Chapter 1 - Introduction and Overview

The book "Triumph of the Optimists: 101 Years of Global Investment Returns" addresses key questions about investment markets and prospects by providing a comprehensive record of historical investment returns worldwide. It spans a 101-year period from 1900 to 2000 and covers four continents and sixteen countries. The book aims to help readers understand the historical performance of equities, bonds, and bills, as well as inflation rates and currency movements.

The authors emphasize the need for a reliable international dataset due to the increasing demand for locally sourced research in a global context, as well as the rise of global mandates for fund managers. The book starts by discussing the challenges of making accurate judgments about future prospects and required rates of return without a comprehensive historical perspective. It highlights the importance of analyzing long-term data to provide insights into expected returns.

The authors examine various aspects of investment, including size and seasonality effects in equity markets, the performance of value and growth stocks, and the significance of dividends in overall stock market performance. They also delve into the equity risk premium, comparing returns on equities to risk-free investments, and discuss its implications for investors, valuation, and investment decisions.

The book concludes by presenting individual chapters for each of the sixteen countries studied, highlighting their historical investment performance. It provides a summary of the findings and insights gained from the extensive research on global financial markets. The authors emphasize the importance of historical data and analysis for understanding past trends and making informed investment decisions for the future.

Chapter 2 World Markets Today and Yesterday.

The United States leads the global equity market in the 2000swith $16.6 trillion(This number is almost 3x today in 2023) in traded shares, representing 46 percent of the total. Japan briefly overtook the US in the late 1980s but later faced a 41 percent decline. The UK's market surpassed Japan's by 2001. GDP correlates with stock market size, but exceptions exist. Well-developed financial sectors and public ownership boost markets, as seen in the US, UK, and Switzerland. Less privatization and state involvement lead to smaller markets, as in China, Italy, and Germany.

Data from 16 countries underpin a worldwide equity index spanning the 20th century. North America dominates, Europe follows, and a north-south divide is evident. The study includes countries with data on equities, bonds, bills, inflation, and exchange rates from 1899 to 2000, forming a basis for understanding GDP-market cap links.

At the start of the 21st century, bonds became a substantial asset class, challenging equities. The global bond market was valued at $31 trillion, slightly below equities' $36 trillion. Developed nations had active bond markets, often larger and more active than equities. Bonds facilitated long-term borrowing, while money markets handled short-term lending.

The US led with a $14.6 trillion bond market (47% of the global total), followed by Japan and Germany. Bonds in USD, Euro, and Japanese yen made up 88% of the global market.

Government bond importance declined, making up 55% of the global market by 2000. Corporate bonds, Eurobonds, and foreign bonds grew.

Market size differences were influenced by macro policies, government borrowing, and financial system structures. Cross-border investment surged, driven by the Eurobond market's growth.

The euro's introduction in 1998 unified Eurobond markets, increasing liquidity and reducing currency risk, leading to potential Eurozone market integration.

Large and liquid stock and bond markets have essential roles: the primary market raises capital for companies through securities issuance, while the secondary market enables trading of existing securities.

The primary market emerged due to the need for more funds than individual investors could provide. This required organized exchanges, transferable securities, and intermediaries.

The secondary market allows investment decoupling, where long-term projects are funded, and investors can sell securities when needed. Stock markets offer diversification, risk reduction, regulation, and information dissemination.

Bond markets work similarly, allowing diverse debt capital raising, and the secondary market enables flexible investing.

Money and bill markets serve short-term borrowing and lending needs. The book covers equity, bond, and bill markets, focusing on historical returns, risks, and future insights.

Despite their earlier existence, stock markets gained prominence gradually. Amsterdam, London, and NYSE were among the early exchanges. 19th-century markets included banks, transportation, mining, and manufacturing stocks, often regionally focused.

Regional exchanges proliferated due to local needs and proximity to firms. National exchanges gained dominance due to improved communication and larger projects. By 1900, exchanges existed in many countries, with 16 key countries covered in the book representing a significant portion of today's market value, compared by GDP.

Cross-border investment was prominent, particularly Europeans investing in less developed regions. International investment declined due to various factors until a resurgence in the 1970s. The book delves into the historical development of stock markets' role in global investments.

In the early 20th century, the United Kingdom had the largest equity market globally, with over six times as many companies listed on the London Stock Exchange (LSE) compared to the New York Stock Exchange (NYSE). The market capitalization of LSE-listed equities in 1899 was $4.3 billion, surpassing the $2.86 billion value of NYSE-listed stocks. The UK had numerous regional exchanges as well. However, the US equity market eventually surpassed the UK's dominance, with 6,340 US stocks quoted on major exchanges by the end of 2000, having a total capitalization of $14.4 trillion. In contrast, the UK had 2,140 companies listed on the London market with a total capitalization of $2.7 trillion. The largest stocks in 1899 were the Pennsylvania Railroad in the US and the London and North Western Railway in the UK. By 2001, General Electric and Vodafone were the largest stocks in the US and UK, respectively, with significantly larger market capitalizations.

The Financial Times editorial from 2001 challenges the idea that information technology is the most transformative force since the Industrial Revolution, citing the 1880-1940 period as more impactful. The editorial examines shifts in stock market sectors over the 20th century:

1. Railroads Dominance: Railroads played a significant role in the early 1900s, with large market values in the UK and US.

2. Emergence of New Sectors: Many companies today operate in sectors that were small or nonexistent in 1900, contributing significantly to market value.

3. Changing Sectors: Sectors like chemicals and tobacco experienced fluctuating prominence over the years.

4. Modern Sector Landscape: Information technology, banking, pharmaceuticals, telecommunications, retailers, and oil and gas are now major sectors.

5. Persistent Sectors: Certain sectors, such as banking and insurance, have maintained importance over time.

6. Differences Across Countries: Disparities in sector weightings between countries impact market performance and risk levels.

In essence, the editorial highlights the historical shifts in sectors, the rise of new industries, and the lasting impact of technology and industry on the stock market.

Market concentration is a contemporary concern in the UK and global stock markets. The UK has seen increased concentration, with large companies dominating indices. Regulatory worries arise as UK mutual funds are limited to 10% per stock. While the UK's concentration grew, it remained below historical highs and was lower than some countries. The US experienced similar trends but with fluctuations and a recent decline.

Challenges arise for index funds and fund managers following benchmarks. Global companies like Vodafone should be considered in a global context. For worldwide investors, market concentration matters less, as the top stocks hold a small portion of the total equity value.

Chapter 3 Measuring long term returns.

The five key principles for measuring long-term equity index performance are:

1. Avoid Bias: Construct indexes without look-ahead bias, using only available information at the time. Minimize bias from skewed constituents or sectors.

2. Total Returns: Measure performance using total returns, considering both dividends and capital gains.

3. Comprehensive Coverage: Strive for representative market coverage, even if complete historical data is unavailable.

4. Proper Weighting and Averaging: Weight constituents by market capitalization and use arithmetic averaging for accurate results.

5. Cross-Country Comparisons: Include diverse countries in analysis, adhering to the above principles and facilitating currency conversion when needed.

The first guiding principle emphasized avoiding bias in evaluating investment strategies. However, many published historical data suffer from survivorship and success bias. This bias is due to retrospective selection of index constituents, leading to an overrepresentation of successful companies and sectors. The widely used de Zoete index for UK stock market performance has been criticized for these biases. Its constituent selection, sector coverage, and start date (1919) distort the true market performance. A reconstructed index using comprehensive data from 1900 to 1954 reveals significantly lower equity returns than previously reported. This underscores the need to examine global financial history to better understand stock market performance.

The availability of stock market indexes for measuring the performance of exchanges like New York and London has been a historical development. Initially, most indexes focused on capital appreciation and overlooked the importance of reinvested dividends. The transition to total return indexes, which include both capital gains and dividends, was gradual, and some countries relied on estimates for early 20th-century equity returns. The construction of these indexes involved careful selection of representative equity and bond indexes, often favoring broader coverage and more comprehensive data sources. The index calculations are based on end-of-year values, with weighting by market capitalization and arithmetic averaging being preferred.

Recent concerns about index weighting include potential overstatements of equity available for trading due to full market capitalization weighting, leading to a shift towards measures of free equity. A global perspective on equity market performance necessitates adjusting for currency differences, inflation rates, and timing variations. A common-currency 20th-century world equity index is constructed, considering local currency returns converted to a common currency (usually US dollars) and adjusted for investor behavior. Weights are based on market capitalization data post-1967 and GDP conversion before that, with rebalancing occurring annually after 1968. A similar process is used to construct a world bond market index, weighted by country size and using GDP weights throughout the century. The resulting indexes are expressed in real terms after adjusting for inflation, providing insights into global market performance from the perspective of a notional US investor.

comparing stock market performance across countries. Researchers often use modern indexes with a common starting date, like the MSCI Indexes from 1970. Single-country studies have proliferated, enabling cross-country comparisons. A comprehensive database covers various asset categories and sixteen countries from 1900 onwards, allowing insights into economic and political differences.

Survival bias arises from focusing on enduring markets, potentially inflating return estimates. Market failure alone doesn't explain high equity returns. "Easy-data bias" occurs when researchers favor accessible, stable data, often leading to overestimations of long-term equity performance. Comparing different studies' start dates with a 101-year index series reveals an average overestimation of about three percentage points.

Using international indexes with extensive coverage and a shared start date mitigates but doesn't eliminate easy-data bias. Still, upward bias in global return estimates persists. The challenge of studying earlier periods is acknowledged, and the potential for new studies on nineteenth-century security prices is noted.

The principles for measuring equity indexes also apply to inflation, bill, and bond returns. The Boskin Commission found that inflation might be overestimated due to quality improvements. We use published measures and show risk differences to counter this. In the past, inflation measures were narrow, but now cover a wider range of items.

For government bonds, factors like maturity, coupon, and tax matter. Bonds in the same maturity tend to move together. Treasury bill returns are easy to measure, but in some countries, we use similar instruments with low risk.

Inflation indexes track currency fluctuations well. Bond indexes focus on key factors, and government bond markets move similarly. Tax details are mentioned for specific countries.

Chapter 4 International capital market history

The United States holds a significant position as a financial superpower, boasting the world's largest equity and bond markets, constituting almost half of global market capitalization. This dominance is attributed to comprehensive research and data availability, initiated by the Center for Research in Security Prices (CRSP) in the 1960s.

Analyzing a 101-year span from 1900 to 2000, US equities outperformed bonds and treasury bills. A $1 investment in equities grew to $16,797, with annualized returns of 10.1%. Bonds and bills yielded lower returns but surpassed inflation, with annualized returns of 4.8% and 4.1% respectively, while inflation averaged 3.2% annually.

Factoring in inflation-adjusted returns, equities grew 711-fold, while bonds and bills grew 1.6-fold and 0.9-fold respectively, over the period. Despite setbacks like World War I, the 1929 Wall Street Crash, the Great Depression, and the 1970s oil shock, US equities consistently excelled. The 1987 crash and the 2000 technology bubble's burst had minor impacts on long-term trends. Considering global perspectives is important, as investment returns in other countries provide a balanced outlook.

The comparison between the United States and the United Kingdom's investment records provides valuable insights. In the early 20th century, London was the world's leading financial center with substantial equity and bond markets. Despite this, the UK faced challenges such as World Wars and decolonization, which weakened its economy. The UK struggled to adapt to a changing global landscape and suffered economic, labor, and productivity issues.

However, the UK's investment performance from 1900 to 2000 was surprisingly similar to the US. UK equities yielded a nominal annualized return of 10.1%, similar to US equities. In real terms, UK equities, bonds, and bills showed a steady growth trajectory, with equities experiencing setbacks during world wars and economic crises. Notably, the largest decline in the UK was in 1973-74 due to the OPEC oil crisis, economic mismanagement, inflation, labor unrest, and political uncertainty. Despite this, UK equities rebounded, and from the end of 1974, the US dollar gains on UK equities surpassed those of any other country studied. Overall, while the UK faced challenges, its investment performance remained comparable to the US, albeit with periodic setbacks.

The study examines US and UK equity market performance from 1900 to 2000 compared to fourteen other countries. Real returns, adjusted for inflation, are used for meaningful comparisons. Countries are ranked by annualized real returns, showing better performers on the right and worse on the left. Despite diverse economic conditions, all sixteen countries had real returns within 3% of the 5.1% average, indicating similarity. However, even small deviations in returns lead to significant differences in final wealth due to compound interest.

Resource-rich countries like Sweden, Australia, South Africa, the US, and Canada showed the best equity market performance. The Netherlands and UK also performed well. Poor performing markets were often linked to major wars, civil conflicts, and hyperinflation.

In essence, the study highlights global variations in stock market performance, with stable nations and resource-rich countries generally yielding better results. US and UK markets ranked favorably, emphasizing the importance of comparing global equity market experiences.

The performance of equities, bonds, and bills in the US and other countries over 101 years. US equities consistently outperformed bonds and bills. This trend was mirrored in 16 countries. Equities generally outperformed bonds even during economic turmoil. Inflation negatively affected both stocks and bonds. The text emphasizes the historical performance and risk implications of these asset categories.

Investors consider both returns and risks in investments. Risk refers to potential losses or not meeting target returns. Volatility, measured by standard deviation, is a common measure of risk.

annual real returns of US equities and bonds (1900-2000). Equities had higher volatility (20% standard deviation) than bonds. Equities deviated significantly from expectations, with about one in six years seeing deviations of 20% or more. Long bonds had 10% volatility.

Figure 4-9 shows the distribution of annual real equity returns. It's roughly bell-shaped, indicating some years had negative returns. Worst year: -38%, best year: 57%.

Figure 4-10 presents rolling ten-year real returns for equities, smoother and rarely negative. But aiming for zero return isn't ideal as safer investments yielded positives.

Returns follow a lognormal distribution, slightly "fat-tailed." Extreme events are more likely. Volatility changes over time, affecting return distribution.

While more precise risk assessment exists, the focus here is on comparing assets and countries. This analysis sheds light on risk and volatility in investments.

Diversification is a potent strategy to lower investment risk by spreading funds across various stocks. It reduces individual stock volatility, evident in the rapid drop of excess standard deviation as portfolio size increases. Diversification effectively lessens unsystematic risk tied to individual stocks.

Historical examples like market crashes and major events underline equity market volatility, even with diversification. International diversification further mitigates risk by expanding investments across countries.

Key takeaway: Diversification is vital to manage risk, yet all equity markets entail risk, even with diversification.

The historical analysis of major US asset classes (equities, bonds, bills) reveals a risk-return relationship. Equities had the highest returns (6.7% annualized, 8.7% average) but were riskier. Bonds, less risky than equities but more than bills, had intermediate returns. This trend extended to sixteen countries.

Hyperinflation-affected countries showed higher volatility. Standard deviation impacted differences between one-year arithmetic means and long-term geometric means.

Regarding equities, the US ranked fifth lowest in risk (20.2% standard deviation) among Canada, Australia, UK, Denmark. High volatility markets like Germany and Japan had wider return ranges and discrepancies between arithmetic and geometric means.

Overall, assets correlated risk and return consistently, influenced by historical events.

Chapter 5 Inflation, interest rates, and bill returns

This chapter focuses on analyzing returns from consumer goods (indicating inflation) and treasury bills (reflecting short-term interest rates). Inflation and interest rates are vital investment benchmarks. The chapter compares US and UK inflation experiences and explores global inflation variations.

The second asset class, treasury bills, serves as a benchmark for risk-free interest rates. The chapter examines US and UK treasury bill returns from 1900 to 2000 and compares real interest rates across sixteen countries.

Notably, inflation impacts investment outcomes, and treasury bills' perceived risk-free status can be challenged during periods of unexpected high inflation.

Over the period from 1900 to 2000, the US experienced an average annual inflation rate of 3.2 percent. The purchasing power of money changed significantly, with $1 in 1900 being equivalent to $24 today. Inflation rates were lower in the first seventy years (2.4 percent) compared to the subsequent period since 1970 (5.1 percent). Notably, there were instances of deflation, particularly during the 1920s and early 1930s, which affected purchasing power. US inflation rates varied greatly over time, with higher volatility and average rates in the first half of the century (2.4 percent) compared to the second half (around 4.0 percent). The UK followed a similar pattern until the mid-1960s, after which UK inflation rates became significantly higher than those in the US. Over the entire 101-year period, UK consumer prices rose 55-fold, 2.3 times more than in the US, largely due to the last 35 years. The average annualized inflation rate for the UK was 4.1 percent, while for the US, it was 3.2 percent.

International inflation trends from 1900 to 2000 in sixteen countries. Notable points include:

Variability: Inflation rates varied significantly among countries, with high inflation in France, Germany, Italy, and Japan, while Switzerland had low inflation.

German Hyperinflation: Germany experienced extreme hyperinflation in 1922–23, causing economic devastation and wiping out wealth.

Inflation Peaks: High inflation coincided with wartime or post-war periods, except for the UK's peak in 1975.

Inflation Patterns: Early 20th century had low inflation with spikes during wars, while the latter half had more widespread inflation.

Recent Trends: From 1990 to 2000, average inflation across countries was around 3.0 percent.

Treasury bills are short-term government bonds with maturities of three, six, or twelve months, offering a low-risk investment option. They are discount bonds, meaning their return is calculated from the difference between purchase price and maturity value. The relationship between interest rates and inflation is complex, not always adhering to the Fisher effect's prediction. Since the 1950s, this relationship has become more consistent due to improved financial markets and inflation measurement. Real interest rates (adjusted for inflation) have been volatile, with periods of negative rates during deflation or government intervention. The late 1970s marked a shift to consistently positive real rates. Different countries experienced varying real interest rates due to inflation and economic conditions, and the 1980s saw a global increase in real rates. The investment landscape has been shaped by these changes over time.

Chapter 6 Bond Returns

The focus is on bonds as a crucial asset class, with a specific emphasis on long-term government bonds. These bonds are considered relatively safe, especially in developed markets, due to their minimal default risk. They provide fixed payoffs and yields for investors who hold onto them until they mature. These bond returns are not only important in themselves but also serve as a reference point for evaluating the equity risk premium.

The text takes a historical perspective, examining the performance of US and UK government bonds from 1900 to 2000. It highlights the actual real returns earned by bond investors and how these returns were influenced by factors like fluctuations in inflation rates and shifts in interest rates. The bond market's trajectory was marked by distinct phases - bear markets, characterized by lower returns, and bull phases, marked by higher returns. Economic events like global conflicts and inflation spikes played a significant role in shaping these market shifts.

Bond Significance and Comparative Analysis: Bonds play a vital role in investment portfolios and are frequently compared to other assets, like equities, to gauge risk and reward dynamics.

Long-Term Government Bonds: Long-term government bonds, due to their minimal default risk, are favored by investors. They guarantee fixed returns for those who hold them to maturity.

Performance Comparison - US and UK Bonds: The text offers a comparative analysis of real returns generated by government bonds in the US and the UK between 1900 and 2000. This assessment provides insights into their historical performance and how they reacted to changing economic conditions.

Impact of Economic Events: The text highlights how economic events such as world conflicts, inflation variations, and shifts in interest rates had a notable impact on bond returns. High inflation rates, for instance, could erode the real returns offered by bonds.

Volatility and Expected Outcomes: Bond returns are subject to volatility due to changes in inflation and actual interest rates. Long-term bond returns tend to be more volatile than those of short-term bills. Additionally, the text suggests that actual bond returns might have fallen short of initial investor expectations.

Alternating Market Phases: The bond market exhibits alternating bear markets, with lower returns, and bull markets, with higher returns. These market phases were influenced by economic factors and trends in inflation.

Comparison of US and UK Bonds: By drawing parallels and distinctions between US and UK bond returns, the text underscores the similarities and differences in their historical performance.

Investor Satisfaction: The text suggests that the actual returns on bonds might have been lower than what investors initially anticipated, particularly considering the increased volatility and unforeseen economic events.

Over a span of 101 years from 1900 to 2000, the performance of real bond returns varied across sixteen countries. Notably, German bonds had the worst performance, exacerbated by instances like hyperinflation in 1923 and post-World War II currency reforms that led to substantial losses for investors. Countries experiencing high inflation rates such as Germany, Italy, Japan, Belgium, and France generally had negative real bond returns.

Switzerland had the highest real bond returns (2.8 percent) due to its low inflation rate, while Denmark and Sweden also had relatively strong returns. The United States ranked well with the fifth position and moderate volatility. The United Kingdom, while having middle-ranking returns, exhibited higher volatility. Germany had the highest volatility in real bond returns, Japan following suit.

The division between the first and second halves of the century was evident. Countries that faced setbacks due to world wars saw recovery and improvement in the latter half. Notably, the best performers in the first half, like Switzerland and Sweden, continued to have positive returns, though somewhat reduced, in the second half. Overall, the historical performance of bond markets highlighted the impact of geopolitical events, inflation, and the significance of peacetime and financial stability.

The behavior of long-term bonds versus short-term bills has significant differences due to their sensitivity to interest rate fluctuations. Bond maturity premia, the extra compensation for holding long-term bonds over short-term bills, were examined to understand this phenomenon.

Some argue against expecting a bond maturity premium, but this overlooks the impact of inflation uncertainty. When uncertainty about inflation exists, even long-term investors might prefer short-term bonds due to uncertain reinvestment rates. Conversely, those with short-term horizons might see long-term bonds as riskier due to uncertainties in future bond prices.

The yield curve and the gap between long bond yields and short-term bill yields were analyzed. Over the 1921-2000 period, long bond yields exceeded short rates by about 1.3% annually, showing an upward-sloping yield curve likely tied to a risk premium.

The bond maturity premium's year-to-year variations indicated that labeling them as "premia" could be misleading. Negative premia could reflect surprises like increased inflation, while positive ones could result from lower expected real interest rates. The term "excess returns" might be more accurate.

Over extended periods, positive and negative surprises could balance out, offering insight into the ex ante required maturity premium. Analyzing rolling 10-year premia revealed patterns linked to bear and bull markets in bonds.

For the United States, the 101-year geometric mean bond maturity premium was 0.7%, indicating that long bonds outperformed short bills by this margin annually. However, these averages hid shifts over time due to factors like economic turbulence.

analyzing bond maturity premia unveils the complex interplay of interest rates, inflation, and investor expectations. The observed trends highlight the intricate relationship between long-term bonds and short-term bills.

Inflation-linked bonds are a unique asset class with historical origins dating back to the 18th century. Despite their early introduction, they remain relatively new in developed markets like Japan and Germany. In the 1990s, several countries introduced these bonds, but they still make up less than 2 percent of the global government bond market. Countries grappling with high inflation, including Argentina and Brazil, have been more open to adopting them.

The UK stands out as an exception, having a well-established inflation-indexed bond market since 1975. These bonds are linked to the Retail Price Index and offer a valuable reference for other major markets like the United States.

In theory, inflation-linked bonds provide guaranteed real returns by tying coupon and principal to inflation. However, UK inflation-linked bonds have underperformed compared to conventional bonds of similar maturity, attributed to unexpected shifts in real interest rates and potential tax effects.

