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CHAPTER 11

EQUITY MARKET VALUATION

Peter C. Stimes, CFA

Altadena, CA, U.S.A.

Stephen E. Wilcox, CFA

Mankato, MN, U.S.A.

LEARNING OUTCOMES

After completing this chapter, you will be able to do the following:

• 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.
• Evaluate the relative importance of growth in total factor productivity, in capital stock, and in labor input given relevant historical data.
• Demonstrate the use of the Cobb-Douglas production function in obtaining a discounted dividend model estimate of the intrinsic value of an equity market.
• Evaluate the sensitivity of equity market value estimates to changes in assumptions.
• Contrast top-down and bottom-up forecasts of the earnings per share of an equity market index.
• Explain and critique models of relative equity market valuation based on earnings and assets.
• Judge whether an equity market is under-, fairly, or overvalued based on a relative equity valuation model.

1. INTRODUCTION

Economic strength or weakness affects equity prices through its effect on risk-free rates, risk premiums, and corporate earnings. These economic drivers of security prices are often considered fundamental because they will affect security returns throughout most investment horizons. It is widely accepted that equity prices are negatively related to risk-free rates and risk premiums and positively related to earnings growth.

There are, of course, other drivers of equity returns and most of these can be considered behavioral. The cognitive and emotional factors experienced by investors can create both positive and negative feedback mechanisms. Market momentum may thus result in both bull market rallies and bear market declines lasting longer than may be justified by fundamental factors. This chapter does not deal specifically with such behavioral drivers. Rather, this chapter illustrates the application of economic forecasts to the valuation of equity markets. While 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.1 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 chapter, and practice problems in the CFA Institute format follow.

2. ESTIMATING A JUSTIFIED P/E RATIO

Investors commonly use the market’s price-to-earnings (P/E) ratio or multiple to gauge the prospects for future equity returns. Sections 2.1 through 2.3 develop the Cobb-Douglas production function (also called the Cobb-Douglas model) for obtaining growth rates for an economy and, thus, the dividend growth rate trajectories for a corresponding equity market. This model is particularly useful in the case of developing markets such as China, where the structure of the underlying economy has experienced, and may experience, fundamental changes (as compared with the relatively stable growth rates of more developed economies).

In Section 2.4 we apply a form of the dividend discount model known as the H-model to the complicated dividend growth trajectory because it is well suited to instances where near term growth rates can diverge significantly from the ultimately sustainable dividend growth rate. We also standardize the results in justified P/E form. This facilitates intertemporal and cross-border market value comparisons. The difference between prevailing P/Es and justified P/Es is a measure of potential investment attractiveness.

As will be shown, the Cobb-Douglas and dividend discount models may also be applied to developed economies and equity markets.

2.1. Neoclassical Approach to Growth Accounting

Growth accounting is used in economics to measure the contribution of different factors—usually broadly defined as capital and labor—to economic growth and, indirectly, to compute the rate of an economy’s technological progress. The neoclassical approach to growth accounting uses the Cobb-Douglas production function.2 This approach can be useful to financial analysts because it gives insights 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 as Equation 11.1, 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 which accounts for that part of Y 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 Equation 11.1.3 Taking the natural logarithm of both sides of the equation gives

Taking first differences of Equation 11.2 and utilizing the fact that, for small changes in any variable x,

we obtain the expression:

Equation 11.3 is the expression which we will employ in our analysis. In Equation 11.3, 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 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 Equation 11.3, with the exception of the growth in TFP, are directly observable or can be derived from national income and product accounts.4 However, growth in TFP is determined using the other inputs as noted by Equation 11.3 and is commonly referred to as the Solow residual.5

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 which are experiencing major changes in political and/or regulatory structures. As examples, 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, developments such as the depletion and degradation of natural resources would detract from growth in TFP.

The robustness and simplicity of the approach we have presented can be tested against the complex and important case of valuing the equity markets in mainland China.

2.2. The China Economic Experience

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 Exhibit 11-1. Note particularly the comparisons of China’s growth in the capital stock, ΔK/K, and growth in the labor input, ΔL/L, to those of the (former) Soviet Union, United States, and 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 percent. This compares with 15 to 20 percent over the comparable periods for the other countries in Exhibit 11-1.

EXHIBIT 11-1 Historical Growth Accounting for China, the (Former) Soviet Union, United States, and European Union

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.

Concerns over the sustainability of China’s growth have emerged in recent years because, as is evident from Exhibit 11-1, 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.

Exhibit 11-1 also 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 investment6 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 $2 trillion.7 Because of this, 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 percent.8) 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 all 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 for European and American economies, this 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 percent per year in recent years, according to the World Bank. Furthermore, major changes in labor force participation rates, largely due to 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 for the Soviet Union, United States, and European Union presented in Exhibit 11-1.

Finally, in addition to these factors, 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 chapter does not address them.

2.3. Quantifying China’s Future Economic Growth

Now that we have covered a simple model for estimating an economy’s growth rate, the next step is to apply the model using our best estimates of the model inputs. As in any forecasting exercise, the specific forecasts must be based on currently available information. Any forecast has an “as of” date associated with it. Comparing the forecasts to actual outcomes subsequently, some inputs or elements of the forecast may appear to be misjudged or dated. With that caution in mind, we can proceed to develop our economic growth projections for China.

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 percent GDP growth rate for China is consistent with the Chinese government’s 8 percent 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 percent 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 European Union. Given the history of other developing countries and the record of economic recovery of developed countries after World War II, this does not seem unreasonable.

EXHIBIT 11-2 Growth Projections (2009–2030)

Source: Zheng, Hu, and Bigsten (2009).

The neoclassical framework we have presented permits analysts to apply their own forecasts of factors of production and with particular emphasis on how such factor trajectories might change over time. Once the analyst has developed a long-term macro forecast, it can then be used in conjunction with traditional valuation models.

