Probability-weighted average

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Last Updated on 04/05/2021 by 75385885

Probability-weighted average is used in several standards to provide a more balances estimate of amounts for which the estimation uncertainty is rather high. The standards and IFRS Jargon involved in determining a probability-weighted average are:

IFRS Standards IFRS reporting item
IFRS 3 Business combinations Contingent consideration
IFRS 13 Fair value measurement Expected cash flows
IFRS 17 Insurance contracts Variable fee approach
IFRS 9 Financial instruments Expected credit losses

Here are the more detailed explanations:

IFRS 3 Contingent consideration

Contingent consideration often involves the buyer transferring additional consideration to the seller if certain performance targets are met in the future. This allows the buyer to share the risk associated with the future of the business with the seller by making some of the consideration contingent on future performance.

For context Determine the transaction price

What factors should be considered in determining the fair value of this type of arrangement?

Valuation methods for contingent consideration range from discounted cash flow analyses to more complex Monte Carlo simulations. The terms of the arrangement and the payout structure will influence the type of valuation model the acquirer uses.

Most valuation methods require an approach incorporating some form of option pricing techniques to incorporate the potential variability in outcomes.

Buyers may consider a best estimate discounted cash flow methodology for cash-settled arrangements. The key issue for a discounted cash flow is: what discount rate best represents the risks inherent in the arrangement? There is, in reality, more than one source of risk involved.

For example, both projection risk (the risk of achieving the projected performance level) and credit risk (the risk that the buyer may not have the financial ability to make the arrangement payment) need to be considered. Each of these risks may be quantifiable in isolation.

Factors such as the potential correlation between the two risks and the relative impact of each risk upon the realisation of the arrangement need to be analysed when the two risks exist in tandem.

An alternative approach would be to develop a set of discrete potential scenarios for future performance. Each of these discrete payout scenarios could then be assigned a probability, and the probability-weighted average payout could be discounted based on market participant assumptions.

The impact of using a probability-weighted average approach would typically result in a lower amount being recognised on the acquisition date and income statement volatility in the post-acquisition period.

IFRS 13 Expected cash flows

Present value (ie an application of the income approach) is a tool used to link future amounts (eg cash flows or values) to a present amount using a discount rate. A fair value measurement of an asset or a liability using a present value technique captures all the following elements from the perspective of market participants at the measurement date:

  1. an estimate of future cash flows for the asset or liability being measured.
  2. expectations about possible variations in the amount and timing of the cash flows representing the uncertainty inherent in the cash flows.
  3. the time value of money, represented by the rate on risk-free monetary assets that have maturity dates or durations that coincide with the period covered by the cash flows and pose neither uncertainty in timing nor risk of default to the holder (ie a risk-free interest rate).
  4. the price for bearing the uncertainty inherent in the cash flows (ie a risk premium).
  5. other factors that market participants would take into account in the circumstances.
    for a liability, the non-performance risk relating to that liability, including the entity’s (ie the obligor’s) own credit risk.

The factors under a. and b. are represented in expected cash flows in a probability-weighted average approach to all possible future cash flows, the expected present value technique.

For contextExpected cash flow

Expected present value technique

The expected present value technique uses as a starting point a set of cash flows that represents the probability-weighted average of all possible future cash flows (ie the expected cash flows). The resulting estimate is identical to expected value, which, in statistical terms, is the weighted average of a discrete random variable’s possible values with the respective probabilities as the weights.

Because all possible cash flows are probability-weighted, the resulting expected cash flow is not conditional upon the occurrence of any specified event (unlike the cash flows used in the discount rate adjustment technique).

