{"id":6409,"date":"2025-04-05T10:53:55","date_gmt":"2025-04-05T06:53:55","guid":{"rendered":"https:\/\/eoninvestment.com\/?p=6409"},"modified":"2026-04-13T16:47:53","modified_gmt":"2026-04-13T12:47:53","slug":"hazard-function-yield-degradation","status":"publish","type":"post","link":"https:\/\/eoninvestment.com\/ka\/2025\/04\/05\/hazard-function-yield-degradation\/","title":{"rendered":"\u10e1\u10d0\u10e4\u10e0\u10d7\u10ee\u10d8\u10e1 \u10e4\u10e3\u10dc\u10e5\u10ea\u10d8\u10d0 \u10d3\u10d0 \u10d0\u10db\u10dd\u10dc\u10d0\u10d2\u10d4\u10d1\u10d8\u10e1 \u10d3\u10d4\u10d2\u10e0\u10d0\u10d3\u10d0\u10ea\u10d8\u10d0<\/span>"},"content":{"rendered":"\n
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Fixed-income assets come with default risk. For example, the default probability statistics for commercial mortgages by years since loan origination look like this:<\/p>\n\n\n\n

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Source:<\/strong> Commercial Real Estate Analysis and Investments<\/em> by D. M. Geltner, N. G. Miller, J. Clayton, P. Eichholtz<\/p>\n\n\n\n

In the event of default, it is often impossible to recover the full amount of the invested capital\u2026 which ultimately leads to a difference between the contractually expected IRR and the actual IRR \u2014 this is called \u201cYield Degradation<\/strong>.\u201d<\/p>\n\n\n\n

In the example below, a 5-year loan defaults in year 4, and only 80% of the expected amount is recovered. As a result, instead of the agreed IRR of 10%, the investor ends up with just 4.89%. The difference between these two figures is what is referred to as Yield Degradation<\/strong>:<\/p>\n\n\n\n

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An interesting point here is that the later<\/strong> the default occurs, the lower<\/strong> the yield degradation tends to be.<\/p>\n\n\n\n

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Understanding this reality leads to the need to calculate the probability of default and incorporate its impact into the pricing of contracts in a meaningful way. In other words, investors should understand what kind of return they can realistically expect on their investment, given the likelihood of default.<\/p>\n\n\n\n

To achieve this, historical statistical analysis is conducted, credit rating systems are developed, and default probabilities are determined. For example (ChatGPT):<\/p>\n\n\n\n

In order to calculate the expected return based on default probabilities, certain mathematical steps are necessary. First, based on statistical data, we define the Hazard Function<\/strong>, then compute the Survival Probability<\/strong>, Cumulative Survival Probability<\/strong>, and Unconditional Default Probability<\/strong> by year. Finally, we arrive at the expected IRR<\/strong> (it’s a bit complex, but manageable in Excel).<\/p>\n\n\n\n

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Definitions:<\/strong><\/p>\n\n\n\n