In applying the framework, we modify the Zheng, Hu, and Bigsten (“ZHB”) projections by using a lower estimate of the growth rate in the labor force, since World Bank data indicate that population growth in China now appears to have declined to below 1.0 percent annually. At the same time, we are inclined to think that savings and investment rates will only decline gradually from over 35 percent of GDP, thereby keeping the growth rate of capital stock much higher than the 8 percent per annum assumed by ZHB. We have no disagreement with the ZHB projection of 2.5 percent per year for TFP growth. If we utilize the labor and capital elasticities from the ZHB study, a reasonable projection for economic growth would therefore be:

This near-term rate is higher than the ZHB forecast, the official forecast of the Chinese government, and the consensus of many economic forecasters. We note, however, that there are several factors that are consistent with our higher near-term forecast. First, actual real growth has cumulatively exceeded the 8 percent Chinese official growth target of the past several years. Second, and more importantly, our forecast is to be thought of as a normalized forecast of sustainable cash flow growth potential.

While our near-term forecast for economic growth is higher than ZHB and the Chinese government, the reasoning set forth in the preceding section leads us to believe that economic growth will gradually decline to levels lower than the ZHB analysis.9 This 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:

2.4. Equity Market Valuation

In this section we 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/E ratios.

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, we 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.10

In theory, we would like to be able to forecast, year by year, each of the underlying factors of production and the change in TFP. In practice, however, we recognize that a less complicated cash flow representation might be more suitable, because it lessens the possibility of compounding forecast errors. 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 Equation 11.4:

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 H-model involves an approximation to the value estimate that would result from period-by-period discounting of cash flows in the phase prior to the mature or terminal phase when a constant growth rate is assumed. The approximation is generally very good in most practical situations and the gain from using an approximation is an easy to evaluate expression.11 In the case of valuation of mature developed equity markets, the Gordon (constant) growth dividend discount model would be more commonly used than the H-model because supernormal growth would not generally need to be modeled in such cases.

In our valuation analysis, we express the discount rate and both growth factors in real, that is, inflation-adjusted terms. A key to valuation is consistency: stating variables consistently on a nominal basis or consistently on a real basis are both feasible approaches. Economists, however, typically prefer to use real variables as they tend to be more stable and, therefore, easier to predict than their nominal counterparts.

We use our growth rate trajectory and apply the H-model to the S&P China BMI Index. This index underlies the SPDR S&P China ETF, which is an exchange-traded fund designed to track the investment performance of the mainland China and (to a much lesser extent) Hong Kong stock markets. Both the underlying stocks and the ETF itself are avenues in which both Chinese and non-Chinese investors may obtain participation in the Chinese equity markets. The index underlying the ETF and the information provided by the ETF’s sponsor (State Street Global Advisors) provide up-to-date information that can enter traditional valuation models.

In evaluating the investment attractiveness of a market index, we utilize a price–earnings ratio or P/E approach. Because of the behavioral factors mentioned in the introduction, prices of equities and equity market composites tend to vary more than underlying normalized earnings and growth prospects. P/E analysis permits us to make useful intertemporal valuation comparisons and has the additional benefit of providing intuition when making comparisons across international borders. As of 15 July 2009, the forward or prospective P/E ratio 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). In the following analysis, we estimate what justified P/E ratios should be under differing inflation-adjusted equity discount rates and for different estimates of the ultimately prevailing terminal inflation-adjusted dividend growth rate to perpetuity.

The (forward) justified P/E is the estimated intrinsic value divided by year-ahead expected earnings; in this case we are estimating intrinsic value using the H-model. Reflecting the meaning of justified here as warranted by fundamentals, price in the justified P/E ratio is assumed in this discussion to equal intrinsic value as estimated by the valuation model, that is, P0 (or P) = V0.12 In all instances, we assume that core inflation-adjusted growth rates decline in a linear fashion over a 30-year time horizon from the 9.25 percent per year we estimate for year one.13 The 30-year time horizon is selected both because it is a round number and because it is not unlike other historical instances where 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 nineteenth century and after World War II.

In Exhibit 11-3 and Exhibit 11-4, we have presented justified P/E ratios. Interpolating visually, the observed 19.1 P/E ratio on 15 July 2009, assuming a terminal 4.25 percent real dividend growth rate to perpetuity, is consistent with a real equity discount rate just under 8.0 percent.

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

This leads immediately to the question of what the proper discount rate should be. To answer this we would like to know a little bit about both the volatility of Chinese equity prices and how such return/volatility prospects compare with other world equity markets.

In Exhibit 11-5, we present cumulative return data for both the S&P China BMI Index and the S&P 500. The data series commence in 2001, the point at which the China BMI Index data are first available, and a point by which mainland Chinese equity markets had become seasoned and widely accessible to non-Chinese investors.14

Over the seven-year period, the cumulative return of Chinese equities far outpaced those of the United States. However, Chinese markets also experienced more of a bubble and subsequent collapse, resulting in a much higher volatility of returns. For China, the annualized return over this time frame approached an inflation-adjusted 13 percent. This outpaced the return one would have expected even from coupling a 2 to 2.5 percent dividend yield with an aggressive core dividend real growth rate of 9 percent. The cumulative return benefited from a positive shift in P/E ratios between the beginning and end of the measurement period. In fact, the P/E expansion and subsequent contraction appear to be the chief cause of the 2007 Chinese bubble and the following collapse.

By comparison, the equity markets in the United States were much less volatile, although the cumulative return, particularly net of inflation, was negative. Assuming a 6 percent inflation-adjusted discount rate for the U.S. equity market (in line with long-term historical realized returns), the cumulative nominal return—incorporating the 2.6 percent average inflation rate—would have resulted in an ending cumulative return index value of around 1.80 in December 2008 (compared with the 2.61 achieved by the S&P China BMI Index). The explanation for the poor performance by U.S. equities was largely attributable to a contraction from the high normalized P/E valuation relationships prevailing in 2001 to the below-average levels at the end of the period. Additional evidence is presented in Exhibit 11-6.

