EXPECTED
RETURNS

Robeco regularly revises its outlook on long-term expected returns.
This document was last updated in September 2020.

This publication is intended for professional investors only

Contents

1.

Long-term expected returns
1.1
Inflation
1.2
Cash
1.3
Government bonds
1.4
Investment grade corporate credits
1.5
High yield corporate credits
1.6
Inflation-linked bonds
1.7
Emerging market debt
1.8
Developed equities
1.9
Emerging equities
1.10 Private equity
1.11 Real estate
1.12 Commodities
1.13 Hedge funds

4
6
7
8
9
10
11
12
12
14
14
15
16
17

2.

Economic growth and financial markets in a steady state
2.1
Labor productivity
2.2
Size of the labor force
2.3
Economic growth, earnings growth and dividend growth
2.4
Economic growth and interest rates
2.5
Inflation

18
19
19
20
23
24

References25

Long-Term Expected Returns | 3

1Long-term
expected
returns

The purpose of this report is to show our long-term return
expectations for a wide set of asset classes. We take anunconditional long-term view, which means that neither
valuation or current economic environment is relevant.
These long-term expected returns can be used as theequilibrium returns for asset and liability management(ALM) studies for long-term investors such as pension or
endowment funds.

4 | Long-Term Expected Returns

Naturally, these estimates are uncertain. Nevertheless, by using thorough empirical andtheoretical research methods, and rounding returns to the nearest quarter, i.e. 0.25%
precision, and volatilities to the nearest 1%, they should reflect net returns for investors
that want to gain exposure to each asset class. For liquid assets, transaction costs andmanagement fees are low and only play a marginal role when rounding expected returns
to the nearest 0.25% precision. Situations where costs actually play a larger role are also
discussed; for example, alternative assets such as private equity, and hedge funds thatcannot be tracked at low cost.
The returns we estimate here are geometric, which are better suited to long investment
horizons. Since we also estimate the volatility risk of each asset class, readers who areinterested can convert the geometric return to an arithmetic expected return.1 Our
estimates are based on the worldwide market capitalization-weighted asset classes. For
historical returns on the invested market portfolio, i.e. the market capitalization-weighted
investment portfolio of all asset classes, see Doeswijk, Lam, and Swinkels (2020). Theyfind a realized geometric real return in USD of 4.45% per year, with a standard deviation of
11.2% and a Sharpe ratio of 0.36 over the period 1960-2017.

1. Assuming log-normally distributed returns, thearithmetic average is the geometric average plus
half of the variance of the returns. See Campbell, Lo
and MacKinlay (1997, p. 15).

Table 1.1: Historical returns for several markets over the period 1900-2017
Inflation

Real returns

Excess returns over cash

Cash

Bonds

Equities

Bonds

Equities

Australia

3.8%

0.7%

1.7%

6.8%

1.0%

6.0%

Austria

12.6%

-7.9%

-3.7%

0.8%

4.6%

9.5%

Belgium

5.0%

-0.3%

0.5%

2.7%

0.8%

3.0%

Canada

3.0%

1.5%

2.2%

5.7%

0.7%

4.2%

Denmark

3.7%

2.1%

3.3%

5.4%

1.2%

3.3%

Finland

7.0%

-0.5%

0.3%

5.4%

0.7%

5.9%

France

6.9%

-2.7%

0.3%

3.3%

3.1%

6.2%

Germany

29.5%

-2.3%

-1.3%

3.3%

1.0%

5.8%

Ireland

4.1%

0.7%

1.6%

4.4%

0.9%

3.6%

Italy

8.1%

-3.5%

-1.1%

2.0%

2.5%

5.7%

Japan

6.7%

-1.9%

-0.8%

4.2%

1.1%

6.1%

Netherlands

2.9%

0.6%

1.8%

5.0%

1.2%

4.5%

New Zealand

3.6%

1.7%

2.1%

6.2%

0.4%

4.4%

Norway

3.6%

1.1%

1.8%

4.3%

0.7%

3.2%

Portugal

7.3%

-1.1%

0.7%

3.5%

1.8%

4.6%

South Africa

5.0%

1.0%

1.8%

7.2%

0.9%

6.2%

Spain

5.6%

0.3%

1.8%

3.6%

1.6%

3.3%

Sweden

3.4%

1.8%

2.7%

5.9%

0.9%

4.0%

Switzerland

2.2%

0.8%

2.3%

4.4%

1.6%

3.6%

United Kingdom

3.7%

1.0%

1.8%

5.5%

0.8%

4.4%

United States

2.9%

0.8%

2.0%

6.4%

1.1%

5.5%

World

2.9%

0.8%

1.8%

5.1%

1.0%

4.2%

Average

6.2%

-0.3%

1.0%

4.5%

1.4%

4.8%

Median

4.1%

0.7%

1.8%

4.5%

1.0%

4.6%

Source: Dimson-Marsh-Staunton database (2017), Robeco. Note that for Austria and Germany have experienced hyperinflation periods in 1922 (Austria) and 1923/24 (Germany).

Long-Term Expected Returns | 5

LONG-TERM EXPECTED RETURNS

We start this study by examining the 2017 database compiled by Dimson, Marsh andStaunton (the DMS database). For each of the 21 countries in this database, we calculate
the compounded rate of inflation, the compounded real rates of return for cash, bonds andequities, and the excess returns over the 117-year period 1900-2016. Table 1.1 shows theresults. We also calculate the average of and a median over the 21 countries.
Note that recently, several other independently developed historical databases havebeen created. The Jordà-Schularick-Taylor MacroHistory database is described by Jordà,
Schularick, and Taylor (2017) and Jordà, Knoll, Kuvshinov, Schularick, and Taylor (2019)and contains country-level annual bond and stock returns starting as early as 1870. The
Global Financial Data database contains data going back as far as 1602, when stock market
trading started in Amsterdam. Swinkels (2020) uses this database to create global bondand equity returns over the period 1800-1914. These relatively new and less exploreddatasets are used as additional novel evidence complementing the evidence from the DMS
database that is central in the sections below.

1.1 Inflation
Inflation around the globe was significantly higher from 1900 to 2000 than that we haveseen over the past two decades. Germany is an outlier with its hyperinflation period in theearly part of the sample period, resulting in an average inflation rate of 29.5% per year.
The median compounded inflation rate equals 4.1%. Although central banks in developed
markets target inflation at close to 2%, we doubt whether, looking at historical records,
they will succeed in achieving in the long run what would be lower than historicallyobserved in any country since 1900.2
Figure 1.1: Distribution frequency of 2,457 annual inflation data (1900-2016, 21 countries, in %)

350
300
250
200
150
100
50
0
-14

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

14

The target inflation rate frequently used by central banks
Source: Dimson-Marsh-Staunton database (2017), Robeco

Another way of describing the history of inflation is to map all 2,457 inflation figures that
we have for 21 countries over 117 years – see Figure 1.1. Using this method, as illustrated in
the distribution frequency, it appears that inflation most often falls in the range of 2 to 3%,with 353 observations, and the median of these individual observations together comes in
at 2.8%. In addition, Figure 1.1 clearly shows an asymmetric distribution: there are far more
years in which inflation is above 2% than below 2%. A future distribution is likely to show thesame asymmetry, as we have yet to meet a central bank that argues in favor of targetinga period of deflation after a period of overshooting its target inflation rate, as this would

6 | Long-Term Expected Returns

2. Note that Swinkels (2020) finds that the four major
markets had an average inflation of only 0.4% from1800 to 1914. An important difference between the
19th and 20th century is that in the 19th century
most currencies were directly linked to gold.

detract from its ability to achieve its target rate. This applies in particular to an environment
where the zero lower bound problem for central banks remains an issue. Blanchard,
Dell’Ariccia and Mauro (2010) along with De Grauwe and Ji (2019) find that a low inflation
target creates the risk of persistent recessions and low growth.
Our view is that when investors make long-term predictions about inflation, they should
consider both past and present inflation targets; see Svensson (2010). We believe longterm inflation to be around 3% as a compounded average: right between the central banks’
inflation target of 2% and the empirical reality of the 4.1% median compounded inflation
over the period 1900 to 2017. It therefore seems to be a conservative estimate, being below
the 4.1% median and the 6.2% average of the 21 individual compounded inflation rates. Notethat the median is less sensitive to outliers (such as Germany) than the average of the data
series. Finally, we would like to point out that our long-term estimate is one for an averagecompounded inflation rate. This results from lengthy periods with inflation of around 2%,
some periods with inflation spikes above 2%, and the occasional deflationary episode.

1.2 Cash
For cash we assume the real rate of return to be 0.5%, roughly in line with the historical
median of 0.7%. Note that the average of -0.3% is heavily impacted by several cases ofhyperinflation. There is a wide dispersion in real cash returns. No fewer than eight out oftwenty-one countries in our sample experienced compounded negative real returns on cash
over the 1900-2016 period.
New York Fed President John C. Williams has devoted an important part of his career
to researching an unobservable phenomenon: the neutral rate of interest, or ‘r-star’ ineconomic jargon. It was first defined by Wicksell (1898) as “…a certain rate of interest on
loans which is neutral in respect to commodity prices, and tends neither to raise nor to lower
them.” Nowadays, the r-star is defined as the short-run real interest rate that is expected toprevail when an economy is at full strength and inflation is stable. It is the rate at which theeconomy neither accelerates nor slows down. Central banks consider it their responsibility tomove their policy rates towards the r-star.
One popular model for estimating the r-star is the Holston, Laubach, and Williams (2017)(HLW) model.
Figure 1.2: Natural rate of interest

Real interest rate (% per year)

4

3

2

1

0

-1
03-00
US current

03-05
US vintage

03-10Eurozone current

03-15

03-20

Eurozone vintage

Source: Holston, Laubach, Williams (2017), Robeco. The series ‘US current’ and ‘Eurozone current’ refer to thehistorical estimates based on the Q1-2020 update. The ‘US vintage’ and ‘Eurozone vintage series contain the last
updated quarterly observations. These are updated from Q4 2015, and vintage data before refer to the Q4-2015
historical time series.

Long-Term Expected Returns | 7

LONG-TERM EXPECTED RETURNS

Figure 1.2 contains the recent time series of the r-star estimate for the US and Eurozone.
The latest estimate provided by the HLW model for the US neutral real rate of interest is
0.53%, with its Eurozone counterpart close to zero. The average HLW r-star since 1961 is
2.77%, which is substantially above our estimate of the real short rate in equilibrium of
0.5%. The HLW r-star is also substantially above the realized short real interest rate overthe period 1961 to 2016 for the US, which equals 0.87% per annum.3 Therefore, we feel
comfortable with our long-run estimate of 0.5%, which corresponds with the long-run
average real interest rate since 1900 for a few dozen countries.4

1.3 Government bonds
We estimate the real return on high-quality government bonds to be 1.25%, which is thesum of a 0.5% real return on cash and a 0.75% term premium on bonds. This real-return
estimate is substantially lower than the historical median of 1.75% and the 1.82% for the
GDP-weighted global bond index. Due to the strong recent performance of bonds, thisfigure has gradually moved higher in recent years, making a 1.25% real return estimate
look conservative in historical terms. For example, Doeswijk, Lam, and Swinkels (2020)
report a real return on government bonds of 2.81% per annum from 1960 to 2017. Our total
expected nominal return on bonds is 4.25%, as our expected long-term inflation rate is 3%.5
The estimate for the long-term return on bonds is 0.25% lower than our estimate for longterm economic growth. Looking deeper, it is also 0.25% lower than the global bond term
premium of 1% observed from 1900 to 2016.6 This discount is validated by our observationthat the median capture of real GDP growth by real bond returns over the past 114 years forthe countries in the DMS database is only 91%, and the average compensation a mere 58%.
This suggests bond investors are not being fully compensated for economic growth risks in
the long run.

1,000

100

10
1900

1920
World (GDP-weighted)

1940

1960

1980

2000

Average (annual rebalancing)

Source: Dimson-Marsh-Staunton database (2017), Robeco

We would like to point out that the real returns generated on bonds have failed to rise
gradually over time. As Figure 1.3 shows, real bond returns were roughly unchanged
from 1900 to 1980. Since then, the real annual compounded return exceeded 6% as ahistorically unprecedented bull market set in. This dynamic historical pattern suggests that
our real return estimate for bonds is more uncertain than for equities.

8 | Long-Term Expected Returns

4. Note that Swinkels (2020) documents a real rate on
cash of no less than 3.7% for the four main markets
from 1800 to 1914, possibly due to the scarcity of
cash during the 19th century. Jordà, Knoll, Kuvshinov,
Schularick, and Taylor (2019) find that the real returnon cash has been very volatile, sometimes evenmore volatile than the real return on risky assets.
They report especially low real rates on cash inperiods of wars and stagflations.

5. For Solvency II regulation, the European Commission
had initially suggested a Ultimate Forward Rate
(UFR) of 4.2%, which is close to our long-term
return estimate on high-quality government bondsof 4.25%. The arguments used by the European
Commission are very different to ours. They expect
a 2% inflation rate and a 2.2% real interest rate in
the long run. Note that the UFR has since decreased
due to a lower historical average real rate on
government bonds. The UFR is 3.75% as of 1 January2020.
6. Swinkels (2020) reports a term premium of 1.1%
from 1800 to 1914 for the four main markets, which
is very similar to the average term premium in the20th century.

Figure 1.3: Real return index for global bonds with different weighting methods

Median

3. Source: Dimson, Marsh, and Staunton (2017)
database.

1.4 Investment grade corporate credits
Historical excess returns for investment grade corporate credits are displayed in Table 1.2.
According to Elton, Gruber, Agrawal and Mann (2001), the credit spread comprises thefollowing three components: specific default risk compensation, the tax premium, andsystematic default risk premium. Additionally, Bongaerts, De Jong, and Driessen (2011) alsofind a liquidity premium in credit spreads. Houweling, Mentink, and Vorst (2005) estimate
the liquidity premium to be between 13 and 23 basis points.
Table 1.2: Estimated excess returns for investment grade credits, high yield bonds and inflation-linked bonds
Excess returns
over bonds

Volatility

PeriodBloomberg Barclays US

0.4%

4.3%

1988-2020

Bloomberg Barclays Pan-European

0.6%

3.6%

1999-2020

ICE Bank of America US

0.4%

5.0%

1997-2020

ICE Bank of America UK

0.6%

5.0%

1997-2020

ICE Bank of America Eurozone

0.6%

3.1%

1997-2020

JP Morgan U.S. Liquid

1.1%

5.3%

2000-2020

Altman (1998)

0.8%

5.4%

1985-1997

Giesecke, Longstaff, Schaefer, Strebulaev (2011)

0.8%

Ng and Phelps (2011)

0.3%

7.9%

1990-2009

Asvanunt and Richardson (2017)

0.5%

3.9%

1988-2014

Investment grade credits

1866-2008

High yield bonds
Bloomberg Barclays US

2.3%

9.4%

1988-2020

Bloomberg Barclays Pan-European

3.6%

11.8%

1999-2020

ICE Bank of America US

2.1%

10.2%

1997-2020

ICE Bank of America UK

4.9%

11.6%

1998-2020

ICE Bank of America Eurozone

2.6%

12.7%

1998-2020

Altman (1998)

2.5%

5.2%

1978-1997

Ng and Phelps (2011)

3.1%

19.2%

1990-2009

Asvanunt and Richardson (2017)

2.5%

9.6%

1988-2014

Barclays US

-0.3

4.7%

1997-2017

Barclays UK

-1.8%

7.1%

1981-2017

Barclays UK

0.5%

5.8%

1997-2017

Hammond, Fairbanks, and Durham (1999)-0.5%

Grishchenko and Huang (2013)-0.3%

Inflation-linked bonds

2000-2008

Source: Bloomberg Barclays, Barclays, ICE Bank of America, JP Morgan, Robeco.

We estimate the total risk premium of credits over government bonds at 0.75%, which is
close to the 0.8% premium in Altman (1998) from 1985 to 1997 and the 0.8% premiumin Giesecke, Longstaff, Schaefer and Strebulaev (2011) from 1866 to 2008. These areslightly higher than the historical excess return in the corporate bond indices publishedby Bloomberg Barclays and reported by Ng and Phelps (2011) from 1990 to 2009 andAsvanunt and Richardson (2017) from 1988 to 2014.7 Our own empirical analysis showsthat from 1988 to April 2020, the excess return for the Barclays U.S. Corporate Bond Index
is 0.4%. For pan-European corporate bonds, the average excess return was 0.6% from 1999
to 2020. ICE Bank of America shows similar excess returns from January 1997 to April 2020.

7. One might be tempted to use Ibbotson’s longer
data series instead of Barclays’. However, Hallerbachand Houweling (2013) argue that the Ibbotson’slong-term credit series is an unreliable source fromwhich to calculate excess returns, as most credits areof extremely high credit quality and the series is not
appropriately duration-matched with the long-term
government bond series.

Long-Term Expected Returns | 9

LONG-TERM EXPECTED RETURNS

We note that the Bloomberg Barclays corporate bond indexes do not contain bonds withless than one year to maturity, and investors are forced to sell bonds when they are rated
below investment grade. Ng and Phelps (2011) find that relaxing these constraints leads toapproximately 0.4% additional return compared to constrained indices. This is a substantial
increase and investors should be aware of this benchmark issue when investing in credit
bonds.
Table 1.3: Risk and return for credit factors
Investment gradeHigh yield

ReturnVolatility

Sharpe ratio

ReturnVolatility

Sharpe ratio

Size

1.81%

3.54%

0.51

7.71%

11.68%

0.66

Low risk

0.87%

2.04%

0.43

3.77%

6.21%

0.61

Value

2.00%

6.38%

0.31

6.24%

13.23%

0.47

Momentum

1.16%

4.24%

0.27

4.13%

9.89%

0.42

Source: Data obtained from www.robeco.com/data and is updated from Houweling and Van Zundert (2017). The four factor series (Size, Low Risk, Value, Momentum) areconstructed by sorting each month-end all index constituents in 10 groups based on the respective measure. An overlapping portfolio method is used to hold on to bonds for thesubsequent 12 months while rebalancing monthly. The series listed are the excess returns over duration-matched Treasuries of the top (D1) portfolio. Results are provided for boththe Bloomberg Barclays U.S. Corporate Investment Grade index (left) and the Bloomberg Barclays U.S. Corporate High Yield index (right). Period January 1994 to December 2019.

Recent research suggests that excess corporate bond returns have a factor structure; see
Houweling and Van Zundert (2017), Israel, Palhares, and Richardson (2018), Bai, Bali, andWen (2019), and Bektic, Wenzler, Wegener, Schiereck, and Spielmann (2019). For example,
there is a low-risk phenomenon in credit bonds. This implies that credits with low distressrisk and a short time to maturity achieve the same returns as the credit bond market as awhole; see, for example, Ilmanen, Byrne, Gunasekera, and Minikin (2004). Several recent
studies, such as Frazzini and Pedersen (2014) and Houweling and Swinkels (2019), confirm
higher risk-adjusted returns for investors in low-risk credits than for the credit market asa whole. But size, value, and momentum factor premiums are also present in corporate
bonds markets. In Table 1.3, we show the updated factor premiums from Houweling and
Van Zundert (2017) from 1994 to 2019. We see that over this extended period, each of thefour factors has delivered Sharpe ratios in the range of 0.27 to 0.51 for US investment gradecredits.

1.5 High yield corporate credits
High yield bonds require a higher default premium than corporate bonds due to the lower
creditworthiness of the issuers and hence their higher risk profile. Altman (1998) also
examines the return on US high yield bonds compared to US Treasuries from 1978 to 1997.
The excess return of high yield over Treasuries during this 20-year period is 2.5%, as canbe seen in Table 1.2. We believe that this figure may overstate the risk premium of highyield. At the start of the sample period, the high yield market was still immature with theassociated liquidity problems and biases. Nevertheless, the sample period from August
1988 to April 2020 has a risk premium for high yield bonds of 2.3% over duration-matchedgovernment bonds. For European high yield indices the excess returns are very similar.
Houweling and Van Zundert (2017) document factor premiums in the high yield bondmarket. In Table 1.3, we show their updated factor premiums from 1994 to 2019. We seethat over this extended period, each of the four factors has delivered Sharpe ratios in therange of 0.42 to 0.66 for US high yield bonds. These Sharpe ratios are slightly higher thanfor investment grade.

10 | Long-Term Expected Returns

It is important to discuss the possible negative impact of transaction costs on investors’ability to achieve our estimated returns for corporate bonds. We note the argument of
Houweling (2012) that the returns for corporate bond indices are difficult to replicate, astransaction costs for corporate bonds are higher than for government bonds, which are
more liquid and cheaper to trade. Houweling reports an underperformance of 16 basis
points for government bonds for the average exchange-traded fund in his study, withinvestment grade bonds underperforming by 56 basis points, and high yield funds by asmuch as 384 basis points on average. Obviously, the liquidity or lack of it for these asset
classes requires extra attention in terms of portfolio implementation. Passive index
investing is likely to underperform the paper indexes substantially in fixed income markets.
We proceed with a 1.75% net premium over government bonds.

1.6 Inflation-linked bonds
The return to maturity on default-free inflation-linked bonds comprises the real interest
rate and the realized inflation rate. Intermediate returns depend on changes in expected
real rates and realized inflation. This differs from the return on default-free nominal bonds,
which consists of a real interest rate, expected inflation, and an inflation-risk premium. The
cost of insurance for inflation shocks should be reflected in a discount in the risk premiumfor inflation-linked bonds relative to nominal bonds.
Theoretically, the inflation risk premium should be positive, as this is related to the positive
skewness in the historical inflation numbers. From March 1997 to October 2017, theinflation risk premium in the US was small (see Table 1.2) as inflation-linked bonds earned
a 0.3% lower return than nominal bonds.8 When the inflation-risk premium is positive andother premia non-existent, we expect inflation-linked bonds to underperform nominal
bonds of the same maturity.
For the UK sample, we find that inflation-linked bonds underperform comparable nominal
bonds by a staggering 1.8% per annum since 1981. However, over the last 20 years of thesample (1997 to 2017), they outperformed comparable nominal bonds. This suggests that
estimating these premiums in newly developed asset classes can be particularly difficult.
Grishchenko and Huang (2013) point to liquidity problems in the Treasury InflationProtected Securities (TIPS) market as the reason for the low inflation risk premium
they document. After adjusting for liquidity in TIPS, they find an inflation risk premiumof between -0.09% and 0.04% from 2000 to 2008, depending on the proxy used for
expected inflation. They estimate the liquidity premium to be around 0.13%.
Driessen, Nijman, and Simon (2017) find a liquidity premium of 0.33% for inflation-linked
bonds. A study by García and Werner (2010) finds an inflation risk premium varying from
0.07% to 0.25% at longer horizons. Hammond, Fairbanks, and Durham (1999) estimate
the risk premium at 0.5%.9 Based on these findings, we estimate the premium of nominal
bonds over inflation-linked bonds to be 0.25%. This results in an ex-ante estimated total
nominal return of 4% for inflation-linked government bonds relative to 4.25% for nominal
government bonds. A disadvantage of inflation-linked bonds is their short historical data
availability. To circumvent the problem of statistical analysis, researchers can resort tohistorical simulation of inflation-linked bond returns. Swinkels (2018) compares several
proposed methods for historical simulation. His results show that inflation-linked bondreturns are most accurately simulated by subtracting inflation predictions from professional
forecaster from the nominal interest rates. Using historically simulated series this way gives
researchers the opportunity to artificially extend the data history of this asset class.

