the fulcrum expected returns model: a primer€¦ · the fulcrum expected returns model united...

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

2


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

3




4


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).

5


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.

6


Table 2: Nominal Expected Returns in Euros.


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%



7


Table 3: Nominal Expected Returns in Pounds Sterling.


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%



8


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.

9


Disclaimer

This material is for your information only and is not intended to be used by anyone other than you. It is directed at

professional clients and eligible counterparties only and is not intended for retail clients. The information contained

herein should not be regarded as an offer to sell or as a solicitation of an offer to buy any financial products, including

an interest in a fund, or an official confirmation of any transaction. Any such offer or solicitation will be made to

qualified investors only by means of an offering memorandum and related subscription agreement. The material is

intended only to facilitate your discussions with Fulcrum Asset Management as to the opportunities available to our

clients. The given material is subject to change and, although based upon information which we consider reliable, it is

not guaranteed as to accuracy or completeness and it should not be relied upon as such. The material is not intended

to be used as a general guide to investing, or as a source of any specific investment recommendations, and makes

no implied or express recommendations concerning the manner in which any client’s account should or would be

handled, as appropriate investment strategies depend upon client’s investment objectives. Funds managed by Fulcrum

Asset Management LLP are in general managed using quantitative models though, where this is the case, Fulcrum

Asset Management LLP can and do make discretionary decisions on a frequent basis and reserves the right to do

so at any point. Past performance is not a guide to future performance. Future returns are not guaranteed and a

loss of principal may occur. Fulcrum Asset Management LLP is authorised and regulated by the Financial Conduct

Authority of the United Kingdom (No: 230683) and incorporated as a Limited Liability Partnership in England

and Wales (No: OC306401) with its registered office at Marble Arch House, 66 Seymour Street, London, W1H 5BT.

Fulcrum Asset Management LP is a wholly owned subsidiary of Fulcrum Asset Management LLP incorporated in the

State of Delaware, operating from 350 Park Avenue, 13th Floor New York, NY 10022.

c©2019 Fulcrum Asset Management LLP. All rights reserved.

10

the fulcrum expected returns model: a primer€¦ · the fulcrum expected returns model united...

Documents