risk free rate and the price of risk as all non-diversifiable risk of a certain asset. The price of risk does not include non-diversifiable risk since investors can avoid those risk by diversifying. In the case of common stocks there will always be risk as some events cannot be diversified such as economic swings (Lintner, 1965). The papers of Sharpe (1964) and Lintner (1965) introduced the CAPM in finance and the following formula that describes the CAPM is the cornerstone of asset pricing under the condition of market equilibrium:
(1) 𝐸(𝑅𝑖) = 𝑟𝑓+ 𝛽𝑖 ∗ (𝐸(𝑅𝑚) − 𝑟𝑓)
As can be seen in the formula the return of an asset is the risk free rate plus the beta of an asset times the expected return of the market minus the risk free rate according to the standard CAPM formula. The power of the CAPM is the simplicity and empirical testability of formula 1.
Since the introduction of the CAPM the model has become the standard in finance and researchers have developed the model and have tested the possible problems with the underlying assumptions. Black (1972) describes the four assumptions generally used for formula 1 as follows:
5 all investors are risk averse. (Every investor's utility function on end-of-period wealth in- creases at a decreasing rate as his wealth increases.) (d) An investor may take a long or short position of any size in any asset, including the riskless asset. Any investor may borrow or lend any amount he wants at the riskless rate of interest.’’
In his paper Black (1972) suggest that the most restrictive assumption is assumption d. Since it is not reasonable to think all investors can borrow any amount they wish at the riskless rate. Furthermore, another paper suggests that the CAPM might not be accurate in a world with possibilities of collateral requirements when going short and possible bankruptcy provisions (Ross, 1977). Another assumption that can restrict the use of the CAPM is assumption a, that all investors have the same opinions about the possibilities of various end-of-period values of assets. In the real world investors might not have the same opinions about the returns of assets. The difference of opinion can be caused by asymmetric
information among investors and can cause a change in the market equilibrium (Diether, Malloy, & Sherbina, 2002).
Furthermore, the β of the CAPM model failed to capture the relationship with average returns in the period between 1963 and 1990 (Fama & French, 1992). While researchers such as Lintner (1965) and Sharpe (1964) suggests that stock returns are positively correlated with β Fama and French (1992) do not find support for this prediction in later periods.
Therefore, an extension to the CAPM is proposed to more efficiently explain cross section asset returns, the three factor model of Fama and French (1993). The additional factors used in this model are the book value to equity factor, a size factor and a momentum factor (Fama & French, 1993). The set of additional factors increases the models explanatory value on asset returns and is often used in modern finance.
Portfolio optimization in regards to the CAPM is often done through mean-variance optimization, the basic concept is to get the lowest possible variance at a certain expected return. Generally if you optimize a portfolio according to mean-variance optimization higher returns have higher variance and thus higher risk, while lower returns have lower variance and thus lower risk. Markowitz (1952) is the first to bring the concept of mean-variance optimization. His paper advocates to dismiss any hypothesis which only focuses on expected return maximization and to dismiss any hypothesis which does not imply the superiority of diversification (Markowitz, 1952). Furthermore, the CAPM allows to pick to select stocks while only needing information of the β of stocks and covariance’s between stocks to
6 Mean-variance optimization is the most prominent theory in finance regarding portfolio optimization and is well researched, however in practice it can be hard to implement. While it sounds simple to only take the β and covariance’s of stocks and diversify accordingly in practice this model leads to unbalanced weights in portfolios (Green & Hollifield, 1992). Furthermore, transaction costs in the real world can make optimization implementation with the mean-variance model even more problematic (Black & Litterman, 1990). Due to practical implementation problems of mean-variance optimization investors might not invest in market efficient portfolios. Therefore, there is the possibility that the market is not perfectly in equilibrium. This might affect the effectiveness of the CAPM model as it is required for the market to be in equilibrium for the CAPM to be the most accurate.