In establishing a reasonable discount rate to apply to our cash flow forecasts, we should take into account the higher volatility of Chinese markets, which has arisen in part because of structural macroeconomic instabilities (discussed previously) and the evolution of their legal and regulatory systems.

The higher observed volatility also has arisen from behavioral shifts in P/E relationships that are more pronounced than those usually seen in U.S. and European markets. Such valuation-induced price volatility is not unusual for any market that is new by historical standards and has been experienced in the past by U.S., European, and Japanese markets in their own long paths to economic maturity. Furthermore, because the bulk of mainland equities are still 75 percent owned (directly or indirectly) by the mainland Chinese government, there is an overhanging risk of intervention or divestiture that might be occasioned by noneconomic motives. However, the possibility of denationalization, such as carried out by the United Kingdom in the 1980s, might be viewed more as a market opportunity than as a risk.

The effect of higher volatility on required returns might be somewhat mitigated to the extent (1) market returns are less than perfectly correlated with other international equity markets and (2) cross-border investing and divesting of equities is freely achievable by investors both inside and outside of China.

On balance, the foregoing factors suggest that the required real equity discount rate be higher in China than, for example, in the United States. This naturally leads us to investigate both what the realized real equity discount rate has been in the United States and what real equity discount rates are predicted based on alternative theoretical models. Historical studies have been undertaken15 which indicate that a prospective inflation-adjusted equity discount rate16 in the area of 5–7 percent is reasonable. Work based on macroeconomic, corporate finance, and financial market equilibrium17 suggests that a slightly higher range might be possible in equilibrium. Purely theoretical models have had mixed results. The utility function models,18 for example, find that real discount rates in the 5–7 percent area are well above what can be justified by underlying market volatility. On the other hand, a theoretical approach19 simply based on prospective wealth accumulation under different volatility assumptions is consistent with the results actually realized in the U.S. historical record.

In the volatile economic and market conditions at the time (2009) this chapter is being written, the higher end of the discount rate estimates seem to be in order for the United States. If we place these at 6–7 percent, 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 percent. This is a necessarily judgmental adjustment 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 11-4 and integrating our view of the real (i.e., inflation-adjusted) equity discount rate with the sustainable dividend growth rates obtained from our macroeconomic framework, we can conclude that the currently observed 19.1 forward P/E ratio for Chinese equities is not unreasonable. As a further check, we note that a 19.1 P/E would be somewhat on the high side for seasoned U.S. and European stock markets. However, reflecting much higher growth prospects over the next several decades, a much higher Chinese P/E ratio would be warranted (although the impact would be somewhat offset by a greater discount rate reflecting higher volatility in China) as compared with U.S. and European markets.

Inherent in our analysis of equity composites is the difficulty of specifying precise price or P/E ratios at which a “buy” or “sell” recommendation is to be made. However, the strength of this kind of relative value approach is that, in a diversified portfolio context, investors can usually make reasonable decisions—at the margin—whether it is then appropriate to raise or lower market exposures relative to the investable universe in the aggregate. The price/value relationships prevailing at the date of the analysis were such that those investing on a fundamental basis should have a weighting in Chinese equities close to their baseline or normal-strategy allocation.20 Stated differently, only those with a very optimistic long-term dividend growth rate forecast and/or a low required discount rate would find the Chinese market to have substantially better than average current attractiveness.

The possible criticisms of our approach should not be overlooked. From a practical perspective, there may be severe problems with the accuracy of data inputs. It is difficult enough to obtain macroeconomic data in developed countries with long-established methods and facilities. In developing markets or in economies experiencing profound governmental and structural change, such as the Eastern Bloc after the fall of the Berlin Wall, the problems of obtaining accurate and, more importantly, historically consistent, data are multiplied. The same fluidity in political and demographic fundamentals also calls into question whether companies’ growth rates will track GDP growth rates. In certain instances, there can be long departures between growth rates, meaning that for long periods of time the share of corporate profits may be rising or declining relative to GDP.

The analysis in this chapter has also focused on inflation-adjusted income, cash flow, and discount rates. In a global economy with reasonably robust currency exchange markets and where monetary growth is targeted to keep inflation at manageable levels, this is probably appropriate. However, hyperinflation, currency instability, and other trade disequilibria have occurred far too frequently from a historical perspective to be overlooked. In the presence of such factors, the confidence of our model’s approach could be diminished.

3. TOP-DOWN AND BOTTOM-UP FORECASTING

When it comes to predicting equity returns, analytical approaches can be divided into two major categories: top-down and bottom-up. In top-down forecasting, analysts use macroeconomic projections to produce return expectations for large stock market composites, such as the S&P 500, 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, market sectors, and for the equity market as a whole.

Exhibit 11-7 sets forth the manner in which top-down and bottom-up approaches are typically implemented. Top-down can be characterized as moving from the general to the specific, while bottom-up forecasting moves from the specific to the general. Depending on the investment strategy and portfolio context, one of the types of forecasting may be more suitable. In other instances, both types of forecasting may be useful. In those cases where both top-down and bottom-up are used, the additional work involved may provide valuable insights.

3.1. Portfolio Suitability of Each Forecasting Type

In theory and practice, it is not necessary for either top-down or bottom-up forecasting to be carried to the final step shown for each method in Exhibit 11-7. For example, if a portfolio focuses primarily on tactical asset allocation among different market composites (and/or different industry groups within such composites), a top-down forecast may not need to focus all the way down to the relative merits of individual securities.

Likewise, there are instances where either the investment strategy or specific portfolio constraints dictate a focus primarily on individual security returns. In such instances, the unique factors pertaining to particular securities may render the need to study industry and market composite unnecessary. In such cases, the bottom-up method stops well short of the top. The partial application of each method is developed in the following examples.

