**Analyst forecasts may not take into account the distribution, particularly the skewness, of potential outcomes. A forecast of the most likely profit can significantly differ from the more relevant probability weighted expected value. **

**Whether a forecast is a mean or a mode is also important in financial reporting. Most IFRS standards, including IFRS 9 regarding loan impairments, require a probability weighted expected value; however, this is not universal. In some cases, such as IAS 37 regarding provisions, the requirements are unclear.**

A recent Financial Times article ‘The anatomy of a very brief bear market’ reports on academic research about the drivers of the Covid-19 related fall in US equity prices and their subsequent recovery. Based on analysts’ earnings and dividend expectations the researchers estimate that the equity risk premium (ERP) for the US market rose by 4.5% at the time of the market low in March 2020. They suggest that the ERP has subsequently fallen back to more normal levels, with any difference from the pre-Covid-19 ERP merely reflecting the impact of now higher leverage. Given the scale of the implied ERP change, the implicit suggestion seems to be that markets acted irrationally in their initial knee-jerk response to Covid-19.

The research is interesting but should be read with caution. The problem is using single point analyst forecasts without, it seems, consideration of how these estimates are derived. There is no one absolute forecast for earnings, cash flows or dividends. Forecast uncertainty and the uncertain future development of drivers, such as customer demand, exchange rates, commodity prices or GDP, mean that there is a distribution of possible outcomes. The question is how to best summarise that distribution.

A distribution of forecasts can be summarised by calculating the probability weighted average of the full distribution (the mean). Alternatively, the most likely outcome out of the range of potential values could be used (the mode)^{1}For a continuous distribution the mode is the highest point in the probability distribution.. If the distribution of potential outcomes is symmetrical then the mean and the mode are identical. However, if distributions are skewed then the two measures differ, and it becomes important to know what is being used and to select what is most appropriate.

Market prices should, and in our view, generally do (albeit at times imperfectly), reflect the full distribution of potential outcomes, together with an assessment of the characteristics of that distribution, including the systemic risk. Accordingly, we think the most appropriate summary statistic is the probability weighted average of the distribution and not the most likely outcome.

The problem with analyst earnings forecasts is that it is often unclear which type of summary statistic is being used. In our experience, most analyst forecast models are a single point estimate of the most likely outcome, i.e. the mode. Some analysts may supplement a ‘base-case’ forecast model with additional ‘upside’ and ‘downside’ scenarios and then factor these additional scenarios into their overall valuation. However, we believe the published earnings forecasts to be the most likely outcome. This is not surprising because analysts are (in-part) judged on their forecast accuracy. By forecasting the most likely outcome they ensure that they maximise the probability of being right. Factoring in a less likely (black-swan type) outcome into a probability weighted expected value almost guarantees that the forecast will turn out incorrect – with the expected value being the only value that is not actually expected.

The result of this approach to forecasting is that a change in the skewness of a distribution may not be reflected, or only partly reflected, in the forecasts themselves. Take the following example where we summarise a distribution using three scenarios with varying probabilities. In the ‘before’ case the distribution is symmetrical, and the mean expected value is the same as the mode most likely outcome. However, in the second ‘after’ case the negative skewness results in a mean that is significantly lower than the mode. While the most likely outcome has fallen by 5%, the expected value has fallen by 23%. It is the expected outcome, together with the change in systemic risk associated with the change in the distribution, that should drive the change in fundamental value.

**How skewness affects the mean and mode of a distribution**

While it may be convenient to illustrate distributions of potential outcomes using just 3 scenarios, in practice distributions of economic variables and potential outcomes in terms of stock valuation are, most likely, continuous. However, the same message applies: if the probability and consequences of downside risk are greater than for upside variations, then the most likely outcome will overstate the more relevant expected value.

Of course, in practice, changes in prices are driven by many complex factors, some rational and grounded in finance, and some irrational driven by, for example, behavioural influences. We are not saying that the equity risk premium did not increase in the Covid-19 downturn. Indeed, the rise in both observed and implied volatilities and the general uncertainty of what was going to happen next would seem likely to increase the ERP. However, it also seems likely that the market was factoring in a different distribution of profit and cash flow outcomes.

The analysts may well have been right that the most likely Covid-19 related downturn effect on profitability is limited in both amount and duration. However, it also seems to us that the downside scenario became more likely and more severe, resulting in something like the skewed distribution we illustrate above. The focus on simply the most likely forecast will not result in a reliable ERP estimate. We doubt very much that the ERP rose by 4.5% February to March 2020 or that the change in prices at this time was necessarily irrational.

