28
Dec

## Replug – Interview with Dr. Viral Acharya

The Government today appointed Dr. Viral Acharya, Professor of Economics at the New York University Stern School of Business, as RBI Deputy Governor for 3 years. We had the pleasure of interviewing Dr. Acharya few years ago on aggregation of risks in a financial system especially with respect to the Indian context. In the below video we share Dr. Acharya’s conversation with Bindu on the subject. You can read the full transcript of the conversation here.

Dr. Viral Acharya in conversation with Bindu Ananth

28
Aug

## 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.

24
Mar

## 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.

Floods

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
• Krishna, Godavari, Mahanadi and Cauvery basin

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.

Droughts

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

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 map based on multi-hazard model12

Earthquakes

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: Estimated Earthquake frequency

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

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.

References:

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

4
Feb

## Estimating the Diversity Score of a Portfolio across Multiple Correlated Sectors: Generalized Herfindahl-Hirschman Index

By Vaibhav Anand and Ramasubramanian S V, IFMR Capital

Diversification is an effective risk mitigation strategy for portfolio risk management. It helps to mitigate risk arising from various factors, including extreme events, except factors which are systemic in nature. Often diversification across counterparties, sectors or geographies is the only risk mitigation tool available to a credit portfolio manager. It is important to measure and monitor the degree of diversification periodically to ensure that concentration risk remains low. However, quantifying the diversification may not be straightforward. Herfindahl-Hirschman Index (HHI) is one such measure but has limitations as it does not take into account correlation among underlying assets. In this post, we discuss a more general and effective measure of diversity score, Generalized-HHI (GHHI), to quantify diversification of a portfolio across multiple correlated sectors and sub-sectors.

In this post we first give a brief overview of how diversification helps to mitigate risk. We also discuss briefly the effect of correlation on portfolio risk. Next, we give a quick introduction to the classical HHI measure. In the last sections we present the GHHI formulation and illustrate its usage to identify a best diversified portfolio. In this blog post, we do not discuss in detail the derivation of GHHI and request interested readers to refer to the Working Paper for a detailed discussion.

How Diversification Helps

We discuss the benefit of diversification using a hypothetical credit portfolio of INR 1000 which can be lent to a single or multiple borrowers. Let us assume that all borrowers have an annual default probability (PD) of 5%. The portfolio manager has three options to lend the entire amount to:

(a) Scenario 1- A single borrower – No diversification
(b) Scenario 2- Equally to ten borrowers with no default correlation among them
(c) Scenario 3- Equally to ten borrowers with a pairwise default correlation of 0.33 among them

Assume no recovery.

Assuming 5% PD for each borrower, the expected loss of the portfolio in all scenarios is same and is equal to INR 50. However, the unexpected risk, measured as the standard deviation of loss here, for the three portfolios will be different.

The loss distributions of Scenario 1 and Scenario 2 are shown in the Figure 1. Scenario 1 has higher standard deviation because it has probabilities bunched only towards the ‘INR 0 loss’ and ‘INR 1000 Loss’ events which is intuitive for a one borrower portfolio- either all good or all bad, whereas a diversified portfolio, under scenario 2, has a better distribution with a very thin tail. For example, under Scenario 2 the probability of INR 1000 loss is nearly 1 in 10,000,000,000,000 as opposed to 1 in 20 in Scenario 1. Remember that Scenario 2 assumes no correlation among borrowers.

Figure 1: Loss Distribution: Scenario 1 and Scenario 2

Let’s see how correlation impacts the loss distribution. The loss distribution of Scenario 2 and Scenario 3 are compared in Figure 2. It can be seen that the latter’s loss distribution has fatter tails. The probability under Scenario 3 of INR 1000 loss is nearly 1 in 240, much higher than that under Scenario 2 but lower than that under no diversification Scenario 1. This tells us that greater than zero default correlation among borrowers increase risk in the portfolio and should be taken into account while quantifying the degree of diversification.

Figure 2: Loss Distribution: Scenario 2 and Scenario 3

Herfindahl-Hirschman Index (HHI)

One commonly used method of measuring the degree of diversification is HHI. HHI is defined as sum of the squares of the portfolio proportions. Consider a loan portfolio P with exposure across 3 counterparties, $latex C_i&s=1$, with corresponding proportions, $latex c_i&s=1$, where $latex i$ = 1 to 3. Then the degree of diversification for P across counterparties can be measured using HHI, where HHI is:

$latex HHI =\sum\limits_{i=1}^3 c_i^2&s=3$

However, the HHI assumes the sectors are independent and does not take into account the correlation among them. We propose a more general metric, the Generalized Herfindahl-Hirschman Index (GHHI), which incorporates correlation among underlying assets.

Generalized Herfindahl-Hirschman Index (GHHI)

The GHHI formulation for a portfolio P with across n assets having pair wise correlation of $latex \rho_{ij}&s=1$ can be written as:

$latex GHHI= {\sum\limits_{i=1}^n} c_i^2 + \sum\limits_{i}^n \sum\limits_{j\neq i}^n 2c_ic_j\rho_{ij}&s=3$

The derivation of the above formulation is not discussed here for the sake of brevity. We request the reader to refer to the Working Paper for a detailed account.

GHHI Vs HHI – Illustration

As an illustration the HHI and GHHI are estimated for four hypothetical credit portfolios, A, B, C, and D, with exposure in 12 counterparties across three sectors S1, S2 and S3. The counterparties are pairwise correlated within a sector with correlations of 0.05, 0.25 and 0.5 respectively. It is assumed that sectors are pairwise uncorrelated. Column 4 to 6 of Table 1 shows the exposure of the four portfolios in different counterparties.

Portfolio A is a seemingly perfectly diversified portfolio with equal exposure to all the available counterparties. In fact, a comparison based on the classic HHI yields a similar conclusion. However, it is shown using GHHI that a more diversified portfolio can be created taking into account the correlation among the counterparties in a sector. The last two rows of Table 1 show the calculated value of diversity scores of each portfolio as well as the effective number of counterparties in each portfolio. Based on HHI, the degree of diversification of the portfolios follows the order: A > B = C = D. Whereas GHHI takes into account the correlation and provides a more accurate order: D > A > C > B, i.e. a portfolio with exposures skewed towards a highly correlated sector, such as S3, will have lower risk mitigation.

Finally, we minimize the GHHI to identify the optimum proportions across assets for the best diversification. The optimal proportions across different sector are indicated in the last column of Table 1.

For a more detailed perspective on this subject please do refer our working paper which you can access here.

7
Dec

## 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.

Framework

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:

Presentation:

Video: