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The Fulcrum Expected Returns Model: A Primer∗
Motivation
Traditional approaches to computing longer-term expected returns rely heavily on the Dividend
Discount Model proposed by Gordon (1959) and Gordon and Shapiro (1956). Oftentimes, this
involves inputting “exogenous assumptions” about quantities—economic growth, the path of interest
rates, the evolution of risk premia—that are thought to affect returns. This approach has several
drawbacks. First, variables like economic growth, interest rates and risk premia are treated as
exogenous with respect to stock returns, when clearly there are feedback loops between all of
them. In other words, the variables are all simultaneously determined in equilibrium, and cannot
be reasonably treated as exogenous. Second, interest rates and growth rates are assumed to be
constant, so the model is best thought of as a “comparative statics” exercise about the very-long run.
Therefore, the model is silent about adjustment dynamics at horizons between now and the long
run, which is much more relevant for investors. Relatedly, they typically embed strong assumptions
about mean reversion, both of interest rates and valuation ratios. Finally, the model is silent about
the uncertainty surrounding the results, which can be quite high.
To calculate expected returns on the major asset classes, Fulcrum instead relies on dynamic
multivariate models estimated using Bayesian methods, see Sims (1980), Doan et al. (1983) and Sims
and Zha (1998). These methods allow us to model the joint dynamics of stock returns, dividends,
interest rates and other macroeconomic variables in an internally consistent way without making
strong assumptions about dynamics, mean reversion or the steady-state values of the variables.
∗This note was prepared by the Fulcrum Macroeconomics Research Group. Corresponding author: Gino Cenedese,<[email protected]>, Department of Macroeconomic Research, Fulcrum Asset Management LLP, 66Seymour Street, London W1H 5BT.
The Fulcrum Expected Returns Model
Furthermore, Bayesian prior information that disciplines the long-run behavior of the variables in
the system can be introduced naturally.
Specifically, the model includes stock prices and dividends, as well as a set of macroeconomic
variables, including short and long-term interest rates. Returns are then calculated from the model’s
forecasts using the Campbell-Shiller log-linearization of the one-period return,
rt+1 ≈ ρ(pt+1 − dt+1) − pt − dt + ∆dt+1 (1)
In words, higher returns come from higher future prices (relative to dividends, i.e. higher future
valuations), lower initial valuations, or higher dividends. Similar equations can be used to compute
returns for fixed income assets on the basis of the model’s forecasts for interest rates and future
long-term yields.
Results for the United States
Fulcrum maintains several versions of expected returns models for the Unites States. The following
figures display the results of one such models, updated with data up to December 6, 2019.
Figure 1 displays the current expected holding period returns at various horizons for the major
asset classes. The horizontal axis represents years and all numbers are annualized averages to ease
comparisons. The model’s forecast of inflation has been subtracted throughout, so all figures are
real returns. The figure offers a cross-sectional view of returns across asset classes, providing us with
a term structure of expected returns. A notable conclusion from the figure is that expected real
returns to bonds are negative, and worse than holding cash instruments, for the forecast horizon.
This result is the consequence of the negative term premium in long-term bonds.
Figure 2 instead offers the time series evolution of expected returns at the three-year horizon.
This allows us to compare the expected returns of each asset class through time. The real expected
three-year return on stocks has averaged 5% over the postwar period, whereas currently it stands
at around 3%. In that sense, stock prices are currently “overvalued”, meaning expected returns
are lower than normal. Compared with the decline in expected returns observed in the late 1990’s,
where expected returns turned negative, the current undervaluation is modest. It is also still better
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The Fulcrum Expected Returns Model
Source: Haver and Fulcrum calculations.
than the negative real returns expected for longer term bonds and the returns on BAA corporate
bonds, which stand just above 1%.
The final figure compares the model’s ex-ante expected returns for stocks (blue) with the returns
that ultimately materialized three years later (red). It serves as a reminder that the volatility of
stock returns is huge, and that realized returns vary much more than expected returns. For instance,
as valuations went ever higher during the late 2000s, prices kept increasing and expected returns
kept going down. Ultimately, of course, the negative returns experienced by an investor who bought
stocks in 1999 were much worse than the model’s already negative expectation.
International Returns
Fulcrum currently does not maintain equivalent models for Europe or Emerging Markets, so the
figures for these two regions are derived using analysts’ judgement, starting from the US figures
above and applying adjustments that reflect differences in risk premia and expected cash flows
across regions and asset classes. For example, the expected European equity return is calculated by
adding the differentials in dividend yields and expected dividend growth between Europe and the
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The Fulcrum Expected Returns Model
Source: Haver and Fulcrum calculations.
Source: Haver and Fulcrum calculations.
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The Fulcrum Expected Returns Model
United States.1 This calculation is theoretically motivated by a simple dividend discount model
of expected equity return differentials. The same reasoning has been applied to Emerging Market
equities.
The following table summarises the expected nominal returns for several regions and asset
classes. For government bonds, it is worth noting that the current expected rate of nominal return
on Treasuries is negative at one-year horizon, and only slightly positive at three-year and ten-year
horizons. These figures are consistent with the current negative real return estimated by the ER
model, as described above. We apply a similar term premium to Bunds, but adjusting for the EUR
cash rate. For Emerging Markets sovereigns and and US and Europe Credit, we also apply risk
premia adjustments relative to US Treasuries. For example, for Emerging Markets we add the
current spread between an EM local government bond index (USD unhedged) and US Treasuries to
the model’s expected Treasury returns.