3.2. Using Both Forecasting Types

When engaged in fundamental securities analysis, it can be wise to use both top-down and bottom-up forecasting. However, when we use both approaches, we often find ourselves in the situation of the person with two clocks, each displaying a different time. They may both be wrong, but they cannot both be right!

It is frequently the case that top-down and bottom-up forecasts provide significantly different results. In such instances, the analyst should investigate the underlying data, assumptions, and forecast methods before employing them as a basis for investment decisions. After all, if forecasts cannot be consistent with each other, at least one of them cannot be consistent with underlying reality.

Because we are fallible human beings, most forecasting discrepancies arise from our own limited knowledge, errors, and incomplete assumptions. Reconciling top-down and bottom-up forecasts is therefore a discipline that can help prevent us from taking inappropriate investment actions. In other words, most of the time, the aggregate market consensus will tend to be more accurate than the individual forecasts that comprise the consensus. The reconciling and revision process is therefore useful in helping us better understand the market consensus.

However, in rare and significant instances, we will find that carefully retracing the steps reveals a gap between the two forecast types that gives rise to significant market opportunities. In such instances, the process of reconciling the two types of forecasts creates instances where we differ significantly and correctly from the consensus.

Recent years have provided major examples of this. In the early 2000s, top-down forecasts provided much more subdued outlooks compared to bottom-up projections for corporate profits, both in the aggregate and for particular industries. In the tech area, both consumer and capital spending on computer equipment were below the projected sales growth that companies, and analysts following them, were individually expecting. After all, individual companies were optimistic about their own prospects. However, in the aggregate, many of their technologies and products competed with each other. Thus, the success of some companies meant the failure of others and this natural, competitive offsetting tendency was correctly reflected in aggregate, top-down sales growth for the industry.

Aggregating the bottom-up forecasts of individual companies, however, produced a wildly inflated forecast of both sales quantities and average prices and profit margins. Thus, the high-tech “bubble” originated from the mistaken principle that all the companies could be above average. For those who recognized the inconsistency of the top-down and bottom-up forecasts, and the accuracy of the top-down forecast, much of the carnage of the bubble collapse was avoided.

More recently, the collapse of equity markets in developed countries was a case where bottom-up forecasts proved their superiority over top-down approaches. In both the United States and the United Kingdom, some banking and real estate analysts perceived the excesses in residential real estate in a microeconomic sense. Those who pushed their analyses to a macro conclusion realized that certain large financial institutions were imperiled, particularly the highly-levered Fannie Mae and Freddie Mac in the United States. Those who understood the pressure on these and other large financial institutions correctly foresaw that then-prevailing worldwide forecasts of economic activity and equity market returns were dramatically overstated.

3.3. Top-Down and Bottom-Up Forecasting of Market Earnings per Share

Two different methods are employed when estimating earnings for a market index, such as the S&P 500 Index. The first is to add up the individual estimates of the companies in the index. This is referred to as the bottom-up earnings estimate. The top-down estimate relies on forecasts for various macroeconomic variables and a model that fits these forecasts to past trends in aggregate earnings.

4. RELATIVE VALUE MODELS

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 switching from bonds to stocks, or vice-versa. As an investor, it is important to focus on the markets in a comparative fashion.

4.1. Earnings-Based Models

In its 22 July 1997 Humphrey-Hawkins report to Congress, the United States Federal Reserve compared 1982–1997 10-year Treasury note yields to 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. However, use of the term “Fed model” is somewhat misleading, as 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 model predicts:

• U.S. stocks are undervalued if the forward earnings yield on the S&P 500 is greater than the yield on U.S. Treasury bonds.
• U.S. stocks are overvalued if the forward earnings yield on the S&P 500 is less than the yield on U.S. Treasury bonds.

For example, if the S&P 500 forward earnings yield is 5 percent and the 10-year T-note yield is 4.5 percent, stocks would be considered undervalued according to the Fed model.

The key criticism of the Fed model is that it ignores the equity risk premium. (Informally, the equity risk premium is the compensation demanded by investors for the greater risk of investing in equities compared to investing in default-risk-free debt.) The validity of this criticism is apparent if one understands the assumptions necessary to derive the Fed model from the Gordon growth model. Equation 11.5 presents the Gordon growth model where V0 is intrinsic value, D1 is the dividend per share to be received one-year from today, r is the required return, and the constant annual dividend growth rate is g.

Assuming markets correctly set price, P0, equal to intrinsic value, then P0 = V0. The expected dividend, D1, can be determined as the payout ratio, p, times expected earnings, E1. Sustainable growth, g, can be estimated as return on equity, ROE, times the earnings retention rate, (1 − p).

Substituting D1 = pE1 and g = ROE(1 − p) into Equation 11.5 and noting that P0 = V0 we are able to derive Equation 11.6. Equation 11.6 provides a Gordon growth model estimate for the forward earnings yield, E1/P0.

The Fed model hypothesizes that the earnings yield, E1/P0, and the yield on Treasury bonds, yT, are equal in equilibrium. One way to produce this equilibrium using Equation 11.6 is to assume that the required return, r, and the return on equity, ROE, are equal to the Treasury bond yield, yT. Making these substitutions in Equation 11.6 shows this result:

Thus, implicit in the Fed model equilibrium are the assumptions that the required return, r, and the accounting rate of return on equity, ROE, for risky equity securities are equal to the Treasury bond yield, yT. Historical evidence and financial theory resoundingly reject the notion that either assumption is true. For example, the long-run average return on U.S. equities has exceeded the long-run average return on T-bonds by a significant amount.22 Because of this, many analysts consider the Fed model flawed.