8. Even though we compare the inflation-linked bondindex with a comparable nominal government
bond, it could be due to differences in duration
between nominal and inflation-linked bonds, their
tax treatment, and the slightly higher credit risk ininflation-linked bonds due to the cash flow patternthat is further into the future

9. For a sample of developed and emerging
market inflation-linked bonds, Swinkels (2012)
estimates returns on maturity matched nominaland government bonds to be virtually the same,
indicating that the inflation risk premium in practiceis small. This could be partially due to the lower
liquidity of inflation-linked bonds compared tonominal government bonds

Long-Term Expected Returns | 11

LONG-TERM EXPECTED RETURNS

1.7 Emerging market debt
Emerging market debt (EMD) is a fast-growing asset class with dynamic characteristics. The
size of the EMD market has grown significantly in recent years. As data availability is limited,
it is impossible to take a firm view on risk and return for this asset class. Moreover, it is not acompletely homogenous asset class.
Table 1.4: Return and risk for emerging debt and other fixed income asset classes (2003-2013; hedged USD unless noted otherwise)
ReturnAnnualized st.dev.

Global developed government bonds

4.4%

2.9%

Global corporate investment grade credits

5.1%

4.5%

Global corporate high yield

7.8%

9.5%

Emerging markets USD debt

8.0%

8.8%

Emerging markets Corporate USD debt

7.4%

8.8%

Emerging markets local currency government debt

4.2%

4.0%

Emerging markets local currency government debt (unhedged)

6.7%

12.5%

Frontier market USD debt

9.4%

13.1%

Source: Bloomberg Barclays, JP Morgan, Robeco. Bloomberg Barclays Treasury (index id: 23), Bloomberg Barclays Global Corporate (index id: 9805), Bloomberg Barclays Global
Corporate High Yield (index id: 23059), JP Morgan EMBI Global, JP Morgan Corporate EMBI, JP Morgan GBI-EM, JP Morgan NEXGEM.

In Table 1.4 we compare global government bonds, credits, high yield, and EMD. We display
external USD-denominated debt for the latter as well as local currency government debt. Thisis our main focus asset class when it comes to EMD, as USD-denominated high yielding asset
prices tend to be highly correlated. This means that less diversification might be obtained thanwith local currency assets, even though they are all risky assets that tend to perform poorly in‘risk off’ environments; see Agur, Chan, Goswami, and Sharma (2019). On a currency-hedged
basis, local currency debt has underperformed global developed bond markets over this18-year period. The volatility risk on a currency-hedged basis is modest at 4.0%. However, whencurrency risks are not hedged (as is usual for this category), the volatility shoots up to 12.5%.
The average return is also higher with 6.7%.
We position EMD between credits and high yield, but closer to high yield. While the volatility
is somewhat higher from 2002 to 2020, the credit rating for emerging markets that can issue
local currency debt is on average investment grade. So we estimate the EMD premium over
government bonds to be 1.50%, which brings the nominal return to 5.75%. This is one notch
below our return estimate for high yield bonds, as we believe the risk profile is closer to highyield bonds than to credits. Once again, we stress that this asset class is young and dynamic,
and so we feel less certain about this estimate than for asset classes that have a longer history
and more data to back up our estimates.

1.8 Developed equities
Ever since Mehra and Prescott (1985) documented the equity premium puzzle, i.e. the relatively
high observed equity premium in the US compared to reasonable values of investor risk
aversion used in economic models, researchers and practitioners have been trying to solve it.
These answers have been found partly by introducing frictions in economic models and partly
from improved (i.e. lower) estimates of the equity premium.
Table 1.1 contains the estimates by the DMS database. From 1900 to 2016, the averageand the median real equity returns were 4.5% for 21 countries per annum, with the market
capitalization-weighted equity market index 5.1% per annum. The risk premium relative to cash
was 4.2% per year for the world index. We assume that this is a reasonable guidance for the

12 | Long-Term Expected Returns

Table 1.5: US factor premiums since 1963
FactorAcronym

ReturnVolatility

Alphat-statistic

Betat-statistic

Market

RMRF

6.44

15.40

-

-

-

-

Size

SMB

2.60

10.46

1.34

1.00

0.20

7.87

Value

HML

3.04

9.96

3.95

3.05

-0.14

-5.83

Profitability

RMW

3.07

7.45

3.73

3.83

-0.10

-5.67

Investment

CMA

3.13

6.91

4.22

4.95

-0.17

-10.74

Beta

BETA

-1.28

22.61

5.09

2.28

-0.99

-23.78

Variance

VAR

5.21

27.05

12.17

4.28

-1.08

-20.41

Momentum

MOM

7.83

14.50

8.76

4.58

-0.14

-4.03

Source: Data library of Kenneth French, Robeco. Period July 1963 to June 2020.

future, but perhaps slightly high because for part of the sample period, these countries were
emerging markets. Moreover, Swinkels (2020) reports a global equity risk premium of only
2.6% for 1800 to 1914. Therefore, we adjust our expected excess return over cash to 3.5% perannum, leading to a developed equity markets return estimate of 7%. We do not separately
discuss regional equity premiums for long-term expected returns.
Table 1.5 contains the excess returns relative to the risk-free rate for the US stock market from1963 to 2020. The arithmetic annualized average was 6.44% for a volatility of 15.40%. The
table also contains several of the documented factor premiums in the US. We see that thesize premium was statistically insignificant with an annualized alpha of 1.34% and t-statisticof 1.00. The other factor premiums were strong over this sample period, and most had amodest negative covariance with the market between -0.1 and -0.2. However, the BETA andVAR premiums were clear exceptions, with market exposures close to -1. This is why the risk
adjustments through, for example, alphas, are more important than the raw return differencein the first column. Note that these estimates do not yet include transactions costs. Thismight be a larger problem for the momentum strategy as this requires trading each stock
approximately once a year (assuming one-year momentum) while the holding period for value
strategies is typically three to five years.
Table 1.6: Global factor premiums since 1990
Developed markets ex US

Emerging markets

FactorAcronym

ReturnVolatility

Alphat-statReturnVolatility

Alphat-statMarket

RMRF

3.83

16.49

-

-

8.07

21.23

-

-

Size

SMB

1.07

7.06

1.44

1.14

2.04

8.20

2.71

1.88

Value

HML

3.12

7.59

3.23

2.33

7.07

9.38

6.61

3.94

Profitability

RMW

4.34

4.74

4.68

5.67

1.91

5.99

2.51

2.33

Investment

CMA

1.45

6.10

1.82

1.69

2.75

6.56

3.46

2.91

Momentum

WML

8.49

12.09

9.34

4.36

9.63

10.22

10.28

5.62

Source: Data library of Kenneth French, Robeco. Developed ex US markets, period July 1990 to July 2020, except WML starts in November 1990. Emerging markets, period July 1989
to July 2020, except RMW starts in July 1991, CMA in July 1992, and WML in January 1990.

