Understanding Probability of Default (PD): A Comprehensive Guide

The probability of default (PD) is the probability of a borrower or debtor defaultingDebt DefaultA debt default happens when a borrower fails to pay his or her loan at the time it is due. The time a default happens varies, depending on the terms agreed upon by the creditor and the borrower. Some loans default after missing one payment, while others default only after three or more payments are missed. on loan repayments. Within financial marketsFinancial MarketsFinancial markets, from the name itself, are a type of marketplace that provides an avenue for the sale and purchase of assets such as bonds, stocks, foreign exchange, and derivatives. Often, they are called by different names, including "Wall Street" and "capital market," but all of them still mean one and the same thing., an asset’s probability of default is the probability that the asset yields no return to its holder over its lifetime and the asset price goes to zero. Investors use the probability of default to calculate the expected loss from an investment.

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Probability of Default and Credit Default Swaps

The market’s view of an asset’s probability of default influences the asset’s price in the market. Therefore, if the market expects a specific asset to default, its price in the market will fall (everyone would be trying to sell the asset). Therefore, the market’s expectation of an asset’s probability of default can be obtained by analyzing the market for credit default swapsCredit Default SwapA credit default swap (CDS) is a type of credit derivative that provides the buyer with protection against default and other risks. The buyer of a CDS makes periodic payments to the seller until the credit maturity date. In the agreement, the seller commits that, if the debt issuer defaults, the seller will pay the buyer all premiums and interest of the asset.

Consider an investor with a large holding of 10-year Greek government bonds. The price of a credit default swap for the 10-year Greek government bond price is 8% or 800 basis points. The investor expects the loss given default to be 90% (i.e., in case the Greek government defaults on payments, the investor will lose 90% of his assets). Therefore, the investor can figure out the market’s expectation on Greek government bonds defaulting. In this case, the probability of default is 8%/10% = 0.8 or 80%.

What are Credit Default Swaps?

Credit default swaps are credit derivatives that are used to hedge against the risk of default. They can be viewed as income-generating pseudo-insurance. A credit default swap is an exchange of a fixed (or variable) coupon against the payment of a loss caused by the default of a specific securityMarketable SecuritiesMarketable securities are unrestricted short-term financial instruments that are issued either for equity securities or for debt securities of a publicly listed company. The issuing company creates these instruments for the express purpose of raising funds to further finance business activities and expansion..

Consider the following example: an investor holds a large number of Greek government bonds. However, due to Greece’s economic situation, the investor is worried about his exposure and the risk of the Greek government defaulting. The investor, therefore, enters into a default swap agreement with a bank. The investor will pay the bank a fixed (or variable – based on the exact agreement) coupon payment as long as the Greek government is solvent.

In the event of default by the Greek government, the bank will pay the investor the loss amount. A credit default swap is basically a fixed incomeFixed Income SecuritiesFixed income securities are a type of debt instrument that provides returns in the form of regular, or fixed, interest payments and repayments of the (or variable income) instrument that allows two agents with opposing views about some other traded security to trade with each other without owning the actual security.

Market vs. Individual Probability of Default

Like all financial markets, the market for credit default swaps can also hold mistaken beliefs about the probability of default. For example, if the market believes that the probability of Greek government bonds defaulting is 80%, but an individual investor believes that the probability of such default is 50%, then the investor would be willing to sell CDS at a lower price than the market.

This would result in the market price of CDS dropping to reflect the individual investor’s beliefs about Greek bonds defaulting. Therefore, a strong prior belief about the probability of default can influence prices in the CDS market, which, in turn, can influence the market’s expected view of the same probability.

Additional Resources

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• BankruptcyBankruptcyBankruptcy is the legal status of a human or a non-human entity (a firm or a government agency) that is unable to repay its outstanding debts
• Debt CapacityDebt CapacityDebt capacity refers to the total amount of debt a business can incur and repay according to the terms of the debt agreement.
• Recovery RateRecovery RateRecovery rate, commonly used in credit risk management, refers to the amount recovered when a loan defaults. In other words, the recovery rate is the amount, expressed as a percentage, recovered from a loan when the borrower is unable to settle the full outstanding amount. A higher rate is always desirable.
• Swap SpreadSwap SpreadSwap spread is the difference between the swap rate (the rate of the fixed leg of a swap) and the yield on the government bond with a similar maturity. Since government bonds (e.g., US Treasury securities) are considered risk-free securities, swap spreads typically reflect the risk levels perceived by the parties involved in a swap agreement.