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**Chapter 11 Equity Market Valuation**

Presenter Venue Date This chapter illustrates the application of economic forecasts to the valuation of equity markets. Although many factors interact to determine whether equity prices are currently rising or falling, economic fundamentals will ultimately dictate secular equity market price trends. Section 2 uses GDP forecasts for a developing country, China, to develop inputs for a discounted cash flow valuation of that country’s equity market. Section 3 contrasts the top-down and bottom-up valuation approaches. Section 4 explains and critiques popular earnings- and asset-based models to relative equity market valuation. Section 5 summarizes the reading. DISCLAIMER: Candidates should understand that this presentation is NOT a substitute for a thorough understanding of the CFA Program curriculum. This presentation is also NOT necessarily a reflection of all the knowledge and skills needed for candidates to successfully complete questions regarding this topic area on the CFA exam.

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**Neoclassical Approach to Growth Accounting**

Cobb-Douglas production function Assuming constant returns to scale, 1 – α = β, and taking the natural logarithm of both sides of first equation gives Taking first differences of second equation and using a property of logarithms results in this approximation: LOS: Explain the terms of the Cobb-Douglas production function and demonstrate how the function can be used to model growth in real output under the assumption of constant returns to scale. Pages The neoclassical approach to growth accounting uses the Cobb-Douglas production function. This approach can be useful to financial analysts because it provides insight into the long-term potential economic growth in individual countries, in larger regions, and for the world as a whole. The Cobb-Douglas estimate of the growth of total production can help to estimate corporate profit growth and develop corporate cash flow projections for stock market composites. The basic form of the Cobb-Douglas production function is set forth in the first equation, where Y represents total real economic output, A is total factor productivity, K is capital stock, α is output elasticity of K, L is labor input, and β is the output elasticity of L. Total factor productivity (TFP) is a variable that accounts for that part of Y that is not directly accounted for by the levels of the production factors (K and L). If we assume that the production function exhibits constant returns to scale (i.e., a given percentage increase in capital stock and labor input results in an equal percentage increase in output), we can substitute β = (1 – α) into the first equation. Taking the natural logarithm of both sides of the equation results in the second equation. Taking first differences of the second equation and using a property of logarithms results in the third equation. Equation 3 is the expression that is used in the analysis.

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**Growth Accounting Formula**

Percentage growth in real output (GDP) ΔY/Y Percentage growth in total factor productivity ΔA/A Percentage growth in the capital stock ΔK/K Percentage growth in labor ΔL/L Output elasticity of capital α Output elasticity of labor 1 − α LOS: Explain the terms of the Cobb-Douglas production function and demonstrate how the function can be used to model growth in real output under the assumption of constant returns to scale. Pages The percentage growth in real output (or gross domestic product, GDP) is shown as ΔY/Y and it is decomposed into its components: ΔA/A is the growth in TFP; ΔK/K is the growth in the capital stock; ΔL/L is the growth in the labor input; α is the output elasticity of capital; and 1 – α is the output elasticity of labor where 0 < α < 1. In practice, all the variables in the growth accounting formula, with the exception of the growth in TFP, are directly observable or can be derived from national income and product accounts. However, growth in TFP can be determined using the other inputs and is commonly referred to as the Solow residual.

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**Total Factor Productivity (TFP)**

Technical Progress and Innovation Changes in Political/Regulatory Structures Improvements in the Division of Labor LOS: Explain the terms of the Cobb-Douglas production function and demonstrate how the function can be used to model growth in real output under the assumption of constant returns to scale. Pages Total factor productivity (TFP) growth means that aggregate output (i.e., GDP) can grow at a faster rate than would be predicted simply from growth in accumulated capital stock and the labor force. Interpreting TFP as a measure of the level of technology, growth in TFP is often described as a measure of “technical progress” and linked to innovation. As examples, such technological advances as the introduction of the steam engine, electricity, the internal combustion engine, telecommunications, microchips, penicillin, and the internet are thought to have contributed to growth in TFP. However, growth in TFP, as a residual in the sense described, can be driven by factors other than improvements in technology. These factors could be particularly significant in economies that are experiencing major changes in political and/or regulatory structures. For example, liberalization of trade policies, abolition of restrictions on the movement and ownership of capital and labor, the establishment of peace and the predictable rule of law, and even the dismantling of punitive taxation policies would be expected to contribute to growth in TFP. Finally, growth in TFP can benefit from improvements in the division of labor that arise from the growth of the economy itself. By contrast, such developments as the depletion and degradation of natural resources would detract from growth in TFP.

