Alternative Thinking | Q1 2022
Capital Market
Assumptions for
Major Asset Classes
Executive Summary
1 Historical comparison is based on a simpler methodology than main estimates, due to data availability;
methodology described in Appendix.
This article updates our estimates
of medium-term (5- to 10-year)
expected returns for major asset
classes. It also includes an analysis
that attempts to reconcile ever-
lower expected returns with
ever-higher realized returns, and
suggests practical strategic steps to
boost portfolio expected returns.
Selected estimates are summarized
in Exhibit 1. U.S. equity and bond
expected returns both moved
lower in 2021, while changes to
their global counterparts were
mixed. The expected real return of
a 60/40 portfolio remains around
2%, less than half its long-term
average of nearly 5% (since 19001).
Exhibit 1: Medium-Term Expected Real Returns for Liquid
Asset Classes
3.8 3.6
4.4 4.3
5.0 5.3
0.4 0.3 0.6 0.4
-0.5 -0.8 -1.0
-0.6
-1.5 -1.6
2.1 1.9
-4
-2
0
2
4
6
8
10
5
-1
0Y
E
xp
ec
te
d
Re
al
R
et
ur
n
%
Dec 2021Dec 2020
U.S.
Equities
Non-U.S.
Dev’d
Equities
Emerging
Market
Equities
U.S. HY
Credit
U.S. IG
Credit
U.S. 10Y
Treasuries
Non-U.S.
10Y Govt
Bonds
U.S.
Cash
Global
60/40
Source: AQR; see Exhibits 3-5 for details. Estimates as of December 31, 2021. “Non-U.S. developed
equities” is cap-weighted average of Euro-5, Japan, U.K., Australia, Canada. “Non-U.S. 10Y govt. bonds” is
GDP-weighted average of Germany, Japan, U.K., Australia, Canada. Error bars cover 50% confidence range,
based on analysis from the 2018 edition and adjusted for current expected volatilities. These are intended
to emphasize the uncertainty around any point estimates. Not only are the return forecasts uncertain, but
also any measures of forecast uncertainty are debatable. Forecasting requires humility at many levels.
Estimates are for illustrative purposes only, are not a guarantee of performance and are subject to change.
Not representative of any portfolio that AQR currently manages.
PSG
Portfolio Solutions
Group
Table of Contents
Contents
Introduction and Framework 3
Updated Estimates
Equity Markets 4
Government Bonds 5
Credit Indices 6
Commodities 6
Alternative Risk Premia 7
Private Equity and Real Estate 8
Cash 9
Revisiting “The 5% Solution” – and practical strategic steps to boost
portfolio expected returns 10
References 14
Appendix 15
Disclosures 16
About the Portfolio Solutions Group
The Portfolio Solutions Group (PSG) provides thought leadership to the broader investment
community and custom analyses to help AQR clients achieve better portfolio outcomes.
We thank Alfie Brixton, Pete Hecht, Thomas Maloney and Nick McQuinn for their work on this paper.
We also thank Antti Ilmanen for helpful comments.
Capital Market Assumptions for Major Asset Classes | 1Q22 3
Introduction and Framework
2 For a discussion of expected arithmetic (or simple) vs. geometric (or logarithmic, or compound) rates of return, see the 2018 edition.
3 We calculate the excess-of-cash return by subtracting an estimate of real cash return; this is effectively the return accessed by
hedged investors irrespective of their base currency. Unhedged USD estimates are shown in the Appendix; other currencies available
on request.
For the past eight years we have published
our capital market assumptions for major
asset classes, with a focus on medium-term
expected returns (see 2014, 2015, 2016, 2017,
2018, 2019, 2020 and 2021). Each year, as
well as the updated estimates, we provide
additional analysis in the form of new asset
classes or other new material. This year’s
article includes an application of our CMA
framework to understand realized stock
and bond returns over the past decade,
and suggests several practical steps to raise
expected returns over the next ten years.
As usual, we present local real (inflation-
adjusted) annual compound rates of return2
for a horizon of 5 to 10 years. Over such
intermediate horizons, starting valuations
tend to be useful inputs. For multi-
decade forecast horizons their impact is
diluted, so theory and long-term historical
averages may matter more in judging
expected returns. At shorter horizons,
returns are largely unpredictable and any
predictability has tended to mainly reflect
momentum and the macro environment.
Our estimates are intended to assist investors
with setting medium-term expectations.
They are highly uncertain, and not intended
for market timing. The frameworks we
present may be more informative than the
numbers themselves. As one cautionary
example, the error ranges shown in Exhibit 1,
based on historical analysis in the 2018
edition, suggest there is a 50% chance that
realized equity market returns over the
next 10 years will under- or overshoot our
estimates by more than 3% per annum.
