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For the long-run: capital-market assumptions 2018

Don't put all your eggs in one basket. That's a time-honored piece of advice, and rightly so. By buying shares in one particular company, for example, you may be taking a lot more risk for the same likely reward that you could get by investing in a wider range of companies. However, buying shares across many different companies and sectors still exposes you to the whole equity market going down. If you seek a steady stream of income in retirement, say, you should consider adding some sovereign bonds. Often, such securities offer the potential to do well precisely when equity markets go down. A recession, for example, hurts corporate earnings and valuations. At the same time, it leads to falling interest rates. This, in turn, is likely to increase the price of the sovereign bonds in your portfolio.

Of course, holding only U.S. Treasuries and American stocks can still leave you exposed to some risks. High rates of inflation, for example, can damage both. Historically, investors have been less prepared to put a high stock market multiple on company earnings at times of high inflation, partly because during such periods, earnings tend to be fairly volatile.

Taking risks in other ways, such as with high-yielding U.S. bonds may also help to stabilize a portfolio further. Such highly leveraged companies tend to benefit from unexpected inflation spikes. Their earnings and revenues go up in nominal terms, while their coupon stays the same, tending to make their debt load more bearable.

Even a portfolio across a wide range of traditional and alternative U.S. assets can suffer from threats affecting the whole economy. Policy errors can drag down economic growth potential and hurt the U.S. dollar. Spreading holdings across a wide range of countries may help to mitigate such risks, including geopolitical ones. And as with U.S. Treasuries, you might be prepared to pay a premium for assets that have proven a safe haven during past periods of turmoil. Gold and pretty much anything denominated in Swiss Franks come to mind.

Diversification makes intuitive sense.

Putting this intuition into practice, however, is most often a matter of judgment. Partly it's about comparing one's own risk with the level of potential risk in investments in particular asset classes in the past by looking at measures of the variability in returns. Partly it's about assessing correlations within and across various asset classes.

There is a third, critical ingredient: expected returns over the planned investment horizon. What returns may the chosen portfolio likely generate, given current market conditions? Are the potential returns satisfactory or sufficient to justify the risk taken? Having reasonable answers to these questions can help to figure out how much risk an investor might wish (or need) to take, and can serve as a useful starting point for constructing portfolios.

In that spirit, we have in recent years put a lot of effort into deriving our own proprietary long-run return assumptions. This publication highlights some of our key findings and results, as well as providing brief introductions to the methodologies we used. In the remaining sections, we cover fixed income, equities and alternatives. We conclude with some final observations.

Fixed-income returns

Figuring out the nominal expected return is pretty straightforward in fixed income, as long as your investment horizon exactly corresponds with the duration of the bonds in question. Simply defined, a bond's duration is the weighted average of how long it will take for an investor to get repaid, i.e. the time until each interest (coupon) and principal payment of a bond becomes due. Given how low interest rates currently are, a bond's duration is very close to its maturity – the remaining time until the principal amount is paid back.

Let's say you buy a 10-year Treasury with a 2.5% yield trading at par. You intend to hold it until it matures. So, you know that you are likely to receive $100 back in 10 years' time (except for the unlikely event that the U.S. government becomes insolvent). You also know that each year, you will collect coupon payments of 2.5% of the face value, i.e. $2.5. The only thing you don't know is what yields you will get when you reinvest the coupons for the remaining term.

Things get a little trickier if you buy a 10-year Treasury today, which you only plan to hold for 5 years. You now have a coupon and a price component to deal with. Fortunately, there is an easy way to at least get a first, baseline estimate of your returns that neatly resolves the issue of reinvesting coupons as well. You simply look up the interest rates on U.S. Treasuries of varying maturities. This gives you the yield curve on U.S. Treasuries as of today. With this chart, you can estimate your expected return. That is assuming the future yield curve will be the same as the current yield curve. This allows you to calculate how much all your bonds are likely to be worth, if you sell them before they mature.

A constant yield curve means that the yield on your initial 10-year Treasury will be only about 2.2% in 2022. If you bought your bond at 2.5% yield, this means that its value has to go to $101.41 over the next 5 years. This price gain is called the roll down effect, and it can be a very important component of bond returns when the yield curve is upward sloping. (The steeper the curve, the bigger the initial impact, which will fade again as the bond matures.)

