Loss Given Default Estimation using Transition Matrix (TM-LGD): A Case Study

By Vaibhav Anand, IFMR Capital

Loan repayment behaviour differs across asset classes based on borrower profile, purpose of loan, geography and nature of security, if any. Certain asset classes show regular and timely repayments with close to 99% collection efficiency but low recovery once a loan reaches a certain delinquency level, say DPD30 (Days past due). On the other hand, there are asset classes with low periodic collection efficiency ranging from 90% to 95%, but ultimate loss on the portfolio may be significantly smaller as compared to the peak delinquency levels showing higher recoveries on delinquent loans. Such differences in repayment behaviour may be driven by cash flow and income volatility of the underlying borrowers as well as delinquency management practices of the lenders among other things. As a result, periodic cash flow shortfalls (or excess) may vary significantly from ultimate loss on the portfolio.

In order to model cash flows accurately, a methodology should be able to model the transitions of loans across different delinquency levels during the tenure. The TM-LGD is one such methodology which does this by first converting the periodic credit behaviour of loans into a ‘transition matrix’ (or TM) and then estimating the periodic cash flows and loss given default (LGD) using Monte-Carlo simulations. Based on the repayment behaviour, a loan may move across different states (delinquent, current, prepaid or pre-closed). Capturing this movement is helpful in estimating the periodic cash flows and ultimate loss on a portfolio. TM captures these transitions across different states using the historical repayment behaviour of the borrowers. Possible transitions for a loan are shown in Figure 1 below. Figure 2 shows an illustrative transition matrix for transitions over a single repayment period.

Figure 1: Possible transitions for a loan

Figure 2: Illustrative TM capturing the transition of loans over one repayment period

The transition matrix can be used to simulate the possible states for all the loans in a portfolio. Each simulation represents a set of paths for all the loans, which denotes a single state of the universe of all the possible states through which the portfolio can evolve during its life. Periodic cash flows and resulting shortfalls (or excess) are estimated using these transitions for each simulation.

Figure 3: Simulating the path of a loan using TM

In this article which was published in the Securitisation & Structured Finance Handbook 2015/16, we present and discuss the TM-LGD model in some detail as well as its implementation and limitations through a case study based on the loss estimation for a securitization transaction with underlying commercial vehicle loans.

Click here to read the case study.


Designing a Framework for Event Risk & Loss Estimation: Understanding Natural Disasters

By Vaibhav Anand, IFMR Capital

In the previous post of this series on Event Risk & Loss Estimation, we discussed briefly the motivation and key modules of a framework for estimating capital against event risk. Before we discuss the approach and components of such a framework in detail, it is important to understand the nature of the extreme events and how such events impact borrowers, lenders and credit portfolios. In this post, we will discuss the former in the context of some of the extreme and not-so-extreme events. Not-so-extreme because either there may be some predictability in the timing of their occurrence or their impact may appear less extreme and more diffused- spatially as well as temporally. We will cover four natural disasters- Flood, Drought, Cyclone and Earthquake – in this post. We will discuss briefly the socio-political events in the next post along with a common investigation framework to evaluate the impact of events on borrowers and lenders.


India receives more than 70% of its rainfall over a period of four months1. In fact, the rainfall may not be evenly distributed during the season. This results in long dry spells followed by heavy rainfall in several geographies. Throughout history floods are the most recurrent natural disasters that cause havoc. A flood is defined as a phenomena in which water over flows its natural or artificial banks onto normally dry land, such as a river inundating its floodplain2. There are mainly four types of flood:

  • Riverine Flood: This type of flooding is caused by overflow of water along the path of a river and mainly affects land area along the river bank. The frequent flooding in the Kosi River, also known as the sorrow of Bihar, is a typical example of riverine flood. The August 2008 flood in Kosi River was caused by a breach of an embankment of the river in Nepal. After the breach, the river changed its course to the one followed by it in 1930s in a very short time causing severe flooding over a large extant of land in Bihar3. Four major riverine flood prone regions are:
    • Ganga basin
    • Brahmaputra basin
    • Narmada – Tapti basin
    • Krishna, Godavari, Mahanadi and Cauvery basin

Figure 1- Flood Hazard
Figure 1: Flood Hazard Map of India4

  • Coastal flood: Flooding caused by the ocean water driven inland by another natural cause such as storms, cyclones, tidal waves caused by earthquake (tsunamis), etc.
  • Urban flood: There could be several reasons for urban flooding such as heavy rainfall, sudden release of water from a bund or dam, tidal waves, etc. However, the main underlying cause is usually the slow absorption of water by the land. The 2005 flood in Mumbai was an example of urban flooding.
  • Flash flood: Such floods manifest in a very small time and usually without warning, hence the name. These are usually caused by heavy rainfall or release of water from a dam. The disastrous floods in the North Indian geography in the last few years were examples of flash floods.