Since we started publishing our CMAs in
2014, estimates for both stocks and bonds
have moved lower due to richening valuations
(see Exhibit 2). All assets’ expected real
returns remain depressed by exceptionally
low real cash rates, but expected premia
over cash are nearer normal levels.3
Exhibit 2: Expected Real Returns for Liquid Asset Classes
Dec-2013 to Dec-2021
-2%
-1%
0%
1%
2%
3%
4%
5%
6%
7%
2014 2015 2016 2017 2018 2019 2020 2021 2022
5
-1
0Y
E
xp
ec
te
d
R
ea
l R
et
ur
n
Emerging Market Equities
Non-U.S. Developed Equities
U.S. Equities
U.S. HY Credit
U.S. IG Credit
U.S. 10Y Treasuries
Non-U.S. 10Y Govt Bonds
Source: AQR; see Exhibits 3-5 for details. “Non-U.S. developed equities” is cap-weighted average of Euro-5, Japan, U.K., Australia,
Canada. “Non-U.S. 10Y govt. bonds” is GDP-weighted average of Germany, Japan, U.K., Australia, Canada. Estimates are based on current
methodologies, are for illustrative purposes only, are not a guarantee of performance and are subject to change. Not representative of any
portfolio that AQR currently manages.
4 Capital Market Assumptions for Major Asset Classes | 1Q22
Equity Markets
4 See the 2017 edition and its online appendix for details and discussion of the methodology.
5 See the 2015 edition for a discussion of mean reversion in stock and bond valuations, and our decision to exclude it. Our analysis
suggests the timing of any mean reversion is difficult to forecast, and there are plausible arguments for yields remaining below
historical levels.
6 For our earnings-based estimate, we apply a 50% payout ratio to all countries, and use g = 1.5% for all countries except for emerging
markets, where we use a higher growth rate of 2%. Adjusted Shiller EP is Shiller EP * 1.075 where the scalar accounts for average
earnings growth during the 10-year earnings window of the Shiller EP.
Our starting point for equities is the dividend
discount model, under which expected real
return is approximately the sum of dividend
yield (DY), expected trend growth (g) in real
dividends or earnings per share (EPS), and
expected change in valuation (∆v), that is:
E(r) ≈ DY+g+∆v. We take the average of two
approaches,4 described below. We assume no
mean reversion in valuations.5
1. Earnings-based: We start from the inverse
of the CAPE ratio (cyclically-adjusted P/E),
which is 10-year average inflation-adjusted
earnings divided by today’s price. We multiply
by 0.5 (roughly the U.S. long-run dividend
payout ratio), and add real earnings growth of
1.5% (roughly the U.S. long-run average). So
earnings-based expected return6 is: E(r) ≈ 0.5*
Adjusted Shiller E/P + gEPS
2. Payout-based: We estimate net total payout
yield (NTY) as the sum of current dividend
yield and smoothed net buyback yield. To this
we add an estimate of long-term real growth of
aggregate payouts that includes net issuance.
This growth estimate, gTPagg, is an average
of smoothed historical aggregate earnings
growth and forecast GDP growth. So our
payout-based expected return is: E(r) ≈ NTY +
gTPagg, where NTY = DY + net buyback yield (NBY)
Our estimates saw mixed changes in 2021 (see
Exhibit 3), with U.S. and global real return
estimates falling slightly as markets richened.
The U.S. estimate is very low by historical
standards.
Exhibit 3: Expected Local Returns for Equities
December 2021
1. Earnings-Based 2. Payout-Based Combined =
Excess-
of-Cash
Return
Adjusted
Shiller EP
0.5 * EP
+ gEPS
Dividend
Yield NBY gTPagg
DY+NBY
+ gTPagg
Real
Return
1yr
Change
U.S. 2.8% 2.9% 1.3% 0.2% 2.7% 4.2% 3.6% -0.2% 5.1%
Eurozone 4.0% 3.5% 2.2% -0.3% 2.5% 4.4% 3.9% -0.2% 5.8%
Japan 4.6% 3.8% 2.1% 0.2% 2.3% 4.6% 4.2% +0.0% 5.1%
U.K. 5.6% 4.3% 3.6% -0.2% 2.4% 5.8% 5.1% -0.1% 6.9%
Australia 4.4% 3.7% 4.0% -0.4% 2.8% 6.4% 5.1% +0.5% 6.3%
Canada 4.1% 3.6% 2.7% -0.9% 2.7% 4.4% 4.0% -0.2% 5.2%
Global Developed 3.2% 3.1% 1.6% 0.1% 2.7% 4.4% 3.7% -0.2% 5.3%
Global Dev. ex U.S. 4.5% 3.7% 2.6% -0.2% 2.5% 4.9% 4.3% -0.1% 5.8%
Emerging Markets 6.6% 5.3% 2.4% -- 2.9% 5.3% 5.3% +0.3% 4.4%
Source: AQR, Consensus Economics and Bloomberg. Estimates and methodology subject to change and based on data as of December 31,
2021. See main text above for methodology. For earnings yield, U.S. is based on S&P 500; U.K. on FTSE 100 Index; Eurozone is a cap-
weighted average of large-cap indices in Germany, France, Italy, Netherlands and Spain; Japan is Topix Index; and “Emerging Markets” is MSCI
Emerging Markets Index. Net buyback yield is past 10-year average. For payout-based estimates, all countries are based on corresponding
MSCI indices. “Global Developed” is a cap-weighted average. For emerging markets, payout-based estimate is dividend yield + forecast GDP
per capita growth. Excess-of-cash return is calculated by subtracting real cash return estimates described later in the article. Hypothetical
performance results have certain inherent limitations, some of which are disclosed in the back. Estimates are for illustrative purposes only, are
not a guarantee of performance and are subject to change. Not representative of any portfolio that AQR currently manages.
