This article requires a subscription to view the full text. If you have a subscription you may use the login form below to view the article. Access to this article can also be purchased.

## Abstract

Empirical literature on value and growth style investing finds value style investing to be a favorable long-term investment strategy. But the value premium, as explained by Basu [1977] and Fama and French [1992], has been subject to important criticism. For example, Peters [1991], Estrada [2005], and Penman and Reggiani [2013a] argued that value and growth investment strategies should not be viewed as mutually exclusive. Their contention further earns credibility when academics fail to explain the value premium in value stocks. In this article, the authors argue that the value premium puzzle is a result of the lack of a valid asset pricing model. They show that that the key problem that lies behind the value premium puzzle is related to standard risk measures and thus related to the discount rate. They further show that investment style biases can be avoided by estimating a fair value that not only considers economic size metrics, but also controls for individual stocks’ heterogeneous risk and reward characteristics independent from market price. The authors introduce *fair value indexation*, designed to avoid systematic biases not just in capitalization-weighted indexes but also in traditional style and fundamentally weighted indexes, while delivering improved long-term risk adjusted returns of very similar liquidity and capacity as capitalization-weighted equity market indexes.

Empirical literature on value and growth style investing finds value style investing to be a favorable long-term investment strategy. But the value premium, as explained by Basu [1977] and Fama and French [1992], has been subject to important criticism. For example, Peters [1991], Estrada [2005], and Penman and Reggiani [2013a] argue that value and growth investment strategies should not be viewed as mutually exclusive. Their contention further earns credibility when academics fail to explain the value premium in value stocks. In this article, we argue that the value premium puzzle is a result of the lack of a valid asset pricing model. We show that that the key problem that lies behind the value premium puzzle is related to standard risk measures and thus related to the discount rate. We further show that investment style biases can be avoided by estimating a fair value that not only considers economic size metrics but also controls for individual stocks’ heterogeneous risk and reward characteristics independent from market price. We introduce *fair value indexation*, designed to avoid systematic biases not just in market capitalization-weighted indexes but also in traditional style and fundamentally weighted indexes while delivering improved long-term, risk adjusted returns to very similar liquidity and capacity as capitalization-weighted equity market indexes.

## VALUE VERSUS GROWTH

Value and growth represent two opposite investment styles when market multiples, such as the price-to-earnings (P/E) ratio and the price-to-book (P/B) ratio, are used to classify investment styles of equities. Investors who invest in value stocks believe that these stocks are temporarily underpriced by the market. Growth stocks, on the other hand, are those companies that have high growth potential in their sales and earnings and are generally highly priced by investors. The debate between value and growth investment styles begins with the value anomaly documented by Basu [1977]. Using the price-to-earnings multiple as a measure of the relative valuation of firms, he found that value stocks, i.e., stocks with lower P/E ratios, outperformed growth stocks with higher P/E ratios. These findings were later confirmed by Fama and French [1992].

Nonetheless, the findings of the value premium in value stocks have not been without criticism. Peters [1991]; Broussard, Michayluk, and Neely [2005]; Estrada [2005]; and Penman and Reggiani [2013a] argue that that price multiples are imperfect valuation measures. Buffett [1992] argues that value and growth investing are “joined by the hip” and that stocks that exhibit low price multiples are just as likely to be as underpriced. The favoritism of value stocks in empirical literature raises the question as to whether the perceived future prospects of growth stocks are indeed overpriced by investors.

From a fundamental performance perspective, value stocks are stocks with below-average growth and profitability and higher volatility due to the lack of competitive advantages in mature industries. Value stocks usually pay higher dividends and have higher debt leverage than growth stocks. Growth stocks, on the other hand, are associated with higher quality, whose earnings are expected to continue growing at an above-average rate relative to the market. They consequently have relatively higher price multiples, such as higher P/E and P/B ratios. Investors who purchase growth stocks receive returns from capital appreciation primarily based on future growth prospects, rather than dividends. Although dividends are sometimes paid to shareholders of growth stocks, it has been more common historically for growth companies to reinvest retained earnings for continued growth.

## THE VALUE PREMIUM PUZZLE

It is an empirically robust finding that value portfolios generate higher returns than growth portfolios. However, this observation is a puzzle within the capital asset pricing model (CAPM) because the betas of value portfolios are similar to, or may even be smaller than, those of growth portfolios. In other words, the CAPM (a model that prescribes what portfolio returns should look like for a given amount of risk) says that value stocks should have much lower returns than what is shown in the data (Fama and French [1996]). The inability of the CAPM to explain the value premium is what academics refer to as the value premium puzzle. Put differently, the value premium puzzle refers to the fact that fundamental size metrics, such as a company’s earnings or cash flow, discounted by the required return generated by the CAPM, do not explain the difference in valuation between value and growth stocks. For that reason, the value premium in value stocks is not yet understood, and thus the existence of a value premium in value stocks is unclear. The academic debate centers largely around whether the outperformance tendency of value stocks is due to market efficiency or inefficiency.

