# Probability of Default

The chance of a borrower defaulting on their payments

## What is Probability of Default?

The probability of default (PD) is the probability of a borrower or debtor defaulting on loan repayments. Within financial markets, 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 swaps 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 security.

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 income (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.

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