A very basic form of probability-weighted expected cash flows is as follows:

Possible expected cash flows Probability Probability-weighted cash flows
CU500 15% CU75 (=CU500 * 15%)
CU800 60% CU480 (=CU800 * 60%)
CU900 25% CU225 (=CU900 * 25%)
Expected cash flow 100% CU780 (= CU75 + CU480 + CU225)

In this simple illustration, the expected cash flows (CU780) represent the probability-weighted average of the three possible outcomes. In more realistic situations, there could be many possible outcomes. However, to apply the expected present value technique, it is not always necessary to take into account distributions of all possible cash flows using complex models and techniques.

Rather, it might be possible to develop a limited number of discrete scenarios and probabilities that capture the array of possible cash flows.

For example, an entity might use realised cash flows for some relevant past period, adjusted for changes in circumstances occurring subsequently (eg changes in external factors, including economic or market conditions, industry trends and competition as well as changes in internal factors affecting the entity more specifically), taking into account the assumptions of market participants.

While expected cash flows (i.e., the probability-weighted average of possible future cash flows) incorporate the uncertainty in the instrument’s cash flows, they do not incorporate the compensation that market participants demand for bearing that uncertainty.

IFRS 17 Variable fee approach

An entity assesses whether a contract has direct participation features using its expectations at inception of the contract and does not reassess the conditions, unless the contract is modified. [IFRS 17.B102]

A contractual right for policyholders to participate in a clearly identified pool of underlying items can arise from the terms of the contract or from law or regulation. The key point is that the policyholder’s right to participate in the returns of the pool of underlying items is enforceable. [IFRS 17.B105]

For contextExample Variable fee approach

Underlying items are defined as Items that determine some of the amounts payable to a policyholder. Underlying items can comprise any items, for example, a reference portfolio of assets, net assets of the entity, or a specified subset of the entity’s net assets.

An entity does not need to hold the underlying items to be eligible for the variable fee approach. However, whether an entity holds the underlying item or not is relevant to the presentation of insurance finance income and expense (see Disaggregating of insurance finance income or expense in Profit or Loss and OCI).

A clearly identified pool of underlying items does not exist when: [IFRS 17.B106]

  • An entity can change the underlying items that determine the amount of the entity’s obligation with retrospective effect.
  • There are no underlying items identified, even if the policyholder could be provided with a return that generally reflects the entity’s overall performance and expectations, or those of a subset of assets the entity holds.

To treat an entity’s share in underlying items as a fee, analogous to fees charged by an investment manager in an investment management contract, IFRS 17 requires that the entity should expect:

  • To pay the policyholder an amount equal to a substantial share of the fair value returns on the underlying items.
  • A substantial proportion of any changes in the amounts to be paid to the policyholders to vary with the changes in the fair value of underlying items.

IFRS 17 provides guidance that the term “substantial” in both requirements should be considered in the context of the objective of insurance contracts with direct participation features being contracts under which the entity provides investment-related services and is compensated for the services by a fee that is determined by reference to the underlying items.

An entity’s expectations of the proportion of changes in the fair value of underlying items accruing to policyholders in different scenarios is considered over the duration of the group of insurance contracts on a present value probability-weighted average basis. [IFRS 17.B107]

For example, if the entity expects to pay a substantial share of the fair value returns on underlying items, subject to a guarantee of a minimum return, there will be scenarios in which: [IFRS 17.B108]

  • Cash flows that the entity expects to pay to the policyholder vary with changes in the fair value of the underlying items, because the guaranteed return and other cash flows that do not vary based on the returns on underlying items do not exceed the fair value return on the underlying items.
  • Cash flows that the entity expects to pay to the policyholder do not vary with the changes in the fair value of the underlying items because the guaranteed return and other cash flows that do not vary based on the returns on underlying items exceed the fair value return on the underlying items.

The entity’s assessment of the variability of contracts that include such guarantees will reflect a present value probability-weighted average of all scenarios.

IFRS 9 Expected credit losses

IFRS 9.5.5.17(a) requires an entity to measure expected credit losses (ECL) in a way that reflects an unbiased and probability-weighted amount that is determined by evaluating a range of possible outcomes.

