A Gross UnderestimateWhy We Believe Bill Gross’ Investment Outlook on Equities is too Pessimistic

Summary As we enter 2013, we felt it would be an appropriate time to revisit one of last year’s most controversial predictions of future equity performance. We acknowledge that equities in general may not continue to deliver the same real rate of return they have over the last century; however, we believe the glum outlook for the asset class forecasted by Bill Gross last year misses the mark. Our estimates of future equity returns—based on three different approaches—all point to a meaningfully higher forecast than Gross’ pessimistic prediction. We arrive at higher estimations first by looking at corporate earnings growth from a bottom-up perspective, which shows that Gross’ estimates do not take into account revenue growth from countries that are still experiencing much faster economic growth. We also take a historical approach, looking back at periods in time with characteristics similar to today’s economic and market environment; our findings suggest that a low interest rate environment and high investor risk aversion do not automatically translate to low equity returns. Finally, we consider potential future returns from the perspective of investor demand, which demonstrates the expected long-term nominal return on equities cannot be lower than yields for bonds, due to the inherent risk premium investors demand for the riskier asset class.

Investment Insights Series l January 2013

Jonathan Coleman, CFACo-Chief Investment Officer

Soonyong Park, CFA, CPAInstitutional Client Strategist

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With all due respect…

We begin by stating that we have great respect for Bill Gross and PIMCO as an asset management organization. For the past several years, some of us have been regular readers of the Investment Outlook and Secular Outlook Series penned by Bill Gross and Mohamed El-Erian and, recently, of Equity Focus by Neel Kashkari. The August 2012 Investment Outlook caught our attention not because Bill Gross was favoring fixed income over equities (his prospective view of a low return environment applied to both equities and bonds), but, rather, because of the following statement:

Together then, a presumed 2% return for bonds and a historically low percentage nominal return for stocks – call it 4%, when combined in a diversified portfolio produce a nominal return of 3% and an expected inflation adjusted return near zero. The Siegel constant of 6.6% real appreciation, therefore, is a historical freak, a mutation likely never to be seen again as far as we mortals are concerned.1

The ‘Siegel constant’ of 6.6% that Bill Gross refers to represents the annualized long-term inflation adjusted return for U.S. equities since 1912 (i.e. the past 100 years) as estimated by Jeremy Siegel of the University of Pennsylvania. With respect to the foregoing quote, the historical 6.6% real return for equities is likely beyond the realm of possibility; in fact, the future expected real return for equities is closer to 1.6% (See Exhibit 1).

Exhibit 1

Real Rate of Return on Equities

Bill Gross’ Nominal Rate of Return for Equities

4.00%

Expected Inflation

10 Year Treasuries: Nominal 1.64%

10 Year Treasuries: Real -0.78%

Average Inflation Rate for the Next 10 Years, as Implied by the Market

2.42%

Expected Real Rate of Return on Equities for the Next 10 Years

1.58%

Source: U.S. Department of Treasury. Rates as of October 1, 2012.

The fact that the developed Western economies are in the midst of a multi-year deleveraging process is beyond

dispute; further, we read and observe the results of the deleveraging process: outright economic contraction and high unemployment rates in Greece, Portugal and Spain and below 3.0% real GDP growth and moderately high unemployment in the United States. Therefore, the estimated 1.6% real GDP growth rate for the U.S. during the deleveraging period is quite reasonable. Notwithstanding, we take exception to Bill Gross’ assertion that the future long-term return for equities cannot exceed the real GDP growth rate for the U.S. economy. To quote Bill Gross:

If wealth or real GDP was only being created at an annual rate of 3.5%...then somehow stockholders must be skimming 3% off the top each and every year. If an economy’s GDP could only provide 3.5% more goods and services per year, then how could one segment (stockholders) so consistently profit at the expense of the others (lenders, laborers and government)?…and if GDP growth itself is slowing significantly due to deleveraging in a New Normal economy, then how can stocks appreciate at 6.6% real? They cannot, absent a productivity miracle that resembles Apple’s wizardly.