A constant yield curve also makes it easy to calculate the returns on reinvested coupons. For the first one due in a year's time, you simply pencil investing $2.5 at the yield level in line with where 9-year Treasuries are currently trading # . Your total expected nominal returns are simply the coupons on the initial bond, roll down, and proceeds from re-investing coupons at yields in line with the current yield curve.

In principle, you can use this approach for any fixed-income instrument that is priced according to a yield curve. Whether a constant yield curve is really the best estimate is a matter of judgment. Another approach would be to use forward rates – what sorts of future yields the market is currently pricing in. From an investment perspective, there are advantages to using this approach; in particular, Diebold and Rudebusch (2013) showed that there is valuable information contained in the yield curves implied by forward rates. The differences tend to be highly significant, as the chart below illustrates.

The current U.S. Treasury yield curve versus implied yield curves

Source: Bloomberg Finance L.P. as of 11/30/17

There are advantages and disadvantages to both. We therefore tend to use a blended approach. So far, so good for U.S. Treasuries. For a portfolio of sovereign bonds from different countries, you would want to include two additional considerations. First, your portfolio is likely to include some sovereigns with non-negligible default risk. And second, some bonds might see their ratings change over time. We use historic data to assess long-term default probabilities, recovery rates and rating migration.

This is particularly relevant for corporate bonds. For example, historic data suggests that A-rated corporate borrowers from around the world have about a 5% probability to see their rating downgraded to BBB within the next year.

Average rating migration of A-rated corporate borrowers globally (1981 - 2015)

Source: Standard & Poor's RatingsDirect, "Default, Transition, and Recovery: 2016 Annual Global Corporate Default Study And Rating Transitions" as of 4/13/17

U.S. corporate bonds, like many other bonds, are priced by their spread compared to very low risk sovereign bonds, in this case U.S. Treasuries. To calculate their returns, you need assumptions on how credit spreads will evolve over time. For example, spreads on U.S. corporate bonds have recently been trading at historically low levels. Such changes tend to be negatively correlated with sovereign bond yields. So, in an environment where we expect the Treasury yield curve to flatten in the near term (due to, for example, growing risks of a U.S. recession), spreads on corporate bonds are likely to widen. At times, this correlation can also turn positive, for example when rates are rising during times of strong economic growth, strengthening corporate balance sheet. As a bond matures, there is also a natural tendency towards spread compression. The shorter the remaining term, the lower, all else equal, the likelihood that the issuer will default.

Yields and spreads of U.S. corporate bonds (A rating)

Source: Bloomberg Finance L.P. as of 11/30/17

Take it all together and add a few twists related to more complex instruments, and it becomes possible to forecast comparable returns across a wide range of fixed-income assets. The results are provided below.

Long-term fixed income returns (7-10 year horizon)

  Asset Class Forecasted Return (in %)1

Eurozone sovereign bonds2


Euro corporate bonds2


Euro high-yield bonds


U.S. Treasuries2


U.S. corporate bonds


U.S. high-yield bonds


Emerging-market external sovereign bonds3


Source: Multi Asset Group, Deutsche Asset Management Investment GmbH as of 11/30/17

1Assuming investors hold those securities until maturity

2Remaining maturity: 5-7 years

3JP Morgan EMBI Global Composite Index

Equities returns

Traditionally, investors have tended to rely on historical average data when assessing equities returns. Typically, they have taken long-term government-bond rates of the country in question as a proxy for the risk-free rate and added an equity risk premium based on average historic outperformance. This would suggest that in the long run, it is worth considering owning equities. However, history clearly shows that 10-year periods of zero or even negative equity returns do occur, as the following chart shows. Consequently, other approaches are needed to derive more realistic and accurate expectations of future long-term equity returns at any given point in time.

10-year rolling return (S&P 500)

Source: Bloomberg Finance L.P., Deutsche Bank AG as of 11/30/17

As with a bond, the expected return of a stock can be decomposed into its respective building blocks. After all, being a shareholder in a company gives you a corresponding claim on its future cash flows. The value of a share is the present value of those expected cash flows. As with bonds, expected returns can take the form of dividends paid during the investment period, plus any share-price appreciation in the meantime. However, tomorrow's share price similarly depends on future dividends, as well as price changes thereafter. With a sufficiently long time horizon, the weight of the price component in the calculation tends towards zero. Given that companies can in principle exist forever, it is therefore natural to consider the value of stock as simply a function of current dividends, future dividend growth rates and the discount rates investors are applying.