Analyzing monthly returns from 1981 to 2000, UK inflation-linked bonds have shown higher volatility than anticipated, behaving somewhat like conventional long-term bonds. Correlations between different asset returns have remained consistent, suggesting potential similarities in the behavior of these bonds in the US had they been available.

inflation-linked bonds remain novel despite their historical roots. Their adoption, performance, and behavior vary globally, with the UK serving as an informative case. These bonds, theoretically low-risk, have faced challenges and underperformance due to unexpected interest rate shifts and tax considerations.

In the exploration of bonds, we've delved into both government and corporate bonds. Unlike government bonds, corporate bonds carry the potential for default due to financial struggles of the issuing company. These distinctions reveal corporate bonds as a significant asset class, offering insights into the default risk premium.

Ratings assigned by agencies like Moody’s and Standard & Poor’s gauge corporate bond quality and default risk. Moody's ranges from Aaa to C, with Baa and below considered "junk bonds." High-grade bonds encompass Aaa and Aa ratings. While default on high-grade bonds is rare, downgrades can lead to eventual default. Junk bonds, however, can experience high default rates, even surpassing 10% in tough times. Default impacts can range from minor delays in interest payments to total payment default.

Due to default risk, corporate bonds are priced lower, yielding higher returns compared to government bonds. The anticipated return of a corporate bond is lower than its redemption yield. A portion of the yield difference is due to expected default losses, with the remainder constituting a risk premium. This premium compensates investors for the assumed default risk. Calculating the default premium involves comparing actual corporate bond returns, accounting for defaults, against government bond returns using the formula: (1 + Long corporate bond rate of return) / (1 + Long government bond rate of return) - 1.

A visual representation, Figure 6-9, illustrates the cumulative real return and default premiums of high-grade US corporate bonds from 1900 to 2000. The data, sourced from various references, demonstrates that corporate bonds yielded higher returns than government bonds over the period. The annualized default risk premium was about 48 basis points per year. High-grade corporate bonds often trade with yields around 1% above government bonds. This indicates that around half of the yield discrepancy is due to defaults and downgrades, while the other half represents the actual risk premium received.

Figure 6-9 also showcases annual default risk premiums, which typically skew positive with an average of 53 basis points. However, these premiums vary greatly, occasionally turning negative. Negative premiums might coincide with years of downgrades or widening yield differentials, while positive premiums align with narrowed yield disparities.

Though detailed corporate bond return data spanning the twentieth century is limited to the US, if available for other countries, it is likely to mirror government bond returns, accompanied by a comparable default risk premium.

Overall quick summary of chapter 6 -

The focus here is on bonds, particularly those from governments that are considered safe. These bonds offer fixed payments and are a reference point for understanding investment risk. The analysis looks back from 1900 to 2000 at how US and UK government bonds performed, shaped by events like wars and inflation.

Inflation-linked bonds, tied to inflation, are newer and less common, but the UK has a well-established market. These bonds haven't always performed as expected due to interest rate shifts and taxes.

Then we dive into corporate bonds, which can be riskier due to possible company defaults. These bonds have ratings that gauge default risk. Corporate bonds give higher returns, compensating for this risk. high-grade US corporate bonds had more returns with an annual default risk premium of about 48 basis points.

Chapter 7 Exchange rates and common currency returns

In the context of our study on long-run investments by domestic investors across sixteen countries, we've focused on comparing international performance in terms of real equity and bond returns. This involves analyzing returns from local investments in equities and bonds, such as US investors in US equities and bonds, and UK investors in UK equities and bonds, all measured in their respective local currencies like dollars, pounds, and marks.

However, for international investors, fluctuations in asset prices need to be converted into the currency used for evaluating portfolio performance. This is particularly important due to the role of exchange rate changes. As an example, when a US investor purchases UK equities, they don't solely earn returns in British pounds; they must also account for currency exchange rate movements to convert those returns back into dollars.

Our study covers exchange rate fluctuations experienced by these sixteen countries over a 101-year period from 1900 to 2000. Throughout this time frame, various exchange rate regimes were encountered, with currencies undergoing periods of stability, revaluation, devaluation, and significant changes in value. This dataset allows us to observe multiple real-world scenarios, providing valuable insights.

Within this historical context, we explore the impact of both short-term and sustained inflation differences on exchange rates. We then adopt the viewpoint of an international investor and delve into analyzing investment returns using a standardized currency, such as dollars, or dollars adjusted for changes in purchasing power.

The study delved into how exchange rates behaved for 101 years. They started off in 1900, with 5.21 Swiss francs and £0.20 sterling equaling US$1.00. Picture an up-and-down graph where going down means a currency dropped in value and going up means it gained against the US dollar.

In the wild German hyperinflation of 1922–23, the German mark dropped so much it went beyond the graph. Other currencies moved, but more slowly. By 2001, the currencies on the graph had dropped a lot. For instance, the Italian lira needed 358 times more US dollars than in 1900. The French franc, Japanese yen, Spanish peseta, and British pound also lost a lot. On the flip side, the Swiss franc gained ground, needing more US dollars for a franc.

Across sixteen countries, they compared how currencies changed against the US dollar. Positive numbers meant a currency gained, negative meant it lost. France, Germany, Italy, Japan, and Spain had big losses and lots of ups and downs. The Netherlands and Switzerland kept their currencies strong. Others lost around -1 to -2 percent. When things were extra jumpy, the regular average was much higher than the typical average, especially for Germany.

In the 20th century, the value of currencies was heavily influenced by different systems. At first, the gold standard provided stability until WWI. Then, the chaos of wars and economic strategies caused turmoil. The Bretton Woods Agreement temporarily reintroduced fixed rates, but it didn't last due to changes and devaluations. Since 1973, we've had floating exchange rates, where currency values fluctuate freely.

The period from 1900 to 1914, known as the Gold Standard Era, was characterized by currencies being tied to gold, ensuring stable exchange rates as governments guaranteed their paper money with specific gold reserves. However, this stability was shattered by the upheaval of World War I and World War II in the subsequent decades.

The gold standard faltered during WWI and wasn't fully reinstated afterwards, resulting in a turbulent landscape where nations experimented with different economic strategies, leading to currency fluctuations and devaluations. The Bretton Woods Agreement of 1946 marked a new phase, attempting to restore stability through fixed exchange rates pegged to the US dollar or gold.

Despite central banks' interventions to maintain these values, the system collapsed by 1971 due to shifting rates and the US devaluing its own currency. Since then, the world has operated under a system of floating exchange rates, where currency values are determined by supply and demand, ushering in an era of constant fluctuations that persists to this day.

Exchange rates, reflecting the value of US dollars against British pounds, play a crucial role in global economics. A lower rate means a stronger dollar, while a higher rate signifies a weaker pound. From 1900 to early 2001, the pound's value dropped by about 70% against the dollar due to higher inflation in the UK compared to the US.

To gain a clearer picture, we use the "real" exchange rate, factoring in inflation. This adjusted rate has remained relatively stable over the long term.

Regarding the relationship between exchange rates and inflation, there's an idea called purchasing power parity (PPP). It suggests that over time, exchange rates should adjust to match inflation differences between countries.

Though factors like tariffs and trade impact PPP's accuracy, the tendency remains: currencies from high-inflation countries tend to depreciate compared to those from low-inflation countries. This trend is evident in Figure 7-4, where exchange rate changes (vertical) align with purchasing power shifts (horizontal) across different times and countries – a total of seventy-five observations.

When exchange rates between countries don't follow the rule of purchasing power parity (PPP), it means that factors beyond just inflation differences are influencing them. For example, if a country discovers a lot of oil or if the price of oil goes up, its currency might become stronger. Changes in productivity, like how efficiently goods are made, can also affect exchange rates without causing too much inflation. Different things a country spends money on, like education or defense, can make its competitive position seem different than it really is. Changes in interest rates between countries can lead to money moving around and affecting exchange rates too.

Even though exchange rates have mostly been steady over long periods, they can still go up and down a lot in the short term. Except for Germany which had major changes, exchange rates compared to the US dollar were relatively stable from 1900 to 2000. But Germany had two big drops during the Second World War and its aftermath, which might not fully reflect the real situation due to wartime issues.

Despite no clear long-term trend, exchange rates can be quite unpredictable from year to year, and the theory of PPP doesn't fully explain these changes. Some extreme changes might be due to unusual situations like wartime controls on inflation or exchange rates. Looking at the numbers (Table 7-2), we see that most countries' exchange rates change each year by only a tiny bit, except for South Africa. This is surprising considering there are measurement errors in inflation numbers and because real exchange rates use two different sets of prices.

When countries shifted to floating exchange rates in 1973, the idea was that currency values would adjust to inflation differences. However, between 1950 and 2000, we found that real exchange rates were more unpredictable during the floating-rate period compared to the earlier fixed-rate period. This surprised those who supported floating rates, as they expected stability.

On average, exchange rate volatility against the US dollar was 2.4 times higher for fifteen countries during the floating-rate period. This was also true for other currencies like the British pound, Japanese yen, and German Deutschemark.

Interestingly, when some countries joined the Eurozone, the volatility of exchange rates within that group became zero due to a shared currency. However, this didn't significantly reduce volatility between Eurozone countries and those outside it. This means that despite hopes for stability, exchange rate fluctuations still greatly influence international comparisons and investment returns.

When floating exchange rates were introduced in 1973, people believed that currency values would adjust freely based on differences in inflation between countries. This meant that if a country had high inflation, its currency would decrease in value, while a country with low inflation would see its currency increase in value. However, the reality didn't match these expectations.

Real exchange rates consider both inflation and nominal exchange rates. We split the time since 1950 into two parts: the fixed-rate period from 1950 to 1971 and the floating-rate period from 1972 to 2000. Surprisingly, we found that real exchange rates were more unpredictable during the floating-rate period than during the earlier fixed-rate period. This finding is consistent with other research too.

This increased unpredictability of currency values has been disappointing for those who supported floating exchange rates. On average, when we looked at fifteen countries (excluding the US), we found that during the floating-rate period, currency values were 2.4 times more volatile compared to the Bretton Woods period. The same trend was observed for specific currencies like the British pound, the Japanese yen, and the German Deutschemark.

Interestingly, some countries joined the Eurozone in the late 1990s, which reduced volatility among Eurozone countries' currencies when trading with each other. However, this reduction didn't extend to currencies outside the Eurozone. So, even though the Eurozone became more stable within itself, currency fluctuations still matter a lot when comparing investment returns internationally.

we studied global real returns on stocks and bonds. These returns reflect local investors' gains in their own currencies. Exchange rate changes matter when investing across borders. For instance, a US investor in UK stocks must consider the pound's value against the dollar.

Historical real exchange rates show how currencies shifted against the US dollar. Converting real returns involves adjusting for these changes. To compare, let's use the example of a US citizen's investment in UK stocks. The UK's annual real stock return is 5.78%, but the pound weakened against the dollar by 0.33% annually. Thus, the US investor's return is about 5.43%. For a UK investor buying US stocks, the return becomes around 7.07% due to currency fluctuations.

A neat way to compare different countries' returns is by translating them into a common currency, like the US dollar. This approach maintains equity market rankings, showcasing the impact of exchange rate changes. For example, Belgium could edge above Italy due to a stronger currency.

Another graph presents real stock and bond returns in US dollars, letting us compare countries based on these returns. US equities yielded a solid 6.7% real return annually, outperforming most. However, PPP didn't ensure consistent positive real returns for international bond investors, as seen in the varied bond market results.

Chapter 7 overall quick summary is

• Exchange Rates and Investor Perspective: International investors need to consider currency exchange rates when evaluating returns across borders.

• Historical Exchange Rate Regimes: Different regimes, like the gold standard and floating rates, influenced currency values over time.

• Inflation and Exchange Rates: Inflation differences affect exchange rates. Purchasing Power Parity theory suggests high-inflation countries see currency depreciation.