Another approach to investing and portfolio management is value investing which contradicts classic financial literature as it is not focused on diversifying a portfolio but rather it focusses on financial (accounting) data of the underlying asset. Value investors believe that analyzing financial (accounting) data and set certain requirements that the firm must meet will reduce their risk in the assets value investors invest in. While the CAPM and mean-variance optimization focusses on the β of stocks and covariance’s between stocks. Furthermore, one of the main assumptions of value investing is that there are mispriced stocks on the market. This contradicts the efficient market theory that suggests the intrinsic value of the firm should be equal to the listed price on the market, in other words everything on stock markets is priced correctly. However, using value investing strategies earlier studies find superior returns for value investors (Novy-Marx, 2013). A possible reason for these superior returns might be that the β of the portfolios of value investors is higher and thus the risk associated with value investing is higher. Bartov and Kim (2004) find that excessive risk taking is not the explanation for the superior returns. While other researchers such as Fama and French (2006) argue that there are indeed risk premiums for portfolios with higher returns. The literature seems divided in this case. Therefore, there is a possibility that the efficient market theory that suggest all stocks are correctly price and the CAPM that suggest that returns can be explained by only using the β of stocks (or the β and some additional factors) might not uphold in all cases.
The core of value investing comes from Benjamin Graham and is further developed by many scholars and professional value investors. In the original framework Graham suggested seven criteria for which the firm underlying the stock must meet (Novy-Marx, 2013).
1. Adequate firm size
7 3. Earnings stability, 10 consecutive years of positive earnings 4. Stable dividends, 20 years consecutive dividend payments 5. Earnings-per-share growth of 1/3 over the last 10 years 6. Price-to-earnings ratio not exceeding 15
7. Price-to-book ratio not exceeding 1.5
These seven criteria are meant to evaluate the cheapness and the quality of the firm. The first five are quality checks and the last two ensuring that the price is reasonable. The two most important themes of the quality dimension in Graham’s criteria are long term stability as can be seen in points 3 to 5 and low levered firms as can be seen in point 2.
The main principles of value investing are the cheapness of a stock and the quality of a firm. Many researchers have discussed optimal cheapness measures and quality measures. Quality measures are less straightforward and Novy-Marx (2013) has done an extensive research with multiple frameworks to value quality and compared the results of those frameworks. Novy-Marx (2013) finds that the gross profitability measure gives the highest returns in a dataset ranging from 1963 to 2012. Furthermore, Novy-Marx (2013) suggests using both cheapness factors and quality factors. According to Jocye and Mayer (2012) first quality check to do is to identify the capital structure of the company. Joyce and Mayer argue that most investors undervalue ‘boring’ firms with high earnings and stability and low leverage. These quality measures seem to have positive excess returns as in Novy-Marx (2013) study the framework based around these measures outperforms the market with 6.4%. Furthermore, Sloan (1996) finds in his paper that aggressive accounting practices regarding accruals might lead to investors overvaluing firms. Kozlov and Petajisto (2013) further validate the importance of quality earnings when considering a firms value. The cheapness and quality dimensions of value investing are heavily researched while
another potential factor is neglected, the intrinsic value of a firm. Most studies mentioned in the previous paragraph use cheapness of the stock and an array of different quality factors or signs. It could be argued that the intrinsic value can be used as a cheapness. Intrinsic value used as a measure for cheapness is straightforward, if the intrinsic value is significantly higher than the current market capitalization then the stock is cheap. If the intrinsic value is calculated correctly the firm value should converge to it. Thus, the need for a quality factor might not be needed. However, in the paragraph above quality factors are heavily
influencing the return of the portfolios. So, calculating intrinsic values with a quality factor might increase portfolio returns.
8 the discounted free cash flow analysis for finding intrinsic values of firms is reliable and that the free cash flow analysis is equivalent to economic value added and net present
valuations. However, Francis, Olssen and Oswald (2000) argue that the abnormal earnings method provide significant better explanation for the intrinsic value of a firm. Lastly, the paper of Lundholm and O’keefe (2001) suggests that the discounted free cash flow model and the residual income model give equivalent firm value. As previously stated, this study uses the discounted free cash flow model. There is not sufficient evidence to discredit the discounted free cash flow model.
Since the discounted free cash flow model is used to calculate intrinsic value, an appropriate quality factor might be the free cash flows themselves. Free cash flows might be a more comprehensive factor than the quality factors mentioned in previous paragraphs since it is essentially an estimate of returns flowing to the owner. Free cash flows are either paid out as dividend or reinvested to create value for the firm and thus the owners of the firm. Ultimately, adding free cash flows as a quality factor might increase the returns of a portfolio. In this study, the quality factor is ten years of positive free cash flow. This
measures the stability of the firm’s free cash flow over a relatively long period of time. The period of ten years is chosen since that seems to be in line with most of Graham’s initial quality measures and stresses the importance of long term stability.