The risk-based explanation put forward by Fama and French [1992, 1993] asserts that value stocks are typically companies in distress, due to higher leverage, lower profitability, and more cyclical earnings. They argue that stock markets are rational, and consequently, the value premium exists because value strategies bear more risk, which is consistent with the CAPM’s positive risk–return tradeoff in equity markets. The argument that value stocks are riskier is further corroborated by Penman and Reggiani [2013b], who contend that the value premium is a consequence of the current accounting practice for accommodating earnings risk. Risky earnings are deferred until the uncertainty is resolved and earnings are realized, which reduces the ratio of earnings to price (E/P) in the short term and compresses the value of earnings relative to book value. Lower earnings in relation to the book value detract from price, and thereby increase the book-to-market (B/M) ratio. This is consistent with Penman et al.’s [2011] conclusion that a high B/M ratio implies high earnings risk and that a value firm carries more risk than a growth firm.

In the absence of an asset pricing model that can support the risk-based explanation, an alternative stream of research suggests that the value premium reflects mispricing. For example, Lakonishok, Shleifer, and Vishny [1994] argue that the value premium arises because the market undervalues distressed stocks and overvalues growth stocks, and when these pricing errors are corrected, distressed value stocks earn higher returns than growth stocks. Dichev [1998] argues that a natural proxy for firm distress is bankruptcy risk. If bankruptcy risk is systematic, one would expect a positive association between bankruptcy risk and subsequent realized returns. However, his study demonstrates that bankruptcy risk is not rewarded by higher returns. Thus, a distress factor is unlikely to account for the size and book-to-market effects. Hence, a risk-based explanation cannot explain the anomalous evidence.

In addition to the two main explanations, several others have been put forward by researchers. For example, Kothari, Shanken, and Sloan [1995] argue that the value premium is a false result caused by methodological issues that emphasize the failure of a significant relation between the B/M ratio and return, which poses a serious challenge to the B/M ratio and the CAPM. Daniel and Titman [1997] suggest that the value premium is due to a firm’s characteristics, rather than the covariance structure. Lee [1999] argues that more effort should be put into the development of a valid risk–return model to determine the appropriate discount rate, and he argues that this problem is perhaps the single most pressing research issue in finance. Penman [2012] suggests that accounting-based valuation and the related endeavor in financial statement analysis deal with the issue of how one pulls information together to determine the expected payoffs to be discounted, but they have little to say about the discount rate.

The debate is at the heart of modern finance because without a valid asset pricing model, which can explain risk across value and growth stocks, a fair value cannot be established. This, in turn, poses problems for institutional asset managers, who invest trillions of dollars for their clients. This article identifies growth with lower risk and shows that when associated with common price multiples, a higher P/E ratio indicates that investors require a lower discount rate. We further show that investing in low P/E (or high E/P and B/M) stocks, with the idea that low prices relative to earnings or book value indicate mispricing, is misguided. Rather, buying low P/E (or high E/P or B/M) stocks may simply mean buying stocks that exhibit above-average risk and below-average growth prospects.

## STANDARD RISK MEASURES

The problem with standard risk measures, such as CAPM–beta and standard deviation (SD), is that they cannot explain the excess risk of value stocks. Exhibit 1, Panel A illustrates the SD and the return-per-unit-risk measure using the Fama–French (FF) annualized returns and SDs from January 1963 through December 2016. The data show that value stocks not only appear to have higher returns but also have lower risk, as measured by return-per-unit-risk measure.

In other words, the SD and the return-per-unit-risk (return/SD), when used to measure risk, suggest that value stocks are less risky. The data obviously contradict the academic findings that value stocks are riskier. A similar problem is inherent in the CAPM. Fama and French [1996] show that beta (β) has no ability to explain the cross-sectional variation in average returns across value and growth stocks. Exhibit 1, Panel B shows both the value premium and the value premium puzzle from January 1963 to July 2011.

Note that the return is higher for value stocks, whereas the CAPM betas (β) stay constant. If the CAPM was an appropriate representation of risk, the betas (β) should have been higher for value stocks. The value premium puzzle suggests not only that beta (β) is a flawed measure of risk but also that the positive relationship between risk and return, as taught by the CAPM,^{1} may be seriously flawed.

## FUNDAMENTAL RISK–REWARD FACTORS

Because of the void of a generally accepted model of asset pricing, academics and practitioners commonly define fundamental value by accounting measures of company size, such as book value, revenues, earnings, cash flow, dividends, etc. When these fundamental size metrics are matched to the market price, they form price multiples, such as the P/E and P/B ratios, which are common valuation shortcuts.

Market practitioners argue that stocks that exhibit low price multiples (e.g., low P/E) imply undervaluation and that high price multiples (e.g., high P/E) imply overvaluation relative to the market. The problem with such an interpretation is that fundamental size metrics (e.g., E), per se, are flawed estimates of individual stocks’ fair value, and as a consequence, common price multiples (e.g., P/E) cannot be used effectively to measure expected return across growth and value stocks. Therefore, the common practitioner’s interpretation that value stocks are underpriced stocks is highly misleading.^{2} Rather, common price multiples, such as the P/E or P/B ratios, express investors’ assessment of individual stocks’ risk-to-reward characteristics. In this context, investors require a higher discount rate for value stocks to compensate for these stocks’ relatively inferior long-term risk-to-reward characteristics. Conversely, investors require a lower discount rate for growth stocks due to their relatively superior risk-to-reward characteristics. The fact that value stocks are not necessarily underpriced stocks is perhaps best explained by Warren Buffett, who states in the Berkshire Hathaway 1992 letter to shareholders:

value investing typically connotes the purchase of stocks having attributes such as a low ratio of price to book value, a low price-earnings ratio, or a high dividend yield. Unfortunately, such characteristics, even if they appear in combination, are far from determinative as to whether an investor is indeed buying something for what it is worth and is therefore truly operating on the principle of obtaining value in his investments. Correspondingly, opposite characteristics—a high ratio of price to book value, a high price-earnings ratio, and a low dividend yield—are in no way inconsistent with a ‘value’ purchase.