Capital Market Assumptions for Major Asset Classes | 1Q22 5
Government Bonds
7 If we assumed a more realistic random-walk (rather than unchanged) yield curve, our estimate would theoretically need to include
convexity and variance drag components (see footnote 9). However, since these terms are small and mostly offsetting for
concentrated bond portfolios, we ignore them here.
Government bonds’ prospective medium-
term nominal total returns are strongly
anchored by their yields. The so-called rolling
yield measures the expected return of a
constant-maturity bond allocation assuming
an unchanged yield curve.7 For example, a
strategy of holding constant-maturity 10-year
Treasuries has an expected annual (nominal)
return of 1.8%, given the starting yield of
1.5% and expected capital gains of 0.3% from
rolldown as the bonds age. Exhibit 4 shows
current local rolling yields for six countries,
converted to local real returns by subtracting a
survey-based forecast of long-term inflation.
We also show expected excess-of-cash returns,
which are effectively the expected returns
accessed by hedged investors irrespective
of their base currency. While real returns
are often the appropriate unit for assessing
expectations versus investment objectives,
excess-of-cash returns are more relevant for
making international allocation decisions, and
for investors with access to leverage.
During 2021, our U.S. estimate fell as higher
yields were offset by a flatter curve and higher
expected inflation. Most other countries’
estimates increased slightly, but remain in
negative territory. Low bond yields should be
considered in the context of exceptionally low
cash rates – indeed, all excess-of-cash returns
are positive. Any adjustment to these expected
returns boils down to expected future changes
in the yield curve level or shape. Capital
gains/losses due to falling/rising yields
dominate returns over short horizons but are
highly uncertain, and matter less over longer
horizons.
Exhibit 4: Expected Local Returns for Government Bonds
December 2021
Y RR I Y + RR - I
Excess-
of-Cash
Return
10-Year Nominal
Bond Yield
Rolldown
Return
10-Year Forecast
Inflation
Expected
Real Return
1yr
Change
U.S. 1.5% 0.3% 2.6% -0.8% -0.3% 0.8%
Japan 0.1% 0.4% 0.8% -0.3% +0.0% 0.5%
Germany -0.2% 0.5% 2.0% -1.7% +0.2% 0.7%
U.K. 1.0% 0.4% 2.5% -1.2% +0.2% 0.7%
Canada 1.4% 0.3% 2.2% -0.4% +0.3% 0.8%
Australia 1.7% 0.7% 2.3% 0.0% +0.3% 1.2%
Global Developed 1.1% 0.4% 2.2% -0.7% -0.1% 0.8%
Global Developed ex U.S. 0.5% 0.6% 1.7% -0.6% +0.4% 0.9%
Source: Bloomberg, Consensus Economics and AQR. Estimates as of December 31, 2021. “Global Developed” and “Global Developed ex
US” are GDP-weighted averages. Rolldown return is estimated from fitted yield curves and based on annual rebalance. Excess-of-cash
return is calculated by subtracting real cash return estimates described later in the article. Estimates are for illustrative purposes only, are
not a guarantee of performance and are subject to change. Not representative of any portfolio that AQR currently manages.
6 Capital Market Assumptions for Major Asset Classes | 1Q22
Credit Indices
8 Consistent with Giesecke et al. (2011) and Ben Dor et al. (2021), who find that over the long term, the average credit risk premium is
roughly half the spread. ‘Bad selling’ refers to the practice of selling bonds that no longer meet the rating or maturity criteria of the index.
9 These terms, both related to volatility, are not as closely offsetting for broad indices as they are for single bonds, due to diversification
effects. Briefly, the convexity term estimates the impact of non-linearities assuming yields will change, while the variance drag term
estimates the impact of compounding effects assuming return volatility will be non-zero.
10 Exhibit 5 shows spreads for Bloomberg Barclays cash bond indices. Synthetic indices (Markit North America CDX) have tended to have
somewhat tighter spreads (but during 2021 this basis was near zero). For EM debt we use US HY OAS rolldown due to data limitations.
11 For more details see the 2016 edition, Levine, Ooi, Richardson and Sasseville (2018), and the AQR data library.
12 From February 1975 to December 2021, an investment in gold futures delivered around 1% real return, approximately the same as cash.
To estimate expected real returns for credit
indices, we first apply a haircut of 50% to both
IG and HY spreads to represent the combined
effects of expected default losses, downgrading
bias and bad selling practices.8 We assume no
change in the spread curve, say, through mean
reversion. We add the expected real yield of a
duration-matched Treasury, and rolldown from
both Treasury and spread curves. Finally, we
include corrections for convexity and variance
drag.9 Exhibit 5 shows our updated estimates for
U.S. credit indices10 and hard-currency emerging
market sovereign debt. Estimates for U.S. credit
fell slightly in 2021, with higher Treasury yields
offset by narrower spreads. The HY-IG spread
remains narrow (HY’s modest spread advantage
over IG is offset by its lower Treasury yield,
rolldown and convexity).
Exhibit 5: Expected Returns for Credit Indices
December 2021
A. Spread
Return
B. Treasury
Real Yield
C. Rolldown
Return
D. Convexity &
Variance
OAS * 0.5 Y - I RT+RC C - V
Expected Real
Return A+B+C+D
1yr
Change
Excess-of-
Cash Return
U.S. IG 0.5% -1.2% 0.6% 0.5% 0.4% -0.2% 1.9%
U.S. HY 1.4% -1.2% 0.2% -0.1% 0.3% -0.2% 1.8%
EM HC Debt 1.7% -1.1% 0.4% 0.5% 1.4% +0.2% 3.0%
Source: Bloomberg, AQR. Estimates as of December 31, 2021. OAS and duration data are for Bloomberg Barclays U.S. Corporate
Investment Grade (IG), U.S. Corporate High Yield (HY) and Emerging USD Sovereign (EM HC Debt) Indices. Index durations are 8.7 years,
3.9 years and 8.8 years respectively. Excess-of-cash return is calculated by subtracting real cash return estimates described later in the
article. Estimates are for illustrative purposes only, are not a guarantee of performance and are subject to change. Not representative of
any portfolio that AQR currently manages.
Commodities
Commodities do not have obvious yield
measures, and we find no statistically significant
predictability in medium-term returns (see
the 2016 edition). Our estimate of 5- to 10-year
expected return is therefore simply the long-run
average return of an equal-weighted portfolio of
commodity futures. This portfolio has earned
about 3% geometric average excess return over
cash since 1877, and a similar return if measured
since 1951.11 We add a (negative) U.S. real cash
return to give our expected real return of 1.4%.
Gold has attracted attention recently, as it
is often viewed as an inflation hedge. We do
not have medium-term return estimates for
individual commodities but would expect gold
to have a substantially lower risk-adjusted return
than a diversified basket over the long term.12
A gold investment has indeed exhibited useful
tail-hedging properties, but arguably it lacks
the premium associated with growth-sensitive
commodities, and it forgoes the considerable
diversification found within the broader asset
class.
Capital Market Assumptions for Major Asset Classes | 1Q22 7
Alternative Risk Premia
13 Style-tilted strategies exhibit many design variations. Our estimates are purely illustrative and do not represent any AQR product or
strategy.
14 Consistent with historical data, we assume low correlations between the styles to produce our Sharpe ratio range for a diversified
composite of long/short styles. As transaction costs depend on implementation and both transaction costs and fees vary with target
volatility, our estimates are based on a transaction-cost-optimized strategy targeting 10% volatility with fees of 1 to 1.5%. Refer to
the 2015 edition for details of our style premia assumptions, which we believe are plausible and conservative. All assumptions are
purely illustrative and do not represent any AQR product or strategy.
15 See Israel, Jiang and Ross (2017), “Craftsmanship Alpha: An Application to Style Investing”.
16 See Asness, Chandra, Ilmanen and Israel (2017), “Contrarian Factor Timing Is Deceptively Difficult”.
17 See Cliff’s Perspective blog, “That’s It, That’s the Blog”, December 2021.
Style-Tilted Long-Only Portfolios
We believe a hypothetical value-tilted,
diversified long-only equity portfolio that is
carefully implemented and reasonably priced
may be assumed to have an expected real
return 0.5% higher than the cap-weighted
index, after fees, with 2-3% tracking error.
An integrated multi-style strategy — which
we assume to include balanced allocations
to value, momentum and defensive styles
— may achieve a higher expected net active
return of around 1% at a similar tracking
error. Finally, we think a defensive or low-risk
equity portfolio may be assumed to have an
expected return similar to that of the relevant
cap-weighted index, but may achieve this
with lower volatility.13 These are long-term
estimates – we discuss tactical considerations
below.
Long/Short Style Premia
Alternative risk premia strategies apply similar
tilts as long-only smart beta strategies, but in
a market-neutral fashion and often in multiple
asset classes. Because long/short strategies
can be invested at any volatility level, it makes
sense to focus on expected Sharpe ratios. The
degree of diversification is essential. A single
long/short style applied in a single asset class
might have an expected Sharpe ratio of only
0.2-0.3. For a diversified composite, we believe
an expected Sharpe ratio of 0.7-0.8, net of
trading costs and fees, can be feasible when
multiple styles are applied in multiple asset
classes. At a target volatility of 10%, such a
hypothetical portfolio would have an expected
return of 7-8% over cash.14 We stress that this
requires careful craftsmanship in portfolio
construction as well as great efficiency in
controlling trading, financing and shorting
costs.15 Strategies that are less well-designed
or poorly implemented may have much lower
expected returns.