From a top-down and supply side perspective, Bill Gross’ line of reasoning around equity returns appears sensible and commonsensical. However, from bottom-up, historical and investor demand perspectives, Gross’ 4% projected nominal equity return for the foreseeable future seems way too low even in a multi-year deleveraging environment. We posit the following three counter arguments to Bill Gross’ position on future equity returns:

1. Corporate revenues and earnings from a bottom-up perspective

2. History of equity returns

3. Equity returns from the investor demand perspective

Corporate Revenues and Earnings from a Bottom-Up Perspective

In his article, Bill Gross relates the long-term real stock market returns to the long-term real GDP growth rate, presumably that of the U.S. since ‘New Normal’ does not apply to developing economies such as China, Indonesia, India, Brazil, and Nigeria. Taking a building block approach, one can estimate the real return from equities in the following fashion:

Real Return from Equities ≈ Dividend Yield T = 0 + Real EPS Growth Rate2 +/- P/E Expansion or Contraction

1Gross, Bill. “Cult Figures.” PIMCO Investment Outlook: August 2012. 2Assume that the payout rate is constant; therefore, the EPS growth rate and the dividend growth are one and the same.

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When one assumes zero return from dividend yield (an unrealistic assumption) and no price-to-earnings ratio expansion or contraction (a realistic assumption since over the long-term, equity valuations tend to be mean-reverting), then the real return from equities reverts to the long-term real earnings-per-share (EPS) growth rate. Further, if one assumes that the latter converges with the real GDP growth rate over the long term, then the real return from equities has to equal the long-term real GDP growth rate. Sensible, right? Even if (this is a big ‘if’) one ascribes to this normative supply side view of equity returns it still begs the question: What is the appropriate real GDP growth rate that one should use as a proxy for the long-term real EPS growth rate? This is one of the areas where we part ways with Bill Gross. In our opinion, and from a bottom-up perspective, the U.S. real GDP growth rate represents a rather poor proxy for the real earnings growth of U.S. companies.

Consider the global sales of S&P 500 companies as estimated by S&P Dow Jones Indices (Exhibits 2 and 2a).

Based on reported regional sales data, S&P estimated that 46% of 2011 sales for S&P 500 companies emanated from abroad; meaning that domestic economic activity accounted for 54% of total corporate sales. The significance of this observation is obvious: It is not U.S. GDP growth but, rather, global GDP growth that drives the corporate EPS growth rate for S&P 500 companies. Therefore, it is inappropriate to use the U.S. real GDP growth rate as the proxy for the real EPS growth rate of U.S. corporations and, by nexus, the expected real return on U.S. equities.

Exhibit 2

Foreign Sales as a Percent of Total Sales for S&P 500 Companies

2011 2010 2009 2008 2007 2006 2005 2004 2003

46% 46% 47% 48% 46% 44% 43% 44% 42%

Source: S&P Dow Jones Indices, S&P 500 2011: Global Sales.

Exhibit 2a

Foreign Sales by Region for S&P 500 Companies

Foreign Sales 2011 Foreign Sales 2010 Foreign Sales 2009

Region (USD Millions) (%) (USD Millions) (%) (USD Millions) (%)

Africa 208,602 7.9 148,103 6.5 160,559 7.9

Asia 407,381 15.5 300,065 13.1 356,739 17.7

Australia 11,953 0.5 6,025 0.3 5,439 0.3

Europe 630,172 24.0 666,398 29.1 516,690 25.6

North America 248,427 9.5 104,115 4.5 157,659 7.8

South America 148,820 5.7 97,628 4.3 108,750 5.4

Foreign Countries 969,181 36.9 966,145 42.2 715,176 35.4

Total $2,624,536 100.0 $2,288,479 100.0 $2,021,012 100.0

Source: S&P Dow Jones Indices, S&P 500 2011: Global Sales.

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In Exhibit 3, we present the International Monetary Fund’s (IMF) Overview of World Economic Outlook Projections as of October 2012.

We think it’s noteworthy that the IMF’s 2013 economic growth projections for the U.S. (2.1%) and the Euro Area (0.2%) are consistent with PIMCO’s ‘New Normal’ outlook. However, IMF’s world output projections of 3.3% (2012) and 3.6% (2013) are well beyond the growth projections for deleveraging economies like the U.S. or Europe. Furthermore, based on S&P’s data on corporate sales, if the global real GDP growth rate represents a better proxy for the corporate earnings growth rate, then, at least for 2012 and 2013, the real return from equities is closer to 3.5% (roughly the midpoint between the 2012 and 2013 world output projections per the IMF), as opposed to 1.5% espoused by Bill Gross.