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**The China Economic Experience**

LOS: Evaluate the relative importance of growth in total factor productivity, in capital stock, and in labor input given relevant historical data. Page 472 China has been widely regarded as the most influential emerging economy, and its growth performance since reform has been hailed as an economic miracle. Historical growth accounting results, as presented in Zheng, Hu, and Bigsten (2009), are reported in the table. Note particularly the comparisons of China’s growth in the capital stock, ΔK/K, and growth in the labor input, ΔL/L, with those of the (former) Soviet Union, the United States, and the European Union. The growth in capital stock stands out particularly for China and is most apparent during the period of economic liberalization that commenced in the early 1990s. According to estimates by the World Bank and other institutions, the gross effective savings in China (loosely defined as investment in plant, property, equipment, and inventories) divided by economic output have been in the neighborhood of 40%. This compares with 15% to 20% over the comparable periods for the other countries. Source: Zheng, Hu, and Bigsten (2009). China’s output elasticity for capital (α) and output elasticity for labor (1 – α) were both estimated to be 0.5.

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**Quantifying China’s Future Economic Growth**

ΔA/A Reform measures? Productivity? ΔK/K Government policies? Price controls? High savings rates? ΔL/L Population growth? Labor force participation rates? LOS: Evaluate the relative importance of growth in total factor productivity, in capital stock, and in labor input given relevant historical data. Pages Concerns over the sustainability of China’s growth have emerged in recent years because, as is evident in the table on the previous slide, the growth in TFP has slowed. Zheng, Bigsten, and Hu (2006) studied the Chinese economy and found that reform measures had a significant positive impact on TFP, but this impact should be considered a one-time event. Those authors make a case that China should now focus on achieving sustained increases in productivity. The previous slide shows that Chinese economic growth has been largely driven by growth in the capital stock. Zheng, Bigsten, and Hu note that government policies in the mid- to late 1990s supported this extraordinary growth in investments. Key input prices were kept low through subsidies, and controlled pricing and a high savings rate allowed for the availability of cheap credit. A huge trade surplus has been another side effect of both high investment and an unsustainably low fixed exchange rate policy designed to support exports. China’s foreign reserves are currently the world’s largest by a considerable amount and have recently surpassed US$2 trillion. Because of this size, China is facing excessive growth in its money supply and there are concerns about potential bubbles in both real estate and share prices. (Recent year-over-year growth in the broad M2 measure of the money supply has been over 25%.) A necessary, eventual “course correction” in exchange rate and monetary policies would reduce or reverse the forces that contributed to a de facto subsidization of capital formation. In addition to the foregoing structural factors, changes in consumer behavior are also likely to cause the Chinese savings/investment rate to moderate. Altogether, government policy changes, structural imbalances, and an increased propensity to consume point to an eventual reduction from the double-digit growth rates of capital stock. At the same time, while the labor force of China has grown at a much more rapid pace than that of the European and U.S. economies, it has been attributable both to higher population growth rates and to a rise in labor force participation rates. The Chinese population growth rate has slowed to less than 1.0% per year in recent years, according to the World Bank. Furthermore, major changes in labor force participation rates, largely because of more people leaving rural occupations and household/childcare activities, represent one-time changes rather than sustainable trends. In sum, these considerations suggest that Chinese economic growth will eventually moderate, which is consistent with the economic history of the Soviet Union, the United States, and the European Union. Finally, in addition to the factors above, an investment analyst might wish to consider other, more qualitative factors in producing a long-term growth forecast (e.g., China’s educational system or pollution side effects of China’s strategy of rapid capital formation). Because adjustments for such factors would typically have a large judgmental element, this reading does not address them.