So to summarize, value investing theory suggest that the return of stocks are based on financial (accounting) data and the risk are based on possible mistakes in using the financial (accounting) data not correctly. While the CAPM and mean-variance optimization suggest that the return and risk of stocks are based on the β of the stocks and the covariances of stocks within portfolios. The CAPM and mean-variance suggest that reducing risk can be done with diversification. Previous studies have suggested that value investing can make superior returns, while other studies debate if the superior returns are due to a higher β and thus more risks are taken in value investing. The efficient market theory suggests that all stocks are priced correctly. However, due to the use of the CAPM in finance while not all conditions are met and the practice of mean-variance optimization while practical
implementation problems might cause portfolios to not be market efficient. Both of those factors might cause investors to overvalue or undervalue stocks on the capital market. Therefore, value investors might have possibilities to invest in mispriced stocks and gain superior returns while reducing risk.
9 model one can calculate the intrinsic value of a firm and create portfolios of stocks that have superior returns while maintaining low risk. Therefore, the first hypotheses of this study can be formed as follows:
Hypothesis 1a: Diversification has significantly less impact on the standard deviation of portfolios with stocks selected via the means of intrinsic value calculation using the discounted free cash flow compared to portfolios of stocks that do not have that criteria. Hypothesis 1b: Portfolios made by selecting stocks that have higher intrinsic value than market capitalization have significantly lower standard deviation compared portfolios that do not have that criteria.
Hypothesis 1c: Portfolios made by selecting stocks via the means of intrinsic value
calculation using the discounted free cash flow have significantly higher returns compared to portfolios of stocks that do not have that criteria.
Considering the importance of a cheapness measure and a quality measure another hypotheses can be made. Using the intrinsic value as cheapness measure and using a ten year period of positive free cash flows as a quality measure portfolios can be made to further increase returns and decrease risks of portfolios. Furthermore, diversification via adding more stocks to the portfolio has no significant impact on the risk of those portfolios. Hypothesis 2a: Portfolios made by selecting stocks with a cheapness measure and a quality measure have significantly higher returns compared to portfolios that do not have that criteria.
Hypothesis 2b: Portfolios made by selecting stocks with a cheapness measure and a quality measure have significantly lower standard deviation compared portfolios that do not have that criteria.
Hypothesis 2c: Diversification of portfolios made by selecting stocks with a cheapness measure and a quality measure have no significantly impact on standard deviation.
3. Research method
10 The FCF framework adopted in this study will be one based on Copeland, Koller and Murin (1994) but will have some changes to it. Most notably the CAPM concepts, such as the weighted average cost of capital (WACC), will be taken out since in value investing the WACC is not based on the β of a certain stock. The idea of the FCF model is that the cash after all required investments is ‘free’ to use by the shareholders. The intrinsic value of the firm using free cash flow is calculated in the following way:
(2) 𝑉𝐹𝐹𝐶𝐹 = 𝐹𝐶𝐹∗(1+𝑔) 𝑟𝑡 − 𝐷𝑡+ ∑ ( FCF∗(1+g)𝑡 (1+rt)𝑡 ) 𝑇 𝑡=1 (3) 𝐹𝐶𝐹𝑡 = (𝑆𝑡− 𝑂𝑡− 𝐷𝑃𝑡− 𝐼𝑡)(1 − 𝑇) + 𝐷𝑃𝑡− ∆𝑊𝐶𝑡− 𝐶𝑡 (4) 𝑔 =LN(SALESt10−𝑆𝐴𝐿𝐸𝑆𝑡−10) Where:
𝑉𝑡𝐹𝐶𝐹 : Intrinsic firm value at time t 𝐷𝑡: Total debt at time t
𝑆𝑡 : Sales revenue of year t 𝑂𝑡 : Operating expenses of year t 𝐷𝑃𝑡 : Depreciation expense of year t 𝐼𝑡: Interest expense at time t
𝑇 : Corporate tax rate
∆𝑊𝐶𝑡 : Change in working capital in year t 𝐶𝑡 : Capital expenditures in year t
𝑔: Growth rate
11 expenses. Since the core value of a company is with its operating efficiency. Furthermore, deprecation expenses is only an accounting expense not a cash flow. Therefore, it is included in the first part of the formula since it reduces the tax expense and is added back in the second part of the equation. Furthermore, the change in working capital and the capital expenditure are deducted from the free cash flow in the end since it is needed to maintain the core operations of the company. Change in working capital can capture the cash flows of accounts. For example, changes in accounts payable are reflected in working capital.