Value and growth stocks typically exhibit opposite risk-to-reward characteristics, i.e., value stocks exhibit above-average risk and below-average growth, whereas the opposite is typically true for growth stocks. Exhibit 2 considers two hypothetical stocks, one value stock and one growth stock, both with net earnings of $10 but with opposite long-term risk-to-reward characteristics. We show that the higher market value of the growth stock, and conversely the lower market value of the value stock, may be explained by these two stocks’ heterogeneous long-term risk-to-reward characteristics. Hence, we argue that it may be premature to conclude that the value stock is more attractive than the growth stock based on valuation.

The question of what a company is really worth is one of the core subjects of value investing theory. Graham [1949] explained the “central concept” of stock investing as the “margin of safety,” which is defined as the difference between a stock’s fair “intrinsic” value and the market price. Graham explained that a margin of safety should be derived from fundamental analysis, and that the margin of safety concept should compensate for the various qualities of a company’s fundamentals and that it must rest “upon simple and definite arithmetical reasoning from statistical data” that provides a “justification or support independent of the fluctuating market prices.” A stock’s fair value is traditionally estimated based on the company’s earnings and cash flows, growth potential, and risk. In its most common form, the discount rate reflects an individual stock’s risk and reward characteristics and interest rates. In this context, assets with high growth and stable earnings (low volatility) should have lower discount rates and thus higher fair value than assets with the opposite characteristics.

Alcock and Steiner [2010] show in an academic study that the volatility of earnings growth (risk as measured by uncertainty) is a significant determinant of the value premium. Furthermore, Warren Buffett shows that earnings growth is a significant factor. Exhibit 3 shows that the Berkshire Hathaway equity portfolio’s earnings growth rate averaged 21.1% annually and that Berkshire’s stock price grew at an annual rate of 22.1%, almost completely mirroring the growth in earnings over the period 1970 to 2010.

Berkshire Hathaway’s earnings growth rate is compelling because it not only suggests a strong relationship between earnings growth and stock price appreciation but also shows that Buffett is the ultimate growth investor since the earnings grew about twice the level of the general stock market during this period. These findings are corroborated by Martin and Puthenpurackal [2008], who find that Berkshire Hathaway’s performance is primarily related to investing in large-cap growth stocks and that the performance does not appear to be driven by traditional value stocks, but rather by stocks whose growth is undervalued by the market.

So far, we have shown that the traditional CAPM cannot explain the value premium in value stocks. We argue that the underlying problem is related to standard risk measures, such as standard deviation and betas (β), which view risk solely from the perspective of market prices and thereby fail to take into consideration specific fundamentals factors, such as earnings growth (reward) and earnings growth volatility (risk). We further contend that another key problem is related to the positive relationship between risk and return, as taught by the CAPM.^{3}

## FAIR VALUE WEIGHTING: A NEW APPROACH TO ASSET PRICING

With the aim of finding a solution to these problems, we establish a holistic multifactor framework for asset pricing based on fundamental analysis. We focus on the discount rate, which is used to account for both company-specific (unsystematic) risk and reward factors as well as systematic risk. We define company specific “risk” as earnings growth volatility (*EGVOL*) and “reward” as earnings growth (*EG*). We determine *EG* by the five-year trailing average earnings growth. *EGVOL* is determined by calculating the standard deviation of the year-over-year earnings growth for the same period. We determine individual stocks’ risk-per-unit-reward factor (*RRF*) by dividing the risk factor (*EGVOL*) by the reward factor (*EG*). We use the current yield of a 10-year Treasury note as a proxy for the risk-free rate (i.e., systematic risk). We determine the risk premium by multiplying *RRF* by the risk-free-rate (*Rf*). Finally, we determine the discount rate by adding the risk premium (*RP*) to *Rf*.

The fair value of individual stocks is determined by dividing a stock’s current ex post net earnings (*E*)^{4} by the discount rate (*DR*), and where the discount rate controls for individual stocks’ heterogeneous unsystematic risk-to-reward characteristics and the risk-free rate (*Rf*). The discount rate can be written as follows:

where *DR* is the discount rate, *EGVOL/EG *×* Rf* is the unsystematic risk premium and *Rf* is the proxy for systematic risk.