We also report the same expected return figures expressed in two other currencies, euro (EUR)
and pound sterling (GBP). To do so, we start from the US dollar figures produced by the expected
equity return model, and convert them in the relevant currencies using the expected exchange rate
change over the relevant horizons. The expected exchange rate changes are derived from a separate
model of currency forecasting,2 which adapts a recent methodology proposed by ECB researchers.3
Briefly, this simple model relies on the empirical fact that real exchange rate deviations from the
level implied by long-run purchasing power parity tend to halve in about three years, and this
adjustment takes place mainly via changes in the nominal exchange rate, rather than inflation
differentials. While admittedly simple, the methodology has good forecasting power over medium
and long horizons. The currency model currently forecasts the EUR to appreciate by 2.4% and
1.3% per year over the next three and ten years, respectively.
1This approach is not necessarily consistent with Fulcrum’s dynamic model developed for the United States, butit can nevertheless be a useful approximation. Fulcrum is currently developing dynamic models for other countriesand regions.
2In principle, one may want to forecast equity and currency returns with a single encompassing model. We leavethis for future research.
3See Ca’Zorzi and Rubaszek (2018).
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The Fulcrum Expected Returns Model
Table 1: Nominal Expected Returns in US dollars.
1 Year 3 Years 10 Years
EquitiesUS 3.97% 3.87% 5.51%Europe 4.01% 4.97% 6.83%Emerging Markets 7.19% 7.97% 9.83%
Long-Term Government BondsTreasuries -1.68% 0.28% 1.43%Bunds -0.45% 0.87% 0.82%EM Local 1.61% 3.57% 4.72%
CreditUS Investment Grade -0.64% 1.32% 2.47%US High Yield 2.29% 4.25% 5.40%Europe Investment Grade 0.60% 1.92% 1.87%
CashUSD 1.56% 1.50% 1.84%EUR 2.79% 2.10% 1.23%
CurrencyEUR/USD 3.26% 2.57% 1.34%
Unhedged continuously compounded returns in per cent per annum. Currency returns denote the nominal
expected exchange rate change of the currency pair. Source: Haver and Fulcrum calculations.
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The Fulcrum Expected Returns Model
Table 2: Nominal Expected Returns in Euros.
1 Year 3 Years 10 Years
EquitiesUS 0.71% 1.30% 4.17%Europe 0.74% 2.40% 5.49%Emerging Markets 3.93% 5.40% 8.49%
Long-Term Government BondsTreasuries -4.94% -2.29% 0.09%Bunds -3.71% -1.70% -0.52%EM Local -1.65% 1.00% 3.38%
CreditUS Investment Grade -3.90% -1.25% 1.13%US High Yield -0.97% 1.68% 4.06%Europe Investment Grade -2.66% -0.65% 0.53%
CashUSD -1.70% -1.07% 0.49%EUR -0.47% -0.47% -0.11%
CurrencyEUR/USD 3.26% 2.57% 1.34%
Unhedged continuously compounded returns in per cent per annum. Currency returns denote the nominal
expected exchange rate change of the currency pair. Source: Haver and Fulcrum calculations.
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The Fulcrum Expected Returns Model
Table 3: Nominal Expected Returns in Pounds Sterling.
1 Year 3 Years 10 Years
EquitiesUS -0.53% 0.35% 3.70%Europe -0.50% 1.45% 5.02%Emerging Markets 2.68% 4.45% 8.01%
Long-Term Government BondsTreasuries -6.18% -3.24% -0.38%Bunds -4.95% -2.64% -0.99%EM Local -2.89% 0.05% 2.91%
CreditUS Investment Grade -5.14% -2.20% 0.66%US High Yield -2.21% 0.73% 3.59%Europe Investment Grade -3.90% -1.59% 0.06%
CashUSD -2.94% -2.01% 0.02%EUR -1.72% -1.42% -0.59%
CurrencyEUR/USD 3.26% 2.57% 1.34%GBP/USD 4.51% 3.52% 1.81%
Unhedged continuously compounded returns in per cent per annum. Currency returns denote the nominal
expected exchange rate change of the currency pair. Source: Haver and Fulcrum calculations.
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The Fulcrum Expected Returns Model
Conclusion
Dynamic multivariate models can be used to advance our knowledge of expected returns across asset
classes. Relative to traditional approaches, they have the advantage of modeling the joint dynamics
of asset prices and macro variables in an internally consistent way, and providing expected returns
at different horizons and points in time. Estimated using Bayesian methods, they are an alternative
way to judiciously incorporate prior information about the long-run behavior of returns, without
resorting to restrictive assumptions about mean-reversion that are not supported by the data.
References
Ca’Zorzi, M. and M. Rubaszek (2018): “Exchange rate forecasting on a napkin,” Working
paper, ECB Working Paper No 2151.
Doan, T., R. B. Litterman, and C. A. Sims (1983): “Forecasting and Conditional Projection
Using Realistic Prior Distributions,” NBER Working Papers 1202, National Bureau of Economic
Research, Inc.
Gordon, M. J. (1959): “Dividends, earnings, and stock prices,” The review of economics and
statistics, 99–105.
Gordon, M. J. and E. Shapiro (1956): “Capital equipment analysis: the required rate of profit,”
Management science, 3, 102–110.
Sims, C. A. (1980): “Macroeconomics and Reality,” Econometrica, 48, 1–48.
Sims, C. A. and T. Zha (1998): “Bayesian methods for dynamic multivariate models,” International
Economic Review, 949–968.
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The Fulcrum Expected Returns Model
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