Overview of Financial Risks and Regulatory Frameworks › Key Parameters

The simulation relies on the following parameters, each of which captures an essential aspect of market risk:

• mu: Vector of expected daily returns for each asset class. These represent our assumptions about the average return we expect from each asset type over time. Equities have the highest expected return (8% annualized), which reflects the equity risk premium, while bonds and currency have lower expected returns.
• cov_annual: Annualized covariance matrix capturing the risk and co-movement of assets. The diagonal elements represent each asset's variance, or the square of its volatility, while the off-diagonal elements represent covariances that determine how assets move together. Lower covariances between asset classes provide diversification benefits.
• weights: Allocation of capital to each asset class (60% Equities, 30% Bonds, 10% Currency). These weights determine how much each asset's returns contribute to the overall portfolio. A higher weight on volatile assets increases portfolio risk, while diversifying across assets with low correlations reduces it.

Credit risk is the potential for losses due to a counterparty's failure to meet its contractual obligations. When you lend money, the borrower might default. When you enter a derivatives contract, your counterparty might fail to make required payments. Unlike market risk, where losses occur because prices move against you, credit risk involves the more fundamental problem of not receiving money you are owed.

The distinction between market risk and credit risk is subtle but important. With market risk, you face potential losses even when all parties honor their obligations: a bond might fall in price simply because interest rates rise. With credit risk, the loss arises specifically from a failure to perform. However, these risks interact: a bond's price might fall because the market perceives increased default probability, blending credit spread risk with pure credit default risk.

Credit risk takes several forms, each with distinct characteristics and measurement challenges:

• Default risk: The outright failure of a counterparty to make required payments. A bondholder faces default risk if the issuing company goes bankrupt. Default is a discrete event, either it happens or it doesn't, which makes it fundamentally different from the continuous price movements of market risk.
• Credit spread risk: Changes in the market's assessment of creditworthiness, even absent actual default. If a company's credit rating is downgraded, its bond prices fall as spreads widen. This is sometimes called "migration risk" because it relates to the borrower migrating between credit quality categories.
• Recovery risk: Uncertainty about the amount recovered in the event of default. Even knowing that a company will default, the bondholder faces uncertainty about how much they will eventually receive. Recovery rates vary widely depending on the seniority of the debt, the assets available for liquidation, and the complexity of bankruptcy proceedings.
• Counterparty credit risk: The risk that a derivative counterparty defaults when the position has positive value to you. This was a central concern during the 2008 crisis, particularly around credit default swaps. Counterparty risk is particularly complex because your exposure changes with market movements, creating "wrong-way risk" when a counterparty's credit quality deteriorates precisely when your exposure to them increases.

As we discussed in Part II on credit default swaps and structured credit products, the instruments designed to transfer credit risk can themselves become sources of systemic risk when correlations between default events are underestimated.

The quantitative foundation of credit risk is the Expected Loss ($\text{EL}$) metric, which decomposes the complex phenomenon of potential credit losses into three measurable components. This decomposition is both conceptually elegant and practically useful because it separates the question "how likely is loss?" from "how much will we lose if it happens?" and "how much do we have at stake?" The formula is:

$$\text{EL} = \text{PD} \times \text{LGD} \times \text{EAD}$$

To understand why this formula takes this form, consider what we need to know to estimate our expected credit loss. First, we need to know the probability that a loss will occur at all, which is the Probability of Default ($\text{PD}$). A loan to a highly creditworthy borrower might have a PD of 0.1%, while a loan to a troubled company might have a PD of 10%. Second, if default occurs, we need to know what fraction of our exposure we will lose, which is the Loss Given Default ($\text{LGD}$). This is calculated as $1 - \text{Recovery Rate}$, where the recovery rate represents the percentage of the loan we expect to eventually collect through bankruptcy proceedings, collateral liquidation, or restructuring. Finally, we need to know how much we have at stake when the default occurs, which is the Exposure at Default ($\text{EAD}$). For a term loan, this is simply the outstanding principal, but for credit lines or derivatives, the exposure may be uncertain and require modeling.

The components of the Expected Loss formula are:

• $\text{PD}$: Probability of Default, the likelihood that the borrower fails to pay. This is typically estimated from historical default rates for borrowers with similar credit ratings, or from market data such as credit default swap spreads.
• $\text{LGD}$: Loss Given Default, the percentage of exposure lost if default occurs ($1 - \text{Recovery Rate}$). Recovery rates vary significantly by industry, collateral type, and position in the capital structure. Senior secured loans typically have higher recovery rates than subordinated debt.
• $\text{EAD}$: Exposure at Default, the total value at risk at the time of default. For drawn loans, this equals the outstanding balance. For undrawn commitments, it requires estimating how much the borrower will draw before defaulting.

The following example calculates Expected Loss for a hypothetical loan portfolio using these components.