But aren't we forgetting something here? What about share buybacks, an increasingly common way for companies, particularly in the U.S. to return cash to shareholders. Actually, both our own analysis and other studies have found that in the long term, the buyback effect is typically outstripped by the dilution effect from new shares being issued, as Bernstein and Arnott (2003) showed.

This is one of three reasons why in the long run, real earnings per share, out of which dividends are paid, are at most likely to grow in line with gross real domestic product per capita. Another reason is that a lot of economic growth results from new companies, not yet listed; stock investments can participate only in the growth of established businesses. Third, retained earnings are often invested at a rate of return that is below externally available investments. Chief executives have plenty of leeway in how they use company funds, and they may not necessarily be in their shareholders interest.

Historical data and macro-economic estimates help to assess the size of these effects in various regions. In order to compare our results with those for fixed income, we also add an inflation component. This is derived from 10-year inflation swaps for developed markets and forecasts by the International Monetary Fund for emerging ones. Finally, we know from past experience that earnings margins can be highly volatile in any given year, and that in the long run, price-earnings ratios tend to be mean reverting. This is why we use a cyclically adjusted price-to-earnings (CAPE) ratio, popularized by Robert Shiller, to assess the likely valuation changes over a longer-term forecasting horizon.

Our resulting estimate of future returns on a 7-year to 10-year horizon is still well above yields on long-dated government bonds. From a global perspective, equities continue to offer the potential for a substantial positive risk premium. Expected returns for developed markets are relatively tightly clustered. Within emerging markets, Latin America might offer attractive rewards if currently depressed earnings and valuations were to revert back to historic means. Asia excluding Japan appears fairly valued and on track towards fairly substantial earnings growth.

Source: Multi Asset Group, Deutsche Asset Management Investment GmbH as of 11/30/17

* Not adjusted for underlying emerging-market local currency risks

The same methodology can also be applied to listed alternative investments, such as real estate investment trusts (REITs) or infrastructure companies. The return components are the same, only with different weightings. For example, REITs offer high dividend yields (around 4.0%), but almost no retained earnings; for legal reasons, they have to distribute their rental income. The annual resulting return assumptions are 5.8% for global REITs and 6.4% for global infrastructure.

Alternative investment returns

For alternatives, we generally assess future returns by combining statistical analysis and our return projections for the traditional asset classes. For hedge funds, this means using a factor-based model in order to figure out key return drivers. We applied such a model to the database of Hedge Fund Research (HFR), which is the one most commonly used by practitioners. Our findings confirm that returns from different types of hedge-fund strategies vary, depending on broader financial market trends. This is why our return assumptions take into account the broader market context – the market regime, as it is commonly known. For example, periods of financial-market stress tend to be especially painful for certain equity strategies, while macro strategies proved fairly resilient. Based on our calculations, we expect a broad portfolio of hedge funds to generate returns of 2.7% per year over the long term. Another key finding is that there is a great deal of dispersion in returns, depending on both the strategy and the manager selected. Fund structures and fee arrangements also have a big impact. That said, we found that selectively adding hedge-fund investments can help diversify and adjust risk in multi-asset portfolios.

In commodities, we currently expect a return of 3.6% per year in the long term. Investing in commodities means buying futures. This allows you to collect interest at the risk-free rate on the amount of your collateral. On top of that, we merely add our long-term expectations for U.S. inflation. This is a bit of simplification in several ways. On the one hand, our approach ignores the potential of real commodities prices to rise (for example due to growing scarcity) or to fall (due to productivity advances) over long periods of time. Effectively, it amounts to saying that real commodities prices will remain constant in the long run. On the other hand, it also assumes no gain our losses due to the shape of the futures curve. Whenever a futures contract expires, it needs to be replaced with a new one. This typically yields small gains, but can also cause substantial losses during periods of commodity-market turmoil. For example, Ilmanen (2011) show the decomposed returns for the S&P GSCI Index since 1969. They found the cumulative gains from 1970 onwards were fully cancelled out by losses from contracts expiring during the late 2000s. For this reason, we take a simplified approach in our long-term strategic asset allocation. For a tactical asset allocation with a shorter time horizon, other methods might be better suited.

For convertibles, we use an average of our equities and credit return assumptions, and adjust for currency hedging costs. Using a simple average appears appropriate, as a balanced strategy for convertibles targets an equity sensitivity around 50%. In total, we estimate the current long-term convertibles bonds return at 4.4%.