When an entity has determined the scenarios to be used consideration then needs to be given to determining the weightings to be applied to each of the scenarios selected.

For contextImpairment of financial assets

This section assumes that the approach taken to calculate ECL is to use discrete forward looking macro-economic scenarios rather than a Monte Carlo or other type of approach.

IFRS 9 does not prescribe how to determine weightings, so different approaches are possible. Judgement will be required as the weightings assigned will depend on various facts and circumstances and will need to be periodically re-assessed.

Relevant considerations in determining the weighting to be applied to each selected scenario include:

  • Objective of weightings: IFRS 9.BC 5.265 states that when there are many possible outcomes, an entity can use a representative sample of the complete distribution for determining the expected value of credit losses. When representative scenarios are selected they therefore represent a subset of the complete distribution of scenariosMost likelythat could occur. Accordingly, each selected scenario should be given a weighting based on the sub-set of scenarios for which the outcome of that selected scenario (i.e. the loss arising, in the case of ECL measurement) is representative. As an example, consider a simplified example where all possible scenarios are placed in order of severity, with the 0th percentile scenario being the worst case scenario and the 100th percentile being the best case scenario, and the 10th percentile scenario is chosen as the ‘downside’ scenario. Within the constraints of the discrete scenarios already selected, if the loss arising in the 10th percentile scenario was considered to be representative of the loss arising for all scenarios between the 0th and 33rd percentiles (for example, as the loss profile is relatively flat between the 0th and 33rd percentile), then that scenario would be expected to be given a 33% weighting for ECL measurement in order to be unbiased as per IFRS 9.5.5.17, not a 10% weighting as might seem appropriate based only on the scenario being at the 10th percentile. This is discussed in more detail in the illustrative example presented at the end of this FAQ. As the selected scenarios are chosen to be representative of the complete distribution, the total of the weightings applied should be 100%.
  • Availability of information: The information required to perform a theoretically ‘perfect’ calculation of weightings, such as the complete loss profile across all possible scenarios, will in practice very rarely, if ever, be available without undue cost or effort. For this reason, expert credit judgement will be required. However, just because there is uncertainty, or because judgement is required, does not necessarily mean that information is not reasonable and supportable or not available without undue cost or effort. In particular, some or all of the following information may be available without undue cost and effort, and can be used to assist an entity in determining appropriate weightings:
    • the entity’s default and loss history;
    • peer or industry data on historic defaults and losses; and
    • the entity’s own modelling of possible impacts of future scenarios on credit risk e.g. regulatory stress test modelling. The extent of information available without undue cost or effort may also vary dependent on factors such as the relative sophistication of the reporting entity and how long the entity has been in existence/undertaken particular lending activities.
  • Periodic reassessment: The different scenarios selected and the weightings applied to them will need to be reviewed and re-assessed at each reporting date or when conditions change (also refer to Considering scenarios and weightings together below). If the latest information that is reasonable and supportable continues to support the weightings used at the last reporting date, then it would be appropriate to leave the weightings unchanged. This might be the case, for example, when an entity prepares interim financial statements and there has been no significant change in the entity’s circumstances or to the external macro- economic environment since its previous annual financial statements. When designing the overall approach to determining weightings on first adoption of IFRS 9, an entity should also consider what future developments will, or will not, cause the weightings to change, along with the analysis that will be produced to support this. This will help ensure a consistent approach can be applied on an ongoing basis.
  • Consider scenarios and weightings together: Scenarios and weightings should be considered together. For example, if at a reporting date a more extreme scenario is selected, everything else being equal, it would be expected that the weighting applied would be lower. However, considering consecutive reporting dates, it should not be presumed that if the economic outlook is worsening then the weightings will also always need to be amended. For example, the weighting applied to a downside scenario could remain constant over time if the downside scenario selected is made more adverse.
  • ECL measurement and significant increase in credit risk: The December 2015 meeting of the IFRS Transition Resource Group for Impairment of Financial Instruments (‘ITG’) clarified that consideration of multiple forward-looking macro-economic scenarios is relevant to both measurement of expected credit losses and the assessmentReclassified of significant increases in credit risk. The approach taken to determining scenario weightings should therefore also consider both these elements.
  • Other disclosures: If determination of the weighting to be applied to forward looking macro-economic scenarios within the ECL estimate is a critical estimate, then the disclosures required by IAS 1.125 and 129 will need to be provided.