Furthermore, in the free cash flow model the tax rate can be either the total operating income tax or the corporate tax rate of the United States. The reason there are two options for the tax rate is the data availability. Unfortunately, the data of total operating income tax is not available for all companies. However, it better represents the free cash flow as some companies may have value added through advantageous tax strategies. Firms can have tax strategies to avoid tax expense or receive tax benefits. Therefore, if it is available it is used in the model and the *(1-TAX) is replaced with – total operating income tax. When the data is not available the U.S. corporate tax rate of 35% percent is used since the data used in this study is prior to the change to the tax rate of the U.S.
The risk free rate in formula 2 is the ten year average treasury rate of the United States. Since in the free cash flow model the weighted average cost of capital is not used as a discount rate the choice fell for the ten year average treasury rate. This best reflects a discount rate since there are no other good options. However, the discount rate can heavily influence the value of free cash flows. Lastly, the United States treasury rate has been chosen since the data in this paper consist solely of U.S. traded companies.
The growth rate is based on sales rather than free cash flows since sales tend to be more stable. The free cash flows can differ quite a lot per year and can therefore, not give reliable growth rates in the long term. Furthermore, free cash flows can be negative in the starting year of the growth rate calculation and positive in the end. This makes constructing a growth rate difficult. Sales on the other hand are always positive and shows how much the business has grown. Considering it has more stability over the years and the information sales can give it can better represent the actual growth rate.
12 (6) 𝑅𝑡=
𝑀𝑐𝑎𝑝𝑡+1−𝑀𝑐𝑎𝑝𝑡 𝑀𝑐𝑎𝑝𝑡 + 𝐷𝑖𝑡 Where:
𝑀𝑐𝑎𝑝𝑖𝑡: Market capitalization at time t for company i
𝐶𝑆𝑃𝑖𝑡: Closing share price at time t at the end of June in year t
𝐶𝑆𝑂𝑖𝑡: Common shares outstanding at time t at the end June in year t 𝑅𝑡: Percentage return investing in year t and selling in year t+1
𝐷𝑖𝑡: Dividends paid out at time t
Formulas 5 and 6 are used to calculate the market capitalization and the return on investment in a company since it is not given in the dataset. Formula 4 is uses the closing price at the end of June is since the financial data is often corrected and at the end of June this data is readily available for investors (Novy-Marx, 2013). June is also chosen since comparability of this study is considered, more studies chose the end of June as the start of the portfolio year, for example, Fama and French (2006). Furthermore, the closing price is multiplied by the number of common shares outstanding to calculate the market
capitalization. Formula 6 describes the returns of the investment. Since you invest at the end of June the formula compares the market capitalization at time t to the market capitalization of t+1. So in the model the return of a certain year is the return for holding shares in the company for one year. Market capitalization instead of share price is used to not let the returns be affected by share splits or other events that could influence the share price but have no influence to the total market capitalization. Furthermore, dividends are added to the returns.
13 diversification benefits of the portfolio types. The amount of stocks in a portfolio and the amount of portfolios per subset is based on the study of Green & Hollifield (1992) where they compare diversification in mean-variance portfolios.
The portfolio returns are value weighted, this means the portfolio invests proportional in stocks compared to their market capitalization. One of the reasons for this is to avoid very small cap firms from highly impacting the returns. Furthermore, this is done to increase comparability of the results to previous research. Arschanapalli, Coggin and Doukas (1998) suggest value weighted returns as well and use market capitalization to determine the value weighted returns. Furthermore, they suggest that overinvestment in very small market capitalization firms can be considered an unhedged portfolio for value investors. Other researchers on this topic use value weighted returns as well such as Piotrosky (2000), Fama and French (2006) and Novy-Marx (2013). Formulas 7 and 8 describe the value weighted return and the portfolio return calculation
(7) 𝑉𝑊𝑅𝑖 = 𝑅 ∗ 𝑀𝑐𝑎𝑝𝑖 𝑀𝑐𝑎𝑝𝑝𝑖
(8) 𝑃𝑖 = ∑𝑖𝑖=1VWRi Where:
𝑉𝑊𝑅𝑖: Value weighted return of company i 𝑀𝑐𝑎𝑝𝑖: Market capitalization for company i 𝑀𝑐𝑎𝑝𝑝𝑖: Market capitalization entire portfolio i 𝑃𝑖: Portfolio returns of portfolio i
Value weighted returns are chosen over flat returns because in the dataset there is a high number of companies with low market capitalization. For example, there are market capitalizations in the dataset of under a million and there are market capitalizations of over 100 billion. There are two reasons why this can be problematic if flat returns are used. First, the low market capitalization companies are volatile and can grow 100 times their original market capitalization skewing the return of the portfolio significantly. Secondly, in practice investors will not invest the same amount of money in very small market capitalization companies as in very high market capitalization companies. This holds true since it is not always possible to invest the same amount due to the fact that investors cannot buy more than 100% of the company.
14 the means between the portfolios and checks whether there are significant differences between those means. Furthermore, a F-test will be done to test whether the standard deviations of the portfolios change significantly.
4. Data
The dataset used in this study is obtained from COMPUSTAT and obtains 200,799 observation of company financial data reports. All stocks traded on United States stock markets are included. The financial data reports consist of financial accounting data at the end of the fiscal year per company. The financial data reports come from the fiscal years between 1999 and 2017. However, the portfolios are only constructed in the years from 2009 to 2016 since the growth rate is calculated based on the sales growth of the past ten years and the quality factor also requires 10 years of prior data. Furthermore, the market capitalization return is calculated with stock information at the end of June each year. June is used since in June most financial reports are final.
Missing data points of the sample are not accounted in the final dataset of this study. Unfortunately, COMPUSTAT did not report full data for every company in the initial 200,799 observations. Observations with the following missing datapoints are not accounted for: Sales, Common shares outstanding and Price per share. These observations are left out if there is no data or if the data presented a 0 in those places. The reason for this is since there is no reason to include companies with 0 sales. Furthermore, if there is missing share price information or missing common shares outstanding information then the market
capitalization cannot be calculated. Data with missing total income tax is not excludes, since then the corporate tax rate in the United States is applied. Data with zero’s in change in working capital, depreciation or capital expenditure is included in the dataset. Since it is possible for companies to have no changes in those accounts.
To be included in the calculations of intrinsic value via the free cash flow model more
specifications must be met. First of all there should be 10 consecutive years of data available for the company to be included. This is a requirement in order to calculate the growth rate for that specific company. Furthermore, only observations are included that have market capitalization data for the next year. This is required to calculate returns of the stocks. Given these data exclusions the final dataset for all company returns includes 23,443
15 datasets have sufficient observations to test if intrinsic value calculations via the free cash flow model can increase portfolio returns.
Table 1
Descriptive statistics on returns of stocks during the years 2009 to 2016 Year Return mean Standard deviation Median Minimal return Maximum return N 2009 0.984 15.533 0.223 -0.949 744.518 3391 2010 0.707 7.418 0.294 -0.967 339.059 3182 2011 0.389 17.913 -0.054 -0.981 973.836 3002 2012 0.447 2.615 0.198 -0.950 89.231 2871 2013 0.867 19.837 0.235 -0.948 1061.636 2887 2014 4.375 223.665 0.015 -1.000 12197.634 2976 2015 0.013 1.266 -0.068 -0.979 47.773 2989 2016 0.708 8.033 0.229 -0.976 266.527 2145 Table 2
Descriptive statistics on returns of stocks that have higher intrinsic value than market capitalization during the years 2009 to 2016
Year Return mean Standard
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2016 0.288 0.508 0.231 -0.730 9.464 857
Table 1 and table 2 represent the descriptive statistics of the returns of company stocks used in this study. Table 1 shows high standard deviations and very high maximum returns, the highest return in table 1 is 1,219,763.39% in 2016. The descriptive statistics in table 2 shows relatively lower standard deviations and lower maximum returns. The exception in table 2 is the year 2010 with a standard deviation of 11.5724 and a maximum return of 33,905.94%. The average returns table 1 and table 2 are significantly influenced by excessive returns, this is especially true in table 1. Furthermore, the average returns are relatively high compared to median returns, the cause for this is that the minimum returns are capped at -100% while the maximum returns can go to Infiniti. Most of these excessive returns are due to very low market capitalizations in the beginning of the year and relatively very high market
capitalizations at the end of the year. These excessive returns can be problematic for the purpose of this study. However, with value weighed returns these excessive returns do not harm the results of this study as the value weighted returns significantly decrease the impact of smaller market capitalization stocks.
