Risk Management in Quant Finance: VaR, Credit Risk, and Beyond

The Job Nobody Notices Until It Goes Wrong

Risk management is the part of finance that most people ignore until a crisis hits. Then it becomes the most important function in the building. The role of quant risk is to measure, monitor, and manage the exposures that could cause serious damage — and to do it before the damage happens.

Quant risk teams sit in every major bank, hedge fund, and asset manager. The work is technically demanding (probability, statistics, linear algebra), consequential (bad risk models can bankrupt firms), and — in the author's opinion — underappreciated.

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Value at Risk (VaR)

VaR answers a deceptively simple question: "What is the most we could lose in a given time period, with a given confidence level?"

For example: "Our 1-day 99% VaR is £2 million" means "We are 99% confident that we will not lose more than £2 million tomorrow."

Three Approaches

1. Parametric (Variance-Covariance)

Assumes returns are normally distributed:

[ \text{VaR}{\alpha} = \mu_p + z{\alpha} \sigma_p ]

where ( z_{\alpha} ) is the normal quantile (e.g., -2.33 for 99%).

This requires the covariance matrix and is fast to compute, but the normality assumption can severely underestimate tail risk.

2. Historical Simulation

Take the actual historical returns, rank them, and pick the appropriate percentile. No distributional assumptions, but implicitly assumes history will repeat itself.

3. Monte Carlo Simulation

Simulate thousands of possible future scenarios using random walks and statistical models. The most flexible approach but computationally expensive.

VaR Limitations

VaR has well-known problems:

• It does not tell you how much you lose beyond the VaR level
• It is not subadditive — two portfolios can individually have VaRs that sum to less than their combined VaR
• The 99% confidence level means the 1% tail is ignored — and that is where the nasty stuff lives

The 2008 financial crisis exposed many of these weaknesses. Banks were technically within VaR limits right up until they were not.

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Expected Shortfall (CVaR)

Expected shortfall (also called Conditional VaR) answers: "Given that we exceeded VaR, what is the average loss?"

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

ES is a more conservative measure that accounts for the shape of the tail. It is now the preferred risk measure under Basel III regulations — the international framework for bank capital requirements.

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Credit Risk

Credit risk is the risk that a borrower defaults on their obligations. It is particularly important for banks (who lend money), bond investors, and anyone trading credit derivatives.

Key Concepts

• Probability of default (PD): the likelihood of the borrower defaulting in a given period
• Loss given default (LGD): how much you lose if default occurs (typically 40-60% for corporate bonds)
• Exposure at default (EAD): how much is at risk
• Expected loss: ( EL = PD \times LGD \times EAD )

Credit Spreads

The extra yield on a corporate bond over a government bond reflects credit risk. Wider spreads mean higher perceived risk of default.

Credit Default Swaps (CDS)

A CDS is insurance against default. The buyer pays a regular premium; if the reference entity defaults, the seller pays out. CDS spreads are a real-time market measure of credit risk.

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The No-Arbitrage Framework

Stepping back from specific risk measures, the no-arbitrage principle is the conceptual foundation of everything:

In a well-functioning market, there are no risk-free profits.

This sounds simple, but its consequences are profound. It implies:

• Forward prices must equal the cost of carry
• Put-call parity must hold
• Derivative prices can be computed as discounted expected values under the risk-neutral measure

Risk-Neutral Pricing

Under the risk-neutral measure ( Q ), all assets earn the risk-free rate on average. The fair price of any derivative is:

[ V = e^{-rT} E^Q[\text{payoff}] ]

This is not an assumption about investor preferences. It is a mathematical consequence of no-arbitrage, and it is the single most important idea in derivatives pricing.

The equivalence between no-arbitrage and the existence of a risk-neutral measure is formalised by the Fundamental Theorem of Asset Pricing — one of the deep results in financial mathematics.

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Market Microstructure and Execution Risk

At a more granular level, algorithmic trading introduces its own risk considerations:

• Slippage: the difference between the expected and actual execution price
• Market impact: large orders moving the price against you
• Latency risk: being too slow in a fast market
• Model risk: the possibility that your trading model is simply wrong

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Stress Testing

VaR and ES measure risk under "normal" conditions. Stress testing asks: what happens under extreme scenarios?

• What if the market drops 20% in a week?
• What if interest rates spike 300 basis points?
• What if correlations all go to 1 (as they tend to in crises)?

Regulators require banks to conduct regular stress tests. The scenarios are often based on historical crises or hypothetical extreme events.

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Risk Management in Python

import numpy as np

# Historical VaR
returns = np.random.normal(0.0005, 0.02, 1000)  # Simulated daily returns
var_99 = np.percentile(returns, 1)
es_99 = returns[returns <= var_99].mean()

print(f"99% VaR: {var_99:.4f}")
print(f"99% ES:  {es_99:.4f}")

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The Full Picture

Risk management pulls together probability, statistics, linear algebra, and financial intuition. It is one of the most intellectually satisfying — and practically important — areas of quant finance.

Quantt covers VaR, expected shortfall, credit risk, and risk-neutral pricing as part of the integrated curriculum. The finance, maths, and technology streams all contribute, because real risk management requires all three.

For further reading, the Bank for International Settlements (BIS) publishes the regulatory frameworks, and Risk.net is the industry's go-to publication for quant risk topics.