These factor strategies do not by definition earn excess returns each year, as they also havesustained periods of negative excess returns; see Blitz (2020). For example, in the periodleading up to the internet bubble, valuation strategies severely underperformed the market
capitalization-weighted index. Moreover, executing these strategies is not as simple asfollowing such an index – several types of choices have to be made regarding rebalancing
frequency and the exact definition of the strategy parameters. Hence, it is difficult to defineLong-Term Expected Returns | 13

LONG-TERM EXPECTED RETURNS

a uniform value premium. The historical evidence on the US is overwhelming, and many
authors have empirically detected the same return factors in other countries; see for example
Rouwenhorst (1998). Table 1.6 contains this international evidence. Except for the size
premium, the other factor premiums are positive and statistically significant.

1.9 Emerging equities
We make a distinction between the equity risk premiums for developed and emerging markets,mainly because most of the investment management industry is organized in this way. Several
researchers have argued that equity risk premiums can be higher for countries that areless integrated into global financial markets; see Errunza and Losq (1985) and Bekaert andHarvey (1995) for examples. Developed markets also tend to have better governance, whichshould result in a higher risk premium for emerging markets. Furthermore, Erb, Harvey, andViskanta (1996) and Damodaran (2009) argue that country credit spreads are related to themagnitude of the equity risk premium in that particular country. Since most emerging markets
have become more integrated into the global financial markets and country credit spreads
have decreased substantially, the estimated excess returns of emerging markets relative todeveloped markets have also decreased in recent years. See Salomons and Grootveld (2003)
for a discussion of the emerging markets equity premium relative to that of developed markets.
The profitability of factor strategies in emerging and frontier markets has been widely
documented in the literature; see for example Rouwenhorst (1999), Van der Hart, Slagter and
Van Dijk (2003), Van der Hart, De Zwart and Van Dijk (2005), De Groot, Pang and Swinkels(2012), and Hanauer and Lauterbach (2019). Table 1.6 confirms these earlier studies with
updated data. Again, the size premium is not statistically significant, while the other factors arestrong.

1.10 Private equity
A large number of studies have tried recently to compare the returns of private equity withthose of listed equities. Kaplan and Schoar (2005) do not find an outperformance for private
equity, with a public market equivalent (PME) of 0.96 for all funds. Phalippou and Gottschalg(2009) draw a comparable conclusion using a larger sample. However, Stucke (2011), using
a different methodology, finds a net outperformance for the same data set as Phalippou
and Gottschalg (2009). Harris, Jenkinson and Kaplan (2014) perform a meta-study using
databases from Burgiss, Venture Economics (VE), Preqin and Cambridge Associates (CA).
They show that for all datasets, except VE, the median buy-out fund has returned a PME of
between 1.2 and 1.27. For venture capital, their findings show outperformance in the 1990s
and underperformance in the 1980s and 2000s. Robinson and Sensoy (2016) findings also
demonstrate outperformance over the S&P 500 for buy-out funds from 1984 to 2010. They
document a similar performance for venture capital to the S&P 500, using data from one
large limited partner. These recent studies suggest that private equity may well perform better
than listed equities but that fund management effects can be important. Korteweg (2019)
summarizes the literature on the performance of different private equity styles and concludes
that after 2000, the net-of-fees returns are not above those of public equity markets.
Driessen, Lin and Phalippou (2012) estimate the beta of buy-outs at 1.5. Ang, Chen,
Goetzmann, and Philippou (2018) find a beta of 1.4 and a strong factor exposure to the size
factor, indicating that private equity fund returns are similar to listed small-cap stocks. Kaplan
and Schoar (2005), Higson and Stucke (2012), Sensoy, Wang and Weisbach (2013), Korteweg
and Sorensen (2017) also note a heterogeneous pattern in the performance of private equity
funds. This implies that results depend strongly on manager selection. Finally, Robinson andSensoy (2016) show more capital calls than distributions during crises. Higson and Stucke(2012) also find this cyclical pattern.

14 | Long-Term Expected Returns

Although Table 1.7 shows an underperformance of 0.9% for private equity over stocks from1998 to 2020, there is no consensus in the academic literature saying that that private
equity returns (net of fees) exceed public equity returns. Most studies point to private equity
outperformance, but the issue of what is left after proper risk adjustment remains up for
debate. Moreover, most of the studies mentioned above are subject to selection and reporting
biases. Hence, we assume the risk premium of private equity as a group to match that of listed
equities.
Table 1.7: Estimated excess returns for private equity, real estate and hedge funds
Excess returns
over cash

over equities

Volatility

Period

4.6%

-0.9%

32.2%

1998-2020

Private equity
LPX America
Driessen, Lin, Phalippou (2012)-4.9%

1980-2003

Higson and Stucke (2012)

4.5%

1980-2000

Ang, Chen, Goetzmann, and Phlippou (2018)2%

1994-2015

Real estate
NAREIT US

4.5%

-1.1%

Fugazza, Guidolin and Nicodano (2006)

4.7%

-1.0%

Francis and Ibbotson (2020)

-0.5%

19.6%

1972-2020
1986-2005

7.8%

1991-2018

Commodities
S&P GSCI

1.0%

23.4%

1970-2020

S&P GSCI

-3.7%

21.5%

1991-2020

Bloomberg Commodity Index

-1.4%

17.5%

1991-2020

Bhardwaj, Janardanan, and Rouwenhorst (2019)

5.2%

14.4%

1870-2018

Levine, Ooi, Richardson, and Sasseville (2018)

4.6%

17.7%

1877-2015

Hedge funds
HFRI Fund-of-Fund Composite

3.6%

-3.4%

8.5%

1990-2019

HFRI Fund-of-Fund Composite

7.3%

-4.6%

8.3%

1990-1999

HFRI Fund-of-Fund Composite

1.2%

4.5%

8.4%

2000-2009

HFRI Fund-of-Fund Composite

2.3%

-9.4%

4.3%

2010-2019

Source: Refinitiv Datastream, www.reit.com, www.hedgefundresearch.com, Kenneth French Data Library, Robeco.

1.11 Real estate
In principle, we view direct and indirect real estate as one particular source of risk and return.
This corresponds to Idzorek, Barad and Meier (2006), who state: “Although all investors
may not yet agree that direct commercial real estate investments and indirect commercial
real estate investments (REITs) provide the same risk-reward exposure to commercial realestate, a growing body of research indicates that investment returns from the two markets
are either the same or nearly so.” Hoesli, Oikarinen, and Serrano (2015) report that returns
on REITs lead those of private real estate returns. Of all alternative asset classes, real estate
has probably received the most attention from academics in the past. A literature review by
Norman, Sirmans and Benjamin (1995) tries to summarize all the findings. Overall, they findno consensus for risk and return characteristics for real estate. However, more than half of theconsulted literature in their paper reported a lower return for real estate compared to equities.
Fugazza, Guidolin and Nicodano (2006) also show lower excess returns for real estate thanfor stocks. Their estimate of -1.0% per year can be seen in Table 1.7. More recently, Francis andIbbotson (2020) report that commercial real estate had a -0.5% performance relative to theLong-Term Expected Returns | 15

LONG-TERM EXPECTED RETURNS

S&P 500 index from 1991 to 2018. Note that their volatility estimate of 7.8% per annum isbased on smoothed returns and economic risks are likely substantially higher.
We proceed with an estimated excess return for indirect real estate that is 1% lower than ourestimate for stocks. Due to the lower leverage in direct real estate compared to indirect realestate, we estimate expected returns to be another 1% lower for that asset class.