• Exchange Rate Volatility: Exchange rates were mostly stable, but short-term fluctuations can be unpredictable. Floating rates introduced in 1973 didn't lead to expected stability.

• Impact on Returns: Currency fluctuations play a significant role in investment returns across borders.

• Common Currency Comparison: Converting returns to a common currency helps compare countries' investment performance.

• Real Stock and Bond Returns: Real returns on stocks and bonds were studied in US dollars, showing varied results across countries.

Chapter 8 International Investments.

The United States holds the largest equity market globally, yet US investors who limit themselves to domestic investments miss out on over half of the world's opportunities. International diversification offers risk reduction benefits due to varied market and currency correlations. Historical evidence shows that constructing world indexes for equities and bonds demonstrates the advantages of diversification. Despite this, many investors maintain a home bias, favoring domestic assets due to historical factors.

International investors face both risk and return considerations when investing abroad. Foreign investments introduce exchange rate risk and local market risk, where fluctuations in currency values can impact returns. Despite currency volatility, historical data indicates that currency risk didn't significantly magnify the risks of overseas investments. For instance, US-based investors holding foreign equities experienced modest currency-related risk due to generally small and slightly negative correlations between equity returns and exchange rate changes. This led to a natural hedge effect that helped offset some risk. Similar patterns were observed with bonds. While investors can hedge currency risk, the historical data suggests that even unhedged international portfolios may not substantially increase overall portfolio risk, particularly in the context of diversified portfolios.

Just like domestic diversification, where a wide portfolio reduces risk, international diversification serves a similar purpose. It helps spread risk by investing in various global markets and currencies, assuming investors lack specific market insights.

We constructed a world equity market index, reflecting returns from 16 countries, weighted by their size. From 1900 to 2000, this index showed that $1 invested in 1900 would have grown to $295 in real, US purchasing power terms, with an annualized real return of 5.8 percent. However, US equity markets outperformed the world index, with $1 growing to $711 at an annualized real return of 6.7 percent. Excluding the US (world ex-US) resulted in even lower returns, with $1 growing to just $162 at an annualized return of 5.2 percent.

Despite US equities' outstanding performance, the main argument for international investment remains risk diversification. Both the world and world ex-US indexes had lower standard deviations than the US, emphasizing the risk-reducing benefits of international diversification.

For bonds, a similar pattern emerged. A world bond index, weighted by GDP, showed that $1 invested in 1900 grew to $3.29 by 2000, with an annualized return of 1.2 percent. US bonds outperformed this, with $1 growing to $5.04 at a real return of 1.6 percent per year. World ex-US bond markets lagged behind, with $1 growing to only $1.66 at an annualized return of 0.5 percent. The underperformance of world bonds, like equities, primarily occurred in the first half of the century.

International diversification also reduced bond investors' risk. The standard deviation of annual real returns for the world bond index was 18.9 percent, but diversifying across the fifteen non-US markets reduced this to 14.3 percent. Including the US in the world bond index further lowered the risk to 10.3 percent, although it remained slightly above the 10.0 percent risk for US bonds. This was mainly because other markets were more volatile in the earlier part of the century.

Over the 20th century, US investors saw benefits in risk reduction through international diversification, but these were offset by lower returns from non-US assets. To determine if the lower returns outweighed the reduced risk, we used the Sharpe ratio, which measures the reward per unit of risk.

Comparing US equities to the world index from 1900–2000, US equities had higher standard deviation (20.16% vs. 17.04%) but also a slightly higher return (5.79% vs. 5.81%) after adjusting for risk. This means US investors would have earned almost identical returns from both domestic and international equity investments over this period.

Alternatively, comparing the Sharpe ratios confirms this, with the US and world ratios being very close (0.287 vs. 0.286). These ratios were even more favorable in the second half of the century.

Looking beyond the US perspective, other countries might have experienced greater gains from international investment. For instance, Australia, France, and Japan would have achieved better reward-to-risk ratios by staying at home due to their strong domestic markets. However, most countries, except Japan and the Netherlands, would have benefited from investing worldwide, with Belgian and Italian investors gaining the most in terms of risk reduction and returns.

The reduction of risk through international diversification is rooted in the fact that global markets do not move in perfect harmony. The correlations between different countries' markets, as shown in , reflect this phenomenon. These correlations have evolved over time due to various factors such as changes in world power dynamics, political shifts, economic growth, trade patterns, and currency regimes.

For instance, the highest correlation exists between the United States and Canada, followed closely by the United Kingdom and Ireland. Geography and historical ties influence these correlations, as seen in Australia's strong links with the UK and Ireland due to historical and trade connections. Germany's correlations are lower, reflecting historical disruptions like wars and hyperinflation, but it has stronger ties with its neighboring countries.

There is no clear relationship between correlations in the first and second halves of the twentieth century, making it challenging to predict future correlations based solely on historical data. However, some patterns emerge: during times of turmoil, such as wars or economic crises, correlations tend to increase, potentially diminishing the benefits of international diversification.

Moreover, Goetzmann, Li, and Rouwenhorst's research shows that correlations have varied significantly over seven distinct sub-periods spanning from 1872 to 2000, further highlighting the dynamic nature of market relationships. For example, the US:UK correlation ranged from near zero to 0.51, and the US:Germany correlation fluctuated from -0.36 to +0.36.

We explore the benefits of international diversification. The red line represents a significant risk reduction over the last century for a dollar-based investor who equally invested in sixteen countries. The risk dropped from 29.1% for a single-country investment to 17.3% for a diversified portfolio, a 41% reduction.

However, this reduction is expected to be lower today due to increased market integration. The yellow line, based on recent data (1996–2000), shows a 27% risk reduction.

The equally weighted approach used in these analyses may not reflect realistic investor behavior. also illustrates the risk reduction for a U.S. investor who starts with a U.S. holding and diversifies gradually.

Provides a global perspective, suggesting that investors worldwide benefit from international diversification. U.S. investors can reduce risk by 10% with 20% international exposure and by 20% by holding the world index, heavily weighted in the U.S.

While individual country estimates should be interpreted cautiously, the overall message is clear: international diversification offers risk reduction benefits of around 10–20%.

Despite 30 years of research advocating cross-border investment, the "home bias" puzzle persists, where investors favor their domestic markets. Figure 8-9 illustrates this with load ratios, showing how much investors overweight or underweight their home market compared to the global equity portfolio.

In 1997, US investors had a load ratio of 186% for the US, indicating a significant overweighting of domestic stocks. Their foreign load ratio was just 19%, showing underinvestment in international equities. Other countries exhibited similar home bias.

However, there has been a gradual shift towards international diversification. US investors increased foreign equity holdings from 1% in 1980 to 12% by 2000. Historical factors like

World War I and capital controls contributed to home bias, but modern barriers are diminishing, making global diversification more accessible.

In the future, the challenge may shift from justifying global investing to explaining why one would deviate from a globally diversified portfolio.

Key points from chapter 8 -

- The US has the largest equity market, but investing only domestically means missing global opportunities.

- International diversification spreads risk through varied market and currency correlations.

- Historical data shows that currency risk didn't significantly increase risks for US investors in foreign assets.

- Global indexes for equities and bonds indicate lower standard deviations, emphasizing risk reduction through diversification.

- The Sharpe ratio suggests US and world equities had similar risk-adjusted returns, especially later in the 20th century.

- Different countries may benefit differently from international investment, but most gain from global diversification.

- Correlations between global markets vary over time, making future predictions challenging.

- International diversification can reduce risk by 10-20% for investors worldwide.

- The "home bias" persists, but there's a shift towards global diversification due to reduced barriers.

- In the future, explaining why one would deviate from a globally diversified portfolio may become the challenge.

Chapter 9 - Size Effects and seasonality in stock returns

This chapter focuses on the effects of size and seasonality, while chapter 10 covers the performance of value and growth stocks, and chapter 11 deals with dividends and dividend growth. We dedicate a chapter to size and seasonality because the size effect has become a well-documented anomaly in global stock markets over the last two decades. It's closely linked to seasonality, particularly the "turn-of-the-year" or "January" effect in the United States.

The size effect originated in the US stock market, as highlighted by Banz (1981). His research showed that smaller US companies historically provided higher returns, even after accounting for greater risk. The return premium for smaller stocks was substantial, with the smallest stocks performing the best. This size effect persisted over a 45-year period.

Banz's work also led to the creation of size-based portfolios on the New York Stock Exchange (NYSE). These portfolios demonstrated that smaller stocks consistently outperformed larger ones.

However, it's worth noting that small stock returns can be "streaky." While they outperformed in the long run, they faced periods of underperformance, particularly during the Great Depression and more recently since 1983. The size effect has been a crucial aspect of equity investment, closely associated with the January effect in the US, and its significance extends to global markets.

Banz's 1981 study raised the question of whether the size effect observed in the United States extended to other countries, prompting research worldwide, including in the United Kingdom. In the UK, the Hoare Govett Smaller Companies Index (HGSC) gained prominence in 1987, covering the bottom tenth of the market by capitalization with data dating back to 1955-86.

The performance of UK small- and micro-cap stocks compared to the overall market from 1955 to 2000. Small-caps, represented by the HGSC, consistently outperformed the market. An initial £1 investment in the UK equity market in 1955 would have grown to £592 by 2001, while the same investment in small-caps would have reached £1,676, demonstrating a significant annualized return difference.

How the size effect varied over time, with small-caps often outperforming the market. In most cases, the Micro Cap™ Index outperformed the HGSC when small-caps did well, further confirming the size effect's consistency across various size bands in the market.

The question of whether the size premium will continue in the future remains unanswered. Historical data for the first half of the twentieth century suggests the presence of a size effect, though not overwhelmingly positive. A more definitive answer requires additional data on smaller UK stocks from that era.

Researchers globally investigated the size premium, initially identified in the United States and confirmed in the United Kingdom. This research, mainly conducted in the 1980s and early 1990s, extended to seventeen countries, including eleven covered here.

Each study defined "small" and "large" stocks differently, resulting in variations in size premium estimates. For instance, in the United States, Banz (1981) found that adjusting stock selection criteria could significantly alter the size premium estimate.

These studies also covered different time periods, making direct comparisons challenging. However, the size premium was consistently observed in most countries, with Korea being an exception.

Researchers in these countries also explored risk factors and concluded that the size premium couldn't be solely attributed to risk. This widespread and substantial size effect, where smaller companies consistently outperformed, established itself as a significant stock market anomaly.

In the early 1980s, researchers discovered the "size effect" in the US and UK stock markets, showing that small-cap stocks outperformed larger ones. This led to a surge in small-cap investments and funds, but the honeymoon period lasted only about two years, followed by a prolonged period of underperformance in both countries.

In 1999, researchers noted a global trend where the size effect reversed in almost every country studied, resulting in size discounts instead of premiums. This reversal was likely driven by fundamental factors, including differences in dividend growth between small-caps and large-caps, as well as changes in sector composition.

The lesson learned was that the size effect is not a constant, and small-caps can perform differently from large-caps over time, making it essential for investors to adapt to changing market dynamics.

Investors have long been intrigued by the idea of finding specific times to buy or sell shares, and this fascination has led to the exploration of various calendar anomalies in the financial markets. These anomalies include the January effect, the summer effect (commonly referred to as "sell in May"), the time-of-the-month effect, the holiday effect, the day-of-the-week effect, the time-of-the-day effect, and even the Presidential death effect. These peculiar patterns have been extensively documented, fueling the interest of investors and researchers alike.

While the analysis of all these anomalies is beyond the scope of this discussion, one anomaly, the January effect, holds particular significance for several reasons. Firstly, it is the most renowned and important among all calendar anomalies. Secondly, it is closely related to the size effect in the United States, where smaller stocks tend to outperform in January. Finally, most research on the January effect has historically focused on the U.S. market due to the lack of suitable long-term size-based indexes elsewhere.

One prevalent theory explaining the outperformance of U.S. small-cap stocks in January is tax-loss selling. According to this theory, stocks that have declined in value throughout the year experience downward price pressure as investors sell them to realize capital losses and minimize tax payments towards the end of the year. Once the year-end tax pressure is lifted, these stocks tend to rebound to fair values. Another theory suggests that fund managers engage in year-end "window-dressing," removing underperforming stocks from their portfolios, which artificially depresses their year-end prices. Both of these theories primarily affect smaller stocks because they are more likely to have experienced price declines, making them smaller by definition. These theories, while widely cited, do not fully align with the concept of market efficiency and are not conclusively supported by empirical evidence.

However, when these theories are applied to different countries, adjustments are needed due to variations in fiscal and financial reporting systems. For instance, in the United Kingdom, the tax year for individuals begins on April 6, and many firms report on an April–March cycle, while others follow an end-December tax and reporting year-end. Therefore, if there is a small-cap turn-of-the-year effect in the United Kingdom, it should be observable in April as well as January.

Comparing the average returns on U.S. large-cap stocks for each calendar month from 1926 to 2000, there is no clear turn-of-the-year effect. Returns in December are not particularly low, and January does not consistently have the highest returns. Conversely, in the United Kingdom, there are more pronounced differences. January exhibits the highest mean return of 3.2 percent; however, excluding the outlier in January 1975, the mean falls to 2.2 percent, ranking it third behind April and December. This data suggests that high returns in April may be linked to the tax-year end, while high returns in January and possibly December may be connected to the calendar-year reporting.

The absence of a U.S. January effect in large-cap stocks is explained by the fact that this effect is primarily observed in small stocks. The U.S. January effect is substantial, with an average premium of 7.1 percent, significantly higher than any other month. In contrast, the UK does not exhibit a year-end size effect, whether tied to tax-year or calendar-year end. Therefore, if any seasonality exists in the UK, it appears to relate to the overall market rather than the size premium, which is the opposite of the U.S. situation.

Key Points:

The size effect, identified by Banz in 1981, shows that smaller stocks historically provide higher returns despite greater risk. Smaller stocks consistently outperform larger ones, but there are periods of underperformance, especially since 1983. The size effect is closely linked to the January effect, where smaller US stocks perform well at the start of the year.

This phenomenon extends globally, with smaller stocks outperforming in various countries, except in Korea. The size effect reversed in many countries around 1999 due to fundamental factors like dividend growth and sector changes. Calendar anomalies, like the January effect, are observed, but their explanations vary and are not conclusively supported by evidence.

In summary, the size effect is significant, but its performance can change over time, and calendar anomalies affect stock market dynamics differently across countries and stock sizes.

Chapter 10 - Value and growth in stock returns

In this chapter, we explore the evolution of the small firm effect and the shift towards value-based investment strategies. Historically, small-cap companies yielded high returns, but this trend changed after the effect became widely known. In the 1990s, value-based strategies gained prominence, focusing on stocks priced low relative to fundamentals like dividends, earnings, or book value.

Experts have long emphasized buying stocks at reasonable prices relative to fundamentals, such as the price-to-dividend ratio, earnings ratio, and book value. Stocks with high dividend or earnings yields and book-to-market ratios are labeled as value stocks, while those with lower values are categorized as growth stocks.

We review the long-term performance of value and growth stocks in various countries, including the United States and the United Kingdom. Historical data shows that value investing consistently outperformed growth investing.

In the United States stock market, value and growth companies are distinguished based on their stock prices relative to fundamental metrics like dividend yields, earnings yields, and market-to-book ratios. Value companies often have lower stock prices but higher dividend and earnings yields. Research has shown that high-yield value stocks historically outperformed low-yield growth stocks.

For instance, from 1926 to 2000, high-yield stocks in the US delivered an annualized return of 12.2 percent, compared to 10.4 percent for low-yield stocks. This value premium remained even after considering tax implications, suggesting that it's not solely due to taxation differences.

Another critical measure of value is the book-to-market ratio. Stocks with high book-to-market ratios have also consistently outperformed low book-to-market stocks. The annualized value-growth premium based on this criterion was 3.2 percent over the same period.

The reasons behind this value premium are debated. Some suggest it's because investors get overly enthusiastic about companies with promising prospects, inflating their prices. Others argue it could be because value stocks, often distressed, reward investors with higher returns due to higher risk. Another perspective considers it a result of chance events.

Analysis of value and growth investing in the UK stock market, we draw upon a robust database spanning nearly five decades and comprising over one hundred thousand firm-years of accounting data. This database, compiled by Nagel (2001), provides a comprehensive view of UK-listed stocks.

Annual Value-Growth Premium: We examine the annual value-growth premium by forming portfolios based on book-to-market ratios and dividend yields. The results show that the value premium was stable until the late 1970s and has since exhibited some variability.

Extending Analysis to 1900: We extend our analysis back to 1900, using dividend yields to define value and growth within the top 100 UK stocks. The results align closely with the post-1955 premium based on book values, underscoring the robustness of the value-growth premium.

Performance Gap in the Top 100 Shares: Within the top 100 shares, there is a significant performance gap between value and growth stocks, which varies from year to year, emphasizing its importance.

Long-Term Performance: Over the 101-year period from 1900 to 2000, value investing outperformed growth, with an annualized value-growth premium of 2.7 percent. This trend holds true globally, showcasing the historical strength of value investing.

Growth Stocks:

• Companies with high growth potential.

• Typically have a high Price-to-Earnings (P/E) ratio.

• Often have lower or zero dividend yields.

• Expected to have high future earnings growth.

• Tend to have a higher market-to-book ratio (often > 1).

• May be more volatile and riskier.

• Attract investors seeking capital appreciation.

• Investment strategy focuses on potential future value creation.

• Examples include technology, biotech, and high-growth startups.

Value Stocks:

• Companies considered undervalued or mature.

• Generally have a low Price-to-Earnings (P/E) ratio.

• Typically offer higher dividend yields or consistent dividends.

• Expected to have slower future earnings growth.

• Tend to have a lower market-to-book ratio (often < 1).

• Generally considered less volatile and lower risk.

• Attract income-oriented or value investors.

• Investment strategy focuses on buying undervalued assets.

• Examples include utilities, traditional manufacturing, and mature firms.

Key points:

Initially, small-cap stocks were known for high returns, but the trend shifted once it became public knowledge. Since the 1990s, value-based investment strategies, which focus on stocks with low prices compared to their fundamentals, have gained prominence. Key Metrics:

• Price-to-Dividend ratio

• Earnings ratio

• Book value

Classification:

• Value Stocks: High dividend/earnings yields, high book-to-market ratios

• Growth Stocks: Low dividend/earnings yields, low book-to-market ratios

Performance:

• Value stocks have historically outperformed growth stocks.

• In the U.S., high-yield stocks yielded an annualized return of 12.2% compared to 10.4% for low-yield stocks from 1926 to 2000.

• The annualized value-growth premium was 3.2% based on book-to-market ratios.

Reasons for Value Premium:

• Over-enthusiasm for promising companies, inflating their prices

• Higher returns due to higher risk associated with value stocks

• Possible influence of random chance events

UK Market Analysis:

• Database from Nagel (2001) used, spanning almost five decades.

• Value premium was stable until late 1970s but has varied since.

• Extending back to 1900, the value-growth premium was consistent at 2.7% annually for the top 100 UK stocks.

Characteristics:

• Growth Stocks: High P/E ratios, low or zero dividends, high market-to-book ratios, higher volatility, focus on future value creation

• Value Stocks: Low P/E ratios, higher dividends, low market-to-book ratios, lower volatility, focus on current undervaluation

Industries:

• Growth: Technology, biotech, startups

• Value: Utilities, traditional manufacturing, mature firms

The chapter underscores the long-term efficacy of value investing both in the U.S. and the UK, supported by robust historical data.

Chapter 11 - Equity dividends

In this chapter,

We explore the significance of dividends in equity investment and valuation. We focus on the income received by long-term investors in the overall equity market, without favoring high-yield stocks.

We discuss the impact of dividend income on long-term returns, highlighting the role of reinvested income. We also analyze dividend growth rates and their importance in valuation models.

Our analysis extends globally and over time, comparing dividend growth rates. We examine the relationship between dividend growth, GDP, and equity returns, revealing surprising findings.

We investigate the fluctuations in dividend yields over time and across countries, noting their decline by the end of 2000. Additionally, we explore the trend of companies shifting away from dividends toward stock repurchases.

Equity markets globally have historically delivered strong long-term returns. But what drives these returns – price movements (capital gains) or dividends? While day-to-day focus often centers on price fluctuations, a closer look reveals that capital gains dominate single-year performance, owing to equity market volatility. Dividend income, although consistent, makes a relatively modest contribution to annual gains or losses.

Over time, however, capital gains tend to outweigh losses. Consider a US equity portfolio starting with $1 in 1900. By 2000, even without reinvesting dividends, it would have grown to $198, an annualized capital gain of 5.4%, surpassing the 3.2% annual inflation rate. Reinvesting dividends, on the other hand, significantly amplifies long-term returns.

Imagine two investors: one reinvests all income, while the other spends it. Over 101 years, the reinvestment strategy yields 85 times more wealth. This phenomenon holds true globally.

Long-term investors, in particular, benefit from dividend income. For them, a portfolio's value closely aligns with the present value of dividends, while capital appreciation's significance diminishes.

This underscores why we emphasize dividends in calculating total returns. Indexes that only consider capital appreciation can't facilitate meaningful comparisons over time or across markets due to fluctuating dividend yields.

Examining the historical path of dividends, we constructed income indexes for the United States and the United Kingdom from 1900 to 2000. In the U.S., real dividends fluctuated significantly in the first half of the century, barely keeping pace with inflation by 1949. Over the next twenty-one years, they grew, but afterward, they fluctuated with no clear trend.

Adjusted for inflation, $1 of dividend income in 1900 grew to $1.78 by 2000, with an annualized real dividend growth rate of 0.58%.

In the UK, real dividends consistently lagged behind inflation for the first sixty years of the century, hitting a low of 0.41 in 1920. After fluctuating around 1.0 in the 1960s, they failed to keep up with inflation in the 1970s but grew strongly for the next twenty-five years before falling back in 2000. Over the entire period, UK real dividends grew at an annualized rate of 0.40%.

Both countries had similar patterns of volatility in dividend growth rates, which appeared to follow a random walk. Looking at average growth rates by decade, the U.S. generally saw positive growth, except during World War I, while the UK had negative growth in three decades, mainly in the first half of the century.

An interesting anomaly was that despite the strong bull market in the 1980s and 1990s, the U.S. had low real dividend growth in those decades, possibly due to a trend of firms paying out less in dividends. In contrast, the UK had higher dividend growth during this period but lower in the 1990s, despite higher equity returns.

We've compared real dividend growth rates across sixteen countries from 1900 to 2000:

• Japan had the largest decline, with a 3.3 percent annual decrease.

• Sweden showed the highest growth at 2.3 percent per year.

• The US and UK ranked fourth and fifth, with positive growth.

• Only Canada and Switzerland had consistent positive growth.

Looking at the first vs. second half of the century:

• Initially, most countries had lower growth.

• Resource-rich nations like Canada, Australia, and South Africa had positive growth in the first half.

• The US, Sweden, and resource-rich nations maintained positive growth throughout.

• Germany reversed from low growth in the first half to high growth in the second.

• There was a moderate negative correlation (-0.27) between growth in the two halves.

Dividend growth is a key factor in finance, with Gordon's constant dividend growth model being a widely-used valuation tool. It states that the price of a stock is the present value of future dividends, which grow at a constant rate. The required return on equity is the dividend yield plus expected dividend growth.

In the late 1990s, analysts assumed high real dividend growth rates (2-5%) to explain high stock market valuations. However, Figure 11-6 shows that, except for South Africa, dividend growth was lower than GDP per capita growth, with even a negative correlation between them.

This finding holds for both the 1900-2000 and 1951-2000 periods, challenging the idea of dividends outpacing GDP growth. There are two possible explanations: measurement issues in GDP estimation and the assumption that GDP growth always benefits equity holders.

Still, there is a strong positive correlation (0.81) between equity market performance and real dividend growth, with countries with high dividend growth generally having better-performing equity markets. However, exceptions exist, suggesting that other factors like payout ratios and required equity returns also influence the relationship.

In the mid-20th century, the yield on US equities fell significantly, largely due to declining dividend payments by US companies. Fama and French (2001) analyzed this trend, known as "disappearing dividends." They found two key factors: an increase in initial public offerings (IPOs), often involving small firms with growth potential that don't pay dividends, and a growing awareness of tax disadvantages associated with dividends.

There was a surge in share repurchases in the US from the mid-1980s, driven by tax advantages. Despite this, dividend payouts didn't decline, and repurchases were complementary rather than a replacement.

Similar trends occurred in the UK, where the percentage of firms paying dividends decreased due to IPOs, but large companies continued to pay dividends. Share repurchases also grew in importance, influenced by tax rules.

Globally, share repurchases were historically uncommon in many countries, but there's a gradual shift towards them, with the UK leading in Europe. However, repurchase activity remains smaller than in the US.

Key Points

While capital gains dominate short-term returns, dividends play a substantial role in enhancing long-term wealth, especially when reinvested.

Historical data from 1900 to 2000 reveals fluctuations in real dividend growth rates in both the U.S. and the UK. The U.S. had an annualized real dividend growth rate of 0.58%, while the UK had 0.40%. Dividend growth showed both volatility and regional disparities, with Sweden and Japan marking the highest and lowest growth rates, respectively.

The chapter contests the notion that dividends outpace GDP growth by showing that, except in South Africa, dividend growth generally lagged behind GDP per capita growth. Nonetheless, a strong positive correlation exists between equity market performance and real dividend growth.

The latter part of the chapter addresses the decline in dividend payouts in the U.S., ascribed to increased IPOs and tax disadvantages. It notes a global trend of companies increasingly favoring stock repurchases, though this has not completely replaced dividends.

The analysis leverages various models and historical data to provide a nuanced understanding of the role of dividends in equity markets, underlining their importance in long-term investment strategies.

Chapter 12 - The equity risk premium

The equity risk premium serves as a pivotal metric in finance, capturing the excess return from stocks over risk-free assets like government bonds or bills. Despite the higher risk involved in equities, investors expect a compensatory reward, often gauged by this premium. The historical equity risk premium is frequently used as a surrogate for future estimates, underlining its importance in shaping financial strategy and valuation. However, the debate persists on whether past performance is a reliable indicator of future premiums.

The equity risk premium is a vital tool for gauging if stock market risks are being sufficiently rewarded. It's typically measured in two ways: against the returns of treasury bills or long-term government bonds. However, treasury bills are most often considered the "risk-free" benchmark, although they aren't entirely free from risks like hyperinflation.

The formula for calculating this premium involves a geometric difference between the equity and risk-free returns, expressed as (1+Equity Return)/(1+Risk-Free Return)−1(1+Equity Return)/(1+Risk-Free Return)−1. For instance, if stocks yield 21% and treasury bills 10%, the equity risk premium would be 10%.

One key point is that this premium is a ratio, and therefore currency-agnostic. It's also indifferent to whether returns are nominal or real.

Historical data suggests a wide range of outcomes, making the term "risk premium" potentially misleading. Some prefer the term "excess returns" to signify returns above or below the risk-free rate. Long-term perspectives are crucial for meaningful interpretations, given the volatility in year-to-year or even decade-to-decade data. Over a century-long period from 1900 to 2000, the U.S. equity risk premium relative to bills averaged 5.8%.

The equity risk premium in the United States in the context of 16 countries over a 101-year period. The U.S. has an above-average but not the highest equity risk premium, with a geometric mean of 5.8%. France leads with a 7.4% premium. The averages for these countries generally fall within a close range. There is no straightforward relationship between equity risk premiums and real equity returns; for example, Italy has an above-average risk premium but below-average real returns due to unexpected inflation. Despite the long data series, there's a significant degree of statistical uncertainty. For the U.S., the true geometric mean of the equity risk premium could range from 3.8% to 7.8% with 68% confidence.

Analysts differ on whether to emphasize recent or long-term data due to changing political and economic conditions. Over shorter time intervals like decades, the dispersion in risk premia is reduced due to time diversification. Table 12-1 in the original text provides comprehensive statistics, including geometric and arithmetic means, standard deviations, and standard errors for each country. The U.S. ranks sixth globally over both annual and decadal horizons. Finally, it's important to interpret historical data with care due to the changing nature of risks and economic conditions.

Generally, the risk premium relative to bonds is lower than the premium relative to bills in most countries, given that bonds are considered to be riskier than bills. However, there are notable exceptions such as Germany, Denmark, and Belgium. In Germany, for example, the premium relative to bonds is much higher, which is an outlier among the countries studied.

Another critical insight is that the high equity risk premiums in Germany and Japan are not necessarily indicative of strong equity markets but rather reflect the low returns from their respective bond markets. Similarly, France’s high risk premium relative to bills can be attributed to its low bill returns, not to outstanding performance in the equity market. These findings illustrate that a high risk premium can sometimes be a function of poor bond or bill returns, rather than an indicator of strong equity performance.

The United States ranks sixth in terms of its equity risk premium, whether calculated relative to bonds or bills. The text also delves into the role of inflation, pointing out that bondholders were more adversely affected than shareholders during periods of high inflation. This adds an additional layer of complexity to the equity risk premium, particularly in countries that have experienced significant inflationary episodes.

The study provides comprehensive statistical measures, including geometric and arithmetic means, standard errors, and standard deviations for risk premiums. However, these numbers come with caveats, especially for countries that have experienced poor bond market performances. For instance, the United Kingdom shows a lower standard deviation of the equity premium when calculated relative to bonds, compared to when calculated relative to bills. This is due to a higher correlation between annual equity returns and long bond returns in the UK, which impacts the variability of the equity risk premium.

Key points:

he ERP serves as a measure of the excess returns that investors can expect from investing in the stock market over risk-free assets like Treasury bills or government bonds. Here's a concise summary of the key points:

What is the Equity Risk Premium?

• The ERP is used to gauge if investors are being adequately compensated for the higher risk associated with equities compared to risk-free assets.

How is it Measured?

• Typically measured against the returns of Treasury bills or long-term government bonds.

• The formula involves a geometric difference: (1+Equity Return)(1+Risk-Free Return)−1(1+Risk-Free Return)(1+Equity Return)​−1.

Characteristics

• It is a ratio, making it currency-agnostic.

• It does not distinguish between nominal and real returns.

Historical Data

• Over the period 1900-2000, the U.S. ERP relative to bills averaged 5.8%.

• Averages for different countries generally fall within a close range, with the U.S. ranking sixth globally.

• There is a wide range of outcomes historically, leading some to prefer the term "excess returns."

Interpretation Challenges

• No straightforward relationship between ERP and real equity returns.

• Significant degree of statistical uncertainty; for the U.S., the true geometric mean could range from 3.8% to 7.8% with 68% confidence.

Time Frame for Analysis

• Analysts differ on whether to use short-term or long-term data for ERP estimates.

Relation to Bonds and Bills

• Generally, the ERP relative to bonds is lower than that relative to bills.

• Exceptions exist; for example, Germany has a much higher premium relative to bonds.

Inflation and Other Risks

• Bondholders are more adversely affected than shareholders during periods of high inflation.

Caveats

• High ERP does not necessarily indicate strong equity markets; it can be a function of poor bond or bill returns.

• Comprehensive statistical measures like geometric and arithmetic means, standard errors, and standard deviations are essential but come with caveats.

The ERP is an invaluable tool but must be interpreted with care, considering the changing economic conditions and various risks involved.

Chapter 13 - The Prospective risk premium

The chapter delves into the critical subject of prospective risk premiums in equities, distinguishing between historical and future-oriented premiums. It highlights the tug-of-war between optimists, represented by authors like Glassman and Hassett who argue for an undervalued equity market, and pessimists like Shiller, who caution against irrationally high market levels.

The market equilibrium is understood to be a balance between these contrasting viewpoints. The text underscores the vital role that the risk premium plays in investment theory and corporate finance, suggesting that understanding this concept is a contemporary issue of great importance. It also explores theoretical perspectives on the size of the premium and emphasizes the focus on expected arithmetic risk premiums for future estimations.

The chapter discusses methods for deriving these estimates from historical data and scrutinizes the opinions of academic experts, who may need to revise their long-term forecasts downward based on new findings. Finally, the chapter uses historical analysis to offer insights into future risk premiums, decomposing past premiums into contributing factors to infer the likely future equity premium, and concludes by summarizing the implications of historical data for future risk premiums worldwide.

The pivotal role of the equity risk premium in financial asset valuation, using the Gordon Growth Model as an illustrative example. This model, which values a stream of dividends discounted at an expected rate of return, demonstrates the sensitivity of asset valuations to small changes in the expected return or risk premium. For instance, a mere half-percent shift in the required return can substantially alter the valuation of an index like the Dow. The text also points out an interesting paradox: low required rates of return, while driving up asset valuations, also heighten market volatility, thereby necessitating a higher risk premium.

Determining the appropriate required rate of return is crucial, with the U.S. Treasury bond often serving as the risk-free rate to which the equity risk premium is added. This risk premium significantly influences market expectations and future returns, confirming its status as perhaps the most important number in finance. By gauging the equity risk premium, one can deduce expected future returns and, by extension, asset valuations. This is fundamental because if the premium is near zero, optimists like Glassman and Hassett are validated, whereas if it's high, pessimists like Shiller find confirmation. The text underscores that the equity risk premium is not only important for the U.S. market but also for understanding global stock markets, as it serves as an unbiased estimator of future returns relative to less risky assets like bills or bonds.

The significance of the equity risk premium in shaping stock valuations and expected returns. A higher required risk premium inevitably lowers the valuation of financial assets, and vice versa. The text warns against naively extrapolating historical (ex post) risk premiums for future (ex ante) estimates, as transitional effects can distort perceptions. Due to the limitations in directly measuring prospective risk premiums—investor surveys are often unreliable and analysts' forecasts are not necessarily unbiased—the text advises using historical data as a starting point while being cautious of its limitations.

The Capital Asset Pricing Model (CAPM) serves as a theoretical underpinning, linking the equity risk premium to investor risk tolerance. A variant of CAPM, the Consumption CAPM, further ties the equity premium to consumption patterns, arguing that a higher correlation between stock returns and consumption would warrant a larger equity premium. Despite these theoretical frameworks, the actual observed equity premium, especially in the U.S., seems anomalously high, giving rise to what is known as the "equity premium puzzle."

The text notes that traditional financial theory suggests a smaller equity premium than what has been historically observed in the U.S., leading to ongoing debates and alternative theories about the appropriate magnitude of the risk premium. The text concludes by emphasizing that there is no universally "correct" figure for the equity risk premium. Instead, it suggests that a nuanced approach, informed by both theory and historical data, is essential for making reasonable estimations about future risk premiums.

The discussion explores the intricacies of the equity risk premium, emphasizing its calculation in relation to treasury bills or bonds. Treasury bills are often preferred as they are considered nearly risk-free. Two methods for averaging returns are highlighted: geometric and arithmetic means. The geometric mean offers a way to summarize historical annualized returns, while the arithmetic mean is better suited for forward-looking expectations.

The geometric mean is computed by multiplying the returns for each period, adding one to each, and then finding the nth root of this product. This provides an annualized return rate for a given time period but does not account for intermediate volatility. On the other hand, the arithmetic mean simply averages all returns and is useful for setting expectations for a randomly selected year. It's noted that the arithmetic mean is always greater than the geometric mean, particularly when the asset's returns are volatile.

For making investment decisions that involve valuing future cash flows, the arithmetic mean serves as the appropriate measure for discounting. An example is provided to demonstrate why the arithmetic mean is preferable for such forward-looking estimations, especially when accounting for return volatility.

Additionally, the discussion delves into the relationship between the variance of returns and the difference between the arithmetic and geometric means. The greater the asset's volatility, the more significant the discrepancy between the two means. This is corroborated by historical data from various countries, showing differences ranging from 1.3% in Canada to 5.4% in Germany.

Finally, the issue of high standard errors is raised, particularly when estimating these means over lengthy periods like 101 years. This underlines the uncertainty surrounding the "best estimate" of the equity risk premium and the necessity of utilizing long time series data to improve estimation accuracy. The equity risk premium is crucial for determining investors' required returns and serves as an essential parameter in valuing uncertain future cash flows.

The discussion presents a detailed examination of estimating the expected equity risk premium. Historical arithmetic mean premia are used as a starting point, calculated over the last 101 years for 16 different countries. Notably, these arithmetic mean premia are higher than their geometric mean counterparts, especially in countries with greater past market volatility. However, the reliability of historical data for future predictions is questioned, as future market conditions and uncertainties could differ significantly from the past.

To account for contemporary perspectives on market volatility, the arithmetic means are recalculated. A common estimated volatility level of 16% is applied to all national markets, with a 14% level for the world index. This allows for a predicted difference between the arithmetic and geometric means based on the new volatility estimates. Although this common level simplifies the calculation, it's acknowledged as an oversimplification given the diverse risk profiles among different national markets.

Based on these adjustments, the estimated arithmetic mean equity risk premium varies from 3.1% for Denmark to 8.7% for France, with a worldwide average of 6.2% relative to treasury bills. When compared to government bonds, the premia are generally lower. The U.S. equity premium relative to bonds is estimated at 6.3%, and the U.K. at 5.7%, with a worldwide average of 5.6%.

These revised arithmetic mean premia serve as the basis for extrapolating expected future market returns. While these figures can offer a guideline, the discussion acknowledges the value of understanding historical performance in greater depth to better inform future expectations. Therefore, rather than solely relying on extrapolation from past data, a more nuanced approach is recommended for estimating expected returns.

The historical risk premium, around 6% globally, should serve as the best estimate for the future. It references several prominent textbooks and researchers who have often suggested using the arithmetic mean of historical equity premia as a predictive tool.

A notable study by Welch surveyed 226 financial economists on their forecast for the U.S. arithmetic equity risk premium over 30 years. The mean forecast was 7.1%, with a range of 1 to 15%. The survey also revealed that consensus estimates were influenced heavily by long-run historical data, specifically from Ibbotson Associates. However, Welch found that respondents' expectations of what the professional consensus was were higher than what the survey actually revealed.

The study underscores the influence of these figures not just in academia but also in professional financial settings, including regulatory environments. Yet, it also questions the appropriateness of such estimates. Respondents in Welch's survey appear to base their expectations on long-run historical data, then adjust based on factors like recent market performance.

When longer historical data spanning from 1900 to 2000 is considered, the arithmetic mean risk premium is estimated to be 7.7%, which is lower than the Ibbotson data spanning from 1926 to 1998. This could imply a need for further downward revision in the experts' forecasts.

The discussion concludes by reiterating the notion that while historical data serves as an anchor, more reliable future estimates might be obtained by adjusting these historical figures to reflect current market volatility levels. In doing so, the adjusted U.S. figure is 7.1% and the world index is at 5.9%. These adjusted figures suggest that experts might need to further revise their forecasts downward, particularly if they continue to use historical data as a baseline for future predictions.

Equity risk premia is a complex endeavor that involves a balance between finance theory and practical decision-making. Using historical data is a common approach because it's grounded in empirical evidence. However, this method assumes that future markets will behave similarly to past markets, which may not always be the case due to changes in market dynamics, regulations, and investor behavior.

Surveys offer real-time insights into market expectations but are difficult to interpret.

Different studies find that financial professionals have varying biases and expectations, making it challenging to draw reliable conclusions from these surveys.

Markets are not static and evolve due to various factors like technological advancements, changes in global politics, and shifts in investor sentiment. These dynamics must be considered when estimating future risk premia. For example, the opportunity for greater diversification, both domestically and internationally, has likely affected investors' risk expectations.

Forward-looking approaches try to incorporate these future changes into risk premia estimates. One method is to dissect historical returns into components, such as dividend growth and changes in valuation multiples, and project these into the future. However, this is also fraught with uncertainty as it relies on assumptions about future market conditions.

Theoretical models like the Gordon Growth Model can provide a framework for estimating future returns, but these too are based on assumptions that can be debated, such as stable growth rates and constant discount rates.

using long-term dividend growth to project future real growth can be naive. Dividend growth is subject to a multitude of factors, including economic conditions and company performance. The approach simplifies this by assuming a uniform growth rate based on historical data.

The method considers any deviation between the projected and actual dividend growth rates as "unanticipated" growth. This measure is then compounded over time to estimate its annualized impact. While this offers a basic measure of unexpected dividend growth, it's still a simplified representation.

In terms of valuation ratios, the change in price-to-dividend ratios is attributed solely to a fall in the required risk premium for equity investment. This is a simplification, as these ratios can also be influenced by other factors, such as market sentiment and future growth prospects.

The approach attempts to break down the risk premium for specific countries like the United States and the United Kingdom. While these estimates offer some insights, they are acknowledged to be simplistic and subject to various limitations. Factors such as tax treatment, frequency of data, and the splicing of index series are not accounted for, which could affect the reliability of these estimates.

Lastly, the text suggests that, given the increasingly international nature of capital markets, a global approach to determining the cost of capital may be more appropriate than a country-by-country approach.

Key points

Importance of Equity Risk Premium:

• The ERP is central to financial theory and practice, affecting both asset valuation and investment strategy.

• It serves as an unbiased estimator of future returns compared to less risky assets like treasury bills or bonds.

Market Views:

• There is a dichotomy between optimists and pessimists regarding the valuation of the equity market, which affects the perception of ERP.

• Market equilibrium is often considered a balance between these viewpoints.

Calculation and Methods:

• Various models like the Capital Asset Pricing Model (CAPM) and the Gordon Growth Model serve as theoretical frameworks.

• Historical data is often used as a starting point for estimating future premiums, but caution is advised due to changing market conditions.

• Arithmetic mean is generally used for forward-looking estimates, while geometric mean summarizes historical annualized returns.

The Equity Premium Puzzle:

• Observed ERPs, particularly in the U.S., have historically been higher than what traditional financial theories would suggest.

• This has led to debates and alternative theories about the appropriate magnitude of the risk premium.

Surveys and Expert Opinions:

• Surveys among financial professionals reveal a range of estimates and show that long-run historical data heavily influences consensus.

• The reliability of such surveys is questioned due to biases and varying expectations.

Country-specific and Global Perspectives:

• ERPs differ across countries, influenced by factors like market volatility, economic conditions, and investor behavior.

• A global approach may be increasingly appropriate given the international nature of capital markets.

Limitations and Uncertainties:

• Direct measurement of future ERPs is challenging due to unreliable investor surveys and potentially biased analysts' forecasts.

• Market dynamics, technological advancements, and changes in global politics make it difficult to project future risk premiums accurately.

Conclusion:

Estimating the equity risk premium is a complex task requiring a nuanced approach that balances theoretical frameworks with empirical evidence. While historical data serves as a useful anchor, it's crucial to adjust these figures to account for contemporary market conditions and uncertainties.

Chapter 14 - Implications for investors

Stocks generally outperform government securities over the long term for several reasons. First, they offer a risk premium, which is a higher return to compensate for the additional risk associated with equities. Second, companies have growth potential, which tends to drive their stock prices up. Third, stocks often pay dividends, enhancing overall returns when reinvested. Lastly, they can serve as a better hedge against inflation.

The concept of "Siegel's constant" estimates a stable historical real return on stocks and suggests a long-term consistency in equity performance. However, this constant and the associated past performance should not be seen as guaranteed indicators of future returns.

It's important to note that the idea of equities outperforming less risky investments isn't universal. Stock markets in countries other than the U.S. have often been more volatile, implying that the risk-reward profile of stocks may vary globally. Finally, equities are not risk-free investments, even in the long term, and investment strategies should be evaluated critically, taking into account various risk factors and market conditions.

The text you provided discusses the limitations of relying solely on historical data for future investment predictions, focusing on the U.S. and U.K. markets. It points out two critical issues: sampling error and survivorship bias. Sampling error arises when a limited number of historical outcomes are available for extrapolation, making the predictions less reliable. Survivorship bias refers to the tendency to only consider successful cases when evaluating performance, thereby skewing results.

The text highlights that while both the U.S. and U.K. markets have shown a positive equity risk premium over the long term (defined as twenty years or more), the dispersion around the median for these premiums is significant. This wide range implies that the actual returns could vary greatly, potentially even resulting in negative returns.

The analysis also observes that estimates of the risk premium often converge on a long-term average, but this should not give undue confidence in future predictions. The lack of a sufficient number of independent observations limits the reliability of these estimates. In essence, while the past performance might indicate a pattern, it is not a guarantee of future outcomes, especially in varying economic and market conditions.

Thus, it's important to account for these limitations when utilizing historical data for investment predictions. Using a comprehensive approach that includes a range of possible outcomes can help mitigate the inherent risks in such forecasts.

The analysis begins by recalling Japan's early 1990s economic bubble as a cautionary tale for over-optimism, highlighting the potential for long-term economic downturns even in seemingly strong markets. A key focus is the variability of risk premiums across countries.

While the U.S. and U.K. have historically shown a consistently positive risk premium over long periods, countries like the Netherlands exhibit a more volatile record. In the Netherlands, a holding period of at least 40 years is necessary for a consistently positive risk premium, in contrast to the 20-year periods that suffice in the U.S. and U.K.

The implications are significant for investors. Many tend to hold poorly diversified portfolios, largely focused on domestic securities. Such an approach exposes them to a broad spectrum of market performance risks, including the potential for negative outcomes.

Therefore, international diversification is recommended, along with preparation for a wider range of return experiences. The conclusion stresses that despite the general optimism around stock prices, particularly during the period around 2000-2001, more modest expectations for future returns are advised.

This perspective aligns with empirical financial research that emphasizes the importance of diversification and cautions that past performance is not indicative of future results. Overall, the message is clear: while stocks may have historically been lucrative investments, especially in developed economies, they are far from risk-free. A prudent approach to investment would involve considering a diverse set of experiences and outcomes.

The analysis examines the long-term equity premium and its expected future values. It builds on Mehra and Prescott's "equity premium puzzle," which notes that stocks have historically provided higher rewards than can be theoretically explained, and Weil's "risk-free rate puzzle," which suggests that safe investments like bills and bonds have been under-rewarded. The study uses a global dataset to mitigate the impact of measurement errors and market survival bias, estimating a future world equity premium at approximately 3.0% (geometric mean) or 4.0% (arithmetic mean).

