Value at risk (VaR) is a staple of insurance regulation and capital modelling. It gives a possible answer to a simple question: How bad could it get, with 99.5% confidence? But it stops there. It doesn't tell you what happens beyond the 99.5% confidence level. For risk professionals managing portfolios with fat tails, volatility clustering, or long-latency claims, that missing detail matters.

Enter conditional tail expectation (CTE), also known as tail value at risk (TVaR), conditional value at risk (CVaR), or expected shortfall (ES). While terminology varies by context (e.g., ES in Basel III, TVaR in Bermuda and Switzerland, CTE in North America), the concept is the same: Instead of reporting the loss at a specified percentile, it gives you the average of the losses worse than that. In this article, we refer to it as CTE.

In practice, where CTE is used, it typically uses a lower cut-off percentile for the calculation than VaR. The argument for CTE over VaR is not about whether capital should be higher or lower overall, but about ensuring greater sensitivity to tail risk, promoting better risk management, and driving better decisions.

Why is VaR still the default?

Solvency II, South Africa’s Solvency Assessment and Management (SAM), and Insurance Capital Standards (ICS) all standardise on a 99.5% one-year VaR approach for regulatory capital. This choice is driven partly by legacy, partly by convenience.

VaR allows modular, hierarchical models that don't require full distribution simulation. Its structure supports the use of closed-form aggregation techniques such as variance-covariance matrices under Gaussian assumptions. This has enabled spreadsheet-based implementations, simpler validation processes, and easier articulation of capital across business units and risks. From a supervisory standpoint, it facilitates consistency and tractability.

Another appeal is its intuitive interpretation: A 99.5% VaR can be loosely framed as a 1-in-200 probability of ruin, aligning with credit rating agency language and enabling mapping to target solvency levels (e.g., BBB or A-equivalent). That framing made it attractive when VaR-based standards were first developed.

There's also inertia. Insurance regulation drew heavily from the banking world in the early 2000s, and at that point, VaR was the dominant risk metric in Basel frameworks. Despite Basel's shift to CTE for market risk, insurance has not yet caught up.

But convenience comes at a cost. VaR creates a regulatory cliff edge at the given percentile. It encourages optimisation up to the cliff's edge and then ignores the potentially catastrophic losses that lie beyond. CTE demands more computation but rewards us with richer insight into what happens after we fall off that cliff.

The case for CTE-based capital frameworks

1. Used in practice, and growing in support

CTE isn't merely theoretical. While not yet the insurance regulatory default, it has growing adoption:

• Canadian LICAT (Life Insurance Capital Adequacy Test) explicitly applies a 99% CTE measure for insurance risks like mortality, longevity, and morbidity (while utilising a combination of percentile-based or stress-test methods for market, credit, and operational risks).
• Switzerland's SST (Swiss Solvency Test) uses full distribution simulations with CTE-style tail risk measures.
• Swiss Re explicitly measures risk capital requirements using "99% shortfall (tail VaR)" for internal economic capital and regulatory purposes.
• Large global insurers increasingly incorporate CTE-style measures in internal economic capital models, though specific implementations vary.
• Bermuda uses CTE-style calibration but through a standardised shock-based regime, not insurer-specific CTE modelling.

CTE features prominently in the CERA, FRM, and PRM qualifications, reinforcing its relevance in professional risk discourse.

CTE-style methods are also permitted in valuation frameworks like IFRS 17, although percentile-based and cost-of-capital methods still dominate

Even under Solvency II or SAM, internal models may use CTE as long as they demonstrate consistency with 99.5% VaR.

2. Banks are already moving on

VaR's limitations became undeniable during the global financial crisis. In 2016, the Basel Committee published revisions to the market risk framework, explicitly noting that "a number of weaknesses have been identified with using VaR for determining regulatory capital requirements, including its inability to capture tail risk." The framework shifted from VaR at 99% confidence to CTE at 97.5% confidence, implemented globally over time, with Europe adopting in 2023 and the US targeting 2025 to 2028.

The transition wasn't without complexity. Banks faced stringent eligibility requirements and increased computational demands. The US is still implementing these changes through "Basel III Endgame" proposals, indicating continued regulatory momentum toward CTE-style measures.

Insurers have been slower to follow suit, but the rationale applies equally. If banking regulators concluded that VaR was inadequate for capturing tail risk after the financial crisis, why should insurance regulators consider it sufficient for catastrophe risks, liability tails, and systemic exposures?

3. Better tail sensitivity

VaR at 99.5% tells you the minimum loss in the worst 0.5% of cases. It doesn't say anything about what happens beyond that, whether losses are 1.5 times or 10 times worse. CTE fills this gap by capturing the severity of extreme events, not just their probability.

This distinction becomes critical when comparing portfolios with identical VaR but vastly different tail behaviour. Consider two property catastrophe portfolios, each with ZAR500M in 99.5% VaR:

• Portfolio A (thin-tailed): Concentrated in moderate earthquake zones with well-understood, bounded exposure. Beyond the 99.5th percentile, losses climb gradually to a CTE of ZAR650M.
• Portfolio B (fat-tailed): Heavy exposure to mega-catastrophe regions where infrequent but extreme events dominate the tail. The same ZAR500M VaR masks a CTE of ZAR1.2B.