Drought, along with flood, is one of the most recurring natural disasters in India. The duality is not surprising since both are linked to rainfall cycles to a large extant. However, unlike floods and other disasters that we will discuss shortly, it is very difficult to identify the onset and end of a drought. In fact, there are multiple definitions of drought proposed from time to time based on the specific ‘water content’ requirement (of soil, for example) for various human activities5.


There are mainly three types of droughts6 and the definitions vary based on the type:

  • Meteorological drought: Situation when the deficiency of rainfall at a meteorological sub-division level is 25% or more of the long-term average (LTA) of that sub-division for a given period. If the rainfall deficiency is less than 50%, it is classified as “moderate” drought; else, it is termed as “severe” drought7.
  • Hydrological drought: It is a prolonged meteorological drought resulting in depletion of surface water from various reservoirs causing severe shortage of water for human and livestock needs8.
  • Agricultural drought: It is a situation when rainfall and soil moisture are inadequate to support healthy agricultural crop growth9. This may be caused by a meteorological drought followed by a hydrological one.

(It is very tempting to suggest a fourth type of drought here- Political Drought- but we will leave it out of this post!)

It can be concluded from the above definitions that a meteorological drought instance may not be disastrous in isolation. However, a series of meteorological droughts or mismanagement of water resources may result in a hydrological drought over time10. This coupled with lack of irrigation resources may result in agricultural drought. Further, it should be noted that agricultural drought is also a relative term- it would depend on the moisture requirement of the crop grown in the affected area. These factors make the impact evaluation exercise for a drought on the economic activities a very difficult task. We will discuss in detail this issue in the next post of the series.

National Climate Centre (NCC) provides a good literature on popular methods for measuring the drought severity over a spatial unit in a report published in 201011. The report also provides the drought indices for 458 districts using the southwest monsoon season rainfall time series over the period 1901-2003.


Cyclones, one of the most recurring extreme weather events across the globe, are weather systems with wind speed exceeding 62 km per hour. Though cyclones are known by different names in different regions (hurricane in North Atlantic and East Pacific, Typhoon in West Pacific, and cyclone in Indian Ocean), the classification is mainly based on the wind speeds. For a detailed classification, one may refer to the Wikipedia page on tropical storms which provides a great deal of information as well as useful references on cyclones12.

India with a coastline of more than 7500 kilometres is one of the worst affected regions in the world with on an average nearly 370 million people exposed to cyclone disasters annually13. Cyclones are multi-hazard systems, i.e. multiple hazards are associated with a cyclone– high speed winds, torrential rains and inland flooding, and storm tide14. However the development, eventual landfall and potential impact of a tropical cyclone can be estimated more accurately relative to other natural disasters such as floods, drought and earthquakes. Though the cyclones can change their course or dissipate suddenly, the modern forecasting systems have enabled the governments and disaster management bodies around the world to take preventive actions to minimize the damage due to cyclones and associated hazards.

National Disaster Management Authority (NDMA) of India published a study in 2010 which suggested a cyclone hazard mapping of coastal districts in India based on the historical (1981-2008) occurrences of cyclones and the multiple hazards associated with them.