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**EXHIBIT 11-2 Growth Projections (2009−2030)**

Source: Zheng, Hu, and Bigsten (2009). LOS: Explain the terms of the Cobb-Douglas production function and demonstrate how the function can be used to model growth in real output under the assumption of constant returns to scale. Pages Zheng, Hu, and Bigsten (2009) offer the GDP growth projections presented in Exhibit 11-2 for China, the United States, and the European Union. The forecast of an 8% GDP growth rate for China is consistent with the Chinese government’s 8% GDP growth target as presented by Premier Wen Jiabao. Zheng, Hu, and Bigsten note their own projections rely heavily on two basic assumptions: (1) Growth in the capital stock cannot exceed GDP growth; and (2) a TFP growth rate of 2% to 3% will prevail for the foreseeable future. These authors believe that the potential for China to absorb new technologies from developed nations is double that for the United States and the European Union. Given the history of other developing countries and the record of economic recovery of developed countries after World War II, this view does not seem unreasonable.

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**Growth Forecast for China**

Total factor productivity + Growth in capital stock + Labor force growth = Real GDP growth Near-term growth forecast: 2.5% + (0.5 × 12%) + (0.5 × 1.5%) = 9.25% Sustainable economic growth rate: 1.25% + (0.5 × 6%) + (0.5 × 0.0%) = 4.25% LOS: Explain the terms of the Cobb-Douglas production function and demonstrate how the function can be used to model growth in real output under the assumption of constant returns to scale. Pages In applying the framework, the authors modify the Zheng, Hu, and Bigsten (ZHB) projections by using a lower estimate of the growth rate in the labor force because World Bank data indicate that population growth in China now appears to have declined to less than 1.0% annually. At the same time, they think that savings and investment rates will only decline gradually from more than 35% of GDP, thereby keeping the growth rate of capital stock much higher than the 8% per annum assumed by ZHB. The authors have no disagreement with the ZHB projection of 2.5% per year for TFP growth. Utilizing the labor and capital elasticities from the ZHB study, a reasonable projection for economic growth would therefore be: Total factor productivity plus Growth in capital stock plus Labor force growth 2.5% × 12% × 1.5% = 9.25% This near-term rate is higher than the ZHB forecast, the official forecast of the Chinese government, and the consensus of many economic forecasters. The authors note, however, that there are several factors that are consistent with the higher near-term forecast. First, actual real growth has cumulatively exceeded the 8% Chinese official growth target of the past several years. Second, and more importantly, the forecast is to be thought of as a normalized forecast of sustainable cash flow growth potential. While this near-term forecast for economic growth is higher than ZHB and the Chinese government, the reasoning set forth in the preceding section leads the authors to believe that economic growth will gradually decline to levels lower than the ZHB analysis. This result is because, as economies develop and as the stock of accumulated capital per person rises, savings rates tend to decline and TFP trends fall to levels closer to those of more highly developed countries. Finally, although labor force growth can exceed population growth for some time (as labor force participation rates increase), in the long run labor force growth is constrained by population growth. China appears to be on its way toward zero population growth (much like Japan and Western Europe). With this in mind, an ultimately sustainable economic growth rate might be: 1.25% × 6% × 0.0% = 4.25%

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**Equity Market Valuation**

Macroeconomic Forecasts Corporate Cash Flow Forecasts Discounted Cash Flow Model Justified P/E LOS: Demonstrate the use of the Cobb-Douglas production function in obtaining a discounted dividend model estimate of the intrinsic value of an equity market. Page 476 In this section, the authors translate macroeconomic forecasts into corporate cash flow forecasts and combine those corporate forecasts with an appropriate discounted cash flow model to estimate the intrinsic value of an equity market in terms of justified P/Es. The growth rate of corporate earnings and dividend cash flow, adjusted for inflation, should bear a close relationship with real GDP growth over the long term. For purposes of this analysis, the authors assume that earnings and dividend cash flow for the underlying comprehensive stock composite grow at the same rate as the core growth rate of Chinese GDP.

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**Using the H-Model to Estimate a Justified P/E**