We note that the discount rate complies with the empirical observations of a negative relationship between risk and reward in equity markets (Ang et al. [2009]). Hence, stocks that exhibit lower fundamental risk, all else equal, will have a lower risk premium, a lower discount rate, a higher fair value, and a higher expected return. Conversely, stocks that exhibit higher fundamental risk, all else equal, will have a higher risk premium, a higher discount rate, a lower fair value, and a lower expected return. In this way, the discount rate complies with the basic notion of value investing, as it assigns higher discount rates (lower fair values) to more risky value stocks and lower discount rates (higher fair values) to less risky growth stocks. This further complies with the notion that investors are buying earnings growth (reward) with an understanding that risk (*EGVOL*) means that actual earnings growth may differ from expectations. This perspective fits with the common view that earnings drive stock prices, i.e., stock prices move when earnings are different from expectations.

We furthermore introduce *risk adjusted earnings* and *risk adjusted earnings yield*. These two new metrics are related to the discount rate. Risk adjusted earnings and the risk adjusted earnings yield can be written as follows:

where *E* is the net earnings and the *RRF* is the risk per unit reward factor.

We should note that the risk adjusted earnings yield differentiates from the traditional earnings yield (i.e., the reciprocal of the P/E) by further making an adjustment for relative volatility (risk) across risky assets (stocks) to the benchmark of a risk-free asset (e.g., Treasury bond).

Exhibit 4 illustrates the discount rate and the fair value for the two hypothetical stocks, one value stock and one growth stock, again with the same net earnings of $10. We show that the value stock’s relatively lower market value ($100) can be explained by the discount rate. That is, the relatively lower market value of the value stock can be explained by its relatively inferior long-term risk-to-reward characteristics (as measured by earnings growth volatility and earnings growth), which translate to a higher risk premium and thus a higher discount rate. Conversely, the relatively higher fair market value ($300) for the growth stock can be explained by their relatively superior risk-to-reward characteristics, which translate to a lower risk premium and discount rate.

Exhibit 4 shows that when the opposite risk and reward characteristics are accounted for, both stocks appear to be fair valued, despite having very different price-to-earnings multiples (i.e., P/Es). We show that under an assumption of rational markets, the fair value (FV) perfectly explains the fair market value (P). We further show that the risk adjusted earnings yield (see Exhibit 4 (4)) equals the risk-free rate. Finally, we show that the conventional E/P matches the discount rate (see Exhibit 4 (1) and (2)), which suggest that the E/P may not be the expected return as commonly argued,^{5} but rather investors’ required return, i.e., the discount rate. (See Appendix A for further discussion on this subject.)

Exhibit 5 illustrates two value stocks, Ford and Intel, and two growth stocks, Microsoft and Cognizant, as of December 16, 2015, using data from Bloomberg. We show that based on the earnings yield, Ford and Intel (the value stocks) appear considerably underpriced (earnings yield 8.33% and 6.67%, respectively), while the two growth stocks, Microsoft and Cognizant, appear to be less attractive. However, when we control for the stocks’ heterogeneous risk-to-reward characteristics, the picture is reversed, i.e., the two growth stocks appear to be slightly underpriced, and the two value stocks appear slightly overpriced. This suggests that Ford and Intel had reached their respective fair values, as of December 2015, and started to mean-revert, while Microsoft and Cognizant, which appear slightly underpriced, continue to grow their earnings at a higher rate and consequently have a higher market return over the past five years. That makes sense, as it would be unlikely that value stocks, after several years of bull markets, would offer investors a sizable free lunch, i.e., a considerably higher earnings yield relative to the two growth stocks and the Treasury yield. Again, we show that traditional valuation metrics (such as the P/E or E/P ratios) are highly misleading.

## FAIR VALUE VERSUS CAPITALIZATION WEIGHTING

Today, it is well accepted that if the market is not perfectly efficient, a market cap-weighted index will overweight all overpriced stocks and underweight all underpriced stocks. Exhibit 6 supports this contention as the market cap-weighted index in fact overweights the overpriced stocks, Ford and Intel, and underweights the underpriced stocks, Microsoft and Cognizant.

Exhibit 6 further shows that the fair value-weighted index avoids this systematic bias as it assigns more weight to the underpriced growth stocks and less weight to the overpriced value stocks (see weight redistribution).

## FAIR VALUE VERSUS FUNDAMENTAL WEIGHTING

Fundamental indexes weight stocks based on accounting-based metrics of company size, such as book value, earnings, cash flow, and dividends, or based on a combination of such metrics. From a portfolio perspective, fundamental indexes do not rank companies solely in line with individual stocks’ accounting figures, but rather companies with high accounting figures, which at the same time exhibit low market values (Kaplan [2008]). As we have discussed, there are multiple issues concerning such an approach. First, a fundamentally weighted index makes the implicit assumption that all stocks in a portfolio trade at a price value multiple of one, e.g., a P/E of 1. In other words, by ignoring individual stocks’ price multiples, a fundamentally weighted index also ignores the fact that individual stocks have different risk (volatility) and growth and profitability characteristics. Second, since a fundamentally weighted index assumes all stocks to have a P/E of 1, it will overweight stocks that exhibit low P/E multiples, i.e., value stocks. Third, and as we have discussed, value stocks are not necessarily underpriced stocks, but rather stocks that exhibit above-average risk and below-average growth prospects. Exhibit 7 demonstrates the differences between a fundamentally weighted index and a fair value-weighted index.