1.12 Commodities
An unleveraged investment in commodities is a fully collateralized position which has threedrivers of returns: the risk-free rate, the spot return, and the roll yield. Erb and Harvey (2006)
point out that the roll return has historically been a very important driver of commodity
returns, but it is unclear what the size of roll returns will be in the future.10 In their extensive
study they find that the average individual compound excess return of commodity futuresis zero. They argue that individual commodities are not homogeneous and that their highvolatility and low mutual correlations result in high diversification benefits. The diversification
benefit comes from periodically rebalancing the portfolio and is reflected in the high historicalperformance of the S&P GSCI Index compared to the return from individual commodities.
Gorton and Rouwenhorst (2006) create an equally-weighted monthly rebalanced portfolio ofcommodity futures with returns similar to those for stocks from 1959 to 2004. Erb and Harvey(2006) raise questions over the representativeness of both the equally-weighted portfolio
and the GSCI index. On the one hand, they show that an equally-weighted stock index
would outperform a market cap-weighted index by far. On the other hand, the GSCI index
composition has changed dramatically over time and now allocates heavy weights to energy
commodities. They suggest that a simple extrapolation of historical commodity index returns
might not be a good estimate for future returns.
Recently, two studies have hand-collected commodity futures data going back to before
1900. Levine, Ooi, Richardson, and Sasseville (2018) collect data for the period 1877 to 2015.
Before 1960, their sample consists of five to ten commodities. They find an average arithmetic
excess return on commodity futures of 4.6% per annum, and 3.1% geometric. Bhardwaj,Janardanan, and Rouwenhorst (2019) go even further, collecting data starting in 1870 withover 20 different commodities contracts before 1960. They find an average arithmetic excess
return of 5.2% for their commodity index, which is slightly less volatile because there is morediversification among its increased cross-section of commodities, as can be seen in Table 1.7.
We observe that the return from systematically rolling over energy-related futures has
historically added substantially to the total return of commodity investing in energy andlivestock until the early 1990s (see Figure 1.5). However, over roughly the past ten years
roll returns on all commodity categories have tended to be negative. Due to the increased
interest of institutions in commodity investors, the future roll return is unlikely to turn positive
again. Lummer and Siegel (1993) and Kaplan and Lummer (1998) argue that the long-term
expected return of commodities equals the return on Treasury bills. From 1970 to 2020, theS&P GSCI index had an excess return of 1.0% relative to cash. Most of that excess performance
was made in the beginning of the sample period, as the excess return from 1991 to 2020 was-3.7%. For the Bloomberg Commodity Index, the return was somewhat higher, but still poorat -1.4%. Many theories for commodity risk premiums exist but most of those are not easily
measurable.
There seems to be substantial evidence for a large risk premium on commodities inhistorical data. However, Tang and Xiong (2012) indicate that there was a structural breakin commodity markets in 2000, also known as the ‘financialization’ or financial integration

16 | Long-Term Expected Returns

10. The upward (contango) or downward(backwardation) sloping term structure of futures
prices creates a negative or positive roll return. It
arises when an almost expiring future is rolled over
to a future with a longer maturity.

of commodity markets. This implies that risk premiums are likely to be lower going forward,
because of more investors willing and able to provide insurance for commodity producers.
This might be partially offset by a higher correlation of commodity future returns withequity markets, which should increase the required return for those providing the hedge.
We use a modest long-term commodity risk premium of 0.5% relative to cash. Note that
this is a geometric risk premium, and because of the high volatility of commodity futures, itsarithmetic return is still substantial (around 2.5%).
Recent research suggests there are factor premiums in commodity markets similar to
those that exist in credit and equity markets. The momentum and carry factor have been
documented by Erb and Harvey (2006), Gorton and Rouwenhorst (2006), Miffre and Rallis(2007) and Shen, Szakmary and Sharma (2007). The low volatility factor is in the spirit offindings by Miffre, Fuertes and Fernandez-Pérez (2015) and Frazzini and Pedersen (2014).
Blitz and De Groot (2014) also find that the case for factor premium investing carries over tothe commodity market. More specifically, they find that a commodity portfolio which simply
invests equal amounts in the various factor premiums achieves a significantly higher riskadjusted performance than a traditional commodity market portfolio, with much smaller
drawdowns.

1.13 Hedge funds
Table 1.7 shows historical excess returns for hedge funds of funds. We use the HFRI Fund ofFunds Composite Index which is net of all fees, equally weighted and includes over 600 funds.
Furthermore, it is broadly diversified across different hedge fund styles.
At first sight, hedge funds appear to show a reasonable performance with a net-of-fees
excess return over cash of 3.6% from 1990 to 2019. Since 2000, this has dropped to around
2%, though biases and the favorable equal weighting affect this figure. The academic
literature contains extensive information on biases in hedge fund indices, as shown in Table
1.8. However, estimates for the market portfolio of hedge funds are scarce. Funds of hedge
funds are often considered to be a good proxy for the market portfolio, since they have fewer
biases than typical hedge funds, but their returns are affected by the double counting ofmanagement fees. Fung and Hsieh (2000) estimate the portfolio management costs for atypical hedge fund of fund portfolio to be between 1.3% and 2.9%. There is no cheaper way toobtain exposure to this asset class.11
Taking all this into account, we believe Bekkers, Doeswijk, and Lam’s estimate (2009) tobe reasonable with an excess return over cash of 1.25%. Note that this is a combination of
possible manager skill and also the systematic exposures that hedge funds seem to have.

11. There are cheaper and more liquid so-called hedge
fund replication strategies available for investors.
We do not include these in our analysis, as they
are usually dynamic strategies using derivatives on
traditional asset classes.

Table 1.8: Biases in hedge fund databases
RobecoMagnitude

PeriodFung and Hsieh (2000)

Backfill

0.7%

1994-1998

Fung and Hsieh (2000)

Survivorship

1.4%

1994-1998

Backfill

2.3%

1996-2002

Survivorship

0.6%

1994-2001

Posthuma and Van der Sluis (2003)
Amin and Kat (2005)
Source: Robeco

Long-Term Expected Returns | 17

2

Economic
growth andfinancialmarkets
in a steadystate

18 | Long-Term Expected Returns

Long-term economic growth stems from increasing laborproductivity and changes in the potential labor force,emanating from cyclical swings in the unemployment rate.
Labor productivity and labor force growth also play animportant role in the earnings growth rate and thus in
financial returns for investors. So we will start by discussing
labor productivity and labor force growth rates and thenmove on to economic and earnings growth. We will conclude
with the theoretical implications this will have for equity andbond returns in the long-term steady state.

2.1 Labor productivity
Labor productivity in a mature economy grows between 1.5% and 2% per year. Productivity
gains can be determined by looking at the real growth in per capita gross domestic product(GDP). In the long run, this matches the increase in labor productivity, if we assume thatthe per capita hours worked remain constant. Apart from periods of significant unrest,
the speed of productivity growth has been remarkably gradual. According to data frommacroeconomist Angus Maddison covering a wider set of 20 Western countries, growthin per capita GDP averaged 1.9% in the period 1870 to 2008. Developing economies cantemporarily show higher labor productivity growth rates. For example, Japan experienced
an average increase of 3.8% between the end of World War II and 1980. However, as an
economy matures, it is harder to realize productivity gains. For example, in the period
1980 to 2015, Japan’s labor productivity increased by 1.5%, which is close to the gains of
1.6% seen in the US over this same period. Some developing countries have shown evenstronger growth rates. China has enjoyed an annual productivity gain of 6.6% since 1980
and India 4.5%. In contrast, Brazil has lagged with a modest gain of just 0.8%. Barro andUrsúa (2008) estimate an average historical growth rate for developing economies of 2.8%
over the period 1960-2006, 0.4% above the growth rate for mature economies over thatsame period. Please note that these numbers are average per capita real GDP growth rates,
and that there can be significant differences between different countries.
If history is a good proxy for what happens in the future, a 1.75% gain for mature economies
seems to be a good starting point. Some commentators such as Robert Gordon argue thatthe past two centuries of economic growth could actually just be ‘one big wave’ of dramaticchange rather than a new era of uninterrupted progress, and that the world is returning
to a regime in which growth is mostly of the extensive sort. The idea that technology-led
growth must either continue unabated or steadily decline, rather than ebbing and flowing,is at odds with history. Nevertheless, the last two centuries have been a ‘special’ period interms of population growth. And although it is difficult to make a link between population
growth and productivity, academic literature indicates a positive relationship which seems
logical to us. As we argue in the next paragraph, population growth will not track thestrong historical growth rates seen in the past and so we reduce the historical estimate to1.5% for our steady-state calculations.