Assumptions: Dividend growth declines linearly from rate gS to rate gL over N years. After N years, dividends grow at rate gL into perpetuity. LOS: Demonstrate the use of the Cobb-Douglas production function in obtaining a discounted dividend model estimate of the intrinsic value of an equity market. Pages Fuller and Hsia (1984) developed a valuation model, known as the H–model, in which dividend growth rates are expected to decline in a linear fashion, over a finite horizon, toward an ultimately sustainable rate from the end of that horizon into perpetuity. It incorporates a growth rate in dividends that is expected to prevail in the initial period gS, a period of years, N, where the dividend growth rate declines in a linear fashion, and a long-term dividend growth rate gL that is expected to prevail to perpetuity beginning at the end of period N. With an initial annualized dividend rate at time zero of D0 and a discount rate to perpetuity of r, the H–model estimate of value,V0, is given by the formula in the slide. The H-model provides a convenient means for modeling initially high (supernormal) dividend growth rates that gradually transition to a lower, long-run growth at a constant mature-stage growth rate. The (forward) justified P/E is the H-model estimate of intrinsic value divided by year-ahead expected earnings. In all instances, the authors assume that core inflation-adjusted growth rates decline in a linear fashion over a 30-year time horizon from the 9.25% per year estimate for year one. The 30-year time horizon is selected both because it is a round number and because it is not unlike other historical instances when national economies experienced fundamental changes in political and economic structure, the notable examples being post−World War II European economies and Japan both in the late 19th century and after World War II.

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**EXHIBIT 11-3 Justified P/E Ratios for Chinese Equity Market at Mid-Year 2009**

Note: Chinese equity market justified P/Es: 30-year transition from 9.25% real dividend growth to various terminal growth rates to perpetuity. LOS: Evaluate the sensitivity of equity market value estimates to changes in assumptions. Pages As of 15 July 2009, the forward or prospective P/E for the underlying S&P China BMI Index was 19.1 (this P/E is the level of the S&P China BMI Index divided by year-ahead expected earnings for that index). Exhibit 11-3 presents justified P/E ratios under differing inflation-adjusted equity discount rates and for different estimates of the ultimately prevailing terminal inflation-adjusted dividend growth rate to perpetuity. Note that the observed 19.1 P/E on 15 July 2009 is consistent with a real equity discount rate just under 8.0% and a terminal real dividend growth rate just over 4.0%.

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**U.S. real equity discount rate = 6−7%? **

EXHIBIT 11-6 Return and Volatility Data, 31 December 2001–31 December 2008 LOS: Evaluate the sensitivity of equity market value estimates to changes in assumptions. Pages In establishing a reasonable discount rate to apply to the cash flow forecasts, the higher volatility of Chinese markets needs to be taken into account. In the volatile economic and market conditions at the time (2009) this chapter was written, the higher end of discount rate estimates seemed to be in order for the United States. If those are placed at 6−7%, the additional relative risk considerations for the Chinese market suggest that a required discount rate for that market might be in the range of 7.5–8.5%. This adjustment is necessarily judgmental but should (1) reflect an analyst’s view of differential riskiness (in the context of a well-diversified international portfolio) and (2) reflect congruence with historical realized return differentials between markets that were then seasoned and those that were then developing. Referring back to Exhibit 11-3 and integrating the authors’ view of the real (i.e., inflation-adjusted) equity discount rate with the sustainable dividend growth rates obtained from the macroeconomic framework, the authors conclude that the currently observed 19.1 forward P/E for Chinese equities is not unreasonable. U.S. real equity discount rate = 6−7%? Chinese real equity discount rate = 7.5−8.5%?

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**Top-Down and Bottom-Up Forecasting**

Macroeconomic Projections Forecast Market Returns Forecast Industry Returns Forecast Security Returns Microeconomic Projections Forecast Security Returns Forecast Industry Returns Forecast Market Returns LOS: Contrast top-down and bottom-up forecasts of the earnings per share of an equity market index. Pages When it comes to predicting equity returns, analytical approaches can be divided into two major categories: top-down and bottom-up. Top-down can be characterized as moving from the general to the specific, whereas bottom-up forecasting moves from the specific to the general. In top-down forecasting, analysts use macroeconomic projections to produce return expectations for large stock market composites, such as the S&P 500 Index, the Nikkei 225, or the FTSE 100. These can then be further refined into return expectations for various market sectors and industry groups within the composites. At the final stage, such information can, if desired, be distilled into projected returns for individual securities. By contrast, bottom-up forecasting begins with the microeconomic outlook for the fundamentals of individual companies. An analyst can use this information to develop predicted investment returns for each security. If desired, the forecasts for individual security returns can be aggregated into expected returns for industry groupings and market sectors and for the equity market as a whole.