As shown in Exhibit 7, a fundamental weighted index, similar to a market cap-weighted index, overweights the overpriced value stocks (Ford and Intel) and underweights the underpriced growth stocks (Microsoft and Cognizant). The reason is that fundamental index weights are uncorrelated to market price and, because of this, are poor proxies for individual stocks’ fair values (Buffett [1992]). Consequently, the observed returns of fundamentally weighted indexes can only be explained by randomizing pricing errors caused by investors in market cap-weighted indexes.

## PERFORMANCE

We examine the performance of the Fair Value Weighted 500 Index (FVW 500) relative to two broad market cap-weighted indexes: the S&P 500 and the Russell 1000. The FVW 500 comprises the 500 largest U.S. constituents as measured by fair value. The FVW 500 overweights stocks that have higher ranked fair value and underweights stocks that have lower ranked fair value. Thus, the FVW 500 is dominated by large-cap stocks that have beta and growth prospects very similar to a broad market cap-weighted index, e.g., the S&P 500. The FVW 500 is rebalanced at the beginning of each calendar year. Exhibit 8 compares the return of the FVW 500 with the market capitalization-weighted market indexes, the S&P 500 and the Russell 1000, for the 15 years from January 1, 2000, to December 31, 2014.

Perhaps not surprisingly, the FVW 500 markedly outpaced the S&P 500 and the Russell 1000 for the period with, on average, 6.19% and 5.70%, respectively. We explain the FVW 500 index excess return by estimating a fair value independent of market price allowing the FVW 500 to effectively overweight underpriced stocks and underweight overpriced stocks. Since the S&P 500 and the Russell 1000 do the opposite, the FVW 500 also allows investors to capture these superior returns with a significantly lower risk, as evidenced by the Sharpe ratio (0.42 versus 0.10 and 0.12 for the S&P 500 and Russell 1000, respectively). This is further evident when we study the performance of the FVW 500 in bull and bear markets (see Exhibits B1 and B2 in Appendix B).

We continue by examining the performance of the FVW 500 relative to the Russell 1000 Value and the Russell 1000 Growth traditional style indexes for the same period. These style indexes are typically created by selecting stocks based on various price multiples, such as the price-to-book market value, where below-average P/B stocks are categorized for the value index and above-average P/B stocks are categorized for the growth index. Both indexes are market cap-weighted and, as a result, they suffer not only from the same shortcomings as market cap-weighted indexes but also from concertation biases represented by industry bets. Thus, traditional style indexes are unrepresentative of the underlying economic exposure and consequently are poorly diversified. Further, the traditional style-based investing approach does not capture the value premium and the rebalancing premium effectively, nor are they sufficiently broad as to fully exploit the value and rebalancing premium across all stocks and all industries (Hsu [2014]). Based on these theoretical flaws, it comes perhaps not as a surprise that the FVW 500 significantly outpaced both these indexes by 3.70% and 8.11% per annum for the period, respectively, and again to a notably lower downside risk (see Exhibits 8 and B12). Thus, the FVW 500 excess return can be attributed to more effectively rebalancing toward underpriced stocks, which over time markedly reduces the downside risk, as indicated by the Sharpe ratio.

We further examine the FVW 500 performance relative to the RAFI 1000 fundamental index. We show that the FVW 500 outpaces the RAFI 1000 by 2.58% on an annual basis for the period, again with a markedly improved Sharpe ratio (0.42 versus 0.28). Once more, we explain the FVW 500 superior risk adjusted return by more efficiently overweighting underpriced stocks and underweighting overpriced stocks. Relative to the RAFI 1000, the FVW 500 also takes significantly less downside risk, which can be explained by the fact that the FVW 500 tilts toward stocks that exhibit lower risk and superior long-term growth prospects, while the RAFI 1000 generally does the opposite, that is, it tilts toward value and small-cap stocks that exhibit the opposite characteristics, i.e., higher risk and inferior long-term growth prospects.

Finally, we compare the FVW 500 to the Berkshire Hathaway Class A stocks for the same period. One can argue that a performance comparison to Berkshire Hathaway would be irrelevant since the Berkshire Hathaway investment portfolio is obviously not passively managed, nor is it rules-based and transparent. While that is true, it is also true that a significant portion of Berkshire Hathaway’s returns can be explained by factors such as value, low volatility, and quality (Frazzini, Kabiller, and Pedersen [2012]), and that combining these factors produces attractive diversification benefits (Bender, Brandhorst, and Wang [2014]). In other words, combining value, low volatility, growth, profitability, and interest rates in a holistic multifactor approach, as shown in this article, better explains the fair value of individual stocks, which is necessary for efficiently capturing the value premium in equity markets.

Exhibit 8 shows that the FVW 500 had a long-term risk adjusted return very similar to the Berkshire Hathaway Class A stocks for the period, on average 0.59% higher and with a slightly lower Sharpe ratio (0.42 versus 0.43).

## PERFORMANCE ATTRIBUTION

The observed excess return of the FVW 500 is consistent with the hypothesis that stock prices are inefficient. We have demonstrated both theoretically and empirically that the mean–variance superiority of fair value-weighted indexes is robust and significant. We argue that the performance advantage comes from improving the accounting-based approach, which focuses largely on specifying the expected accounting outcomes to be discounted by focusing on the discount rate under the mantra of asset pricing.