2.2 Size of the labor force
The growth of the labor force has been an important stimulus for economic growth.
Projections from the United Nations show that population growth will gradually fall from
1.2% per year in 2015 to 0.2% per year in 2100. The graph below gives a breakdown of theactual and projected population and labor-force growth in developed regions up to 2100.
In most analyses, the labor force is defined as the population aged between 15 and 64
years old. If we apply this definition, we see labor force growth projections for developed
regions entering negative territory. However, we do not believe this definition is realistic.
As people are expected to live longer, we can expect the retirement age to increase. For
example, the life expectancy for a 65-year old living in 2015 is 19 years. For a 70-year old
living in 2075 this figure is 20 years. Assuming the retirement period stays the same, it isunlikely that you will be able to retire at 65 in 2075. We assume that the retirement age will
increase by 2/3 of the increase in life expectancy. Adjusting for this higher retirement age
and for the number of youngsters remaining in education longer, we arrive at an adjusted
labor force projection. This projection is remarkably close to 0% (see Figure 2.1).

Long-Term Expected Returns | 19

ECONOMIC GROWTH AND FINANCIAL MARKETS IN A STEADY STATE

Figure 2.1: Average population growth in developed regions
1.4%
1.2%
1.0%
0.8%
0.6%
0.4%
0.2%
0.0%
-0.2%
-0.4%
-0.6%
19511960
Population

19611970

19711980

19811990

Labor force (15-64)

19912000

20012010

20112020

20212030

20312040

20411950

20512075

20762100

Labor force (adjusted)

Source: United Nations, Robeco

The global labor-force growth projections will remain in positive territory. We calculate theaverage yearly increase to be 0.5% between 2020-2100. Much of the growth will take placein frontier markets. This global number will likely overstate the effect of population growthon financial markets as we believe we should give more weight to developed regions. For
this reason, we use 0.25% as an estimate for labor-force growth in our further analysis.

2.3 Economic growth, earnings growth and dividend growthBased on a productivity growth of 1.5% and a labor force growth of 0.25%, we end up witha steady-state growth rate of 1.75% for the world economy. The question is, how much ofthis growth will be translated into shareholder returns in the steady-state scenario. Much
depends on the assumptions we make on the level of dilution that occurs at the various
stages of transition between economic growth, earnings growth and actual returns.
The first form of dilution takes place at the earnings level and occurs right across the whole
economy. Earnings are diluted in the form of taxes, reducing the potential growth forshareholders. Looking at the economy as a whole, you can present this as a transfer fromthe profit to the non-profit part of the economy. As we are looking at the returns in a steadystate environment, it seems logical to assume that the net earnings growth will be equal
to the growth of the underlying economy. If this does not prove to be the case, it means
either that earnings are becoming a dominant factor for the economy as a whole (if net
earnings growth is consistently above economic growth), or that they have diminished to
nothing. The notion that net earnings growth should equal economic growth is the central
assumption taken in the literature.
The more relevant question here is: how much of the economy’s earnings growth is linked
to listed companies, as these form the basis for shareholders’ returns. It stands to reason
that the earnings growth available to shareholders in listed companies will be lower thanthat for non-listed companies. One reason is that listed companies are skewed towards theolder, less dynamic parts of the economy. The rapid start-up growth seen in new industries
mostly takes place outside the listed arena. More importantly, however, established listedcompanies issue new shares on a regular basis (either to finance acquisitions, or as part ofpayments schemes), which dilutes existing shareholders’ claim to the earnings growth. Thisis the second stage of dilution.

20 | Long-Term Expected Returns

So how is it possible that earnings growth for the economy as a whole is structurally higher
than it is for listed companies? Doesn’t this imply that listed companies are gradually
being marginalized? This would be true if the split between listed and not-listed companies
remained static, but of course this is not the case: successful companies normally eventually
opt for a listing. Having missed out on the first high-growth phase, equity investors will only
be able to tap into this new growth potential by rebalancing their portfolios.
One final point to address relates to the earnings and growth measures we should
compare. As we are interested to see how much GDP growth will ultimately feed throughto the equity investor, the logical measure for earnings would be earnings (or dividends)
per share, as this takes new share issuance into account and adjusts for the changing
composition of the general stock market. For the growth measure, real GDP seems to bea better option than per capita GDP: equity investors are not interested in what the directsource of growth is, but in the level of that growth. Most people seem to compare percapita GDP with earnings per share. But this seems to imply a link between ‘capita’ and‘share’ which we find difficult to see. So we stick to a comparison between real GDP growthand earnings (or dividends) per share.
So how big is this dilution effect? Literature on this subject is relatively scarce, but the most
relevant study was carried out by Bernstein and Arnott (2003). They find the dilution factor
to be as high as 80% for the period 1900-2000, based on data on dividend growth versus
real growth. To be more specific: equity investors only get 20% of the underlying earnings
growth seen in the economy. We do not think that this is a realistic conclusion. For one,
dividend payout ratios are far from static. Fundamental shifts in these and reforms in termsof tax treatment can lead to structural changes in the absolute and relative distribution
to investors. A decline in the payout ratio (as seen in the US) will result in lower dividend
growth, which is not related to dilution. Looking at data from the Shiller database, forexample, the dividend payout ratio for US stocks had steadily declined from around 80%
in the late 19th century to less than 40% at the start of the current century. Clearly this has
an impact on the dividend growth calculations. In recent years, a preference for increased
payouts to shareholders seems to indicate a reversal in this trend. We also have difficulty
reproducing the numbers given for the US. According to the Shiller database, real dividends
per share have risen by 1.3% annually, not the 0.6% Bernstein and Arnott present in theirpaper. Although this 1.3% is still way below the real GDP growth of 3.3%, if we were toadjust for the structural decline in the payout ratio, we would arrive at dividend growthof around 2.5%. Unfortunately, we have not been able to analyze other countries using
another dataset from a different source to compare the outcome with the results of theBernstein and Arnott study.
We have carried out an equity dilution analysis for the period 1871 to 2015 with earningsand dividend data from Robert Shiller’s website and economic growth data from
MeasuringWorth. Table 2.1 shows the compounded growth rates. Based on the US data, wefind a dilution factor of 50% compared to GDP growth. This is in line with research carriedout by Brightman (2012), who states that “Half of the growth in total corporate earnings
flows to new investors through the formation of new companies and new share issuanceby existing companies”. This means that we expect earnings for equity investors to rise
between 0.75% to 1% in the steady state.