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**Typical Approach to Top-Down Analysis**

Market Analysis Examine valuations in different equity markets to identify those with superior expected returns. Industry Analysis Evaluate domestic and global economic cycles to determine those industries expected to be top performers in the best-performing equity markets. Company Analysis Identify the best stocks in those industries that are expected to be top performers in the best-performing equity markets. LOS: Contrast top-down and bottom-up forecasts of the earnings per share of an equity market index. Page 485 Top-Down Analysis Market analysis: Examine valuations in different equity markets to identify those with superior expected returns. Compare relative value measures for each equity market with their historical values to identify those markets where equities are relatively cheap or expensive. Examine the trends in relative value measures for each equity market to identify market momentum. Compare the expected returns for those equity markets expected to provide superior performance with the expected returns for other asset classes, such as bonds, real estate, and commodities. Industry analysis: Evaluate domestic and global economic cycles to determine those industries expected to be top performers in the best-performing equity markets. Compare relative growth rates and expected profit margins across industries. Identify those industries that will be favorably impacted by expected trends in interest rates, exchange rates, and inflation. Company analysis: Identify the best stocks in those industries that are expected to be top performers in the best-performing equity markets.

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**Typical Approach to Bottom-Up Analysis**

Company Analysis Identify a rationale for why certain stocks should be expected to outperform, without regard to the prevailing macroeconomic conditions. Industry Analysis Aggregate expected returns for stocks within an industry to identify the industries that are expected to be the best performers. Market Analysis Aggregate expected industry returns to identify the expected returns for every equity market. LOS: Contrast top-down and bottom-up forecasts of the earnings per share of an equity market index. Page 485 Bottom-Up Analysis Company analysis: Identify a rationale for why certain stocks should be expected to outperform, without regard to the prevailing macroeconomic conditions. Identify reasons why a company’s products, technology, or services should be expected to be successful. Evaluate the company’s management, history, business model, and growth prospects. Use discounted cash flow models to determine expected returns for individual securities. Industry analysis: Aggregate expected returns for stocks within an industry to identify the industries that are expected to be the best performers. Market analysis: Aggregate expected industry returns to identify the expected returns for every equity market.

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**EXHIBIT 11-8 Standard and Poor’s Forecasts, July 2009**

LOS: Contrast top-down and bottom-up forecasts of the earnings per share of an equity market index. Pages Standard and Poor’s July 2009 top-down and bottom-up forecasts for operating earnings per share appear in Exhibit Note that the bottom-up forecasts are more optimistic than the top-down forecasts. What considerations might encourage a market analyst to rely more on a top-down or bottom-up forecast of S&P 500 operating earnings? Bottom-up forecasts are based on consensus earnings estimates from equity research analysts covering the S&P 500 stocks. Top-down estimates are often based on econometric methods rather than fundamental analysis of the companies comprising the index. Analysts frequently wait for information from the companies they follow to change their forecasts. Thus, bottom-up estimates may be more optimistic than top down heading into a recession and more pessimistic than top down coming out. If the belief exists that companies are reacting slowly to changes in economic conditions, then a market analyst may prefer a top-down forecast. However, top-down earnings forecasting models also have limitations. Most such models rely on the extrapolation of past trends in economic data. As a result, the impact of a significant contemporaneous change in a key economic variable or variables on the stock market may not be accurately predicted by the model. If the belief exists that the economy is on the brink of a significant change, then a market analyst may prefer the bottom-up forecast.

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**Relative Value Models Relative Value Models Earnings-Based Fed Model**

Yardeni Model P/10-Year MA(E) Asset-Based Tobin’s q Equity q LOS: Explain and critique models of relative equity market valuation based on earnings and assets. Page 491 Relative value investing is consistent with the popular trading maxim that investors should buy what is cheap and sell what is expensive. The relative value models presented in this section can be used to support the tactical asset allocation decision. They can help to identify times when investors would be well served by switching from bonds to stocks, or vice versa. As an investor, it is important to focus on the markets in a comparative fashion.