We offer the important insight that common price multiples (such as the P/E) do not account for risk and reward factors independent from market price. Hence, the market price (P), the numerator in the equation, is adjusted (by investors) for risk and expected return, but the denominator (the fundamental size metric) remains unadjusted, (E). This leads to the conclusion that value stocks carry more risk than growth stocks and that this additional risk is not adequately accounted for in the traditional valuation framework. Thus, the lower P/E of value stocks can only be explained by investors requiring a higher discount rate due to higher risk.

The asset pricing approach, as we have introduced in this article, provides for a risk-based explanation for the relatively lower market value of value stocks but not for the empirically observed value premium in value stocks, as our findings suggest that the lower P/E (the higher earnings yields) of value stocks are a result of inadequate risk adjustments. Hence, we argue that value stocks are fair valued at a lower P/E (higher E/P), and that the opposite is true for growth stocks. This suggests that the academics who are arguing the risk-based explanation are both right and wrong—right in the way that value stocks are riskier, but wrong when it comes to explaining the value premium. The value premium does not arise from systematic risk, as suggested by the CAPM (see Fama and French [1996]); rather, it is company-specific risk that explains differences in valuation across value and growth stocks. Hence, we argue that the value premium observed to date can only be explained by mispricing.

The key benefit of fair value weighting is that it allows for capturing the “bona fide” value premium in equity markets. This value premium allows investors to capture the value premium in all stocks. In other words, the value premium can be captured not only in value and small-cap stocks but also, most importantly, in growth and large-cap stocks. Additionally, we argue that this value premium (2.0) is more robust and significantly higher than the value premium found merely in value and small-cap stocks.

## TURNOVER, LIQUIDITY, AND CAPACITY

The FVW 500 is rebalanced as of January 1 each calendar year. The resulting turnover only modestly exceeds the turnover for capitalization-weighted indexes. Since the fundamental fair value indexes are concentrated in large, liquid companies, the relatively low rebalancing turnovers translate into rebalancing costs that are nearly as low as those for capitalization-weighted indexes.

We examine index characteristics that can help us assess the liquidity and capacity of fair value-weighted indexes. In conjunction with the information on annual portfolio turnover, this allows us to assess the impact of transaction costs on the excess returns generated by fair value-weighted indexes. We measure the capacity by dividing the fair value weights’ average capitalization by the capitalization-weighted average capitalization. (See Appendix C for an additional comparison of fair value vs. market cap weighting for a sample of 30 stocks.)^{6} The resulting *CAP ratio* measure helps us assess the investment capacity of the fair value-weighted index. For example, a CAP ratio of 1.00 suggests that the weighted average capitalization of the companies in the fair value-weighted index is equal to that of the market cap-weighted index. The fair value-weighted index scores a CAP ratio of 0.97 as compared with a market cap-weighted index of 1.00. This suggests that a fair value-weighted index portfolio has liquidity of 97% that of the market capitalization index. Hence, a fair value-weighted index (FVW 500) has a liquidity and investment capacity very similar to a market cap-weighted index.

The average annual index turnover of the fair value-weighted index is 8.5%, considerably lower than that for fundamentally weighted indexes and roughly 3.2% higher than a market capitalization-weighted index, which we attribute to pure rebalancing of index weights. The extra turnover, as explained by the FVW 500 index portfolio, must account for changes in fundamental factors from the beginning-of-the-year policy weights. This increases the turnover from 6.3% in the market cap-weighted index to an average of 8.5% for the FVW 500. Another pertinent issue is the erosion of the excess return relative to the capitalization-weighted index due to transaction costs. Assuming a 2% two-way transaction cost (or 1% each way, including both transaction fees and price impact), the average annual excess return over the S&P 500 for the period 2000–2014 would fall from 6.19% to 5.78%.

The implementation characteristics of a fair value-weighted index hence satisfy the biggest investor concerns of liquidity, investment capacity, and trading costs. Exhibit 9 illustrates the weighted average market capitalizations and the average turnover estimates for the fair value-weighted index and four well-known smart-beta index strategies.

## INTUITION OF FAIR VALUE INDEXATION

We believe the performance of fair value-weighted indexes to be free of data mining. The metrics used are straightforward ex post factors commonly used by investors in market cap-weighted indexes in assessing the fair value of individual stocks. We use no subjective stock selection or weighting decisions in the index construction process, and the index simply comprises the 500 largest stocks as measured by their fair values. Part of the motivation of our research is that both the efficient market hypothesis and the conventional CAPM are theories that may seriously misguide investors. Another reason is that value investing is still largely misunderstood, and no systematic and rules-based framework exists for assessing a stock’s fair value. The importance of estimating a fair value is often referred to as the Holy Grail in investing; this is because the essence of value investing is to buy stocks for less than their intrinsic “fair” value. Hence, if a fair value cannot be adequately estimated, the value premium cannot be harvested efficiently in equity markets, nor can investors adequately allocate assets across stocks and bonds, or mitigate downside risk (Perold [2007]).