Two additional criticisms of the Fed model are that they ignore inflation and earnings growth opportunities. Asness (2003) criticized the Fed model because it compares an arguably real variable, the earnings yield, to 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.23 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 (as reflected by expected earnings, E1). In the United States, long-term compound average earnings growth has been 3–4 percent nominal and 1–2 percent real.24 Thus, the model ignores a significant portion of total equity return.25

In spite of the several criticisms, the Fed model still can provide some useful insights. It does suggest that equities become more attractive as an asset class when interest rates decline. This is consistent with the predictions of any discounted cash flow model and is supported by market evidence. In practice, the model typically makes use of expected earnings (a future cash flow) as an input, which is again consistent with traditional discounted cash flow analysis.

Some analysts find a comparison of the earnings yield and Treasury bond yield to be most useful when the relationship is toward the extremes of its typical range. For example, some analysts compare the current difference between the earnings yield and the Treasury bond yield with the historical average difference. Stocks are viewed as more attractive as an investment when the current period difference significantly exceeds the historical average difference.

The Yardeni model addresses some of the criticisms of the Fed model. In creating the model, Yardeni (2002) assumed investors valued earnings rather than dividends. With the assumption that markets set price equal to intrinsic value, P0 = V0, a constant growth valuation model that values earnings is presented in Equation 11.8. E1 is an estimate of next year’s earnings, r is the required return, and g is the earnings growth rate. Equation 11.8 shows that, given the assumptions of the model, the earnings yield, E1/P0, is equal to the required return, r, minus the growth rate, g.

As a data input for the required return, r, Yardeni used the 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 (the credit spread between the A-rated bond, yB, and the yield on a Treasury bond, yT), not the unobservable equity risk premium. Thus, while 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 0.10.26 However, depending on market conditions, d can vary considerably from its historical average. Equation 11.9 presents the Yardeni model stated as the justified (forward) earnings yield on equities.

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 Equation 11.9 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. Example 11-11 shows such an analysis.

Examples 11-11 and 11-12 were taken from U.S. equity markets. To date, nearly all analysis using the Yardeni model has been limited to the U.S. equity market. If adequate data are available, especially for forecasted earnings growth, the Yardeni model could be applied in any equity market.

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. Exhibit 11-14 presents P/10-year MA(E) from January 1881 to January 2009. The mean value of P/10-year MA(E) for this time period was 16.3 and the January 2009 P/10-year MA(E) was 15.8 suggesting 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.

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 11-15 updates the Campbell-Shiller results through 2009. 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 11-15 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 percent given the January 2009 P/10-year MA(E) of 15.8. The R-squared for the regression is 0.1488, which indicates that P/10-year MA(E) explains only 14.88 percent 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.

With a 10-year projected real price growth of 17.9 percent, the annualized growth rate is less than 1.7 percent per year. Given a dividend yield of about 2.9 percent and assuming share repurchases effectively add 1 percent to the annual real cash flow to shareholders, the inflation-adjusted expected return would be approximately 5.6 percent, which is below the 6–7 percent compounded average inflation-adjusted return over long periods in the United States (Siegel 2005). Thus, in contrast to the Fed model and the Yardeni model, the Campbell and Shiller model implies below-average prospective returns.

The conflicting signals between and among various valuation models may provide valuable insights, especially if they cause us to rethink how the parameter estimates and the numerical inputs give rise to the different results. For example, assume that changes in accounting rules lead to significant differences in how earnings are reported over time. Thus, the P/10-year MA(E) at some given point in time might not be comparable with other time periods. A high or low P/10-year MA(E) relative to the long-term average at present could be due to differences in prior accounting rules, thereby resulting in stocks actually being more undervalued or overvalued than they currently appear.

4.2. Asset-Based Models

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. By contrast, a Tobin’s q below 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. Strong economic arguments exist that both Tobin’s q and equity q, discussed later, should be mean-reverting series.

The calculation of Tobin’s q often poses difficulties. At the company level, it is usually possible to get a fairly accurate estimate of market value (the numerator of Tobin’s q) by summing the values of the securities a company has issued, such as its stocks and bonds. It is much more difficult to obtain an accurate estimate of replacement costs of the company’s assets (the denominator of Tobin’s q). Liquid markets for many assets (e.g., many kinds of industrial equipment) do not exist. Moreover, such items as human capital, trade secrets, copyrights and patents, and brand equity are intangible assets that are often difficult to value. Typically, researchers who try to construct Tobin’s q ignore the replacement cost of intangible assets in their calculations.

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.

To date, much of the market-level analysis using Tobin’s q or equity q has been conducted in the U.S. equity market, but analysis based on European and Asian equity markets is increasingly available.

Exhibit 11-16 presents quarterly Tobin’s q data and quarterly equity q data for the U.S. equity market over the time period 1952 to 2008. 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.

A summary of the relative value models appears in Exhibit 11-17.

5. SUMMARY

In this chapter we have investigated several ways in which economic theory can be applied to the valuation of equity markets. Among the major points are the following:

• The growth accounting equation allows one to decompose real GDP growth, ΔY/Y, into components that can be attributed to the observable factors: the growth of the capital stock, ΔK/K, the output elasticity of capital, α, the growth in the labor force, ΔL/L, the output elasticity of labor, 1 − α, and a residual factor—often called the Solow residual—that is the portion of growth left unaccounted for by increases in the standard factors of production, ΔA/A.