Finally, one alternative investment type worth highlighting are U.S. bank loans to highly leveraged companies. Nowadays, such loans tend to be broadly syndicated to a diverse group of institutional investors. The coupons for leveraged loans, unlike most other debt instruments in the U.S., are floating. Moreover, such loans are typically secured by the company’s physical assets (property, plant and equipment), resulting in attractive risk-adjusted returns. Our strategic return projection for leveraged loans of 5.4% is based on two transparent building blocks: our short-term U.S. Treasury bills and the long-term average loan spread over 3-month Treasury bills.


In recent years, investors have been forced to take more risk than they might have previously felt comfortable with. The methodological framework underpinning our long-run return assumptions helps explain why. Through quantitative easing (QE), central banks have pushed down yields on long-term government bonds, commonly used as a proxy for a country's risk-free rate. Partly as a result, constructing a portfolio with positive expected returns requires taking a lot more risk today, than in years gone by. In coming months, we plan to follow up on this analysis by providing additional details.


Bernstein, W.J. and Arnott, R.D. (2003): "Earnings growth: The two percent dilution." Financial Analysts Journal, no. 59.5, pp. 47-55

Bauer, M.D. and Rudebusch, G.D. (2015): "Resolving the Spanning Puzzle in Macro-Finance Term Structure Models", Federal Reserve Bank of San Francisco Working Paper

Campbell, J.Y. and Shiller, R.J. (1991): "Yield Spreads and Interest Rate Movements: A Bird’s Eye View", Review of Economic studies, no. 58.3, pp. 495-514

Cazalet, Z. and Zheng, B. (2014): "Hedge Funds in Strategic Asset Allocation", White Paper, no. 11, Lyxor Asset Management

Cochrane, J.H. and Piazzesi, M. (2005): "Bond Risk Premia", American Economic Review, no. 95.1, pp. 138-60

Dai, Q. and Singleton, K.J. (2008): "Expectation Puzzles, Time-Varying Risk Premia, and Dynamic Models of the term structure", NYU Working Paper, no. S-AM-00-01

Diebold, F.X. and Li, C. (2006): "Forecasting the Term Structure of Government Bond Yields", Journal of Econometrics, no. 130.2, pp. 337-365

Diebold, F.X. and Reudebusch, G.D. (2013): "Yield Curve Modeling and Forecasting: The Dynamic Nelson-Siegel Approach", Princeton University Press

Fernandez, P.L. and Fernandez Acin, I. (2014): “Market Risk Premium used in 88 countries in 2014: A survey with 8,228 answers", SSRN Working paper

Fama, E.F. and Bliss, R.R. (1987): "The Information in Long-Maturity Forward Rates", American Economic Review, no. 77.4, pp. 680-692

Fama, E.F. (2004): "The Behavior of Interest Rates", CRISP Working Paper No. 553

Mehra, R. and Prescott, E.C. (1985): "The equity premium: A puzzle", Journal of monetary Economics, no. 15.2, pp. 145-164

Ibbotson, R. G. and Chen, P. (2003): "Long-run stock returns: Participating in the real economy", Financial Analysts Journal, pp. 88-98

Ilmanen, A. (1995): "Time Varying Expected Bond Returns in International Bond Markets", Journal of Finance, no. 50.2, pp. 481-506

Ilmanen, A. (2011): "Expected returns: an investor's guide to harvesting market rewards", John Wiley & Sons

Koopman, S.J. and van der Wel, M. (2014): "Forecasting the U.S. Term Structure of Interest Rates Using a Macroeconomic Smooth Dynamic Factor Model", Journal of Applied Econometrics, no. 29, pp. 65-90

Nelson, C. and Siegel, A.F. (1987): "Parsimonious Modeling of Yield Curves", Journal of Business, no. 60, pp. 473-489

Stambaugh, R.F. (1988): "The Information in Forward Rates: Implications for Models of the Term structure", Journal of Financial Economics, no. 21.1, pp. 41-70

Svensson, L.E.O. (1994): "Estimating and Interpreting Forward Interest Rates: Sweden 1992-1994", IMF Working Paper, no. 94.114, pp. 1-49


In actual fact, both 9-year and 10-year Treasuries happen to be trading at about 2.4% at the time of writing.

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