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**Fed Model Predictions of the model:**

Stocks are undervalued if their forward earnings yield is greater than the yield on government bonds. Stocks are overvalued if their forward earnings yield is less than the yield on government bonds. Limitations: Ignores the equity risk premium. Compares a real variable with a nominal variable. Ignores earnings growth. LOS: Explain and critique models of relative equity market valuation based on earnings and assets. Pages In its 22 July 1997 Humphrey-Hawkins report to Congress, the United States Federal Reserve compared 1982− year Treasury note yields with the earnings yield of the S&P 500 and showed a very close correlation between the two. The Fed model, so named by Edward Yardeni of (at the time) Prudential Securities, was based primarily on the results of this report. Use of the term “Fed model,” however, is somewhat misleading because the model has never been formally adopted by the Federal Reserve as a policy-making tool. The Fed model is a theory of equity valuation that hypothesizes that the yield on long-term U.S. Treasury securities (usually defined as the 10-year T-note yield) should be equal to the S&P 500 earnings yield (usually defined as forward operating earnings divided by the index level) in equilibrium. Differences in these yields identify an overpriced or underpriced equity market. The key criticism of the Fed model is that it ignores the equity risk premium. Implicit in the Fed model equilibrium are the assumptions that the required return and the accounting rate of return on equity for risky equity securities are equal to the Treasury bond yield. Historical evidence and financial theory resoundingly reject the notion that either assumption is true. Two additional criticisms of the Fed model are that it ignores inflation and earnings growth opportunities. Asness (2003) criticized the Fed model because it compares an arguably real variable, the earnings yield, with a nominal variable, the T-bond yield. According to this argument, the earnings yield is real because it is a ratio of current period prices. The T-bond yield is nominal because it is reflective of the expected rate of inflation as first noted by Fisher (1930). In the presence of inflation, investors should compare the earnings yield with a real interest rate. Asness provides evidence that the Fed model has often been a poor predictor of future equity returns. Another criticism of the Fed model is that it ignores any earnings growth opportunities available to equity holders beyond those forecasted for the next year. In the United States, long-term compound average earnings growth has been 3–4% nominal and 1–2% real. Thus, the model ignores a significant portion of total equity return.

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Exhibit The Fed Model: Difference between the S&P 500 Forward Earnings Yield and Yield on 10-Year T-Notes (Monthly Data: January 1979–December 2008) LOS: Judge whether an equity market is under-, fairly, or overvalued based on a relative equity valuation model. Page 492 The difference between the S&P 500 earnings yield (based on forward operating earnings estimates) and the 10-year T-note yield for the time period January 1979 through December 2008 is presented in Exhibit The Fed model predicts that investors will be indifferent between investing in equities and investing in government bonds when the difference between the two yields is zero. Note that the average difference between the two yields was 0.70% during this time period. The positive difference between the two yields was at its greatest in December Thus, the model predicted that equities were significantly undervalued at that time, following the stock market sell-off during the second half of Similarly, the largest negative differences occurred prior to the collapse of the stock market bubbles in October 1987 and early 2000. Source for data:

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**Yardeni Model Moody’s A-rated corporate bond yield**

Consensus five-year earnings growth forecast for the S&P 500 Weighting factor measuring the importance the market assigns to the earnings projections (average is about 0.10) Concerns: The risk premium captured by the model is largely a default risk premium and not the future equity risk premium, which is unobservable. The consensus five-year earnings growth forecast for the S&P 500 from Thomson Financial may not be sustainable. Evidence suggests that the weighting factor varies significantly over time. LOS: Explain and critique models of relative equity market valuation based on earnings and assets. Page The Yardeni model addresses some of the criticisms of the Fed model. In creating the model, Yardeni (2002) assumed constant growth but that investors valued earnings rather than dividends. As a data input for the required return, r, Yardeni used Moody’s A rated corporate bond yield, yB, which allowed for risk to be incorporated into the model. The risk premium captured by the model, however, is largely a default risk premium, not the unobservable equity risk premium. Thus, although an improvement over the Fed model, the Yardeni model still does not fully capture the risk of equities. As an input for the growth rate, g, Yardeni used the consensus five-year earnings growth forecast for the S&P 500 from Thomson Financial, LTEG. Note that g is truly a perpetual or sustainable growth rate and that a five-year forecast for growth may not be sustainable. The Yardeni model introduces an additional variable, the coefficient d. It represents a weighting factor measuring the importance the market assigns to the earnings projections. Yardeni (2000) found that the historical values for d averaged about However, depending on market conditions, d can vary considerably from its historical average. A justified forward earnings yield that is below, equal to, or greater than the forward earnings yield value implied by current equity market index values (using consensus forward earnings estimates, for example) would indicate that equities are undervalued, fairly valued, or overvalued in the marketplace. A valuation judgment can also be made by using the equation on the slide solved for P0, which gives the Yardeni model expression for the fair value of the equity market: E1/(yB – d × LTEG). The judgment would be that the equity market is undervalued, fairly valued, or overvalued if the fair value estimate is above, equal to, or below the current equity market level.