Figure 2- Cyclone Hazard
Figure 2: Cyclone hazard map based on multi-hazard model12


Earthquakes are arguably the most fatal of the natural disasters. There is high amount of uncertainty attached to the timing, location and severity of an earthquake which makes preventive measures very difficult if not near impossible. Unlike floods, droughts or cyclones, there are no seasonal patterns or clustering in earthquake occurrences15. Earthquakes are caused by the sudden release of built up pressure in the earth’s crust in the form of an energy explosion that fractures the earth’s surface and creates seismic waves. The resulting ground acceleration is the main cause of damage caused by the earthquakes which impacts buildings, roads and other ground infrastructure. Like cyclones, earthquakes too have associated hazards, most common being the tidal waves, also known as tsunamis. The 2004 Tsunami was caused by one of the strongest earthquakes with magnitude of nearly 9.1 on Moment Magnitude Scale (MMS). The other two of the most disastrous earthquakes that India faced had magnitudes of 7.7 (Bhuj, 2001) and 6.2 (Latur, 1993).

Earthquake magnitude can be measured using seismograph (seismogram is the output graph of a seismograph!) which records the ground vibration. One of the most popular scales of measurement is the Richter scale, named after the seismologist Charles Richter16. The relation between the amount of energy and the scale reading is nonlinear. An increase of one magnitude signifies a ten times higher ground motion and nearly thirty times the energy17. Earthquakes with magnitude lower than 5.5 are usually not dangerous and may not cause any damage. An interesting fact is the frequency of earthquakes is far higher than intuition would allow us to guess; however, fortunately, most of these earthquakes have very low magnitude. A table based on the estimates of United States Geological Survey (USGS) is shown below.

Figure 3- table
Figure 3: Estimated Earthquake frequency

The earthquake hazard map of India divides the region in five seismic zones.

Figure 4- Seismic
Figure 4: Seismic Zones of India18

Evaluating the impact on portfolio

Can we actually use a common investigation framework to evaluate the impact of such events? Though the extreme events listed and discussed above, and others not mentioned here, may differ significantly in nature, a common framework for investigation can be used to understand how such events impact portfolio performance of a credit institution. In the next post of the series we will discuss such an investigation framework.

We would like to thank Divyasree PK of IIT Madras who worked on the topic during her internship at IFMR Capital.


  1. http://agricoop.nic.in/DroughtMgmt/DroughtManual.pdf
  2. http://saarc-sdmc.nic.in/pdf/flood.pdf
  3. http://www.indiaenvironmentportal.org.in/files/The%2018%20August%202008%20Kosi%20river%20breach.pdf
  4. http://www.cddrm-ncdc.org/e39621/e39678/
  5. http://ijset.com/ijset/publication/v1s4/p%20149-157%20surendra%20published%20paper.pdf
  6. National Commission of Agriculture in India
  7. National Commission of Agriculture in India
  8. http://www.nrsc.gov.in/pdf/Chap_13_Droght.pdf
  9. http://www.nrsc.gov.in/pdf/Chap_13_Droght.pdf
  10. http://sandrp.in/otherissues/Maharashtra_Drought_2012_13_worse_than_1972_March2013.pdf
  11. http://www.imdpune.gov.in/ncc_rept/RESEARCH%20REPORT%2013.pdf
  12. http://en.wikipedia.org/wiki/Tropical_cyclone#Hurricane_or_typhoon
  13. http://ncrmp.gov.in/ncrmp/Cyclone_Impact.html
  14. http://ndma.gov.in/images/cyclones/cyclonepronedistrict.pdf
  15. However, there are some studies which suggest that weather changes or human activities may seasonally impact the seismic activity, e.g. https://www.sci.hokudai.ac.jp/grp/geodesy/top/research/files/heki/year03/Heki_EPSL2003.pdf
  16. The Moment Magnitude Scale (MMS), developed in 1972, is commonly used now. However, both the scales are logarithmic and have similar characteristics for medium magnitude earthquakes. For a good account please refer to the Wikipedia page: http://en.wikipedia.org/wiki/Moment_magnitude_scale#Comparison_with_Richter_scale
  17. http://saarc-sdmc.nic.in/pdf/earthquake.pdf
  18. http://www.hpsdma.nic.in/ResourceList/Maps/EqIndia.pdf


Designing a Framework for Event Risk & Loss Estimation

By Vaibhav Anand, IFMR Capital

This post is the first post in a new blog series that would delve and deliberate on different aspects of designing a framework that would enable a credit institution to identify the exposure to extreme events and to estimate the potential losses due to such events. 