• The existence of TFP growth, ΔA/A, means that total output can grow at a faster rate than would be predicted simply from growth in accumulated capital stock and the labor force. TFP is typically linked to innovation and technical progress. However, changes in work organization, government regulation, and the literacy and skills of the work force, as well as many other factors, also affect TFP.
• The inputs for the H-model include the initial growth rate, 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 D0 and a discount rate to perpetuity of r, the formula for intrinsic value, V0 according to the H-model is:

• In top-down forecasting, analysts use macroeconomic forecasts to develop market forecasts and then make industry and security forecasts consistent with the market forecasts. In bottom-up forecasting, individual company forecasts are aggregated to industry forecasts, which in turn are aggregated to produce a market forecast.
• Bottom-up forecasts tend to be more optimistic than top-down forecasts. Top-down models can be slow in detecting cyclical turns if the current statistical relationships between economic variables deviate significantly from their historic norms.
• 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.
• A common criticism of the Fed model equilibrium is that it fails to incorporate the equity risk premium. The earnings yield can also be a poor measure of the true value of equities if significant growth opportunities exist. Some authors have also argued that the Fed model comparison is flawed because the earnings yield is real while the Treasury yield is nominal.
• The Yardeni model addresses some of the criticisms of the Fed model. As inputs, Yardeni used the Moody’s A-rated corporate bond yield, yB, the consensus five-year earnings growth forecast for the S&P 500 from Thomson Financial, LTEG, and the coefficient d, which represents a weighting factor measuring the importance the market assigns to the earnings projections. Yardeni found that the historical values for d averaged about 0.10. The formula for the Yardeni model is:

• Limitations of the Yardeni model include that the risk premium captured by the model is largely a default risk premium and not the future equity risk premium, which is unobservable. Also, the consensus five-year earnings growth forecast for the S&P 500 from Thomson Financial may not be sustainable and evidence suggests that the weighting factor varies significantly over time.
• Campbell and Shiller’s P/10-year MA(E) has become a popular measure of market valuation. The numerator of P/10-year MA(E) is the real S&P 500 and the denominator is 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 work of Graham and Dodd.
• Tobin’s q is calculated at the individual company level as the market value of a company divided by the replacement cost of its assets. Smithers and Wright created an equity q that is the ratio of a company’s market capitalization divided by net worth measured at replacement cost. Market-level measures may be computed for Tobin’s q and equity q by a process of aggregation; these market-level measures may be used to form a valuation judgment about an equity market. Assuming that Tobin’s q will revert to the comparison value, a Tobin’s q below, at, or above the comparison value is interpreted as the market being under-, fairly, or overvalued. Strong economic arguments exist that both Tobin’s q and equity q should be mean-reverting series.
• In practice, estimating replacement cost can be problematic due to the lack of liquid markets for many assets. Moreover, such items as human capital, trade secrets, copyrights and patents, and brand equity are intangible assets that are difficult to value.

PROBLEMS

1. Elizabeth Villeneuve is a senior economist at Proplus Financial Economics Consulting (Proplus). She is responsible for the valuation of equity markets in developing countries and is reviewing the preliminary report on Emerge Country prepared by one of her analysts, Danielle DeLaroche. Emerge Country is now experiencing stronger economic growth than most developed countries.

DeLaroche has summarized in Exhibit A some of the assumptions contained in the report. In modeling the growth in the country’s real output, she has used the Cobb-Douglas production function under the assumption of constant returns to scale and, in valuing the equity market, she has used the standard Gordon growth model with constant dividend growth rate.

Exhibit A Assumptions for the Equity Index of Emerge Country

Annual dividend per share in 2008	450 CU*
Forecasted earnings per share in 2009	750 CU*
Forecasted annual growth in TFP	1.5%
Expected real growth rate of dividends to perpetuity	5.5%
Required real discount rate to perpetuity	7.5%

*CU = currency unit of Emerge Country

A. Based on the information in Exhibit A, calculate the equity index price level of Emerge Country implied by the Gordon growth model, as of 31 December 2008.

Villeneuve is familiar with the Gordon growth model but not the H-model.

B. Identify two variables that are needed in the H-model and not needed in the Gordon growth model.

As an illustration of a relative value approach that can be used to support tactical asset allocation, DeLaroche has estimated that the forward operating earnings yield of the equity index in Emerge Country is 6 percent and that the medium-term government bond yield is 7 percent. She then applies the Fed model to the situation in Emerge Country.

C. Based on the Fed model, determine whether the equity market is undervalued or overvalued and identify three criticisms of the Fed model.

Because most of Proplus’s clients use strategies that require fundamental security analysis, Proplus uses both top-down and bottom-up approaches in all reports dealing with equity return forecasts.

D. Contrast the two forecasting approaches used by DeLaroche as they relate to industry analysis.

2. Don Murray, an economist, is president of the investment committee of a large U.S. pension plan. He is reviewing the plan’s recent investment returns and finds that non-U.S. equity returns have been much higher than U.S. equity returns. Before making any changes to the plan’s asset allocation, he has asked to meet with Susan McLean, CFA, who is responsible for the equity portion of the pension plan assets. Murray wants to discuss with McLean the current valuation levels of various equity markets.

Murray develops his own growth projections for the United States and for a hypothetical country (Hyp Country) that enjoys a well-developed economy but whose population is aging. These projections are shown in Exhibit B. In addition, Murray projects that output elasticity of capital equals 0.3 and 0.5 for the United States and Hyp Country, respectively.

EXHIBIT B Growth Projections (2010–2029)

A. Based on the information in Exhibit B, calculate the projected GDP growth for the United States for the period 2010–2029. Use the Cobb-Douglas production function and assume constant returns to scale.

Murray identifies two possible measures that the government of Hyp Country could implement and he wants to know how these measures would affect projected GDP growth for Hyp Country.

Measure 1: Lower the retirement age from 65 to 63, gradually over the next four-year period

Measure 2: Reduce subsidies to higher education over the next five years

B. For each of the growth measures identified by Murray in Exhibit B, indicate which growth factor is most affected. Justify your answers.

Murray is surprised that the bottom-up forecasts produced by McLean for the United States in the last five years have been consistently more optimistic than her top-down forecasts. As a result, he expresses doubt about the validity of either approach.

C. State one justification for using both top-down and bottom-up models even when these models produce different forecasts and state one justification for using the bottom-up approach by itself.

Murray suggests replacing earnings-based models with asset-based models in valuing equity markets. In response, McLean recommends using Tobin’s q ratio and equity q ratio, although both are subject to estimation errors when applied to valuing a particular company.

D. Identify two problems that McLean may have in estimating the Tobin’s q ratio and the equity q ratio for the pension plan assets that she manages.

