Definition of "Hazard Rate" depending on the study session?

chouk07 · May 20, 2018, 7:17pm

The Hazard rate is described in two topics :

Reduced form models of corporate credit risk : the inputs for reduced models can be estimated using historical data, this is called hazard rate estimation
CDS : the hazard rate is the conditional probability of default i.e. the probability of default given that default has not already occurred

So, how should we understand the “hazard rate” ? Are we talking about the same concept here ?

sw3023 · May 21, 2018, 12:07am

I think they are the same.

Mathematically, it means “conditional probability of default”

tickersu · May 22, 2018, 10:26pm

Yet another instance of the CFA Institute botching fundamental statistical concepts. Hazard rates are not to be interpreted as probability. The numerator is a probability and the denominator is a change in time. This quantity can exceed 1 and is interpreted as rate of events per unit of time.

sydneyguy · May 22, 2018, 11:20pm

The Hazard Rate is the conditional probability of default: which means Probability of default when the default has already not happened.

tickersu · May 23, 2018, 12:52am

I know what the CFA book tells you, but the CFA book is incorrect. They are often incorrect on matters of statistics. Conflating a hazard rate for a probability is a fundamental misunderstanding of the concept (probability is utilized in the calculation, but it is not the final quantity).

This is abundantly clear in statistical texts that discuss survival analysis. For now, seethis paper.

See equation 1 on page 2 and please read the subsequent paragraph. “Dividing the numerator (a probability) by the denominator (a magnitude of time), we obtain a rate of event occurrence per unit time. Because the hazard function is a rate function, it is therefore positive in value without an upper bound; in particular, unlike a probability, its value can exceed one.”

sydneyguy · May 23, 2018, 5:08am

tickersu:

sydneyguy:

The Hazard Rate is the conditional probability of default: which means Probability of default when the default has already not happened _ divided by change in time _ (and is actually the limit of this as delta t approaches zero).

I know what the CFA book tells you, but the CFA book is incorrect. They are often incorrect on matters of statistics. Conflating a hazard rate for a probability is a fundamental misunderstanding of the concept (probability is utilized in the calculation, but it is not the final quantity).

This is abundantly clear in statistical texts that discuss survival analysis. For now, seethis paper.

See equation 1 on page 2 and please read the subsequent paragraph. “Dividing the numerator (a probability) by the denominator (a magnitude of time), we obtain a rate of event occurrence per unit time. Because the hazard function is a rate function, it is therefore positive in value without an upper bound; in particular, unlike a probability, its value can exceed one.”

I will just worry about what the textbooks are saying, for the purpose of studying for the exam. What you have described here might be true though.

tickersu · May 23, 2018, 9:31am

sydneyguy:

tickersu:

sydneyguy:

The Hazard Rate is the conditional probability of default: which means Probability of default when the default has already not happened _ divided by change in time _ (and is actually the limit of this as delta t approaches zero).

I know what the CFA book tells you, but the CFA book is incorrect. They are often incorrect on matters of statistics. Conflating a hazard rate for a probability is a fundamental misunderstanding of the concept (probability is utilized in the calculation, but it is not the final quantity).

This is abundantly clear in statistical texts that discuss survival analysis. For now, seethis paper.

See equation 1 on page 2 and please read the subsequent paragraph. “Dividing the numerator (a probability) by the denominator (a magnitude of time), we obtain a rate of event occurrence per unit time. Because the hazard function is a rate function, it is therefore positive in value without an upper bound; in particular, unlike a probability, its value can exceed one.”

I will just worry about what the textbooks are saying, for the purpose of studying for the exam. What you have described here might be true though.

I don’t think that’s a bad idea for exam purposes. I can assure you, for real life, what we’ve discussed here is true. The CFA curriculum isn’t the place to learn statistics. They don’t have a strong grasp of many elementary concepts, let alone the more challenging ones.