Historical vs. CDS Hazard Rates: Exploring the Difference and Negative Excess Kurtosis

The statement suggests that historical hazard rates, which measure the probability of default for a bond over a certain period of time, tend to be lower than hazard rates computed from credit default swaps (CDS). Additionally, it implies that the difference between historical and CDS hazard rates is higher for high-quality bonds. One of the reasons provided for this difference is the presence of negative excess kurtosis in bond returns.\n\nTo understand this statement, let's examine each component in detail:\n\n1. Historical hazard rates: Historical hazard rates are calculated by analyzing the default history of a bond or a group of bonds over a specific time period. These rates take into account historical defaults and provide an estimate of the likelihood of future defaults based on past performance. Historical hazard rates are typically computed using historical default data from rating agencies or other reliable sources.\n\n2. Hazard rates computed from credit default swaps (CDS): CDS are financial instruments that provide insurance against the default of a bond or a reference entity. They allow investors to transfer the credit risk associated with a bond to a third party in exchange for regular premium payments. CDS spreads, which represent the cost of this insurance, can be used to calculate hazard rates. Higher CDS spreads indicate higher perceived default risk and therefore higher hazard rates.\n\n3. Higher difference for high-quality bonds: The statement suggests that the difference between historical hazard rates and CDS hazard rates is higher for high-quality bonds. High-quality bonds typically have lower default risk and are considered safer investments. As a result, their historical hazard rates tend to be lower than their CDS hazard rates.\n\n4. Negative excess kurtosis in bond returns: Excess kurtosis measures the degree of peakedness or flatness in the distribution of returns. Negative excess kurtosis implies that the distribution is less peaked and has thinner tails compared to a normal distribution. In the context of bond returns, negative excess kurtosis indicates that extreme events, such as defaults, are less likely to occur.\n\nThe reason provided for the difference between historical and CDS hazard rates is that bond returns have negative excess kurtosis. This suggests that the historical default experience may not fully capture the potential for extreme events in bond markets. CDS market participants, on the other hand, may have a more forward-looking view of default risk and incorporate a higher probability of extreme events in their pricing.\n\nThere could be other factors contributing to the difference between historical and CDS hazard rates as well. For example, market participants may have different information sets, different risk preferences, or varying interpretations of historical data. Additionally, liquidity and market dynamics can also influence CDS pricing and, consequently, hazard rates.\n\nIn conclusion, the statement highlights that historical hazard rates are generally lower than hazard rates computed from CDS, especially for high-quality bonds. The presence of negative excess kurtosis in bond returns is suggested as one reason for this difference. However, it is important to consider other factors that may contribute to the disparity in hazard rates, such as market dynamics and participants' risk perceptions.