Current valuations
Aggregate valuations across multiple
styles are near long-term averages. Among
individual styles, the equity defensive style
has cheapened after appearing rich for many
years, while the equity value style continues to
look extremely cheap, despite a performance
rebound in 2021. Indeed, spreads between
value and growth stocks are now comparable
to their previous peak during the Dotcom
Bubble. Our research suggests there is quite
a weak link between the value spreads of
style factors and their future returns, making
it difficult to use tactical timing based on
valuations to outperform a strategic multi-
style portfolio.16 However, we believe the
current extreme cheapness of value warrants
an overweight to that style in multi-factor
strategies.17
8 Capital Market Assumptions for Major Asset Classes | 1Q22
Private Equity and Real Estate
18 See Ilmanen, Chandra and McQuinn (2020) for a detailed discussion of the framework, our input choices, and the sources, as well as
a literature review. Strictly speaking, the framework applies to the current vintage rather than the entire PE market. This paper also
discusses the theoretical rationales and historical average returns to assess expected PE returns.
19 See the 2019 edition for details of this alternative method.
20 See Ilmanen, Chandra and McQuinn (2019) for full details of our methodology and assumptions.
Illiquid assets are inherently harder to model
than public markets, and this is exacerbated
by a lack of good quality data. Nevertheless,
in recent years we extended our discounted-
cashflow-based approach into the illiquid
realm and we update these estimates below.
For private equity (PE) our estimate is for U.S.
buyout funds. We present net-of-fee expected
returns, as fees are a substantial component of
returns for illiquid assets. Each of our inputs is
debatable, as data limitations necessitate lots
of simplifying assumptions, and each input
can substantially affect the final estimate.
Exhibit 6 illustrates our framework and
current inputs.18 First, we estimate unlevered
ER using the DDM: E(r) ≈ yU + gU, where yU =
unlevered payout yield and gU = real earnings-
per-share growth rate. Then, we estimate
the levered return by applying leverage and
the cost of debt, and finally we add expected
multiple expansion and subtract fees.
Our yield-based real return estimate is 5.9%
net of fees, higher than last year due to higher
leverage and lower cost of debt. An alternative
approach, which applies simple size and
leverage adjustments to a public proxy and
assuming zero net alpha, generates a lower
estimate of 5.5%.19 Taking a simple average of
the two approaches gives a final estimate of
5.7%, compared to our U.S. large cap equity
estimate of 3.6%.
Exhibit 6: Expected Real Returns for U.S. Private Equity
yu gu
ru = yu
+ gu D/E kd
rl = ru +
(D/E) *
(ru - kd) m
rg = rl
+ m f rn = rg - f
Income
Yield
Real
Growth
Rate
Real
Return
Debt to
Equity
Real Cost
of Debt
Levered
Real
Return
Multiple
Expansion
Gross
Real ER Fees
Net Exp.
Real
Return
1yr
Change
U.S. PE 2.0% + 3.0% = 5.0% 103% 0.0% 10.1% + 0.8% = 10.9% 5.0% = 5.9% +1.2%
Source: AQR, Pitchbook, Bloomberg, CEM Benchmarking. Estimates as of September 30, 2021. Strictly speaking, our inputs are log
returns and should be converted to simple returns before leverage is applied, then converted back to log returns. This ‘round-trip’ has
only a small impact, so we omit it here. For real cost of debt we apply a floor at 0%. Estimates are for illustrative purposes only, are not a
guarantee of performance and are subject to change. Not representative of any AQR product or strategy.
We estimate expected returns for unlevered
U.S. direct real estate (RE) as represented by
the NCREIF indices. We caveat that returns
for individual RE funds can vary vastly from
the industry average (this is also true of PE).
As with our DDM-based approach for equities,
we sum payout yield and expected long-term
growth rate.20 Exhibit 7 shows a slight rise in
our expected real return for RE (unlevered to
make it comparable to the unlevered returns
reported by NCREIF) to 2.6%.
LeverageUnlevered Levered
Capital Market Assumptions for Major Asset Classes | 1Q22 9
Exhibit 7: Expected Real Returns for U.S. Private Real Estate
NOI C ≈ NOI / 3 CF ≈ NOI - C g ER = CF + g

NOI
Yield
Capital
Expenditure
Cashflow
Yield
Real
Growth
Unlevered Real
Return
1yr
Change
U.S. Real Estate 3.9% 1.3% 2.6% 0.0% 2.6% +0.1%
Source: AQR, NCREIF Webinar Q3 2021. Estimates as of September 30, 2021. Estimates are for illustrative purposes only, are not a
guarantee of performance and are subject to change. Not representative of any AQR product or strategy.
Cash
21 Survey-based forecasts from Consensus Economics point to cash rates 50-100bps higher than our market-based estimates, as well
as higher bond yields, as they have for many years. But we find no evidence that estimates based on survey data have been more
accurate than our market-based assumptions.
As discussed in the 2020 edition, our yield-
based cash return assumption is a weighted
average of current short-term and long-term
yields. We are effectively averaging between
the pure expectations and pure risk premium
hypotheses. Giving a larger weight to the
10-year yield implies market rate expectations
explain a larger portion of the yield curve slope
than the required term premium, a conjecture
arguably justified by relatively low inflation
uncertainty and the role of forward guidance
from central banks.
