The surprising accuracy of naive extrapolation compared to explicit multi-year earnings forecasts

The surprising accuracy of naive extrapolation compared to explicit multi-year earnings forecasts
Contents
  1. Summary: the seven findings that matter
  2. Worse than predicting zero
  3. When the random walk wins
  4. Against a machine learning benchmark
  5. What returns the most optimistic deliver
  6. What if the bias were rational?
  7. What to do with this in practice
  8. Frequently asked questions
  9. What we do not know
  10. References

Analysts’ long-run earnings growth forecasts are less accurate than a naive model that simply predicts zero growth. That is not a provocation: it is the literal conclusion of an evaluation published in an accounting and finance journal. And there is more: the random walk beats analysts over long horizons and in small firms, and a naive extrapolation of their own one-year forecast is more accurate than their explicit two- and three-year forecasts. At the same time, the comparison with machine learning models concludes that analysts remain superior to the linear models actually in use. This article sets out what has been measured.

Summary: the seven findings that matter

Each row names the study and the year. It is worth separating accuracy from bias: they are two different problems.

Finding Result Study and year
Long-run accuracy Worse than predicting zero growth Harris, J. Business Finance & Accounting (1999)
Main source of that inaccuracy Random error, not bias Harris (1999)
Where the random walk wins Long horizons, small or young firms Bradshaw et al., Review of Accounting Studies (2012)
The most accurate two- and three-year forecast Naive extrapolation of the one-year one Bradshaw et al. (2012)
Direction and evolution of the bias Optimistic, and growing with the horizon Van Binsbergen et al., Rev. Financial Studies (2022)
Comparison with linear statistical models Analysts are superior to them Van Binsbergen et al. (2022)
Returns of the most optimistic stocks Lower than those of the most pessimistic Bordalo et al., The Journal of Finance (2019)

What you will find here

  • The comparison with the dumbest possible model, and who wins.

• The precise conditions under which the random walk beats an analyst.

• What happens when analysts are compared with machine learning.

  • What returns the stocks with the most optimism around them deliver.
  • The argument that the optimistic bias could be rational instead of a mistake.

Worse than predicting zero

Richard Harris analyzed how accurate, biased, and efficient long-term earnings growth predictions made by analysts for American companies really are, publishing his findings in Journal of Business Finance & Accounting. The opening sentence of his results gets straight to the point: forecast accuracy is shown to be extremely low.

And the comparison that makes it memorable: analysts’ long-run earnings growth forecasts are less accurate than those of a naive model in which earnings growth is forecast to be zero.

The study further notes that, in line with short- and medium-term predictions, long-term forecasts are both biased and inefficient, alongside indications that analysts fail to fully factor in the insights regarding future earnings embedded within current share valuations.

The nuance almost nobody quotes

Here is the part that prevents the finding from becoming a caricature: the bias and inefficiency of the forecasts contribute very little to their inaccuracy, which turns out to be mainly a consequence of random error.

Put another way: the problem with analysts over the long run is not that they push the figures in one direction; it is that a company’s earnings five years out are largely unpredictable. The study itself identifies where they do work: the most reliable growth forecasts are low forecasts issued for large firms with a low price-earnings ratio and a high market-to-book ratio.

Study What it analysed What it found What it does not support
Harris (1999) Long-run growth forecasts in the US Less accurate than predicting zero growth It is long-run growth, not annual forecasts
Bradshaw et al. (2012) Annual forecasts against the random walk The random walk wins in specific horizons and firms Does not assess the usefulness of forecasts for investing
Van Binsbergen et al. (2022) Analysts against a machine learning benchmark Growing optimistic bias, but better than linear models The statistical benchmark is not observable in real time without a model
Bordalo et al. (2019) Portfolios sorted by forecast optimism The most optimistic return less than the most pessimistic It is a test of a belief-formation model
Lim (2001) Analyst utility model and individual data The optimistic bias can be optimal and rational It is a model with empirical testing, not an experiment

When the random walk wins

Mark Bradshaw, Michael Drake and two co-authors re-examined in Review of Accounting Studiesthe widely held belief that analysts’ earnings per share forecasts are superior to random walk time-series forecasts.

Their outcome maps out precisely the boundaries where this assumption breaks down: basic random walk projections outperform expert predictions across extended timeframes, among more compact or newer businesses, and whenever forecasters anticipate negative or substantial shifts in earnings per share.

And they add a comparison that is almost comic: they also compared a third longer-horizon earnings forecast based on a naive extrapolation of analysts’ one-year-ahead forecasts. Surprisingly, that naive extrapolation provides the most accurate estimate of long-run earnings at two and three years.

The authors’ conclusion serves as a methodological caution: these insights transform previous generalisations regarding the supremacy of analysts’ predictions, indicating they are incomplete, deceptive, or both.

Against a machine learning benchmark

Jules van Binsbergen, Xiao Han alongside Alejandro Lopez-Lira unveiled within The Review of Financial Studies an alternative approach to quantify this issue: a real-time gauge regarding conditional biases embedded in earnings forecasts, which is established as the gap separating analysts’ projections from a statistically optimal, unbiased benchmark constructed via machine learning.

By that yardstick, the diagnosis on bias is clear: analysts’ conditional expectations are on average upward biased, a bias that increases with the forecast horizon.

Observation What it shows Practical use
Direction of the bias Upward, on average Discount optimism by default
Evolution with the horizon Increases the further out you look Three-year forecasts are the worst
Relation to future returns Negative cross-sectional predictability More optimism, lower returns afterwards
Where the most biased cluster In the short legs of many anomalies Matches what funds sell short
What their managers do More likely to issue equity They exploit the high valuation

Yet the very same study concludes with an important defense of analysts that deserves mention: standard linear earnings models fail out of sample, underperforming the forecasts generated by financial analysts. Put differently, analysts fall short of an ideal machine learning benchmark while still outperforming current statistical alternatives.

