Valuation risk

Taxonomy of valuation risk

Valuation risk is a financial risk. However, it is different in nature from other financial risks, like market risk. The latter is measured as the potential loss deriving from the evolution of the prices of an entity's financial instruments over time and is calculated as the potential difference in the instrument price at the valuation date and after a certain number of days in the future (the "holding period"). This implies two key conceptual and methodological differences vs. valuation risk:

• Valuation risk is the uncertainty about the difference between the fair value reported for a financial instrument at the valuation date and the price that could be obtained on that same date if the instrument were effectively traded. It is therefore an instantaneous risk that is measured at a specific point in time; its measurement does not involve any time interval.
• Market risk and other financial risks are measured by simulating adverse movements of the risk factors affecting the value of an entity's financial instruments during the holding period, implicitly assuming that the pricing models used by the entity correctly reflect the instrument value and that capacity is maintained along all the holding period. On the opposite, valuation risk represents the uncertainty over the capacity of the pricing models to correctly represent the instrument prices.

The example of banks

Banks are the entities most likely to be exposed to valuation risk as a result of their massive holdings of financial instruments classified as Level 2 or 3 of the fair value hierarchy. In Europe, at the end of 2020 the banks under the direct supervision of the European Central Bank (ECB) held fair-valued financial instruments in an amount of € 8.7 trillion, of which € 6.6 trillion classified as Level 2 or 3. Level 2 and Level 3 instruments respectively amounted to 495% and 23% of the banks' highest-quality capital (so-called Tier 1 Capital). As an implication, even small errors in such financial instruments' valuations may have significant impacts on banks' capital. See valuation control.

In February 2020 the European Systemic Risk Board warned in a report that banks' substantial amounts of financial instruments with complex features and limited liquidity are a source of risk for the stability of the global financial system.

A 2017 report by the Basel Committee on Banking Supervision, an international regulator for the banking sector, noted that IFRS 13 leaves entities significant discretion in determining financial instrument fair value and identified this discretion as a potential source of moral hazard: "The evidence consistent with accounting discretion as contributing to moral hazard behavior indicates that (additional) prudential valuation requirements may be justified."

Areas where discretion may be applied in the determination of financial instrument fair value include:

• Definition of active market
• Choice of pricing models and methodologies
• Classification of inputs used in pricing models as observable or non-observable
• Estimation of the level of significance of unobservable inputs used in pricing models

Banking regulators have taken actions to limit discretion and reduce valuation uncertainties. A row of regulatory documents has been issued, providing detailed prudential requirements that have many points of contact with the accounting rules and have the indirect effect of limiting the discretion left to banks in valuating financial instruments.

The ECB in a Supervision Newsletter of 2021 identified valuation risk as a priority and noted that its inspections had "highlighted severe weaknesses in banks' internal valuation risk frameworks." The ECB acknowledged "The interconnectedness of the accounting and prudential frameworks" and consistently adopted in its inspections on banks a comprehensive perspective covering both the accounting space ("valuation uncertainty, observability of valuation inputs, model risk, fair value classification, recognition of profits when instruments are first recorded in the balance sheet (often referred to as day one profits), independence of price verification, market data quality control") and the prudential space ("prudent valuation practices").

Issues in estimating banks' valuation risk exposures

A 2017 paper of the Bank of Italy noted significant challenges in the assessment of banks' exposure to valuation risk as a result of insufficient published data. The Basel Committee on Banking Supervision also highlighted this lack of transparency in the above-mentioned 2017 report: "Accounting values may embed a significant degree of uncertainty and, as a result, may impede the market's ability to assess a bank's risk profile and overall capital adequacy."

Subsequent research confirmed that more informative analysis of banks' valuation risk exposures, fair value measurement methodologies and practices, risk management processes, and prudential capital allocation would only be made possible by a significant overhaul in banks' disclosures.