Risk premium is one of the components of the cost of providing credit. It is important to understand the nature of underlying risk for estimating the real cost of credit. Historical repayment behaviour may provide significant insights to enable reasonable estimation of credit risk; however, the estimates may be limited to losses experienced in the past. For example, it is possible for a credit institution based in North-West India to have never experienced losses due to a devastating earthquake in its ten year long vintage. But it is not prudent to rule out the potential losses due to an earthquake in future; particularly when the geography is prone to experience devastating earthquakes. The key is to assess the potential risk of events which may have low probability of occurrence, in fact may not have occurred in last 20-30 years at all, but have potential for high impact.

Natural disasters come to mind immediately but these are not the only ones that should be reckoned with to estimate the real risk. Man-made disasters such as industrial accidents, terrorist attacks, and riots are some obvious examples of non-natural disasters. However, other man-made activities such as deforestation, mining, and construction may also lead to seemingly natural disasters. An article in The Hindu daily provides an interesting discussion on this causal relationship.

The focus of this blog series is not to delve into the reasons of such extreme events but rather to initiate a discussion on the design of a framework which would enable a credit institution to identify the exposure to extreme events and to estimate the potential losses due to such events. However, before designing a framework it is important to identify events the framework should address.

Extreme Events

The extreme events discussed here typically have following characteristics:

  • Uncertainty on the time of occurrence: There is usually a reasonable uncertainty on when the event could occur. For example it may be known 72 hours before a cyclone could hit the eastern coast but there may not be any inkling of the cyclone, say, a week in advance. Scientific advances have made it possible to predict some of these events but the time frame between the warning and the occurrence is usually very small.
  • Nature of Impact: Impact is almost always disastrous in nature. However, an unexpected technological innovation could effectively throw an established technology giant out of business, hence a disastrous event for the company, but nevertheless a positive event in a broader frame of reference! But, in this blog we are not focussing on such good-bad or bad-good events.
  • Large scale of impact: The event has to have an impact on a very large scale. A land slide impacting a couple of houses, though tragic and disastrous for the families, may not qualify as an extreme event.

However, the impact need not be instantaneously realised. For example, droughts qualify as extreme events but usually make the impact over a longer period of time, unlike earthquakes.

Also, an event, disastrous in nature on a large scale, may occur periodically, e.g. floods in certain rivers may impact the geography almost every year. Such events, though classified as extreme events, will need different approach for risk measurement. Residents and institutions in geographies regularly affected by periodic events develop, over the time, various mitigation strategies to minimize economic losses. We plan to discuss in some detail such cases in a later post in this series.


The framework should enable a credit institution to measure its portfolio exposure to extreme events and to estimate the expected and unexpected losses due to such events. Ideally it should mimic the linkages between the occurrence of the event and the eventual losses in the portfolio.

Figure 1: Linkages between the event and the eventual losses

The key components of such a framework should include:

  • Mapping Module: To standardize and map the exposure and risk factors like location vulnerability and industry clusters to geographies at a granular level. This is a data intensive module and forms the backbone of the framework.
  • Impact Module: To estimate the loss if an event actually occurs. This, in our opinion, is the trickiest bit to put in place; partly because the loss data is not available always and partly because the nature of impact and the eventual response depend on various factors such as asset class, underlying industry, credit policies, relief activities, past experience, and risk mitigation tools available to borrowers and institutions.
  • Simulation Module: To simulate! Based on the probability and severity assumptions, the module can use the Monte Carlo simulations to generate various extreme event scenarios and estimate the eventual loss distribution.

In the subsequent blog posts we plan to discuss in detail each of the above modules.

As part of our blog series on the recently held Spark sessions, Vaibhav presented his thoughts on the framework at one of the talks. You can view the video & the presentation from his session below:




What impacts the performance of a securitised Commercial Vehicle pool?

By Ramasubramanian SV, IFMR Capital

As a follow-up to our earlier post where we had talked about our first securitisation in the Commercial Vehicle (CV) Finance space, in this post we briefly provide an overview of the industry and discuss the key risk factors affecting the CV industry along with factors that impact the performance of a portfolio of CV loans.