VaR suggests equivalent risk. CTE reveals that Portfolio B requires more than double the economic capital to achieve the same security level.

SCR multiple comparisons become misleading

Under Solvency II, both portfolios would show identical Solvency Capital Requirements (SCRs) of ZAR500M. If each holds ZAR1B in capital, both appear to have a comfortable 2 times SCR multiple. But Portfolio A has genuine resilience with only ZAR650M expected tail loss, while Portfolio B faces ZAR1.2B in expected tail losses—making its apparent 2 times cover ratio illusory.

Reinsurance purchase decisions

An insurer setting reinsurance limits equal to the 99.5th percentile (ZAR500M) might feel adequately protected with a 2 times SCR multiple. But Portfolio B's true tail exposure of ZAR1.2B means that even modest parameter uncertainty or low-frequency events beyond the 99.5th percentile could trigger losses far exceeding both the reinsurance cover and available capital. The SCR multiple provides false comfort when the real tail exposure is masked.

This matters particularly for:

• CAT risks where frequency-severity models exhibit heavy tails
• Liability lines with skewed distributions and uncertain development patterns
• Reinsurance structures that attach beyond the 99.5th percentile
• Cyber risk where systemic events can trigger correlated mega-losses

4. Reinsurance pricing and arbitrage

The VaR-CTE difference creates systematic mispricing in reinsurance markets, enabling cedants to game their apparent risk profile while transferring genuine tail exposure at below-market rates.

Mechanics of the arbitrage

Consider a cedant optimising its portfolio to minimise 99.5% VaR for regulatory capital purposes. By selecting risks with thin regulatory tails but fat economic tails, they can appear well capitalised while offloading true tail risk through reinsurance treaties priced on economic (CTE-based) models.

Concrete example

A specialty insurer writes cyber policies with ZAR10M limits. Their internal model shows:

• 99.5% VaR: ZAR50M (based on attritional losses and moderate events)
• 99.5% CTE: ZAR120M (reflecting potential for systemic cyber events)

A catastrophe excess of loss treaty with ZAR40M retention and ZAR60M cover appears expensive relative to the ZAR50M VaR—suggesting the cedant retains most of the risk. But the reinsurer prices this treaty recognising that systemic events could trigger the full ZAR100M limit across multiple policies simultaneously. The ZAR60M cover represents genuine tail protection worth far more than VaR-based analysis suggests.

Market implications

This mispricing enables:

• Underpriced treaties where cedants transfer tail risk too cheaply
• Capital arbitrage where regulatory capital drops but economic risk remains
• Market distortions as reinsurers cross-subsidise between VaR-optimised and economically priced business

Sophisticated reinsurers increasingly use CTE-based pricing models, creating a fundamental disconnect with VaR-optimised cedants. The resulting arbitrage opportunities can persist until regulation catches up with economic reality.

5. Sub-additivity and capital allocation

VaR's lack of sub-additivity is a significant practical flaw, directly affecting capital allocation, portfolio construction, and merger analysis. A coherent risk measure should satisfy sub-additivity, meaning:

RM(X + Y) ≤ RM(X) + RM(Y)

When sub-additivity fails, combining seemingly well-diversified portfolios can increase required capital, contradicting basic intuition about diversification.

Why VaR fails sub-additivity

This issue emerges when tail dependencies between portfolios manifest at extremes, even if invisible at moderate confidence levels. VaR captures only the individual portfolio's 99.5th percentile losses and misses joint extreme events where simultaneous losses occur.

Realistic insurance example—regional hurricane risks

Consider an insurer holding two hurricane-exposed portfolios:

• Portfolio A: Florida hurricane risk
  • Standalone 99.5% VaR: USD200M
  • Based on individual storm frequency and severity modelling
• Portfolio B: Caribbean hurricane risk
  • Standalone 99.5% VaR: USD150M
  • Based on local historical storm data and modelling
• Combined portfolio: When modelled together, acknowledging regional clustering and tail correlation of extreme storms:
• Combined 99.5% VaR: USD380M
• Sub-additivity violation: USD30M (since USD380M > USD200M + USD150M)

The violation arises because severe hurricanes often affect both regions simultaneously through shared meteorological patterns and storm tracks, creating tail dependency not captured individually.

Capital allocation implications

VaR's sub-additivity failure leads to practical challenges:

1. Unstable allocations: VaR-based allocation can yield nonsensical or negative allocations, failing to consistently sum to the total risk.
2. Gaming opportunities: Business units might exploit diversification "blind spots," manipulating apparent risk profiles.
3. Mispricing in merger and acquisition (M&A): VaR-based due diligence might underestimate required post-merger capital due to missed tail correlations.

CTE as a coherent alternative

CTE inherently satisfies sub-additivity, ensuring stable, economically meaningful capital allocations. Standard Euler-based or gradient-based allocation methods work seamlessly with CTE, producing allocations that are non-negative and consistently sum to the total risk.