Critical lack of disclosed data has been identified in the following areas:

• Qualitative information about the governance and controls on valuation risk
• Segmentation of Level 2 instruments (which represent the bulk of banks' holdings of instruments potentially exposed to valuation risk) by significance of the unobservable inputs used for their valuation
• Details on unobservable inputs, their use in the valuation models, their significance for pricing, and the sensitivity of financial instrument valuations to changes in unobservable inputs
• Contribution of liabilities to valuation risk, i.e. whether liabilities mitigate a bank's valuation risk exposure (because they are exposed to the same valuation risk factors as assets, with a similar functional form and sensitivity, and with opposite sign) or instead contribute to it

Valuation risk measurement

The consensus methodology for measuring risks relating to financial instruments follows the approach prescribed for regulated financial entities like banks and insurance companies, which are required to measure the risks in their balance sheets and set aside capital that will allow them to absorb the losses should the risks materialize (generally referred to as "economic capital"). This methodology requires building a probability distribution of the relevant risk factors and pick the value corresponding to a predefined confidence interval.

For valuation risk, this implies building a probability distribution of exit prices. This task is challenging due to the sheer nature of valuation risk, i.e. the fact that a database of exit prices is hardly available. There is no commonly accepted methodology, and additional research will be required. Initial approaches proposed in literature include:

• Whenever possible, build benchmark curves for key risk factors by leveraging market-traded instruments whose risk factor exposure shows similarities with the instrument being evaluated
• Build hypothetical exit prices based on assumptions about the return that investors are expected to ask for the specific risk (an approach similar to one often used for pricing non-performing loans)

With respect to the amount of economic capital to be effectively allocated for a given instrument, one methodological approach suggests that valuation risk on one side, and all other risks relating to the same instrument on the other side are mutually exclusive. In fact, valuation risk for a financial instrument is measured under the assumption that the entity sells it (or transfers it to a third party, in case of a liability); once that instrument has been traded, the entity is no longer exposed to market, credit or other risks for that instrument and can release any capital previously posted against them. Under this assumption, if an entity suffers a loss due to valuation risk, its prudential capital will be affected by two impacts of opposite sign:

• A negative impact due to the loss incurred in the trade, that directly dents into available capital
• A positive impact due to the release of the capital previously set aside for the traded instrument for all risks other than valuation risk

Under this approach, an entity may allocate economic capital for valuation risk for a given financial instrument to the extent that the risk of loss due to price uncertainty (valuation risk) exceeds the total amount of economic capital set aside for all other risks, as expressed by the following formula:

<span class="mwe-math-element" typeof="mw:Extension/math" about="#mwt110" data-mw='{"name":"math","attrs":{},"body":{"extsrc":"Capital_{VR}(i,t_{Exit})=max[Loss(i,t_{Exit})-Capital_{OR}(i,t_{Exit}),0]"}}' id="mwhQ"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Capital_{VR}(i,t_{Exit})=max[Loss(i,t_{Exit})-Capital_{OR}(i,t_{Exit}),0]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> <mi>a</mi> <mi>p</mi> <mi>i</mi> <mi>t</mi> <mi>a</mi> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> <mi>R</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>i</mi> <mo>,</mo> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> <mi>x</mi> <mi>i</mi> <mi>t</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>=</mo> <mi>m</mi> <mi>a</mi> <mi>x</mi> <mo stretchy="false">[</mo> <mi>L</mi> <mi>o</mi> <mi>s</mi> <mi>s</mi> <mo stretchy="false">(</mo> <mi>i</mi> <mo>,</mo> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> <mi>x</mi> <mi>i</mi> <mi>t</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>−<!-- − --></mo> <mi>C</mi> <mi>a</mi> <mi>p</mi> <mi>i</mi> <mi>t</mi> <mi>a</mi> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>O</mi> <mi>R</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>i</mi> <mo>,</mo> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> <mi>x</mi> <mi>i</mi> <mi>t</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>,</mo> <mn>0</mn> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Capital_{VR}(i,t_{Exit})=max[Loss(i,t_{Exit})-Capital_{OR}(i,t_{Exit}),0]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/30efd0a66729ddf0ae25c6e3c8b161b881a86b86" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:64.082ex; height:2.843ex;" alt="{\displaystyle Capital_{VR}(i,t_{Exit})=max[Loss(i,t_{Exit})-Capital_{OR}(i,t_{Exit}),0]}"/></span>