Long-Term Expected Returns | 21

ECONOMIC GROWTH AND FINANCIAL MARKETS IN A STEADY STATE

Table 2.1: Dilution of earnings per share (EPS) and dividends per share (DPS) in the United States
Real

Dilution

PeriodSource

GDP

EPS

DPS

EPS

DPS

1900-2000

Robeco

3.3%

1.6%

1.3%

-52%

-60%

1871-2015

Robeco

3.4%

1.7%

1.5%

-50%

-55%

1900-2000

Bernstein and Arnott (2003)

3.3%

-

0.6%

-

-80%

Source: MeasuringWorth, Shiller, Robeco

Figure 2.2 presents a schematic overview of the theoretical building blocks for global
equity returns. The components are derived from the growth model developed by Gordon(1959), in which the expected equity returns are split between dividend income andcapital appreciation. As we assume no valuation changes in this steady-state equilibrium(meaning no structural P/E increases or decreases), the capital appreciation shouldbe equal to the real diluted earnings growth we calculated at the end of the previous
paragraph (P. growth = E. growth).

Figure 2.2: Schematic overview of the theoretical building blocks for global equity returns

Global long-term growthof labor productivity = 1.5%

Global growthof labor force = 0.25%

Global economic growth = potential dividend growth = 1.75%-/- dividend dilution through new economic activity = 0.75%

Dividend growth = 1%

Dividend income = 3%

Earnings yield = 6%
Part of earnings paid as dividends = 50%

Long-term inflation = 3%

Expected global equity return = 7%

Source: Robeco

This brings us to the second element of real returns: what is the equilibrium dividend
yield we can expect in the steady state? As it turns out, this is a key question, as numerous
reports underscore the importance of dividends in determining total return. Looking at
Shiller’s data, for example, the average (median) dividend yield for the US market over theperiod 1871 to 2015 was 4.4% (4.3%), comprising roughly two thirds of the real total returnof 6.8% over that period. Although this sounds high, when compared with other areas of
the world, the US is actually at the lower end of the scale. Dimson, Marsh and Staunton(2006) present a table with dividend yields for sixteen countries for the period 1900-2005.
This shows that the geometrical mean for the whole sample was 4.5%, compared to a total

22 | Long-Term Expected Returns

real excess return over cash of 5.0%. This figure is to a certain extent misleading as it isan average, where a country like Belgium has the same weight as one like the US. Still,there is no denying that dividend yields have played an important if not dominant role indetermining the overall level of returns.
So, what is the steady-state dividend yield? The way to assess this is to look at the payout
ratio (D/E; the percentage of earnings that is being paid out in the form of dividends) andthe earnings yield (E/P; the reversal of the P/E ratio). If you multiply these two yields you
get the dividend yield (D/P). Looking at the Shiller database, the average payout rate has
been 61%, while the median reached 58%. It is clear that these numbers have been inflatedby the very high payout ratios in the first half of the period: if we look at the period afterWorld War II, the average and median are 51%. This appears to be more in line with otherperiods, with average and median dividend payout ratios of 47% for the MSCI World since1970. The average earnings yield for the US since 1871 is 7.4% and the median is 6.8%.
Again, these numbers have been positively impacted by the first half of the sample: looking
at the postwar period, the average (7.0%) and median (6.0%) earnings yields are much
more in line with the longer-term averages we see for the world as a whole: since 1970
these figures for the MSCI World have been 6.5% and 5.9% respectively. Based on theseobservations we end up with an equilibrium dividend yield of 3 to 3.5%. If we combine thiswith the earlier ‘neutrally priced’ dividend yields, we feel that a dividend yield of 3% is a
prudent longer-term assumption.
It is easy now to derive the real return on equities. We add the dividend yield of 3% andthe dividend growth rate of 0.75 to 1% to arrive at a real return of close to 4% for global
equities.

2.4 Economic growth and interest rates
The nominal interest rate can best be seen as the sum of the real interest rate and the
expected rate of inflation (Fisher, 1930). Academic literature provides a link between
economic growth and real interest rates (Ramsey, 1928). Cornell (2012) describes a modelthat gives the expected risk-free interest rate as a function of time preference, per capita
consumption growth, aggregate risk aversion, and the volatility of per capita consumption
growth. Generally, higher economic growth is expected to lead to higher interest rates andvice versa. For example, assuming that higher economic growth leads to higher future
income and hence higher future consumption, a higher interest rate will be required todelay household consumption. If not, households will consume more today by borrowing
against expected future growth. To expand this example slightly, if expected growth isuncertain or households are risk averse, one would expect them to be more cautious about
increasing consumption today, which would lead to lower rates.
Rachel and Smith of the Bank of England (2015) provide a number of arguments for today’s
low interest rate environment. Most of these arguments can be incorporated into Cornell’s
model. For example, demographic changes have shifted weight from starters to employees
closer to retirement in most developed countries. This has three effects. First, consumption
growth is expected to decline as these employees have already experienced their biggest
real income increases in an earlier phase of their career; second, there will be more needfor consumption smoothing as retirement comes closer (i.e. time preference changes) andfinally risk aversion is expected to rise as people get older. All these factors lead to lower
interest rates. It should be noted that interest rates can rise again when the number of
elderly increases and the uncertainty about future consumption growth diminishes asincome (i.e. pension) becomes more certain.

Long-Term Expected Returns | 23

ECONOMIC GROWTH AND FINANCIAL MARKETS IN A STEADY STATE

For our steady-state estimate for nominal interest rates we need to look beyond today’s
market to establish what the expected rate will be in a world in equilibrium. Following
Cornell’s model, we first look at the historical compensation investors have demandedfrom real GDP growth (assuming this translates into consumption growth). We calculate
the historical compensation to be 90% of real per capita GDP growth for developed
markets. This implies that the expected real GDP per capita growth of 1.5% leads to a real
return on bonds close to 1.35%. We believe this estimate to be a good indication for futurecompensation with one exception. The compensation is calculated using a dataset which
is not in line with forward-looking demographics (see for example United Nations (2015)).
Rachel and Smith (2015) calculated that changing demographics would have a severe
impact on real rates, causing them to fall significantly. In looking to the future, we believe
this correction to be too high as the number of elderly will increase substantially leading
to higher interest rates. Depending on longevity and retirement age trends, the earlier
correction could reverse. However, we do not believe there will be a complete reversal andso we incorporate a small correction to the historical estimates leading to a real return of
1.25% (i.e. 80% capture of real per capita GDP). This lower figure is also consistent with ourbelief that there is a relatively lower risk associated with investing in government bonds,
than in investing in the growth of the real economy. Hence, there is a safety discount forinvesting in government bonds.
A real return of 4% for equities and 1.25% for government bonds, means that we expect
a steady-state excess return of 2.75%, which is at odds with the historically observed
excess return of 3.4% (see Table 1.5). It should be kept in mind though that this historicalexcess return figure is at least partly due to the fact that equities became more expensive
during the period in question. From a steady-state perspective, we do not expect this priceincrease to be repeated and it might in fact be reversed. This will lead to a lower excess
return on equities in our steady-state scenario.

2.5 Inflation
Most economic theories take a real (i.e. inflation-adjusted) perspective on economic
growth. Money is often seen as a unit which reflects the prices of goods, but which
carries no information in itself. There appears to be a growing consensus among central
banks that 2.0% is an optimal level of consumer price inflation and that this target is
not symmetrical. Deflation is generally considered to be a more serious threat that has
to be prevented at all costs. This suggests a bias towards maintaining a somewhat loose
monetary policy in a bid to err on the side of caution as illustrated by current circumstances.
Representatives of the International Monetary Fund have even advocated an inflation
target of 4.0%. All in all, we expect policymakers in a steady-state environment to actually
have a preference for a higher level of inflation than the stated target of below but close to
2.0%. We should also take into account the fact that an inflation overshoot in one year, willalmost certainly not be compensated by attempting an undershoot in later years, as thiswould increase deflationary risks. Finally, policy preferences have clearly shifted towards
growth enhancement, even at the cost of somewhat higher inflation (as has been theexperience in emerging markets). All in all, in our opinion, an inflation estimate in line withthe empirically observed 3.0% is not a bad one.

24 | Long-Term Expected Returns

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