Returning to the building block approach at the beginning of this section where we unrealistically assumed a zero return from dividend yield, consider a more realistic scenario with the following assumptions:

1. Beginning dividend yield = 2.0%

2. Real corporate earnings growth for the next 10 years = 3.5%

3. Return from P/E expansion or contraction = 03

Based on the foregoing assumptions, the supplied real return on equities for the next 10 years approximates 5.5%, meaningfully higher than the 1.6% implied by Bill Gross. When we add 2.4%—the market implied breakeven inflation rate on 10-year Treasury Inflation-Protected Securites (TIPS) from Table 1, we arrive at

Exhibit 3

IMF World Economic Outlook Projections

Year over Year Q4 over Q4

ProjectionsDifference from July 2012 WEO Update Estimates Projections

2010 2011 2012 2013 2012 2013 2011 2012 2013

World Output1 5.1 3.8 3.3 3.6 -0.2 -0.3 3.2 3.0 4.0

Advanced Economies 3.0 1.6 1.3 1.5 -0.1 -0.3 1.3 1.1 2.1

United States 2.4 1.8 2.2 2.1 0.1 -0.1 2.0 1.7 2.5

Euro Area 2.0 1.4 -0.4 0.2 -0.1 -0.5 0.7 -0.5 0.8

Germany 4.0 3.1 0.9 0.9 0.0 -0.5 1.9 0.9 1.4

France 1.7 1.7 0.1 0.4 -0.2 -0.5 1.2 0.0 0.8

Italy 1.8 0.4 -2.3 -0.7 -0.4 -0.4 -0.5 -2.3 0.0

Spain -0.3 0.4 -1.5 -1.3 -0.1 -0.7 0.0 -2.3 0.2

Japan 4.5 -0.8 2.2 1.2 -0.2 -0.3 -0.6 1.6 2.1

United Kingdom 1.8 0.8 -0.4 1.1 -0.6 -0.3 0.6 0.0 1.2

Canada 3.2 2.4 1.9 2.0 -0.2 -0.2 2.2 1.7 2.2

Other Advanced Economies2 5.9 3.2 2.1 3.0 -0.4 -0.4 2.4 2.3 3.6

Newly Industrialized Asian Economies 8.5 4.0 2.1 3.6 -0.6 -0.6 3.0 3.2 3.5

Emerging Market and Developing Economies3 7.4 6.2 5.3 5.6 -0.3 -0.2 5.7 5.5 6.2

Source: 2012 IMF Global Economic Outlook. 1The quarterly estimates and projections account for 90 percent of the world purchasing-power-parity weights. 2Excludes the G7 economies (Canada, France, Germany, Italy, Japan, United Kingdom, United States) and euro area countries. 3The quarterly estimates and projections account for approximately 80 percent of the emerging market and developing economies.

3Over the long-term, this is a reasonable assumption since valuation measures revert to the long-term mean.

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an expected nominal return on equities of 7.9%; again, meaningfully higher than the 4.0% nominal return estimated by Bill Gross.

History of Equity Returns

In isolation, the normative approach to estimating future equity returns from the previous section appears sensible; however, it is instructional to compare it against the history of equity returns. As set forth in Exhibit 4, the Siegel constant of 6.6% for the past 100 years is almost spot on with the realized returns for the S&P 500 Index from 1926–2011.

Exhibit 4

S&P 500 Index Real Rate of Return (1926-2011)

The Seigel Constant 6.60%

S&P 500 Index (1926-2011)

Historical Compound Rate of Return 9.80%

Historical Change in CPI 3.00%

Historical Real Return 6.80%

Source: Dimensional Fund Advisors Matrix Book 2012. Data presented reflects past performance, which is no guarantee of future results.

If we blindly assume that the long-term realized real returns for the S&P 500 Index is the best unbiased estimate of future returns for the next 10 years, then one should expect 9.2% (see Exhibit 5) in nominal returns from the S&P 500 Index—higher than the supplied nominal return of 7.9% that was previously mentioned.