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EXHIBIT Overvaluation (+) and Undervaluation (−) of S&P 500 Index vs. Fair Value Estimate Using Yardeni Model with d = (Monthly Data: January 1985–December 2008) LOS: Judge whether an equity market is under-, fairly, or overvalued based on a relative equity valuation model. Pages As Exhibit shows, the Yardeni model predicted the S&P 500 was undervalued by 39.25% in December The Yardeni model also did a good job predicting the overvaluation and subsequent pullbacks of October 1987 and the early 2000s. However, the model signaled the equity market was significantly undervalued in 2007 even though U.S. and other world equity markets collapsed dramatically in the wake of a major financial crisis.

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P/10-Year MA(E) Campbell and Shiller’s (1998, 2005) 10-year Moving Average Price/Earnings [P/10-year MA(E)] has become a popular measure of market valuation: Numerator of P/10-year MA(E) is the real S&P 500 price index. Denominator is the moving average of the preceding 10 years of real reported earnings. Stock index and earnings are adjusted for inflation using the Consumer Price Index (CPI). Purpose of the 10-year moving average of real reported earnings is to control for business cycle effects on earnings. LOS: Explain and critique models of relative equity market valuation based on earnings and assets. Pages Campbell and Shiller’s (1998, 2005) 10-year Moving Average Price/Earnings [P/10-year MA(E)] has become a popular measure of market valuation. The authors defined the numerator of P/10-year MA(E) as the real S&P 500 price index and the denominator as the moving average of the preceding 10 years of real reported earnings. “Real” denotes that the stock index and earnings are adjusted for inflation using the Consumer Price Index (CPI). The purpose of the 10-year moving average of real reported earnings is to control for business cycle effects on earnings and is based on recommendations from the seminal Graham and Dodd (1934) text. Many analysts believe that P/10-year MA(E) should be considered a mean-reverting series. The mean value of P/10-year MA(E) for the January 1881 to January 2009 time period was 16.3 and the January 2009 P/10-year MA(E) was 15.8, suggesting that the U.S. equity market was slightly undervalued at that time. The highest value for P/10-year MA(E) was 42.5 in 2000 and the lowest value for P/10-year MA(E) was 5.3 in 1921.

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**EXHIBIT 11-15 P/10-Year MA(E) and Predicted 10-Year Real Price Growth**

LOS: Judge whether an equity market is under-, fairly, or overvalued based on a relative equity valuation model. Pages Campbell and Shiller (1998, 2005) made the case that the U.S. equity market was extremely overvalued in the late 1990s and provided evidence that future 10-year real price growth was negatively related to P/10-year MA(E). Exhibit updates the Campbell-Shiller results through Each plotted data point represents an annual observation for real price growth for the next 10 years and P/10-year MA(E) for that same year. A trend line is plotted and shows the ordinary least squares regression relationship between 10-year real price growth and P/10-year MA(E). The table in the upper right-hand corner of Exhibit shows the predicted 10-year real price growth given some value for the explanatory variable P/10-year MA(E). The regression results predict that 10-year real price growth will be 17.9% given the January 2009 P/10-year MA(E) of The R2 for the regression is , which indicates that P/10-year MA(E) explains only 14.88% of the variation in 10-year real price growth. Furthermore, the traditional regression statistics for this regression are unreliable because of the serial correlation induced by the overlapping time periods used to compute returns.

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**P/10-Year MA(E): Advantages and Disadvantages**

Controls for inflation Controls for business cycle effects Evidence supports a negative relationship with future equity returns Disadvantages Changes in accounting methods may lead to comparison problems Current period data may provide better estimates of value Evidence suggests high and low levels can persist for long time periods LOS: Explain and critique models of relative equity market valuation based on earnings and assets. Page 505 Predictions of the model: Future equity returns will be higher when P/10-year MA(E) is low. Strengths • Controls for inflation and business cycle effects by using a 10-year moving average of real earnings. • Historical data support an inverse relationship between P/10-year MA(E) and future equity returns. Limitations • Changes in the accounting methods used to determine reported earnings may lead to comparison problems. • Current period or other measures of earnings may provide a better relative estimate for equity prices than the 10-year moving average of real earnings. • Evidence suggests that both low and high levels of P/10-year MA(E) can persist for extended periods of time.

