08 Mar 2025 5 min read

The problem with VaR

Value at Risk (VaR) is a financial metric designed to quantify the maximum expected loss of an investment portfolio over a specified time horizon at a given confidence level. While it is a cornerstone of risk management across industries, its limitations are glaring in the context of biotech, pharma, and healthcare. These sectors are dominated by fat-tailed risks, extreme outcomes, and non-linear dependencies, which fundamentally undermine VaR’s utility.

In biotech and healthcare, the stakes are high: R&D expenditures often exceed hundreds of millions of dollars, timelines stretch over a decade, and outcomes range from transformative breakthroughs (e.g., Humira, Keytruda) to complete failures. VaR, by its very design, ignores the rare but extreme events that define the risk and reward landscape of these industries.

The Basics of VaR: A Simplistic Measure

VaR is typically defined as the maximum loss within a certain confidence level (1−α1) over a given time horizon. Mathematically:

$$
P(L \leq \text{VaR}) = 1 - \alpha
$$

Where:

L is the portfolio loss,
VaR is the maximum loss at confidence level 1−α1.

For example:

A 95% daily VaR of $10 million implies that, with 95% confidence, the portfolio will not lose more than $10 million in a single day.

VaR is commonly calculated using three approaches:

Historical Simulation: Uses past returns to estimate potential losses.
Variance-Covariance Method: Assumes normally distributed returns.
Monte Carlo Simulation: Simulates potential returns based on assumed distributions.

In biotech and healthcare, all these methods fail for one simple reason: fat-tailed risks and extreme events dominate outcomes, and VaR is fundamentally unequipped to handle such distributions.

1. Fat-Tailed Risks: The Core Problem with VaR

VaR’s most significant limitation in biotech and pharma is its inability to account for fat-tailed distributions, where rare events—both positive and negative—dominate the risk profile. Fat-tailed distributions are characterized by their slow decay, often described by power laws:

$$
P(X > x) \sim x^{-\alpha}, \quad \alpha > 1
$$

In such distributions:

Right tail (positive extreme events): Blockbuster drugs like Keytruda or Humira generate outsized returns, often exceeding billions in revenue.
Left tail (negative extreme events): Catastrophic failures, such as clinical trial setbacks or regulatory rejections, can result in massive losses.

VaR assumes thin-tailed (e.g., Gaussian) distributions, where extreme events are improbable and can be ignored. In fat-tailed domains like biotech:

Variance may not converge (α<2), making parametric methods unreliable.
Extreme losses are vastly underestimated, leading to a false sense of security.

Why This Matters in Pharma and Healthcare

The healthcare industry frequently encounters tail events:

Blockbuster Breakthroughs: A single drug approval can redefine a company’s trajectory, as seen with CAR-T therapies or mRNA vaccines.
Regulatory Shocks: Sudden FDA or EMA rejections can wipe out years of R&D investment.
Systemic Risks: Pandemics or major litigation can lead to correlated losses across an entire portfolio.

VaR smooths over these extremes, providing an incomplete and often misleading picture of risk.

VaR provides no insight into what happens beyond the confidence threshold (1−α). For example, a 95% VaR might indicate a maximum loss of $10 million, but it tells you nothing about the magnitude of losses in the worst 5% of cases. In biotech and healthcare, these extreme cases are where catastrophic risks lie.

Left-Tail Risks in Biotech

A Phase III trial failure for a lead candidate can destroy up to 90% of a biotech company’s valuation.
Reimbursement or pricing challenges in major markets (e.g., the U.S. or EU) can severely limit market access, rendering a drug commercially unviable.
Competitive breakthroughs can render entire platforms obsolete overnight.

Right-Tail Risks in Healthcare

Blockbuster drugs often generate disproportionate returns, driving the majority of portfolio performance. For example, 80% of revenue in pharma can come from 20% of drugs—a textbook manifestation of fat-tailed outcomes.

VaR ignores these realities by truncating its analysis at the confidence threshold, leaving investors blind to the full spectrum of tail risks.

3. Time Horizon and Path Dependency

Biotech and healthcare investments often involve long, uncertain timelines:

Preclinical to commercialization: 10–15 years.
Revenue ramp-up: 3–5 years post-approval.

VaR’s short time horizons (e.g., daily, weekly) fail to account for the cumulative risks that accrue over these extended periods. Risks in biotech are path-dependent:

Early-stage clinical successes or failures significantly alter future cash flow projections.
Funding gaps or partnership delays can amplify risks downstream.

VaR, designed for stable financial portfolios, assumes that losses are independent and evenly distributed over time. In biotech, where risks are cumulative and non-linear, this assumption breaks down entirely.

4. Correlation Spikes and Non-Linear Dependencies

VaR assumes stable correlations between portfolio components. However, in healthcare, systemic events often cause correlations to spike, amplifying losses. For example:

A regulatory change (e.g., FDA tightening approval standards) can impact multiple drugs in development, leading to simultaneous failures.
A major pricing reform (e.g., U.S. Medicare price negotiations) can devalue entire therapeutic categories.

These non-linear dependencies render VaR unreliable, as it assumes a static covariance matrix that fails to capture dynamic shifts in correlations during crises.

5. The Illusion of Precision

VaR provides a single numerical value, giving the illusion of precision while obscuring its assumptions. In biotech and healthcare:

Thin-tailed models (e.g., normal distributions) systematically underestimate tail risks.
Historical data often lacks sufficient examples of extreme events, leading to biased estimates.

For example, VaR might state that a portfolio’s maximum loss at 95% confidence is $20 million. However:

This number says nothing about the potential for a $200 million loss in the worst-case scenario.
Investors may underprepare for extreme tail risks, resulting in catastrophic financial consequences.

6. VaR’s Mathematical and Statistical Failures

From a mathematical perspective, VaR is fundamentally flawed in fat-tailed environments:

Infinite Variance: In distributions with α<2, variance diverges, making parametric VaR models invalid.
Central Limit Fallacy: VaR assumes losses aggregate toward a normal distribution, which is not the case in biotech, where outliers dominate.
Clipping at Confidence Thresholds: By truncating analysis at 1−α, VaR ignores the very events that define risk in biotech.

Better Alternatives to VaR

Given its limitations, VaR should not be the primary risk metric in biotech or healthcare. Alternatives include:

1. Expected Shortfall (ES)

Expected Shortfall (also known as Conditional VaR) calculates the average loss beyond the VaR threshold:

$$
ES_\alpha = E[L \mid L > \text{VaR}_\alpha]
$$

This provides a more complete picture of tail risks.

2. Extreme Value Theory (EVT)

EVT explicitly models the tails of the distribution using the Generalized Pareto Distribution (GPD):

$$
P(X > x \mid X > u) = \left(1 + \xi \frac{x - u}{\sigma}\right)^{-1/\xi}, \quad \xi > 0
$$

EVT is ideal for estimating the likelihood and magnitude of extreme events in biotech.

3. Stress Testing and Scenario Analysis

Stress testing models the impact of extreme but plausible events, such as:

A portfolio-wide clinical trial failure.
A major regulatory reform or policy shift.

Conclusion

VaR’s reliance on thin-tailed assumptions, its inability to account for fat-tailed risks, and its ignorance of path dependency make it fundamentally unsuitable for biotech and healthcare. By truncating analysis at confidence thresholds and failing to capture the true nature of tail risks, VaR provides a dangerously incomplete picture of risk. To succeed in these sectors, investors must adopt metrics that embrace uncertainty, focus on tail outcomes, and respect the transformative power of rare events. In biotech and pharma, VaR isn’t just flawed—it’s irrelevant.