Our message in terms of forecasting and deriving target values is not to solely use the most likely outcome. Scenarios and, particularly, the skewness of the distribution of potential outcomes matter. Single point estimates and forecasts should reflect all potential outcomes and be calculated as a probability weighted expected value.

It is not just the focus on the most likely outcome that compromises the usefulness of analyst forecasts. We also think that in many cases forecasts are based on the ‘success scenario’. Management guidance tends to assume the successful implementation of their strategy, which may itself introduce an upward bias. In addition, forecasts tend to be based on alternative performance measures (non-GAAP or non-IFRS) and consequently ignore certain expense items. It is true that some of these excluded expenses may be truly ‘non-recurring’ but many more will be ‘sometimes recurring’ or ‘recurring but volatile’.^{2}See our article *Disaggregation is key to understanding performance* for more about non-recurring items and non-GAAP measures. Excluding such items from forecasts is common. A better approach is to use expected values and take into account these items in the overall assessment of the probability weighted expected future cash flows and profit.

**Financial reporting estimates – mean or mode?**

If investors need to focus on probability weighted averages when constructing valuation models, then it would help if the data in financial statements upon which these forecasts are (in part) based are also expected values.

There are many assets and liabilities in IFRS financial statements where measurement is based on estimated future cash flows. Most of these are explicitly or implicitly based on an expected value calculation, but this is not always the case. In some situations, the mode is used and, in others the accounting standards are not very clear, and diversity may arise. We think it is important that investors understand the measurement basis of the financial reporting metrics used in analysis and valuation.

For fair value measures, market prices automatically take account of the distribution of outcomes, assuming those prices are rational. Where fair values are based on models rather than observed prices (level 3), the same distribution must also be taken into account.

The same applies to most other IFRS current value measures that are not strictly fair values. For example, when measuring an impairment of tangible or intangible fixed assets using the ‘value in use’ approach of IAS 36, there is an explicit requirement that the valuation should be “the weighted average of all possible outcomes”.

**Loan loss provisions**

A good example of a recent change in financial reporting, where IFRS has moved from a poorly defined measurement approach (management could use the mode, mean or pretty much anything else) to a clear probability weighted expected value, is the impairment of loans and other financial assets.

In IFRS 9 *Financial Instruments*, impairment allowances using the expected credit loss (ECL) methodology are based on probability weighted expected values. This must take into account the range of potential outcomes, including allowing for differing economic scenarios to the extent that these impact the probability and resulting loss from loan defaults. This more forward-looking expected credit loss approach replaced the previous so-called incurred loss methodology that was applied in IAS 39.^{3}IFRS 9 became effective in 2018. However, most insurance companies have the option to defer application of IFRS 9 until IFRS 17 becomes effective in 2023.

The problem with IAS 39 is the requirement that the incurred loss provision should be based on economic conditions at the reporting date, not taking into account economic forecasts, such as a potential increase in unemployment, or their distribution. In addition, an allowance could only be recognised where there existed “objective evidence” that a loss had occurred. This did not have to be an actual default as is often quoted, but the approach was certainly a lot less forward looking than is the case for ECL under IFRS 9.

The probability weighted expected value approach in IFRS 9 increases the subjectivity of an already difficult estimate for banks. However, in our view, this subjectivity is more than offset by the greater relevance of the ECL measure and the greater responsiveness of the allowance when credit conditions change.

HSBC provides a good example of ECL based on forecast economic assumptions, coupled with a probability weighted expected value approach. The first table below shows the key economic variables that the company has used in estimating expected losses at 30^{th} June 2020. The second shows the range of these key economic variables for the different scenarios used in the expected value calculation, together with the related probabilities. The final table shows the result of these economic assumptions in terms of the expected credit loss allowance.

**Extracts from HSBC 30**^{th} June 2020 expected credit loss disclosures

^{th}June 2020 expected credit loss disclosures

HSBC uses four scenarios in determining their probability weighted average ECL allowance, including two downside scenarios. The skewness of the distribution can be seen by the different probabilities applied to the upside and downside scenarios, which translates into a higher ‘reported ECL’ than would be the case just considering the ‘central scenario’.

The distribution of potential outcomes presented in the HSBC disclosures illustrates how different the required allowance could be in subsequent periods. However, the good thing about IFRS 9 compared with IAS 39 is that the full expected ECL allowance is made as soon as credit conditions deteriorate, rather than there being a drag on earnings for several periods under the former IAS 39 “too little too late” incurred loss approach. The effect of a subsequent unexpected increase or reduction in the allowance should be the same in value terms. However, given the skewness of the distribution the probability of a future reduction in the allowance is actually greater than the probability of an increase. Of course, this is based on the unlikely event that the distribution chosen by the company is actually correct.