Commercial Vehicle (CV) industry in India has surged over the past decade and the market is expected to grow at a CAGR of over 15% until 2016 (Source: Society of Indian Automobile Manufacturers (“SIAM”)) with many companies competing to expand. Commercial vehicle is a type of motor vehicle that is used for transporting goods or carrying passengers with former contributing around 87% in India. Commercial vehicles are classified into Light, Medium & Heavy depending upon its gross vehicle weight. The CV industry enables quick, easy departure of goods and accepts smaller loads than railways and also commercial vehicles can access remote and hilly areas where rail lines cannot be constructed.

The main growth drivers for CV Industry are modernisation of the trucking industry, structural shift to Hub & Spoke model, improved road infrastructure, growing freight capacity and increase in exports from remote areas enabling the producers/manufacturers to move their goods to ports. The key risk factors for this industry are low freight demand and truck rentals, non-availability of cargos, fuel price, risk prone area of occupation, sudden transport strike, competition with alternate mode of transport (Railways) and any new government regulations related to restrictions based on age of the vehicle and other environmental safety issues. Also, recent study on CV industry by ICRA found that the India’s GDP and IIP numbers are very closely correlated with the development of Commercial Vehicle Industry, which in turn has made this industry the lifeline of Indian Economy.

CV Financing and Securitisation

CV Financing Industry in India has seen an impressive growth and in the last five years till 2012-13, CV loan disbursements grew by around 11 per cent (Source: CRISIL Research, Retail Finance- Auto, June 2013). Major players in CV Financing in India are Tata Motors Cholamandalam Finance, Sundaram Finance, AU Finance, Shriram Transport Finance, Magma, L&T, M&M and Religare. The key factors that could impact vehicle financing in India are growth in vehicle sales, finance penetration and average ticket size (players offering marginally higher LTV because of competition from other players). The process of pooling the loans given by these CV financiers and selling the securities backed by cash flows from the loans to investors is termed as ‘Securitisation’ of CV pools and the bank or finance company that has originated the pool of receivables/loans is termed as ‘Originator’. While selecting the loans for securitisation, Originator should take into account the factors such as loan tenure, Interest rates, vehicle type (LCV/UCV), geographical diversity, recovery rates, etc.

[visualizer id=”109872383″]

Risk Factors affecting the CV portfolio performance

We performed a small study to identify the factors that significantly affect the Securitised CV pool performance (delinquencies) and have illustrated the way in which these factors affect the delinquencies.

Data was collected from the Pool Performance reports (from Jun’ 08 to Dec’12) published by Rating Agencies (CARE, ICRA and CRISIL) with a total number of 194 transactions of 14 different Originators. The factors, which could affect the pool performance, were identified based on three broad categories such as Transaction Details, Initial Pool Details and Pool Performance Details. Once data and factors were identified, regression of these factors with 90+ and 180+ delinquencies was performed and the significance level of factors affecting the delinquencies was observed.

We found that originators have greater impact on delinquencies than any other factor. This implies that the characteristics and business model of originator seems to be the most important deciding factor for the CV pool performance. Even though none of the coefficients of other pool parameters are found to be significant, certain parameters like presence of new CV (NCV) in the pool, weighted average seasoning of the pool and ticket size of the loans seem to have positive impact on pool performance. However, the single regression results do not consider the inter dependencies between the factors. For example, presence of NCV in the pool and high-ticket size of the loans can go hand in hand. Further, an originator may spend significantly more effort in the credit evaluation of a high-ticket loan resulting in better origination.

Below a detailed presentation of the study:


IFMR Capital: Securitizing Microloans for Non-Bank Investors

By Vaibhav Anand, IFMR Capital

Columbia Business School has developed a case study documenting the background and the story behind the launch of IFMR Trust Pioneer II, the first rated microfinance securitization transaction to be placed with the capital market investors. Prof. Suresh Sundaresan, Chase Manhattan Bank Professor of Economics and Finance at Columbia University authored this case with the help of the IFMR Capital team. The case study will be used as part of the coursework at Columbia Business School this May and will be available, thereafter, to purchase from the Columbia CaseWorks website.

The case discusses how IFMR Capital adopted the structured finance approach to create new funding options for microfinance institutions. The case analyses the launch of IFMR Trust Pioneer II to answer questions related to the appropriate transaction structure for non-bank investors, leveraging existing market infrastructure, alignment of interests of the stakeholders, and scalability of the microfinance securitization model.

The case abstract is available here.