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**ASSET-BASED MODELS: TOBIN’S q AND EQUITY q**

Tobin’s q = Market value of a company ÷ Replacement cost of assets = (12, ) ÷ 28, = 0.79 Equity q = Equity market capitalization ÷ Net worth measured at replacement cost = 9, ÷ (28, – 12,887.51) = 0.62 LOS: Explain and critique models of relative equity market valuation based on earnings and assets. Pages Tobin’s q ratio, pioneered in Brainard and Tobin (1968) and Tobin (1969), is an asset-based valuation measure. Tobin’s q has been used for several purposes, including decision making concerning physical capital investment and equity market valuation. The first application is the simplest: At the company level, Tobin’s q is calculated as the market value of a company (i.e., the market value of its debt and equity) divided by the replacement cost of its assets. According to economic theory, Tobin’s q is approximately equal to 1 in equilibrium. If it is greater than 1 for a company, the marketplace values the company’s assets at more than their replacement costs, so additional capital investment should be profitable for the company’s suppliers of financing. In contrast, a Tobin’s q less than 1 indicates that further capital investment is unprofitable. Tobin’s q has also been calculated at an overall market level. In that case, the denominator involves an estimate of the replacement cost of aggregate corporate assets and the numerator involves estimates of aggregate equity and debt market values. Some analysts have used a market-level Tobin’s q to judge whether an equity market is misvalued. This application involves a comparison of the current value of market-level Tobin’s q with its presumed equilibrium value of 1 or with its historical mean value. Assuming that Tobin’s q will revert to the comparison value, a Tobin’s q below, at, or above the comparison values is interpreted as the market being undervalued, fairly valued, or overvalued. Smithers and Wright (2000) created an equity q—that is, the ratio of a company’s equity market capitalization divided by net worth measured at replacement cost. Their measure differs from the price-to-book value ratio because net worth is based on replacement cost rather than the historic or book value of equity. Based on a market-level equity q, Smithers and Wright made the case that the U.S. equity market was extremely overvalued in the late 1990s. The principles of that application parallel those given for Tobin’s q. Strong economic arguments exist that both Tobin’s q and equity q should be mean-reverting series.

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**EXHIBIT 11-16 Equity q and Tobin’s q Quarterly Data: 1952 Q1–2008 Q4**

LOS: Judge whether an equity market is under-, fairly, or over-valued based on a relative equity valuation model. Pages Exhibit presents quarterly Tobin’s q data and quarterly equity q data for the U.S. equity market over the time period of 1952 to Last quarter 2008 values for these two variables relative to their respective means suggest that the U.S. equity market was slightly undervalued at that time. However, both series had declined to significantly lower levels relative to their means in the early 1950s and early 1980s. Data source:

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**Tobin’s q and Equity q: Advantages and Disadvantages**

Rely on a comparison of security values with asset replacement costs and theory suggests the relationship is mean-reverting Evidence supports a negative relationship with future equity returns Disadvantages: Difficult to accurately measure replacement cost for many assets Evidence suggests high and low levels can persist for long time periods LOS: Explain and critique models of relative equity market valuation based on earnings and assets. Page 505 Predictions of the model: Future equity returns will be higher when Tobin’s q and equity q are low. Strengths: • Both measures rely on a comparison of security values with asset replacement costs (minus the debt market value, in the case of equity q); economic theory suggests this relationship is mean-reverting. • Historical data support an inverse relationship between both measures and future equity returns. Limitations: • It is difficult to obtain an accurate measure of replacement cost for many assets because liquid markets for these assets do not exist and intangible assets are often difficult to value. • Evidence suggests that both low and high levels of Tobin’s q and equity q can persist for extended periods of time.

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**Summary Cobb-Douglas production function Growth accounting formula**

Total factor productivity, capital stock, labor input H-model estimate of equity market value Top-down and bottom-up analysis Earnings-based equity market valuation models Asset-based equity market valuation models

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Chapter 13 Equity Valuation

Chapter 13 Equity Valuation

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