Exhibit 8 shows real cash return estimates
were little changed during 2021 (after sharp
falls in 2020), remaining negative for all major
markets. If expected returns for equities and
bonds are low, they are even lower for cash –
and this important fact will be true for almost
any methodology.21
Exhibit 8: Expected Local Real Returns for Cash
December 2021
S L I (L*2/3 + S*1/3) - I
3-Month Yield 10-Year Yield 10Y Forecast Inflation
Expected Real
Cash Return
1yr
Change
U.S. 0.0% 1.5% 2.6% -1.6% -0.1%
Japan -0.1% 0.1% 0.8% -0.8% +0.0%
Germany -0.7% -0.2% 2.0% -2.4% +0.0%
U.K. 0.1% 1.0% 2.5% -1.8% +0.2%
Australia 0.0% 1.7% 2.3% -1.2% +0.4%
Canada 0.2% 1.4% 2.2% -1.2% +0.3%
Source: Bloomberg, Consensus Economics and AQR. Estimates as of December 31, 2021. Estimates are for illustrative purposes only,
are not a guarantee of performance and are subject to change. Not representative of any portfolio that AQR currently manages.
10 Capital Market Assumptions for Major Asset Classes | 1Q22
Revisiting “The 5% Solution” – and
practical strategic steps to boost
portfolio expected returns
Mea culpa – dusting off a decade-old paper
22 Asness and Ilmanen, Institutional Investor May 2012.
Ten years ago we published an article titled
The Five Percent Solution22 that lamented the
impact of low yields on expected real returns,
and proposed unconventional solutions. We
wrote: “Current market yields and valuations
make it very unlikely that traditional
allocations will achieve 5 percent real return
in the next five to ten years.” Using simpler
versions of the measures presented in these
pages, we said the expected real return for a
U.S. 60/40 portfolio was 2.4%. How did that
prediction work out?
During the decade from January 2012 to
December 2021, that U.S. 60/40 portfolio
delivered not 5% but a stunning 8.5% annual
real return (6.8% for a global equivalent). How
did that happen, and does it invalidate our
yield-based approach to estimating medium-
term returns?
Reconciling ever-lower expected returns to ever-higher realized returns
The main story is that rich markets got richer.
The U.S. Shiller CAPE started the period at
20.5 (already the 79th percentile historically)
and almost doubled to 39 by the end of it (99th
percentile). The 10-year Treasury yield started
at 1.9% – its lowest ever at the time – and
defied many confident predictions of rises
to end the period slightly lower. Global bond
yields saw more substantial falls.
Exhibit 9 shows how the 60/40 portfolio
delivered that 8.5% return given its 2.4%
starting yield. The largest contributor to the
‘unexpected return’ or forecast error was
equity richening (4.1%), followed by faster
than expected EPS growth (1.5%). Realized
inflation matched the 2.2% forecast.
Exhibit 9: Forecasts as of December 2011 vs. Subsequent Realized 10-Year Returns
4.0% 2.4%
6.6%
4.1%
2.5%
1.5%
14.0%
-0.1%
8.5%
-5%
0%
5%
10%
15%
U.S. Equities U.S. Treasuries U.S. 60/40A
nn
ua
liz
ed
R
ea
l R
et
ur
n
Yield-based forecast Valuation change EPS growth error Inflation error Unattributed error
U
ne
xp
ec
te
d
R
et
ur
n
Source: AQR. Realized returns are calculated for period January 1, 2012 to December 31, 2021. Yield-based forecasts are based on
simple methodology as described in the Appendix. Valuation change is annualized change in CAPE ratio for equities and annualized
return impact of yield change for Treasuries. EPS growth error is realized annualized real EPS growth minus starting assumption of
1.5%. Inflation error is average realized inflation minus forecast. Unattributed error is error not accounted for by these components. For
illustrative purposes only. Not representative of any portfolio that AQR currently manages.
Capital Market Assumptions for Major Asset Classes | 1Q22 11
As we emphasized in another paper a few
years later, Market Timing: Sin a Little, market
valuations can drift for long periods, and it’s
hard to judge fair value in real time. This is
why we assume no mean reversion in our
estimates (forecasts that do assume mean
reversion have suffered even larger errors).
Even so, any richening or cheapening will tend
to send expected returns (informed by starting
valuations) and realized returns in opposite
directions.
What would have to happen for 60/40 to deliver 5% real over the next 10 years?
Our CMA framework allows us to break
down and quantify what needs to happen
for markets to defy “low expected returns”
gloomsters like us yet again. Here is one
possible (if unlikely) scenario:
• Equities deliver 7.9% real return, instead of
our forecast 3.6%
— Market richens another 20%, Shiller
CAPE exceeding Tech bubble peak
(worth 1.9% pa)
— Real EPS growth is 3.9% instead of
assumed 1.5% (worth 2.4% pa)
• Bonds deliver 0.6% real return instead of
our forecast -0.8%
— Yields fall 100bps from current levels,
with U.S. 10-year yield at 0.5% (worth
0.8% pa)
— Inflation averages 2% instead of the
forecast 2.6% (worth 0.6% pa)
Exhibit 10 illustrates this rosy scenario. Some
investors may plausibly believe the 2020s will
be a decade of ever-rising valuations, strong
growth and low inflation. If so, traditional
portfolios could perform strongly again. If
not – and of course the pink arrows in the
chart can also go in the other direction – what
changes to strategic asset allocation could
improve portfolio expected returns in the
current yield environment? We turn to this
question in our final section.