What returns the most optimistic deliver

Pedro Bordalo, Nicola Gennaioli and two co-authors revisited a classic finding in The Journal of Finance and explained it with a belief-formation model. The starting fact: the returns of stocks with the most optimistic analyst long-run earnings growth forecasts are lower than those of stocks with the most pessimistic forecasts.

Their explanation rests on the representativeness heuristic: analysts forecast fundamentals from observed earnings growth, but overreact to news by exaggerating the probability of the states that have become more likely.

The authors document the joint dynamics of fundamentals, expectations and returns of those portfolios, and note that a quantitative estimation of the model accounts for the main patterns in the data.

What if the bias were rational?

Terence Lim suggested in Journal of Finance an interpretation that keeps optimism from being dismissed as mere incompetence. His framework outlines a quadratic loss utility function where analysts balance bias against improved access to corporate leadership and precision.

Something counter-intuitive follows: optimal forecasts with minimum expected error are optimistically biased, and exhibit predictable cross-sectional variation related to analyst and firm characteristics.

And the empirical tests involving individual analyst predictions align with the model’s forecasts, leading to this final deduction: upward and foreseeable bias can actually function as a rational feature within optimal profit estimates, meaning earlier research relying on traditional definitions of unbiasedness might have hastily discarded analyst projections as flawed or unreasonable.

That reasoning aligns with a separate finding: there is heightened demand for private corporate details regarding businesses whose profits are difficult to forecast, and if optimism facilitates entry to executive insights, analysts will publish rosier projections specifically for such companies.

What to do with this in practice

Ordered by the strength of the evidence behind each point:

• Ignore five-year growth forecasts. They are less accurate than assuming zero growth.

• Discount optimism, and more the further out you look. The upward bias increases with the forecast horizon.

  • Be skeptical of general agreement regarding tiny or emerging companies. This is precisely where unpredictable market behavior outperforms expert forecasts.

• Be wary of the portfolio the consensus loves most. Stocks with the most optimistic forecasts have returned less than the most pessimistic ones.

• Do not throw away the one-year forecasts. They remain better than the linear models in use, and extrapolating them beats the explicit three-year forecast.

Frequently asked questions

Do analysts get their earnings forecasts right?

Over the long run, very little. An assessment measuring the precision, bias, and effectiveness of long-term earnings growth projections for US firms reveals that accuracy is exceptionally low, demonstrating that these forecasts underperform even a naive model assuming zero growth.

Is it bias or difficulty?

Mainly difficulty. The same study documents that the forecasts are biased and inefficient, but that bias and inefficiency contribute very little to their inaccuracy, which is mainly a consequence of random error. The most reliable are low forecasts for large firms with a low price-earnings ratio and a high market-to-book ratio.

When is a simple model better?

In three specific, measured situations, simple random walk forecasts outperform analyst predictions over extended horizons, for smaller or younger companies, and whenever analysts anticipate negative or substantial shifts in earnings per share. Furthermore, a straightforward extrapolation of the one-year projection delivers the most precise estimate of earnings at the two- and three-year marks.

Does an optimistic bias exist, and what is its price tag?

There exists, expanding alongside the horizon, and it carries implications for the market. When evaluated against an objective benchmark created through machine learning, conditional expectations from analysts display, on average, a positive skewness—an error that magnifies over time, correlates with negative cross-sectional return forecasts, and concentrates heavily within the short legs of numerous anomalies.

Does that mean forecasts are useless?

No, and there are two reasons to qualify it. The same paper that documents the bias concludes that commonly used linear earnings models do not work out of sample and are inferior to those provided by analysts. And the model published in Journal of Finance argues that a positive, predictable bias may be a rational property of optimal forecasts, so classical studies may have dismissed them prematurely.

What we do not know

• How much of the bias is incentive and how much is belief. Rational models and overreaction models explain the same data.

• Whether machine learning improves real decisions. The unbiased benchmark is built after the fact with a model; using it in real time is another problem.

  • How this carries over outside the United States. Much of the evidence comes from US markets with dense analyst coverage.

• How much of the consensus already embeds the discount. If the market knows forecasts are optimistic, part of the bias should already be in the price.

References

1. Harris, R. D. F. The Accuracy, Bias and Efficiency of Analysts’ Long Run Earnings Growth Forecasts. Journal of Business Finance & Accounting, 1999. DOI: 10.1111/1468-5957.00273

2. Bradshaw, M. T., Drake, M. S., Myers, J. N. and Myers, L. A. A re-examination of analysts’ superiority over time-series forecasts of annual earnings. Review of Accounting Studies, 2012. DOI: 10.1007/s11142-012-9185-8

3. Van Binsbergen, J. H., Han, X. and Lopez-Lira, A. Man versus Machine Learning: The Term Structure of Earnings Expectations and Conditional Biases. The Review of Financial Studies, 2022. DOI: 10.1093/rfs/hhac085

4. Bordalo, P., Gennaioli, N., La Porta, R. and Shleifer, A. Diagnostic Expectations and Stock Returns. The Journal of Finance, 2019. DOI: 10.1111/jofi.12833

5. Lim, T. Rationality and Analysts’ Forecast Bias. Journal of Finance, 2001. DOI: 10.1111/0022-1082.00329

This material is purely informational and does not amount to financial guidance or an investment proposal. The referenced research examines distinct markets and timeframes which cannot be equated, and none of these studies permits the dependability of any specific prediction to be foreseen.

By Ava Stringer

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