**Use of the ‘most likely’** amount in financial reporting

Not all IFRS standards use probability weighted averages for uncertain items. IFRS 15 *Revenue Recognition* requires the use of either an expected value or the most likely amount when estimating customer consideration that is variable^{4}Variable consideration arises when, for example, there are bonus payments or penalties applied to customer consideration, depending on the performance of the supplier. The sale of licences may have variable payments depending on the use of that licence and the gains made by the licensee. IFRS 15 also applies a degree of conservatism to variable consideration, including the requirement that uncertain revenue can only be recognised where the seller does not expect there to be a “significant reversal”. This takes revenue further away from a true probability weighted expected value. While we appreciate the need for a conservative approach to revenue recognition with regard to governance and stewardship, we do not think this constraint, compared with an unbiased probability weighted expected outcome, produces the most relevant measures of performance for investors. The selection is based on which measure “an entity expects to better predict the amount of consideration to which it will be entitled …”. IFRIC 23 *Uncertainty over Income Tax Treatments* applies a similar approach to measuring tax and deferred tax amounts if there is uncertainty over how the tax authorities will view certain transactions.

In both cases where the outcome is binary the standards say that the most likely amount may be the better approach, whereas if the outcome is a range of possibilities or, in the case of revenue recognition there are many contracts with similar characteristics, then the probability weighted average is preferred.

The choice of mean or mode may not matter much for investors when it comes to revenue recognition, considering the volume and generally short-term nature of transactions^{5}A bigger impact for revenue recognition may be the constraint applied where consideration is uncertain. IFRS 15 requires that variable consideration may be recognised as revenue only “to the extent that it is highly probable that a significant reversal will not occur when the uncertainty associated with the variable consideration is subsequently resolved.” The resulting conservative measurement of revenue may lead to reported profit understating the true economic gains, although it is likely that the effect on profit could only be material for companies with significant revenue growth.. This may not be the case for taxation where the effect could be more significant. In our view, a probability weighted expected value approach would be better in all situations.

IAS 37 *Provisions* covers a range of non-financial liabilities such as environmental provisions, warranties, restructuring costs and legal obligations. The standard requires that these liabilities be measured at the “best estimate of the amount required to settle the obligation”. Settlement could be either through transfer to a third party or, more likely, through cash payment. The problem is that ‘best estimate’ is not defined and there is evidence that different approaches are used in practice. Some accountants claim that the result of applying the standard is close to a probability weighted average; however, this may not be the case for those liabilities that are more binary in nature, where there may be greater use of the most likely amount.^{6}Even where the ‘best estimate’ is based on the most likely outcome, IAS 37 suggests that this be adjusted if the distribution is not symmetrical. However, this process is unclear and advice as to how this should be done differs. This IASB board meeting paper explains in more detail some of the measurement challenges in IAS 37, if you are interested!

A further issue with IAS 37 is that liabilities are only recognised where it is estimated that the probability of a cash outflow is more than 50%. Where a number of similar items are involved, such as warranty provisions, this is not a problem because, for the portfolio as a whole, a cash payment would be likely, even though for each individual warranty it may not.

The problem for investors is where the obligation relates to a unique situation such as a legal claim. In this case, while the most likely outcome may be zero, the probability weighted average may be significant. The contingent liability footnote will give details but, unfortunately, not the expected outcome. The exception is where the obligation is acquired as part of a business combination, in which case the probability weighted expected outcome (in the form of a fair value) is recognised in the balance sheet and subsequently updated.

**Insights for investors**

**Analyst forecasts are merely one point in a distribution of potential outcomes. Many of these forecasts may be the ‘most likely’ outcome and not the more relevant probability weighted average.**

**A change in the distribution of potential future profit and cash flow, particularly the degree of skewness, may affect the probability weighted expected performance (and therefore value), even though the most likely outcome is unchanged.**

**Focus on probability weighted expected values and not most likely outcomes. The distribution and variability of potential outcomes matters, particularly the impact on systemic risk and downside potential.**

**While many accounting measures based on forecasts of future cash flows are probability weighted averages, this is not always the case. Pay particular attention to how uncertain provisions and uncertain tax obligations are measured; they may not reflect the full range of potential outcomes.**

**Variable consideration in revenue transactions may not reflect the true probability weighted expected outcome. The inherent conservatism in this situation may create a lag in revenue recognition, although the effect is likely to only have the potential to be significant for high growth companies.**