Exhibit 5

Estimate of the S&P 500 Index Return

S&P 500 Index (1926 - 2011)

Historical Real Return 6.80%

Average Inflation Rate for the Next 10 years, as Implied by the Market

2.42%

Estimated Nominal Return 9.22%

Source: Dimensional Fund Advisors Matrix Book 2012. Data presented reflects past performance, which is no guarantee of future results.

It begs the question though, is the long-term average the best unbiased estimate of future returns for the next 10 years? Would it not be more appropriate to estimate today’s future expected return on equities based on a historical period with similar characteristics? Between 1929–1932, the S&P 500 Index lost 64% of its value and for the subsequent 10 years, the short-term interest rate averaged 0.14%. Not having lived through the Great Depression, we cannot personally attest to the macro environment or investor psychology. However, we believe it’s safe to assume that the macroeconomic environment and investor psychology were similar to or in worse shape than the current market environment: Equity investors were probably extremely risk averse and their confidence in equities shattered to pieces. This is what Milton Friedman said of the environment following the Great Depression:

It changed the atmosphere within which businessmen and others were making their plans, and spread uncertainty where dazzling hopes of a new era had prevailed. It is commonly believed that it reduced willingness of both consumers and business enterprises to spend; or, more precisely, that it decreased the amount they desired to spend on goods and services at any given levels of interest rates, prices and income… Such effects on desired flows were presumably accompanied by a corresponding effect on desired balanced sheets, namely, shift away from stocks and toward bonds, away from securities of all kinds toward money holdings.4

It is important to note that even in that depressing environment, the S&P 500 Index averaged 8.2% in nominal terms and 6.3% in real terms from 1933 to 1942 (see Exhibit 6). History from the Great Depression era shows that a low interest rate environment and high investor risk aversion did not automatically translate to low equity returns.

Exhibit 6

Estimate of the S&P 500 Real Return (1933-1942)

Average 1-Month T Bill Rate (1933-1942) 0.14%

S&P 500 Index (1933-1942)

Historical Compound Rate of Return 8.20%

Average Change in CPI 1.90%

Historical Real Return 6.30%

Source: Dimensional Fund Advisors Matrix Book 2012 and Kenneth R. French Data Library. Data presented reflects past performance, which is no guarantee of future results.

4Friedman, Milton and Anna Jacobson Schwartz. “The Great Contraction 1929 – 1933.” Princeton: Princeton UP, 2008.

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According to Dr. Meir Statman, a leading researcher in behavioral finance, investors’ views of future equity returns is inversely related to their estimation of equity risk; that is, the higher the risk estimation for equities the lower the estimate of future equity returns. When forecasting a 4% nominal return for equities, it may be that Bill Gross is exhibiting multiple behavioral biases of fear and overconfidence under the ‘WYSIATI’ rule in underestimating future equity returns.

WYSIATI – ‘What You See Is All There Is’ – is an acronym coined by the Nobel Laureate Daniel Kahneman. Under the WYSIATI rule, people’s experiences are “. . .determined by the coherence of the story they manage to construct from available information…neither the quantity nor the quality of the evidence counts for much in subjective confidence. The confidence that individuals have in their beliefs depends mostly on the quality of the story they can tell about what they see, even if they see little. We often fail to allow for the possibility that evidence that should be critical to our judgment is missing – what we see is all there is.5”

When asserting that the long-term real return from equities cannot exceed the long-term real GDP growth rate, Gross does not allow for the possibility “…that evidence that should be critical to…” his judgment is missing. Moreover, he appears to draw his confidence from the coherence and quality of his story (sub par real GDP growth rate under the ‘New Normal’ scenario) and only from the available data—mainly the real corporate earnings and GDP growth rates for the United States.

We provide the following caveat before moving on to the next section. While instructional and comparable, we caution investors from placing too much confidence or emphasis in the historical data, especially the 1933-1942 period. We only have one historical sample, and a sample of one cannot possibly be statistically significant.