Where:

• ${\displaystyle Capita{l}_{VR}(i,t_{Exit})}$ is the amount of economic capital to be set aside for valuation risk for instrument ${\displaystyle i}$ at time ${\displaystyle t_{Exit}}$
• ${\displaystyle Loss(i,t_{Exit})}$ is the hypothetical loss assumed to occur on time ${\displaystyle t_{Exit}}$ from the trade of instrument ${\displaystyle i}$
• ${\displaystyle Capita{l}_{OR}(i,t_{Exit})}$ is the total amount of economic capital set aside for all risks other than valuation risk for instrument ${\displaystyle i}$ at time ${\displaystyle t_{Exit}}$ before the trade
• ${\displaystyle t_{Exit}}$ is the evaluation date, i.e. the date when instrument ${\displaystyle i}$ is assumed to be traded

Another way of expressing the same concept is that the total economic capital to be allocated for a financial instrument, including valuation risk and all other risks, is equal to the biggest of the economic capital allocated to valuation risk and the economic capital allocated to the other risks, as per the following formula:

<span class="mwe-math-element" typeof="mw:Extension/math" about="#mwt134" data-mw='{"name":"math","attrs":{},"body":{"extsrc":"Capital(i,t_{Exit})=max[Capital_{VR}(i,t_{Exit}),Capital_{OR}(i,t_{Exit})]"}}' id="mwmg"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Capital(i,t_{Exit})=max[Capital_{VR}(i,t_{Exit}),Capital_{OR}(i,t_{Exit})]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> <mi>a</mi> <mi>p</mi> <mi>i</mi> <mi>t</mi> <mi>a</mi> <mi>l</mi> <mo stretchy="false">(</mo> <mi>i</mi> <mo>,</mo> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> <mi>x</mi> <mi>i</mi> <mi>t</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>=</mo> <mi>m</mi> <mi>a</mi> <mi>x</mi> <mo stretchy="false">[</mo> <mi>C</mi> <mi>a</mi> <mi>p</mi> <mi>i</mi> <mi>t</mi> <mi>a</mi> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> <mi>R</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>i</mi> <mo>,</mo> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> <mi>x</mi> <mi>i</mi> <mi>t</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>,</mo> <mi>C</mi> <mi>a</mi> <mi>p</mi> <mi>i</mi> <mi>t</mi> <mi>a</mi> <msub> <mi>l</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>O</mi> <mi>R</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>i</mi> <mo>,</mo> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>E</mi> <mi>x</mi> <mi>i</mi> <mi>t</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Capital(i,t_{Exit})=max[Capital_{VR}(i,t_{Exit}),Capital_{OR}(i,t_{Exit})]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f19fd680b08aecb92682fd7eeb5644c9ad36e2ce" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:62.918ex; height:2.843ex;" alt="{\displaystyle Capital(i,t_{Exit})=max[Capital_{VR}(i,t_{Exit}),Capital_{OR}(i,t_{Exit})]}"/></span>

Where:

• ${\displaystyle Capital(i,t_{Exit})}$ is the total amount of economic capital to be set aside for instrument ${\displaystyle i}$ at time ${\displaystyle t_{Exit}}$
• ${\displaystyle Capita{l}_{VR}(i,t_{Exit})}$ is the amount of economic capital calculated for valuation risk for instrument ${\displaystyle i}$ at time ${\displaystyle t_{Exit}}$ (corresponding to ${\displaystyle Loss(i,t_{Exit})}$ in the previous equation)
• ${\displaystyle Capita{l}_{OR}(i,t_{Exit})}$ is the total amount of economic capital calculated for risks other than valuation risk for instrument ${\displaystyle i}$ at time ${\displaystyle t_{Exit}}$ before the trade
• ${\displaystyle t_{Exit}}$ is the evaluation date, i.e. the date when instrument ${\displaystyle i}$ is assumed to be traded