Use the following information to answer Questions 3 through 10.

Claudia Atkinson, CFA, is chief economist of an investment management firm. In analyzing equity markets, the firm has always used a bottom-up approach but now Atkinson is in the process of implementing a top-down approach. She is discussing this topic with her assistant, Nicholas Ryan.

At Atkinson’s request, Ryan has prepared a memo comparing the top-down approach and the bottom-up approach. Ryan presents three conclusions:

Atkinson explains to Ryan how the Cobb-Douglas function can be used to model GDP growth under assumptions of constant returns to scale. For illustrative purposes, she uses the data shown in Exhibit C.

EXHIBIT C Hypothetical Data for a Developing Country

Atkinson wants to use the data shown in Exhibit C as an input for estimating justified P/E ratios. Ryan expresses some criticisms about using such historical data:

• “In a context of hyperinflation, the approach may not be appropriate.”
• “The companies’ growth rates may not match GDP growth for long periods.”
• “Government-implemented measures may not be taken into account in any of the growth factors.”

Atkinson intends to use relative value models in order to support the firm’s asset allocation recommendation. The earnings-based approach that she studies is the Fed model. She asks Ryan to write a summary of the advantages of that model. Ryan’s report makes the following assertions about the Fed model:

• “The model can be used for non-U.S. equity markets.”
• “The model captures the net present value of growth investment opportunities available to investors.”
• “The model is most informative when the excess of the earnings yield over the Treasury bond yield is close to the historical average.”

Atkinson thinks that the Yardeni model might address some of the criticisms of the Fed model and bring certain improvements. She will use that model as an alternate approach.

Because different results from various equity market valuation models may provide relevant information, Atkinson will present a third earnings-based approach, namely the P/10-year MA(E) model. Ryan identifies many positive features in that model, including the following:

• “The model controls for inflation.”
• “The model is independent of changes in accounting rules.”
• “The model controls for business cycle effects on earnings.”

When evaluating the equity market in the United States, Atkinson uses the following asset-based models: Tobin’s q ratio and equity q ratio. She calculates the equity q ratio of Nonfarm Nonfinancial Corporate Business based on the Federal Reserve data shown in Exhibit D.

EXHIBIT D Nonfarm Nonfinancial Corporate Business for Fourth Quarter of 2008 (billions of U.S. dollars)

Assets at market value or replacement cost	27.3
Assets at book value	23.4
Liabilities	13.3
Equities at market value	9.0

Atkinson notes that the Tobin’s q ratio that could be derived from Exhibit D is less than 1. She asks Ryan what conclusion could be drawn from such a low ratio if it had been obtained for a specific company.

3. Which conclusion presented by Ryan about the top-down approach and the bottom-up approach is most likely correct?

A. Conclusion 1.

B. Conclusion 2.

C. Conclusion 3.

4. Based on Exhibit C, which of the components of economic growth has contributed most to GDP growth during the 1970–1989 time period?

A. Labor input.

B. Capital stock.

C. Total factor productivity.

5. Which of the following criticisms expressed by Ryan about the use of historical data is the least valid?

A. In a context of hyperinflation, the approach may not be appropriate.

B. The companies’ growth rates may not match GDP growth for long periods.

C. Government-implemented measures may not be taken into account in any of the growth factors.

6. Which of the following advantages listed by Ryan with respect to the earnings-based approach studied by Atkinson is most likely correct? The model

A. Can be used for non-U.S. equity markets.

B. Captures the net present value of growth investment opportunities available to investors.

C. Is most informative when the excess of the earnings yield over the Treasury bond yield is close to the historical average.

7. The most likely improvement from using the Yardeni model instead of the Fed model is that the Yardeni model captures:

A. A pure equity risk premium.

B. A pure default risk premium.

C. The effect of long-term earnings growth on equity market values.

8. Which of the following features of the P/10-year MA(E) model as stated by Ryan is least likely to be correct? The model

A. Controls for inflation.

B. Is independent of changes in accounting rules.

C. Controls for business cycle effects on earnings.

9. Based on the data shown in Exhibit D, the equity q ratio is closest to:

A. 0.6429.

B. 0.8168.

C. 0.8911.

10. The best conclusion that Ryan can provide to Atkinson regarding the calculated value for Tobin’s q ratio is that, based on comparing it to an equilibrium value of 1:

A. The replacement cost of assets is understated.

B. The company appears to be overvalued in the marketplace.

C. The company appears to be undervalued in the marketplace.

Use the following information to answer Questions 11 through 16.

Egon Carmichael, CFA, is a senior analyst at Supranational Investment Management (Supranational), a firm specializing in global investment analysis. He is meeting with Nicolas Schmidt, a potential client representing a life insurance company, discussing a report prepared by Supranational on the U.S. equity market. The report contains valuations of the U.S. equity market based on two approaches: the justified P/E model and the Fed model.

When Carmichael informs Schmidt that Supranational applies the neoclassical approach to growth accounting, Schmidt makes the following statements about what he considers to be some limitations of that approach:

For use in estimating the justified P/E based on the Gordon constant growth model, Carmichael develops the assumptions displayed in Exhibit E.

EXHIBIT E Justified P/E Ratio for the U.S. Equity Market: Assumptions

Required real rate of return	5.0%
Inflation-adjusted dividend growth rate	2.5%

Using these assumptions, Carmichael’s estimate of the justified P/E ratio for the U.S. equity market is 13.2. Schmidt asks Carmichael, “All else equal, what would cause the justified P/E for the U.S. equity market to fall?”

Supranational’s report concludes that the U.S. equity market is currently undervalued, based on the Fed model. Schmidt asks Carmichael, “Which of the following scenarios would result in the Fed model most likely indicating that the U.S. equity market is overvalued?”

Schmidt points out that the Fed model has been the subject of criticism and recommends that Carmichael use the Yardeni model to value the U.S. equity market. Before employing the Yardeni model, Carmichael asks Schmidt to identify criticisms of the Fed model that are addressed by the Yardeni model.