Fair value-weighted index methodology builds on a holistic multifactor approach to asset pricing, that is, the knowledge of factors, their relationships, and how they fit together to explain asset pricing. The key factors involved are size-based fundamental factors, such as earnings and/or cash flows, growth, profitability, volatility, and macroeconomic factors, such as interest rates and inflation. These factors, when adequately combined, provide for a framework that better explains the fair value for individual stocks. Thus, a fair value-weighted index builds on the same basic logic as a market cap-weighted index as both indexes consider not only economic footprints, but also individual stocks’ heterogeneous risk and reward characteristics. The difference between the two is that a fair value-weighted index considers such factors independent of a stock’s market price. Hence, the FVW 500 can be viewed as a smart-beta replica of a market cap-weighted index (e.g., the S&P 500), with very similar liquidity and investment capacity, while offering investors the opportunity to harvest the bona fide value premium in equity markets.

## CONCLUSION

We have demonstrated that the value premium in value and small-cap stocks, despite strong empirical evidence, is highly suboptimal. Value stocks can be overpriced just as likely as they can be underpriced. Conversely, growth stocks can be underpriced just as likely as they can be overpriced when common price multiples are used to measure equity returns based on valuation. As a result, the value premium in value and small-cap stocks is highly inefficient since it can only be captured by chance and only in stocks that exhibit higher risk and inferior long-term growth prospects.

We contend that the discount rate, as introduced in this article, provides a straightforward and practical solution to the long-standing value premium puzzle in finance. We show that formulating a fundamentals based fair value, which controls for heterogeneous risk and reward factors independent of market price, allows investors to capture a more robust value premium in equity markets. This novel value premium can be captured in all stocks independent of investment styles. In other words, this value premium can be captured not only in value and small-cap stocks but most importantly also in growth and large-cap stocks.

Fair value-weighted indexes have, similar to market cap-weighted indexes, a large-cap–growth tilt. However, contrary to a market cap-weighted index, a fair value-weighted index overweights underpriced stocks and underweights overpriced stocks regardless of whether such stocks exhibit high or low earnings volatility, are large- or small-cap stocks, or are classified as value or growth stocks. In other words, the valuation tilt is dynamic; that is, a fair value-weighted index overweights large-cap growth stocks only when value stocks are overpriced, and vice versa. Consequently, fair value-weighted indexes add value by providing an effective rebalancing premium toward underpriced stocks while retaining the key benefits of market cap-weighted indexes, such as broad market representation, high liquidity, high investment capacity, and low-cost access to equity markets. If avoiding unintended factor bias and improving risk adjusted returns are the goals of institutional investment management, then fair value-weighted indexes would be preferred to market capitalization-weighted indexes and evidently also to today’s alternatives, such as traditional value and growth style indexes and fundamentally weighted indexes.

## APPENDIX A

We use the fair value, as introduced in this article, to argue that common price multiples, when used to measure expected returns based on valuation, are theoretically flawed. To illustrate, suppose we have four hypothetical value stocks (Stocks A, B, C, and D) all with the same net earnings of $10, and all fair valued assuming rational markets. Stock A is a typical value stock, which exhibits a below-average P/E ratio of 10 (and thus an above-average E/P of 10%), below-average earnings growth of 5%, and above-average earnings growth volatility of 15%. This together translates to a risk premium of 7.5% and an overall discount rate of 10%, assuming the Treasury yield is 2.5%.

Exhibit A1 shows that Stock A (the base case) is fair valued at $100 with a risk adjusted earnings yield of 2.5%, which is in equilibrium with the Treasury yield. Note that in equilibrium (i.e., when the stock is fair valued) the discount rate (j) equals the earnings yield (d) and the risk adjusted earnings yield (l) equals the Treasury yield (i.e., the risk-free rate) (i), which explains the equity–bond risk–reward equilibrium asset pricing approach, as we have introduced in this article. To illustrate how risk affects price multiples, we make changes only to the factors that affect the discount rate, which include earnings growth volatility, earnings growth, and interest rates, as we proxy the 10-year Treasury yield (see Exhibit A1, e, f, and i) under the assumption of rational stock markets.

Stock B exhibits significantly higher volatility risk than Stock A: risk is up from 15% to 30% (see f), which translates to a higher discount rate (j) and consequently to a lower fair value, $57.14 (k). Assuming that investors are rational (factoring in the higher risk), the market price will adjust from $100 (see a) to $57.14, matching the fair value (k). *This makes sense*, since higher risk should lead to a higher discount rate and thus a lower fair market value. *However, what doesn’t make sense* is that Stock B’s earnings yield increases relative to Stock A’s (increased from 10% to 17.5%) (see d), suggesting that Stock B is significantly more attractive than Stock A.

The flaws of common price multiples (such as P/E) become even more evident when we analyze Stock C. Stock C has not only higher risk but also lower reward (a lower growth rate) (see e) relative to Stock A, which together translates to even more inferior risk-to-reward characteristics (see g). As a result, the risk premium and the discount rate are considerably higher for Stock C and, consequently, the fair market value decreases from $100 to $30.77 (k). Again, we show that the earnings yield increases (32.5%) (see d) when the market price adjusts downward, indicating that Stock C is even more attractive (underpriced) than Stock A and Stock B. That simply doesn’t make sense.