Worked example

NB This example is intentionally simplified so as to illustrate the principle that scenario weightings should be based on the outcome arising from the selected scenario. It is not intended to provide a view on any other aspect of ECL calculation.

It also assumes that all necessary information, in particular the complete loss profile, is reasonable and supportable and available without undue cost and effort, which in practice will rarely, if ever, be the case.

A bank holds a single loan asset and it is assumed that:

  • All possible scenarios can be placed in order of severity, with the 0th percentile scenario being the worst case scenario and the 100th percentile being the best case scenario;
  • Three scenarios have been justified as being appropriately representative of the complete distribution, being the 10th percentile (downside), 50th percentile (base case) and 90th percentile (upside) scenarios; and
  • The appropriate stage for the loan has already been determined taking account of the impact of multiple scenarios and forward looking information.

To calculate the ECL taking account of multiple scenarios, each selected scenario is given a weighting based on the sub-set of scenarios for which the outcome arising in that selected scenario (i.e. the loss) is representative.

Therefore;

  • If the loss arising in the 10th percentile downside scenario of 95 is considered to be representative of the losses arising in all scenarios between the 0th and 34th percentiles (where losses range between 100 and 62), then that scenario would be given a 34% weighting;
  • If the loss arising in the 50th percentile base case scenario of 30 is considered to be representative of the losses arising in all scenarios between the 34th and 57th percentiles (where losses range between 62 and 16), then that scenario would be given a 23% weighting; and
  • If the loss arising in the 90th percentile upside scenario of 2.5 is considered to be representative of the losses arising in all scenarios between the 57th and 100th percentiles (where losses range between 16 and 0), then that scenario would be given a 43% weighting.

The graphic following from these assumptions in this scenario is as follows, along with the full loss profile:

Probability-weighted average

Using this approach, the ECL would be estimated as being the sum of:

95 (loss in downside scenario) × 34% weighting =  32.3
30 (loss in base case scenario) × 23% weighting = 6.9
2.5 (loss in upside scenario) × 43% weighting = 1.1

This gives an estimated ECL of 40.3 which is a close approximation of the ECL of 41.0 that would result by considering the loss arising in every single scenario, which is equal to the area under the line of losses in the diagram above.

This contrasts with the result in the same example if each selected scenario is instead given a weighting linked to the percentile that scenario corresponds to. One way of applying such an approach would be to:

  • Apply a weighting of 10% to the 10th percentile downside scenario, as the likelihood of a scenario occurring that is equally or more severe is 10%;
  • Apply a weighting of 10% to the 90th percentile upside scenario, as the likelihood of a scenario occurring that is equally or more positive is 10%; and
  • Apply a weighting of 80% to the 50th percentile base case scenario, being the balancing figure in order for all the weightings to sum to 100%.

The graphic following from these assumptions in this scenario is as follows:

Probability-weighted average

Using this approach, the ECL would be estimated as being the sum of:

95 (loss in downside scenario) × 10% weighting = 9.5
30 (loss in base case scenario) × 80% weighting = 24
2.5 (loss in upside scenario) × 10% weighting = 0.25

This gives an estimated ECL of 33.75, which is 18% less than the ECL of 41.0 that would result by considering the loss arising in every single scenario.

Where such a difference is material such an approach would not produce an unbiased estimate of expected credit losses as required by IFRS 9.5.5.17.

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Last Updated on 04/05/2021 by 75385885

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