Table 3
Descriptive statistics on returns of stocks that have higher intrinsic value than market capitalization and ten consecutive years of positive free cash flows during the years 2009 to 2016
Year Return mean Standard
deviation Median Minimal return
17 Table 3 shows the descriptive statistics of the returns with the quality factor added. The number of observations are greatly decreased with the quality factor added. There are less outliers and the standard deviations are relatively small in table 3. The highest median return can be found in table 3 with a return of 34.22%. Table 3 shows no negative median returns, while table 1 and table 2 do have negative median returns.
5. Results
Table 4
*, ** and *** means it is significant at the 10%, 5% and 1% respectively Randomly selected portfolios all
stocks
Randomly selected portfolios stocks intrinsic value > market capitalization Number of stocks per
portfolio 10 30 50 10 30 50
Number of portfolios 90 30 18 90 30 18
Panel A Year Average returns and standard deviation (italic)
2009 0.241 0.270 0.272 0.162 0.142 0.125 0.256 0.402 0.402 0.157 0.102 0.073 2010 0.352 0.290 0.319 0.283 0.230 0.209 0.192 0.125 0.097 0.263 0.190 0.181 2011 -0.069 -0.049 -0.068 -0.035 -0.047 -0.064 0.259 0.116 0.104 0.146 0.103 0.094 2012 0.232 0.187 0.172 0.221 0.187 0.139 0.181 0.163 0.092 0.142 0.096 0.106 2013 0.327 0.462 0.412 0.271 0.242 0.196 0.469 0.774 0.741 0.485 0.179 0.070 2014 0.036 0.023 0.024 0.044 0.055 0.083 0.188 0.103 0.135 0.146 0.103 0.100 2015 -0.074 -0.049 -0.050 -0.035 -0.021 -0.037 0.207 0.123 0.118 0.147 0.123 0.097 2016 0.143 0.206 0.130 0.206 0.155 0.179 0.168 0.154 0.090 0.165 0.092 0.052 Panel B Year
P-values of differences between returns and standard deviation (italic) of the portfolios with the same selection process (the portfolio of 10 stocks is the base
18 2012 0.198 0.042** 0.142 0.008*** 0.521 0.003*** 0.018** 0.165 2013 0.364 0.642 0.634 0.167 0.000*** 0.006*** 0.000*** 0.000*** 2014 0.634 0.744 0.656 0.178 0.000*** 0.124 0.036** 0.079* 2015 0.432 0.501 0.598 0.952 0.002*** 0.011 0.266 0.051* 2016 0.063 0.637 0.037** 0.199 0.623 0.005*** 0.001*** 0.000***
Table 4 shows the p-values of the returns and standard deviations compared to the portfolios with 10 stocks of each portfolio type. The returns of portfolios that include all stocks in their selection and portfolios that only include stocks with higher intrinsic value in their selection seem similar in raw returns. The highest average return for the portfolios with stocks of higher intrinsic value is 28.3% as can be seen in table 4 panel A. This return is made in 2010 and is the average of 90 portfolios consisting 10 stocks. The lowest average return for the portfolios with stocks of higher intrinsic value is -6.4% in 2011. This is the average of 18 portfolios consisting 50 stocks. When there is no model applied the maximum average return is 46.2% in 2013 and the minimum average return is -7.4% in 2015. In appendix A the statistical differences of the returns are shown. In 2009 and 2010 the returns of the
portfolios with ten stocks that have higher intrinsic value are significantly lower at a 5% confidence level. Furthermore, the portfolios with ten stocks that have higher intrinsic value only perform significantly better in 2016 at a 5% confidence level.
