Estimating Future Returns and Risk Across Asset Classes

Dora Ercegović

Estimating Return

Portfolio construction starts with estimating how much each asset is expected to return. The most intuitive way to estimate expected return is to average an asset’s past returns over a chosen lookback window. But past returns reflect economic and market conditions that may not persist. Historical averages are therefore unreliable estimates of what an investor can expect to earn in the future.

This instability comes from the returns themselves. They swing widely around their long-run average, so a few unusually good or bad years can move the estimate a long way. Since expected returns feed directly into portfolio construction, those differences can change which assets look attractive and how much of each the portfolio holds.

There is another way to approach the problem. Rather than estimate each asset’s expected return from its own historical average, we can start with the return investors require for bearing market risk and then ask how exposed each asset is to that risk.

The Global Market Portfolio

The global market portfolio combines major asset classes across global markets, weighted by market value. It approximates the market portfolio in the Capital Asset Pricing Model (CAPM), which includes all risky assets.

In CAPM, investors share the same expectations about returns and risk and seek the highest expected return for their chosen level of risk.

The efficient frontier shows the highest expected return available from combinations of risky assets at each level of risk. Combining a risky portfolio with the risk-free asset traces a straight line. The Capital Market Line is the line that touches the efficient frontier at the tangency portfolio, offering the highest expected return above the risk-free rate per unit of risk. In CAPM, all investors choose this portfolio for their risky holdings. Since together they hold all risky assets in the market, this shared portfolio must also be the market portfolio.

The global market portfolio under CAPM
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Select a point to explore its position.
The global market portfolio at the tangency point Expected return is on the vertical axis and total risk on the horizontal axis. The upper branch of the curved boundary is the efficient frontier. The Capital Market Line rises from the risk-free rate and touches the frontier at the global market portfolio. The minimum-variance portfolio sits at the leftmost point of the boundary, and an efficient portfolio is marked further along the frontier. An inefficient portfolio sits directly below the efficient one, with the same risk and a lower expected return.
The upper branch is the efficient frontier for risky assets. The two vertically aligned portfolios show how expected return can differ at the same risk. Risk in this diagram is measured by the standard deviation of returns. Shapes are illustrative, not measured from real portfolios.

The difference between the global market portfolio’s expected return and the risk-free rate is the market risk premium: the additional return investors require for bearing market risk. Short-run historical returns can be heavily influenced by temporary market conditions, making them unreliable for estimating this premium. Long-run data spans a wider range of market conditions and provides a more reliable basis for the estimate, though it cannot guarantee future returns.

From Market Risk Premium to the Expected Return of an Asset

To understand why exposure to the global market portfolio matters for the expected return of an asset, we need to distinguish between risks that diversification can reduce and those it cannot. Idiosyncratic risk is specific to an individual asset and can be reduced through diversification.

Systematic risk, by contrast, comes from market-wide movements and cannot be eliminated simply by holding more assets. CAPM assumes investors are compensated for bearing this systematic risk, but not for risk that can be diversified away. Beta measures an asset’s exposure to that market-wide risk.

Beta is estimated by comparing the asset’s returns above the risk-free rate with the global market portfolio’s returns above that rate. These are called excess returns. A beta of 1 means that a one-percentage-point change in the global market portfolio’s excess return has been associated, on average, with a one-percentage-point change in the asset’s excess return. A beta above 1 indicates greater sensitivity to market movements; a beta below 1 indicates less. Beta captures an asset’s sensitivity to market movements. However, each asset also carries idiosyncratic risk, so its actual return can differ substantially from what its beta and the global market portfolio’s return would suggest.

Beta connects an asset’s market exposure to its expected return. CAPM expresses this as the risk-free rate plus a share of the market risk premium:

Here, Rf is the risk-free rate, E[RM]−Rf is the market risk premium, and βi (beta) determines how much of that premium is assigned to the asset. The result, E[Ri], is an estimate of the asset’s expected return.