Different levels of market volatility are considered, and risk premiums are projected over various future time horizons. The analysis reveals a significant probability of achieving a negative risk premium even over long investment periods. For example, with a market volatility standard deviation of 16%, there's an 18% chance of equities underperforming treasury bills over a 20-year span. This probability increases with higher market volatility and less diversified portfolios.

The analysis also considers the equity premium relative to bonds, noting that the probability of a negative equity premium increases if measured against bonds instead of bills. The study concludes that while equity investments are worthwhile in the long run, they come with substantial downside risk. The risk of underperformance decreases with longer investment horizons, but due to the power of compound interest, the worst-case scenarios become more severe over time. Therefore, equity investment is not as compelling for short- or medium-term strategies. The findings suggest a nuanced approach to equity investment, beyond simplistic views that stocks are either "overpriced" or "cheap."

The analysis culminates with several key implications for investors, which are informed by an in-depth look at long-term capital market trends. The first significant point focuses on asset allocation. Traditional asset allocation in the U.S. often advises a 60:40 ratio of stocks to bonds. However, with a revised, lower equity premium, this conventional wisdom suddenly appears more reasonable. The reduced equity premium implies that the opportunity cost of staying out of the stock market is now lower, making bonds a more viable investment for the future.

The second major consideration involves tax management. While taxes may not play a substantial role in market price formation, they do have a pronounced impact on individual returns. Therefore, the study advocates for efficient tax management. Utilizing tax-exempt or tax-deferred accounts can maximize returns, and this is true across different tax rates. The focus here is on how investors can retain more of their earnings, which is particularly crucial when dealing with smaller equity premiums.

Lastly, the study turns its attention to the fees associated with mutual funds. Given that the anticipated future annualized equity premium is close to 3%, the high fees that many mutual funds charge can essentially negate the benefits of investing in equities. The report anticipates that this realization will exert downward pressure on mutual fund fees. A shift is expected toward either funds that seek to outperform the market significantly or those that offer a low-cost structure.

Balancing investment strategies is a nuanced task that both institutional and individual investors face. Scientifically backed research suggests that while indexation can mitigate risks like implementation shortfall, it's not a one-size-fits-all solution. Institutions that possess the requisite skill and resources could combine passive and active strategies, as proposed by

Treynor and Black in 1973, to maximize their risk-reward ratio. While anomalies in stock returns, such as the size effect or momentum trading, offer tempting opportunities for active management, they often prove to be temporary and unreliable, as indicated by studies like

Hirshleifer (2001). On the other hand, international diversification remains a viable risk-mitigation strategy, even in an era of increasing global market correlations. Therefore, a multi-faceted approach that judiciously integrates these various elements could offer the most scientifically robust and economically meaningful path for investors.

key points: chapter 14

1. **Risk Premium**: Stocks generally offer a higher return than government securities over the long term due to a risk premium. However, this is not guaranteed and can vary by market and time period.

2. **Siegel's Constant**: While it provides a stable historical real return on stocks, it's not a reliable indicator for future returns.

3. **Global Variability**: Risk premiums and market performance can vary significantly from country to country. For example, the Netherlands requires a 40-year holding period for a consistently positive risk premium, compared to 20 years in the U.S. and U.K.

4. **Sampling Error and Survivorship Bias**: These limitations make historical data less reliable for future investment predictions.

5. **Equity Premium Puzzle**: Stocks have historically provided higher rewards than can be theoretically explained, raising questions about future expectations.

6. **Negative Risk Premium**: There is a significant probability that equities may underperform safer investments like treasury bills over long periods.

7. **Asset Allocation**: Given the revised, lower equity premium, a 60:40 ratio of stocks to bonds appears more reasonable than before.

8. **Tax Management**: Efficient tax management can significantly impact individual returns, especially in a lower equity premium environment.

9. **Mutual Fund Fees**: High fees can negate the benefits of investing in equities, suggesting a potential downward pressure on mutual fund fees.

10. **Strategic Considerations**: Combining passive and active strategies can optimize the risk-reward ratio. However, market anomalies often prove to be temporary and unreliable.

In summary, while equities have historically offered lucrative returns, especially in developed markets, they come with substantial risks. A nuanced, diversified approach informed by scientific research is advisable for investors.

Chapter 15 - Implications for Companies

In light of the extensive research on the long-term performance of various asset categories across different national and economic contexts, several key implications emerge for both investors and corporate managers. For estimating the cost of capital, firms can refine their risk assessments by leveraging historical data on asset classes and consider the benefits of global diversification. Regulatory responses to these long-term findings may necessitate adjustments in compliance and economic policies, impacting corporate valuation models. On the question of capital structure, the historical data may challenge the traditional view that debt holds a cost advantage over equity, which could influence future financing decisions. Additionally, the need for paying dividends might be reconsidered based on long-term asset performance and changing investor expectations. In summary, both corporate financial managers and investors should employ data-driven decision-making, be prepared for shifts in economic and regulatory landscapes, and exercise flexibility in their strategies.

Your extensive discussion brings forth several critical shifts in understanding the equity risk premium and the cost of capital, which have significant ramifications for corporate decision-making and investment strategies.

Previously, the equity risk premium was estimated to be higher, often around 7-9%, influencing both corporate and investor behavior. This high premium shaped not only investment decisions but also corporate valuations and capital budgeting. However, recent evidence suggests that these older models likely overestimated the equity risk premium, and thus the cost of capital.

Real interest rates have also evolved, showing a rise over the last century but a decline in more recent years. This change further influences the cost of capital and, by extension, investment decisions. The implications of these shifts are profound. Companies that continue to rely on outdated, higher estimates of the equity risk premium are at risk of under-investing or delaying critical projects. This could weaken their competitive positioning, especially against new entrants who operate under a more accurate, lower cost of capital.

The benchmark for internal valuations should align with current market expectations, which are shaped by a lower risk-free rate and a more realistic equity risk premium. This alignment is crucial for making accurate investment decisions, whether they are local or global. By correctly estimating these parameters, companies can focus on projects that truly add value, rather than chasing unrealistically high returns based on outdated data.

It is essential that corporate managers understand these shifts and incorporate this more nuanced understanding into their decision-making processes. Financial market history, while not a perfect guide to the future, serves as a starting point for understanding capital markets and thus for focusing investments that genuinely add to a company’s market value.

Understanding the precise cost of capital, influenced by a correctly estimated equity risk premium, is pivotal for making sound corporate investment decisions. When companies rely on outdated or inflated hurdle rates, they risk overlooking profitable projects, leading to under-investment. This notion extends beyond national borders, advocating for a global approach to setting the cost of capital, especially given the interconnectedness of today's financial markets.

Furthermore, regulators should also adapt their frameworks, particularly in sectors where returns are capped to prevent market abuse, aligning them with updated risk premium estimates. This is not just a corporate concern; even pension plans need to reassess their strategies. Actuarial valuations should be updated to reflect lower expected returns on equities, compelling a reevaluation of asset allocation in pension portfolios. Failure to update these crucial financial metrics can result in suboptimal investment decisions, regulatory challenges, and an erosion of shareholder value. Therefore, staying attuned to the latest financial market research is essential for both corporate decision-makers and regulators.

The complexity of corporate financial decision-making, especially in the domains of capital structure, dividend policy, financial reporting, and currency hedging. While it may seem tempting for financial managers to tweak their capital structure based on the "apparent" costs of debt and equity, the Modigliani-Miller propositions caution against such an approach. Instead, managers should focus on elements like tax implications, the risk of financial distress, and agency costs.

Similarly, the allure of manipulating dividend policies or book-to-market ratios to ostensibly lower the cost of capital is misleading. Such cosmetic changes are unlikely to have the desired effect and could send mixed signals to the market, affecting valuations negatively. Accounting conventions and book values, therefore, should not be the drivers of a firm's value; fundamental factors are the key determinants.

Finally, on the topic of currency hedging, while long-term exchange rates may adjust to inflation rates, short-term volatility can pose significant risks. Hedging could serve as a practical tool for corporations to manage these risks, allowing them to focus on their core business activities without the distraction of currency fluctuations.

In essence, corporate finance decisions should be rooted in a firm's fundamental attributes and long-term strategies, rather than short-term market perceptions or accounting maneuvers. The focus should be on true value creation, taking into account a myriad of factors including tax considerations, risk profiles, and market conditions.

Key points :

1. Equity Risk Premium: Updated research suggests that the traditionally high equity risk premium estimates are likely inflated, affecting the cost of capital and investment decisions. Both corporate managers and investors need to adapt to this new understanding.

2. Real Interest Rates: Changes in real interest rates over time can also affect the cost of capital. Companies relying on outdated, higher estimates may risk under-investing, thereby losing competitive advantage.

3. Global Approach: The interconnectedness of financial markets argues for a global approach in setting the cost of capital. Outdated models based on individual country data could lead to suboptimal investment choices.

4. Regulatory Implications: Regulators should consider these updated estimates when setting allowable returns for regulated industries, as they directly influence corporate valuations.

5. Pension Plans: Lower expected returns on equities necessitate a reevaluation of asset allocation strategies within pension portfolios.

6. Capital Structure: Traditional views on the cost advantages of debt over equity may be challenged, influencing future corporate financing decisions.

7. Dividend Policy: The data suggests that manipulating dividend policies or financial reporting to appear more attractive is unlikely to lower the real cost of capital.

8. Currency Hedging: While long-term exchange rates adjust to inflation, short-term volatility remains a risk. Hedging can be a practical tool to manage this risk.

9. Fundamental Focus: Financial decisions should be grounded in a firm's fundamental attributes and broader economic factors rather than short-term market perceptions or accounting tricks.

In summary, both corporate managers and investors should adapt their strategies and decision-making frameworks in light of the evolving data, ensuring that they are aligned with current market conditions and realistic estimates.

Chapter 16 - Conclusions

The book aims to identify enduring laws in the inherently complex and volatile financial markets. It differentiates these laws from temporary traits, which may appear stable but are subject to change. The structure includes a summary of key findings, a review of main messages, and country-specific appraisals of market performance. The book's approach aligns with scientific methodologies, focusing on data-driven, multi-country analyses.

The book addresses four key questions related to the performance of stock markets, bonds, and bills throughout the 20th century, considering both domestic and international contexts. The data covers 16 significant global markets and incorporates factors like foreign exchange and inflation.

One major finding is that equities consistently outperformed other asset classes in every country studied. However, they also presented higher risks, evident from their higher standard deviation compared to bonds and bills.

Inflation emerged as a significant factor affecting bond returns, especially in countries like Germany, Japan, Italy, France, and Belgium, where bonds and bills yielded negative real returns over the century.

The study acknowledges its limitations, including potential biases like "easy data bias" and survivorship bias. These could inflate long-term return estimates but are considered in the analysis. Despite these limitations, the book provides a comprehensive and scientifically rigorous insight into long-term financial market trends.

The book emphasizes the importance of quality data for understanding historical investment performance across different economic and political environments. One key variable you document is the equity risk premium, which was lower in the first half of the 20th century compared to later years. This insight challenges prevailing expectations about future market performance.

You attribute the high risk premiums of the last fifty-one years to factors like technological changes, improved corporate governance, and reduced investment risk due to global stability and increased diversification opportunities. These factors have led to rising stock prices, but you caution that such a trend may not continue. Your research suggests that the expected equity risk premium is between 2.5–4 percent on an annualized basis, which is notably lower than earlier estimates.

The implications are significant: investors expecting high returns based on past performance may need to adjust their expectations. High stock prices can only be justified if we accept that the expected equity risk premium will remain at a permanently low level. Therefore, future equity returns may fall below recent investor expectations, and the bullish market conditions of the 1990s are unlikely to be replicated.