The standard deviations of the portfolios are significantly different in most cases and in all years the portfolios with higher intrinsic value stocks have significantly lower standard deviation compared to portfolios of the same size that consider all stocks. Especially the portfolios with ten stocks with higher intrinsic value have significantly lower standard deviation as is shown in appendix A. This is the case in the years of 2009, 2010, 2011, 2014, 2015 and 2016 at the 5% confidence level. In the years of 2009, 2010, 2012 and 2013 the standard deviation is significantly lower at the 5% confidence level in the case of portfolios consisting 30 and/or 50 stocks with higher intrinsic value.
Panel B in table 4 shows the P-values of differences in return between the different portfolio sizes within each portfolio type. The portfolios consisting of 30 and 50 stocks are compared to the portfolio consisting of ten stocks and those portfolios have the same stock
19 respectively. The returns are significantly higher at the 5% confidence level for portfolios that consider all stocks in 2016 for the portfolios that consist of 30 stocks. The portfolios with stocks that have higher intrinsic value have significantly lower returns at the 5% confidence level in 2012 and 2016 for portfolios consisting of 50 stocks and 30 stocks, respectively.
Furthermore, the standard deviations of portfolios consisting of 30 or 50 stocks compared to the portfolios consisting of 10 stocks are in most cases significantly lower at the 5%
confidence level. The only cases where the standard deviations significantly increase is in 2009 and 2013 for portfolios that consider all stocks.
These results shown in table 4 do not support hypotheses 1a that portfolios of stocks selected with higher intrinsic value have less benefit than portfolios of stocks that do not have that criteria. Both portfolio types have significantly less standard deviation as portfolio sizes increase, while the returns of those portfolios are not significant different in most cases. These results indicate that the theory of diversification do apply to investors that only select stocks on the basis of intrinsic value calculated via the discounted free cash flow. However, the results shown in table 4 and appendix A do support hypothesis 1b that portfolios with stocks selected with higher intrinsic value have significantly lower standard deviation in the case of portfolios consisting of ten stocks. In most cases the reduction in standard deviation do not come at the cost of returns. These results show that the risks in small portfolios can be reduces with careful selection of stocks. The benefits of selecting stocks with higher intrinsic value than market capitalization do diminish when portfolio sizes increase. Therefore, the practical use is limited as it is easier to diversify than to calculate intrinsic values of stocks.
20
Table 5
*, ** and *** means it is significant at the 10%, 5% and 1% respectively
Randomly selected portfolios stocks intrinsic value > market capitalization and 10 years of positive free cash flow
Number of stocks per portfolio 10 30 50
Number of portfolios 90 30 18
Panel A Returns and standard deviation (italic)
2010 0.264 0.197 0.223 0.179 0.167 0.138 2011 0.009 0.000 -0.047 0.120 0.104 0.072 2012 0.229 0.253 0.230 0.133 0.094 0.075 2013 0.191 0.182 0.213 0.129 0.100 0.087 2014 0.046 0.058 0.056 0.106 0.067 0.074 2015 0.055 0.055 0.004 0.182 0.143 0.117 2016 0.170 0.176 0.181 0.162 0.148 0.094 Panel B
P-values of differences between returns and standard deviation (italic) of the portfolios with the same selection process (the portfolio of 10 stocks is the base value)
21 Table 5 shows the returns and standard deviations of portfolios with stocks that have higher intrinsic value than market capitalization and ten consecutive years of positive free cash flows and the P-values of differences between returns and standard deviations of the portfolios with 30 and 50 stocks compared to the portfolios of 10 stocks. The highest average return is 26.4% in 2010 of the portfolios consisting of 10 stocks. The P-values of returns and standard deviations of the portfolios in table 5 compared to the portfolios consisting of stocks with no criteria can be found in appendix B. The returns of the portfolios with higher intrinsic value and the quality factor are significantly lower in 2010, the returns are significantly higher in 2011, 2012 and 2015 at the 5% confidence level for various portfolio sizes. The standard deviation of the portfolios with higher intrinsic value and the quality factor are significantly lower in 2011, 2012, 2013 and 2014 at the 5% confidence level as well. This is true for all portfolio sizes in 2013 and 2014 while the standard deviation of portfolios consisting of 50 stocks is not significant in 2011 and 2012 and the standard deviation of portfolios consisting of 30 stocks is not significant in 2011 at the 5% confidence level.