Finally, in the Stock D scenario, we assume that the Federal Reserve raises interest rates (Rf) (see i) due to inflation. As a result, the discount rate increases, the fair market price (P) decreases, and as a result, the earnings yield (E/P) increases to 12%, making Stock D look more attractive than Stock A. Even if we increase the net earnings, assuming that Stock D (not illustrated in Exhibit A1) can fully offset the rise in interest rates by raising the price of its product or service offering, say from $10 to $12 ($12/12% = $100), Stock D’s earnings yield would still increase from 10% (the base case) to 12%. That is because the net earnings (E) increase while the stock price (P) declines, indicating (incorrectly) that the stock is more attractive after the Federal Reserve raised interest rates than it was before. Again, this is evidence of the methodical problems inherent in common price multiples when such metrics are used to measure expected returns across stocks.

From a theoretical perspective, the problem is that common price multiples, such as the P/E, use unadjusted fundamental metrics of firm size, such as net earnings (E), as a proxy for fair value. Note that a stock’s market price (P), by definition, reflects investors’ assessments of the stock’s risk and future growth prospects and is thus adjusted by investors, while the fundamental size metric (E) does not adjust for such factors. The result is that when risk increases (or reward decreases) or interest rates rise, the earnings yield increases, making the stock look more attractive. This is a serious flaw that may mislead investors to invest in stocks that may be not only overpriced but most certainly exhibiting above-average higher risk and below-average growth and profitability relative to the market. That is, as it sounds, not optimal.

Our research shows that, under an assumption of stock market efficiency, the earnings yield is rather an investor’s required discount rate. To illustrate, say a stock has net earnings of $10, and the earnings yield is 10% (P/E 10); then the stock’s market value can be written as $10 divided by 10% equals $100. In other words, the earnings yield is equivalent to the discount rate (see Stock A, d and j, in Exhibit A1). Thus, we argue that the earnings yield (and obviously also the P/E) is not an appropriate measure of valuation; rather, the earnings yield represents investors’ required return (i.e., the discount rate).

However, if stock markets are inefficient (i.e., market prices do not equal fair values), the required return (i.e., the earnings yield) may be either too high or too low, creating opportunities for investors to capture the value premium in equity markets. This finding also has implications for asset allocation across equity and fixed-income securities, as it suggests that the so-called “Fed” model is theoretically flawed (see Exhibit A1, d versus l). See also Asness [2003] and Estrada [2009], who address the same problem.

## APPENDIX B

## APPENDIX C

## ENDNOTES

We would like to express our deepest appreciation to Jennifer Bender, PhD, managing director of research for Global Equity Beta Solutions at State Street Global Advisors, for her valued feedback.

We should note that we have two patents pending for the construction of fair value-weighted indexes, which are based on a rules-based and systematic assessment of individual stocks’ fair value based on fundamental analysis. We also hold trademarks in the United States with the U.S. Patent and Trademark Office (USPTO) and in Europe.

↵

^{1}The CAPM states that the risk-to-expected-return tradeoff is systematic, rather than unsystematic. Furthermore, the CAPM teaches that the relationship between risk and expected return is positively correlated. As a result, the CAPM teaches that only high beta stocks (riskier stocks) can offer higher returns relative the market.↵

^{2}For example, Russell Investments describes the “value factor” as the oldest form of active value investing dating back to the days of Benjamin Graham and David Dodd. See https://russellinvestments.com/au/insights/library/inside-smart-beta--making-sense-of-investment-factors.↵

^{3}CAPM says risk and reward are correlated in a positive fashion. The exact opposite is true in value investing. The greater the potential for reward, the less risk there is (Buffett [1984]). Real investment risk is measured not by the percent that a stock might decline in price in relation to the general market in a given period, but by the danger of a loss of quality and earnings power through economic changes (Graham [1949]).↵

^{4}From a portfolio construction perspective, it is contemplated that if a stock’s current net earnings are negative (i.e., a company reports a loss) the net earnings may be substituted by the stock’s current free cash flow. It is furthermore contemplated that additional fundamental metrics and/or profitability measures may be used in a combination when estimating a stock’s growth rate (reward). Finally, if a firm’s calculated fair value does not exceed the firm’s trailing twelve months book value, it is contemplated that the book value may be used as the fair value weight. That is often the case for so called deep value stocks. A further discussion on this subject goes beyond the purpose of this article.↵

^{5}Investors often compare the earnings yield (E/P) of a broad market index (such as the S&P 500) to prevailing interest rates, such as the current 10-year Treasury yield. They argue that if the earnings yield is less than the rate of the 10-year Treasury yield, stocks as may be considered overvalued. Similarly if the earnings yield is higher, stocks may be considered undervalued relative to bonds. We note that a similar reasoning is inherent in the so-called Fed model.↵

^{6}It is contemplated that a fair value-weighted index may have a higher or lower total capitalization than a market cap, weighted index under different market regimes. A higher capitalization relative to the market is particularly evident in late-stage bear markets and a lower capitalization is similarly evident in late-stage bull markets. However, under normal market conditions, a fair value-weighted index capitalization is fairly correlated to the market capitalization.

- © 2017 Pageant Media Ltd