6. Honesty about tail uncertainty

Estimating 99.5% VaR already forces tail assumptions, but VaR creates a false sense of precision. It suggests we know exactly what happens at the 99.5th percentile while remaining silent about everything beyond that cliff edge.

CTE makes the implications of our tail assumptions visible. If you're uncomfortable with your CTE estimate, that discomfort reflects genuine model uncertainty that VaR simply hides. A 99.5% VaR of ZAR100M paired with a, say, 99% CTE of ZAR500M signals that your tail is fat and uncertain, information that's crucial for decision making but invisible in VaR-only frameworks.

This transparency forces honest conversations about model limitations, parameter uncertainty, and the genuine difficulty of extreme event forecasting. Better to be explicitly uncertain than falsely confident. VaR's apparent precision often masks fundamentally unknowable tail behaviour, while CTE's broader range reflects the true uncertainty inherent in extreme risk estimation.

Long-term capital management’s (LTCM’s) 1998 failure¹ and the 2007–2008 global financial crisis² demonstrated the need for better models of tail behaviour, less use of Gaussian assumptions and Gaussian copulas.

CTE still requires sensible modelling choices for the tail. While selecting inappropriate parameters for alternative copulas can still produce misleading results, CTE frameworks at least allow us to test sensitivity and adjust realistically. Broader use of CTE could push forward better methods for parameter estimation and tail modelling.

Challenges and barriers to adopting CTE

CTE brings implementation challenges and requires careful consideration of trade-offs. However, many perceived barriers are overstated, and the computational and conceptual hurdles are surmountable with proper planning and resources.

1. Computational requirements vary by context

Full distribution simulation can be computationally intensive, particularly where nested stochastics are required. But this is mostly relevant for life insurers with complex guarantees or with-profits structures. For many non-life portfolios, and for much life insurance business, CTE can be implemented using efficient proxy models.

2. Complexity and comprehension

CTE lacks the intuitive appeal of "1-in-200" VaR language. Explaining tail averages, dependence structures, and fat-tailed behaviour risks alienating stakeholders. Ironically, the partial interpretability of VaR may be more dangerous than the arcane complexity of CTE, which at least makes it clear that expert judgement is essential.

3. Tail modelling remains fragile

Modelling VaR already involves tail assumptions. But CTE weights the extreme tail more heavily. Poor fit in the far tail has a greater capital impact. So although the modelling work isn't fundamentally different, the stakes are higher, and scrutiny should increase accordingly.

A common objection to CTE is that it implicitly includes extremely remote scenarios—well beyond 1-in-1,000 or 1-in-10,000 events—where the company is likely already insolvent or the financial system may have collapsed. Why should we hold capital today for such hypotheticals?

However, sensibly chosen distributions will apply negligible weight to the truly apocalyptic. But poor models or choices of loss distributions (with unbounded or infinite-variance tails) can distort results.

4. Implementation and resourcing

Moving from VaR to CTE isn't just a metric swap. It often requires redesigning aggregation layers, rebuilding infrastructure, retraining staff, and overhauling governance. This is a valid concern, particularly in markets where analytical capacity is limited.

Some jurisdictions may benefit from leapfrogging VaR, but others may still find VaR a pragmatic stepping stone.

5. Perceived disconnect from regulatory VaR requirements

Some worry that using CTE for internal purposes creates a disconnect from regulatory capital metrics. But VaR can be easily extracted from a well-designed CTE model, with the benefit of greater confidence and insight. CTE better supports robust risk appetite frameworks and internal decision making, and widespread internal adoption can make eventual regulatory transition easier.

One practical approach is to use VaR for day-to-day risk monitoring and communication but validate key decisions with CTE, especially for capital allocation and stress testing.

6. Limited adoption can miss a core benefit

Some regulators have partially adopted CTE but missed a core benefit. They use CTE to calibrate their standardised scenario-based approaches, replacing VaR-calibrated stress tests with CTE-calibrated ones. While this sounds progressive, it misses one of CTE's main advantages: sensitivity to the actual tail and risk mitigation (like reinsurance) in place for the specific insurer.

Conclusion: Where to from here?

CTE adds complexity. It needs better tail modelling and simulation-based infrastructure. In return it brings transparency, realism, and resilience, thus supporting better risk and capital management.

For actuaries and risk managers serious about internal models, reinsurance structuring, or more realistic capital planning, CTE presents meaningful advantages.

As computational capacity improves and the regulatory landscape evolves, CTE is transitioning from a tool used by a minority of quantitatively sophisticated risk management specialists to a mainstream necessity for robust capital assessment.

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¹ LTCM's sophisticated models assumed low correlations between markets, but the Russian crisis caused "simultaneous price shifts in the same direction in many markets that produced a high correlation between previously uncorrelated markets." This correlation breakdown turned their "diversified" portfolio into a concentrated bet.

² David X. Li's Gaussian copula model became the industry standard for pricing collateralised debt obligations (CDOs). The model couldn't account for tail dependence in housing markets, where extreme events (widespread defaults) were far more correlated than the Gaussian framework suggested. This blind spot contributed to massive mispricing of structured credit products.