Panel B of table 5 shows the P-values of the differences between return and standard deviations of diversifying portfolios with stocks consisting of higher intrinsic value and the quality factor. The returns are only significantly lower than the portfolio consisting of ten stocks in the portfolios consisting of 50 stocks in 2011 at the 5% confidence level. The standard deviation is significantly lower of portfolios consisting of 50 stocks in 2011, 2012, 2015 and 2016 at the 5% confidence level. Furthermore, the standard deviation is
significantly lower of portfolios consisting 30 stocks in 2012 and 2014 at the 5% confidence level. The standard deviation of the other portfolios are not significantly different at the 5% confidence level compared to the portfolio consisting of ten stocks.
22 Furthermore, the results shown in panel B of table 5 show that in four out of seven years diversification lowers the standard deviation significantly by either diversifying creating portfolios of 30 stocks or 50 stocks. Therefore, hypotheses 2c is not supported by the results of this study. These results further support the notion of diversification. Diversification can benefit all invest, also when investing with value investing principles.
6. Conclusion
In this study the benefits of diversification is tested in three types of portfolios, portfolios with no criteria for stocks, portfolios with stocks that have higher intrinsic value than market capitalization and portfolios that have higher intrinsic value than market capitalization and ten consecutive years of positive free cash flows. The intrinsic value of stocks is calculated via the discounted free cash flow method. The main findings of this study are that creating portfolios with the criteria for stocks mentioned above and diversifying the portfolios does significantly decrease the standard deviation of those portfolios while returns are largely unaffected.
Furthermore, creating portfolios with stock criteria of higher intrinsic value does significantly decrease the standard deviation of those portfolios and is not at the expense of significantly lower returns when comparing portfolios of small sizes. However, the benefits of lower risk when selecting stocks with higher intrinsic value than market capitalization do diminish when portfolio sizes increase. Furthermore, portfolios that have the criteria of ten
consecutive years of free cash flows the standard deviations get significantly lower at the expense of returns compared to portfolios with no criteria.
These results support current literature that diversification can decrease risks while
maintaining the same returns and do not support one of the main research question of this study that diversification has no effect on standard deviation when carefully selecting stocks with certain criteria. Furthermore, the criteria selected in this study do not increase returns. On the contrary the returns decrease when using the criteria used in this study. This suggests that using intrinsic value as a cheapness factor and ten consecutive years of free cash flows as a quality factor is not effective for investors that seek higher returns. While other
researchers have found significant higher returns with using value investing principles, this study did not find those returns.
23 Furthermore, the discount rate of the free cash flow model might not be optimal. The
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26
Appendices
Appendix A Table 6
*, ** and *** means it is significant at the 10%, 5% and 1% respectively
Randomly selected portfolios stocks intrinsic value > market capitalization
Number of stocks per
portfolio 10 30 50
Number of portfolios 90 30 18
P-values of differences between returns and standard deviation (italic) of the portfolios with the same number of stocks
2009 0.013** 0.094* 0.145 0.000*** 0.000*** 0.000*** 2010 0.048** 0.149 0.032** 0.003*** 0.027** 0.013** 2011 0.280 0.935 0.909 0.000*** 0.509 0.690 2012 0.641 0.998 0.314 0.024** 0.005*** 0.569 2013 0.430 0.132 0.234 0.744 0.000*** 0.000*** 2014 0.746 0.233 0.146 0.017** 0.973 0.221 2015 0.151 0.369 0.722 0.002*** 0.984 0.419 2016 0.012** 0.126 0.056* 0.888 0.006*** 0.029** Appendix B Table 7
*, ** and *** means it is significant at the 10%, 5% and 1% respectively
Randomly selected portfolios stocks intrinsic value > market capitalization and ten consecutive years of positive free cash flows Number of stocks per
portfolio 10 30 50
Number of portfolios 90 30 18