This can produce very different expected returns across assets. Equities generally have more exposure to market risk than high-quality government bonds. The chart below shows how this difference translates into higher expected returns through beta.

How CAPM maps beta to expected return
Under CAPM, model-implied expected return scales with beta along a single line, starting from the risk-free rate at beta zero.
The long-run betas of 0.34 for government bonds and 1.47 for equities are calculated from historical volatilities and correlations over 1960–2017 (Doeswijk, Lam & Swinkels, 2020). In CAPM, beta zero receives only the risk-free rate; higher beta adds a larger share of the market risk premium. The vertical axis is deliberately unlabelled because the chart shows the relationship rather than a particular expected-return estimate.

Estimating Risk

Portfolio construction also requires assessing the risk of holding assets together. Risk itself is estimated separately, from how much assets fluctuate and how they move in relation to one another.

Two assets can have the same average return yet fluctuate very differently around it. Volatility describes how widely returns fluctuate around their average.

When assets are held together, their risk also depends on whether their returns rise and fall together. Correlation captures that relationship, from −1 for perfectly opposite movements to +1 for perfectly aligned movements.

Volatility and correlations tend to persist over time, making historical data useful for estimating risk. A sufficiently large sample improves estimation precision, and portfolio allocations are generally less sensitive to errors in these estimates than to errors in expected returns. Both volatility and correlation can still change as market conditions evolve.

The historical asset-class volatilities and correlations below illustrate both; in practice, they are estimated for the individual assets themselves.

How much asset classes fluctuate
Historical annual volatility of broad asset classes, 1960–2017.
Historical real-return volatilities (annual standard deviations) of broad asset classes from Doeswijk, Lam & Swinkels (2020), 1960–2017.
How asset classes move together
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Historical correlations between broad asset classes, 1960–2017.
Historical real-return correlations between broad asset classes from Doeswijk, Lam & Swinkels (2020), 1960–2017. This is a correlation matrix: its diagonal is always 1.

How Frontira Does This

Frontira uses a global market portfolio spanning equities, bonds, real estate, and commodities, weighted by market value. Expected returns are anchored to a long-run market risk premium of 3.98% a year, drawn from Doeswijk, Lam & Swinkels’ study of 1960–2017.

Each ETF’s beta is estimated from three years of daily returns and blended 50/50 with a long-run beta for its asset class to reduce sensitivity to the recent window. These long-run betas are calculated from the same study’s asset-class volatilities and correlations with the global market portfolio.

To estimate each ETF’s expected return, Frontira multiplies the 3.98% market risk premium by the blended beta. It then adds the latest €STR (euro short-term rate), its reference for the risk-free rate, and subtracts the ETF’s annual fees, measured by its total expense ratio (TER).

Volatility and correlation are estimated from the same three years of ETF returns, capturing individual fluctuations and co-movement across funds. Expected returns, volatilities, and correlations are recalculated daily using the latest available data.

References

Chopra, V. K., & Ziemba, W. T. (1993). The effect of errors in means, variances, and covariances on optimal portfolio choice. The Journal of Portfolio Management, 19(2).

Doeswijk, R., Lam, T., & Swinkels, L. (2020). Historical returns of the market portfolio. The Review of Asset Pricing Studies, 10(3), 521–567. https://doi.org/10.1093/rapstu/raz010

European Central Bank. Overview of the euro short-term rate (€STR). https://www.ecb.europa.eu/stats/financial_markets_and_interest_rates/euro_short-term_rate/html/eurostr_overview.en.html

Fama, E. F., & French, K. R. (2004). The capital asset pricing model: Theory and evidence. Journal of Economic Perspectives, 18(3), 25–46. https://doi.org/10.1257/0895330042162430

Markowitz, H. (1952). Portfolio selection. The Journal of Finance, 7(1), 77–91. https://doi.org/10.1111/j.1540-6261.1952.tb01525.x

Sharpe, W. F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk. The Journal of Finance, 19(3), 425–442. https://doi.org/10.1111/j.1540-6261.1964.tb02865.x