Finally, Carmichael presents a third earnings-based approach, the P/10-year MA(E) model, and describes many positive features of that model.

Schmidt mentions that the international life insurance company that he represents might be interested in the equity forecasts produced by Supranational. He says that his company’s objective is to accumulate sufficient assets to fulfill the firm’s obligations under its long term insurance and annuity contracts. For competitive reasons, the company wants to quickly detect significant cyclical turns in equity markets and to minimize tracking errors with respect to the equity index. Schmidt asks Carmichael to identify the forecasting approach that is most appropriate.

11. Which of the statements expressed by Schmidt about the neoclassical approach to growth accounting is correct?

A. Statement 1.

B. Statement 2.

C. Statement 3.

12. Carmichael’s most appropriate response to Schmidt’s question about the justified P/E ratio is:

A. Lower volatility of the U.S. equity market.

B. Higher inflation-adjusted dividend growth rate.

C. Higher correlation of U.S. equity market with international equity markets.

13. Carmichael’s most appropriate response to Schmidt’s question about the Fed model is:

A. Scenario 1.

B. Scenario 2.

C. Scenario 3.

14. In response to Carmichael’s question about which criticisms of the Fed model are addressed by the Yardeni model, Schmidt’s most appropriate response is that the Yardeni model does take account of the criticism that the Fed model:

A. Assumes that investors value earnings rather than dividends.

B. Ignores long-term earnings growth opportunities available to shareholders.

C. Assumes that the required rate of return on equity equals the Treasury bill rate.

15. Which of the following features is least applicable to the third earnings-based approach presented by Carmichael? The model:

A. Controls for inflation.

B. Is independent of changes in accounting rules.

C. Controls for business cycle effects on earnings.

16. Carmichael’s best answer to Schmidt’s question about a recommended forecasting approach is to use:

A. A top-down approach.

B. A bottom-up approach.

C. Both top-down and bottom-up approaches.

1Forecasts and opinions offered in this chapter are those of the authors (or the writers cited) and are not positions of CFA Institute.

2See Cobb and Douglas (1928).

3As a result, if both capital and labor change by a percentage x, then the total change in output is αx+(1 − α)x = x. The use of constant returns to scale is predicated on empirical results from several large economies over various time periods during the nineteenth and twentieth centuries.

4Capital, α, and labor, (1 − α), output elasticities may differ across national economies.

5See Solow (1957). The Solow residual is thus simply:

6In lieu of higher consumption spending, particularly on imported goods.

7Preston (2009).

8Xin and Rabinovitch (2009).

9Our forecast is for a 30-year time period and was made in the summer of 2009. As noted in Exhibit 11-2, the ZHB forecast was for 2009–2030. We believe the choice of a longer time horizon for our forecast is also supportive of the choice of a lower terminal growth rate.

10In principle, the sector of publicly traded companies could grow somewhat above or below the overall growth rate of GDP, because it is a subset of the overall economy. However, the approach used in the text should serve as a good approximation for analytical purposes.

11Valuation differences between the H-Model and a period-by-period approach should be minimal so long as the differences between long-term and interim growth rates are of single-digit magnitude and the “interim” period length is not much longer than 30–40 years. In any event, the possible valuation error from adopting a simpler model is reasonable in comparison with the incremental valuation error that can arise from introducing an excessive number of valuation parameters, i.e., year-by-year cash flows.

12Analysts and practitioners may, if desired, proceed directly to forecasting a justified market index level based on the H-Model, the current dividend rate, and the growth-factor inputs. (Strictly speaking, the H-Model does not directly utilize earnings per share, although, indirectly, the trajectory of dividend growth is assumed to be supported by growth in EPS.) Under our approach, the relative differences in P/E ratios in Exhibit 11-3 and 11-4 translate directly into the relative differences between observed and justified market levels.

13The geometric average growth rate during the 30-year period is around 6.7 percent. Also of interest, the average compound growth rate for the first 20 years is not far off from the ZHB 20-year 8 percent annual growth rate.

14To check the reasonableness of the data, we computed the cumulative total returns for the Morgan Stanley Capital International (MSCI) China Index and found them in good accord with the S&P China BMI Index.

15Ibbotson and Sinquefield (1989), Siegel (1992), Arnott and Bernstein (2002), Siegel (2005).

16Geometrically compounded.

17Ibbotson, Diermeier, and Siegel (1984), Stimes (2008).

18Mehra and Prescott (1985), Mehra (2003).

19Arnott (2004).

20Which could, of course, be zero.

21For company EPS estimates, Darrough and Russell (2002) showed bottom-up forecasts are systematically more optimistic than top-down forecasts. The authors contend this occurs because analysts rely heavily on management’s assessment of future profitability and such estimates often are overly optimistic.

22Bodie, Kane, and Marcus (2007) show that the geometric average annual return on U.S. large capitalization stocks was 10.23 percent over the 1926 to 2003 time period. The geometric average annual return on long-term Treasury bonds was 5.10 percent during this same time period.

23Wilcox (2007) and Palkar and Wilcox (2009) note that accounting and debt adjustments must be made to GAAP-based reported earnings before they can be considered real.

24Based on a dataset maintained by Professor Shiller (www.econ.yale.edu/∼shiller/data.htm), the compound (geometric mean) annual earnings growth rate was 3.52 percent from 1872–2008. In the more recent shorter term, the growth rate has been higher: from 1990–2008, the rate was 3.55 percent but stopping at 2007 (i.e., from 1990–2007), reflecting an unusually long period of sustained growth, it was 6.89 percent. The long run rate is probably most appropriate here.

25The required return on equity for a no-growth company that pays all of its earnings out as dividends is the earnings yield (based on a constant EPS).

26Note that rearranging the terms in Equation 11.9 so that they produce a formula for d results in

Thus historical values for d can be estimated from market data.