# Difference between revisions of "Roll Rates"

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== Definition == | == Definition == | ||

− | '''Roll Rates''' help quantify the [[Delinquency]] and [[Default]] behavior of [[Credit Portfolio | credit portfolios ]] with large number of borrowers. The name suggests the ''rolling'' (transfer) of borrowers from one state of delinquency to another. | + | '''Roll Rates''' help quantify the [[Delinquency]] and [[Default Event | Default ]] behavior of [[Credit Portfolio | credit portfolios ]] with large number of borrowers. The name suggests the ''rolling'' (transfer) of borrowers from one ''state'' of delinquency to another. |

+ | |||

+ | Mathematically the computation of roll rates is related to the estimation of a [[Transition Matrix]], more specifically the transition rates between the various states of the adopted [[State Space]]. The size n of this square (n x n) matrix corresponds to the number of distinct [[Past Due]] days that are selected as informative (each on of them considered to be one distinct state). | ||

+ | |||

+ | == The Roll Rate Matrix == | ||

+ | A collection of all relevant roll rates is called a ''Roll Rate Matrix''. The matrix is defined by | ||

+ | * the period (observation time internal) that is used | ||

+ | * an enumeration of states that capture all possible states at the beginning and the end of the time interval | ||

+ | * a set of transition probabilities (roll rates) from any state to any other state during that time interval | ||

+ | |||

+ | === The Period === | ||

+ | A 30-Day (monthly) observation period is typical (even though essentially an arbitrary convention) | ||

+ | |||

+ | === The List of States === | ||

+ | The collection of states will include (depending on the nature of the borrowers and credit products) the union of the following sets: | ||

+ | * An enumeration of distinct Current states (if there are more than one) | ||

+ | * An ordered list of Delinquent states. While any granularity is possible in principle, it is quite typical that the shortest period is 30 days past due, whereas the longest can be 90 days past due or 180 days past due. | ||

+ | * An enumeration of distinct Default states (including such possibilities as Forbearance, Foreclosure etc) | ||

+ | |||

+ | === The Graph of Possible Transitions === | ||

+ | The graph of possible transitions lays out possible paths between states. An [[Absorbing Default State]] will not have paths leading back to performing status | ||

+ | |||

− | |||

− | |||

− | |||

− | |||

Dividing the current month's delinquency bucket by the prior delinquency bucket, calculates the month's roll rates in the previous month. | Dividing the current month's delinquency bucket by the prior delinquency bucket, calculates the month's roll rates in the previous month. | ||

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== See Also == | == See Also == | ||

* For credit portfolios that are managed using a [[Credit Rating System]] (more common for [[Corporate Loan]] or Bond portfolios) one can also estimate the [[Rating Migration Matrix]]. While roll matrices and rating migration matrices are related (e.g. delinquency may be an input to ratings) a roll rate matrix is based on observable states, whereas an internal or external rating has a subjective element | * For credit portfolios that are managed using a [[Credit Rating System]] (more common for [[Corporate Loan]] or Bond portfolios) one can also estimate the [[Rating Migration Matrix]]. While roll matrices and rating migration matrices are related (e.g. delinquency may be an input to ratings) a roll rate matrix is based on observable states, whereas an internal or external rating has a subjective element | ||

+ | * [[How to Calculate a Roll Rate Matrix]] | ||

[[Category:Transition Matrix]] | [[Category:Transition Matrix]] | ||

[[Category:Credit Risk]] | [[Category:Credit Risk]] |

## Revision as of 18:34, 14 June 2019

## Contents

## Definition

**Roll Rates** help quantify the Delinquency and Default behavior of credit portfolios with large number of borrowers. The name suggests the *rolling* (transfer) of borrowers from one *state* of delinquency to another.

Mathematically the computation of roll rates is related to the estimation of a Transition Matrix, more specifically the transition rates between the various states of the adopted State Space. The size n of this square (n x n) matrix corresponds to the number of distinct Past Due days that are selected as informative (each on of them considered to be one distinct state).

## The Roll Rate Matrix

A collection of all relevant roll rates is called a *Roll Rate Matrix*. The matrix is defined by

- the period (observation time internal) that is used
- an enumeration of states that capture all possible states at the beginning and the end of the time interval
- a set of transition probabilities (roll rates) from any state to any other state during that time interval

### The Period

A 30-Day (monthly) observation period is typical (even though essentially an arbitrary convention)

### The List of States

The collection of states will include (depending on the nature of the borrowers and credit products) the union of the following sets:

- An enumeration of distinct Current states (if there are more than one)
- An ordered list of Delinquent states. While any granularity is possible in principle, it is quite typical that the shortest period is 30 days past due, whereas the longest can be 90 days past due or 180 days past due.
- An enumeration of distinct Default states (including such possibilities as Forbearance, Foreclosure etc)

### The Graph of Possible Transitions

The graph of possible transitions lays out possible paths between states. An Absorbing Default State will not have paths leading back to performing status

Dividing the current month's delinquency bucket by the prior delinquency bucket, calculates the month's roll rates in the previous month.

## Issues and Challenges

Estimating a roll rate matrix constitutes a simple type of a credit Risk Model. The underlying assumption is that future accounts will continue to flow through delinquent buckets as they have in the past. In reality changes in the economic environment or other possible risk factors affecting a given portfolio may introduce significant dynamics (variability) in the roll rates

## See Also

- For credit portfolios that are managed using a Credit Rating System (more common for Corporate Loan or Bond portfolios) one can also estimate the Rating Migration Matrix. While roll matrices and rating migration matrices are related (e.g. delinquency may be an input to ratings) a roll rate matrix is based on observable states, whereas an internal or external rating has a subjective element
- How to Calculate a Roll Rate Matrix