Exhibit 10: Possible Scenario for Unexpected Returns, Delivering 5% Real in the
Next 10 Years
3.6%
1.8%
1.9%
1.1%
2.4%
1.4%
7.9%
0.6%
5.0%
-1%
1%
3%
5%
7%
9%
U.S. Equities U.S. Treasuries U.S. 60/40
A
nn
ua
liz
ed
R
ea
l R
et
ur
n
Yield-based forecast Valuation change EPS growth error Inflation error
U
ne
xp
ec
te
d
R
et
ur
n
Source: AQR. Yield-based forecasts are as described earlier in this article. For illustrative purposes only – this scenario is not a forecast.
Striped fill indicates positive valuation change fully offsets negative forecast. Not representative of any portfolio that AQR currently
manages.
12 Capital Market Assumptions for Major Asset Classes | 1Q22
The 4% solution? Practical strategic
steps to boost portfolio expected returns
23 For example, the bond and commodity additions described above can be approximately replicated without any direct leverage, using a
35% allocation to a risk parity strategy targeting 10% volatility, funded mainly from bonds and partly from equities.
We now consider several incremental changes
that could, according to the assumptions
presented in these pages, raise the expected
return of a traditional portfolio without a
material impact on portfolio risk. The three
steps are illustrated in Exhibit 11.
Step 1 begins with a factor tilt. Specifically,
we reallocate half of the 60% (cap-weighted)
equity allocation to defensive equities.
According to our assumptions (and supported
by a raft of evidence) this may be expected to
maintain the expected return while reducing
portfolio risk, providing a risk budget for our
other enhancements. At the same time, we
apply modest leverage to the bond allocation,
adding another 40% of NAV to our bond
exposure. This takes advantage of positive
risk premia and improves the portfolio’s risk
balance.
Step 2 adds a 10% commodity allocation in
the form of a derivatives overlay. This brings
portfolio risk back up to where it started,
and adds another positive risk premium that
has tended to be especially diversifying in
inflationary scenarios.
Finally, Step 3 adds an allocation to
diversifying dynamic strategies. These could
include alternative risk premia (ARP), trend
following, global macro and others. We use our
ARP assumption as a proxy.
Exhibit 11: Practical Steps That May Increase Portfolio Expected Return
10%
10%
10%
0%
40%
80%
120%
160%
Global 60/40 Step 1
Allocate to Defensive
Equities, Add Bonds
Step 2
Add Commodities
Step 3
Add Diversifying
Liquid Alternatives
C
ap
it
al
A
llo
ca
ti
on
Global Equities Global Defensive Equities Global IG Fixed Income Commodities Liquid Alternatives
60%
30% 30% 30%
30% 30% 30%
40%
80% 80% 80%
Source: AQR. For illustrative purposes only. Not representative of any portfolio that AQR currently manages.
The role of leverage: These steps are designed
to combine better diversification with the use of
moderate leverage to convert that diversification
into higher expected returns. For investors unable
or unwilling to use direct leverage in this way (even
via derivatives), a similar effect can be achieved
using delegated leverage in strategies such as risk
parity.23 Some investors pursue higher returns
via levered equity exposure (private equity). This
approach can also help improve diversification if it
is combined with a dollar tilt away from equities to
fund diversifying strategies. We believe investors
should be wary of raising expected returns simply
by adding to their portfolio’s dominant risk.
Capital Market Assumptions for Major Asset Classes | 1Q22 13
Exhibit 12 shows the impact on expected real
return and risk. According to our assumptions,
these diversifying steps raise the expected
real return from 2% to almost 4%, at a similar
level of risk. To achieve 5% real return in this
environment, investors may have to accept a
higher level of risk. The alternative is to increase
savings and accept lower returns for their
investments. These unpalatable choices may be
an unavoidable consequence of pervasive low
riskless real rates.
Exhibit 12: Impact of Proposed Steps, According to Our Assumptions
2.0%
2.6%
3.0%
3.7%
0%
2%
4%
6%
8%
10%
0%
1%
2%
3%
4%
Global 60/40 Step 1
Allocate to Defensive
Equities, Add Bonds
Step 2
Add Commodities
Step 3
Add Diversifying
Liquid Alternatives
V
olatility
Re
al
R
et
ur
n
Real Return Volatility
Source: AQR. Real returns are based on assumptions described herein. Volatilities are based on monthly historical data since January
1990. For illustrative purposes only. Not representative of any portfolio that AQR currently manages.
The solutions outlined above are very similar
to those prescribed in our paper a decade ago:
use financial tools to embrace and monetize
diversification across many sources of returns.
Back then, we added recommendations for careful
portfolio construction and risk management, and
rigorous cost control. Those also apply today.