Equity Returns from an Investor Demand Perspective

Earlier, we approached the estimation of equity returns from the supply side. Now, we will approach the estimation of equity risk from the demand side; that is, what kind of risk premium should investors demand from equities? To be more precise, what should equities’ risk premium be over corporate bonds? Since equities rank junior to all bonds in a corporate balance sheet, equity holders must be compensated for assuming the most risk among all capital providers. A mistake that Bill Gross made in estimating future equity returns is that he only

considered the supply side and completely ignored the demand side.

Exhibit 7

Equity Risk Premium Over Corporate Bonds (1926-2011)

Historical Compound Rate of Return

S&P 500 Index 9.80%

Long-Term Corporate Bonds 6.00%

Historical Equity Risk Premium over Long-Term Corporate Bonds 3.80%

Source: Dimensional Fund Advisors Matrix Book 2012. Data presented reflects past performance, which is no guarantee of future results.

Between 1926 and 2011, the realized (ex-post) equity risk premium over long-term corporate bonds approximated 3.8% (see Exhibit 7). As of October 2012, the yield-to-worst on Barclays Aggregate Long Corporate and High Yield Indexes stood at 4.3% and 6.5%6, respectively. Therefore, when we combine the long-term historical equity risk premium with the current yield-to-worst on Barclays Aggregate Long Corporate Index we arrive at an expected nominal equity return of 8% (see Exhibit 8).

Exhibit 8

Barclays Aggregate Long Corporate and High Yield Index

Long Corporate: Current Yield-to-Worst 4.30%

Historical Equity Risk Premium (1926-2011) 3.80%

Estimated Nominal Equity Return 8.10%

Average Inflation Rate for the Next 10 Years, as Implied by the Market 2.42%

Estimated Real Return 5.68%

High Yield: Current Yield-to-Worst 6.45%

Average Inflation Rate for the Next 10 years, as Implied by the Market 2.42%

High Yield Bonds Real Return 4.03%

Source: Barclays Capital as of October 1, 2012, Dimensional Fund Advisors Matrix Book 2012.

5Kahneman, Daniel. Thinking, Fast and Slow. New York: Farrar, Strauss and Giroux. 2011. 6The yield-to-worst measure ignores the loss associated with future bond defaults. For purposes of our discussion, we ignore the impact of bond defaults and recoveries.

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Although possible on an episodic and temporary basis, we believe over the long term the expected nominal return on equities cannot be lower than 6.5%, the yield-to-worst on the Barclays Aggregate High Yield Index, because even high yield bonds rank senior to equities in the corporate capital structure. Moreover, since equities are deemed riskier than high yield bonds, the former must have higher expected returns than the latter; otherwise, there would be no incentive for investors to hold equities over high yield bonds.

ConclusionWe took several approaches to estimating future equity returns for the next 10 years, and each point to a higher estimate than Bill Gross’ forecast. The normative approach to deriving future equity returns resulted in approximately 5.5% (real) and 7.9% (nominal) equity returns. When using an approach based on historical returns, we estimated future real and nominal equity returns in the following ranges: 6.3% - 6.8% (real) and 8.2% - 9.2% (nominal). Finally, when approached from an investor demand perspective, we estimated the future real and nominal equity returns as follows: 4.0% - 5.7% (real) and 6.5% - 8.1% (nominal). All three approaches resulted in estimated nominal equity returns that are meaningfully higher than the nominal 4% return forecasted by Bill Gross.

Prospectively, we may not obtain the Siegel constant of 6.6% from equities (too optimistic); however, Bill Gross’ ~1.5% real return on equities seems equally unlikely (too pessimistic). That’s probably why Neel Kashkari – the head of global equities at PIMCO – felt compelled to write a follow-up piece in September to revise their estimate upward by stating: “…we believe it [equities] is going to generate more modest returns [real] going forward, in the 3% - 4% range…” The true outcome, most likely, lies somewhere in between the forecasts of Jeremy Siegel and Bill Gross.

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Past performance is no guarantee of future results.

The opinions are those of the authors as of December 2012 and are subject to change at any time due to changes in market or economic conditions. The comments should not be construed as a recommendation of individual holdings or market sectors, but as an illustration of broader themes.

In preparing this document, the author has relied upon and assumed, without independent verification, the accuracy and completeness of all information available from public sources.

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