Maybe the next 10 years will see a continuation
of the recent golden era for traditional portfolios,
with all the inputs to our return estimates once
again surprising on the upside, and we’ll be writing
another mea culpa in 2032. But we wouldn’t bet
on it.
14 Capital Market Assumptions for Major Asset Classes | 1Q22
References
Asness, C. and A. Ilmanen, 2012, “The Five Percent Solution,” Institutional Investor.
Asness, C., A. Ilmanen and T. Maloney, 2017, “Market Timing: Sin a Little,” Journal of Investment
Management, 15(3), 23-40.
Asness, C., S. Chandra, A. Ilmanen and R. Israel, 2017, “Contrarian Factor Timing Is
Deceptively Difficult,” Journal of Portfolio Management Special Issue.
Ben Dor, A., A. Desclée, L. Dynkin, J. Hyman and S. Polbennikov, 2021, “Systematic Investing
in Credit,” Wiley.
Giesecke, K., F. Longstaff, S. Schaefer and I. Strebulaev, 2011, “Corporate Bond Default Risk: A
150 Year Perspective,” Journal of Financial Economics, 102, 233-250.
Ilmanen, A., S. Chandra and N. McQuinn, 2020, “Demystifying Illiquid Assets: Expected
Returns for Private Equity,” Journal of Alternative Investments, 22(3).
Ilmanen, A., S. Chandra and N. McQuinn, 2019, “Demystifying Illiquid Assets: Expected
Returns for Real Estate,” AQR white paper.
Israel, R., S. Jiang and A. Ross, 2017, “Craftsmanship Alpha: An Application to Style Investing,”
Journal of Portfolio Management Multi-Asset Strategies Special Issue.
Levine, A., Y. Ooi, M. Richardson and C. Sasseville, 2018, “Commodities for the Long Run,”
Financial Analysts Journal, 74(2).
Capital Market Assumptions for Major Asset Classes | 1Q22 15
Appendix
Translating Local Real Returns to Expected Total Returns for a Given Base Currency
In the rest of this paper we report local real and excess-of-cash returns. In Exhibit A1 we
translate these into nominal arithmetic returns by adding local expected inflation and variance
drag terms. We also quote unhedged U.S. dollar estimates for non-U.S. equities, in line with
common investing practice. Currency return assumptions are based on expected inflation
differentials. Expected returns for other base currencies are available on request.
Exhibit A1: Expected Total Nominal Arithmetic Returns for a U.S. Dollar Investor
7.3%
8.4%
10.2%
2.9% 3.0%
1.8%
2.5%
1.0%
5.3%
0%
2%
4%
6%
8%
10%
12%
U.S.
Equities
Non-U.S.
Equities
Unhedged
Emerging
Market
Equities
Unhedged
U.S. HY U.S. IG U.S.
Treasuries
Non-U.S.
Treasuries
Hedged
U.S.
Cash
Global
60/40
Ex
pe
ct
ed
T
ot
al
U
SD
R
et
ur
n
Source: AQR. Estimates as of December 31, 2021 are USD-denominated total nominal annual arithmetic rates of return. “Non-U.S.
developed equities” is cap-weighted average of Euro-5, Japan, U.K., Australia and Canada, unhedged. U.S. and Non-U.S. Treasuries are
represented by the respective Bloomberg Barclays indices. Global 60/40 is a 60%/40% weighted average of the developed equities listed
above and developed government bonds listed above, respectively. Estimates are for illustrative purposes only, are not a guarantee of
performance and are subject to change. Not representative of any portfolio that AQR currently manages.
Sources and Methodology for Long-Term Historical Expected Returns
Sources for historical equity and bond expected returns are AQR, Robert Shiller’s data
library, Kozicki-Tinsley (2006), Federal Reserve Bank of Philadelphia, Blue Chip Economic
Indicators, Consensus Economics and Morningstar. Prior to 1926, stocks are represented by a
reconstruction of the S&P 500 available on Robert Shiller’s website which uses dividends and
earnings data from Cowles and associates, interpolated from annual data. After that, stocks are
the S&P 500. Bonds are represented by long-dated Treasuries. The equity yield is a 50/50 mix
of two measures: 50% Shiller E/P * 1.075 and 50% Dividend/Price + 1.5%. Scalars are used to
account for long term real Earnings Per Share (EPS) Growth. Bond yield is 10-year real Treasury
yield minus 10-year inflation forecast as in Expected Returns (Ilmanen, 2011), with no rolldown
added.
Methodology for Forecast Error Analysis (Exhibit 1)
We first produce historical time series of yield-based estimates for U.S. equities and U.S.
Treasuries using the method described in the previous paragraph (analysis starts in 1900, but we
use data from 1870s onwards). We test their predictive power using quarterly overlapping 10-year
periods since 1900 and measure the distribution of errors. See the 2018 edition for more details.
Error ranges in Exhibit 1 are based on interquartile ranges of these distributions, adjusted for
current volatility estimates.
16 Capital Market Assumptions for Major Asset Classes | 1Q22
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The investment strategy and themes discussed herein may be unsuitable for investors depending on their specific investment objectives
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Capital Market Assumptions for Major Asset Classes | 1Q22 17
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