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


An Initial Analysis of the Atal Pension Yojana

By Vishnu Prasad & Anand Sahasranaman, IFMR Finance Foundation

The Finance Minister, in his budget speech for 2015-16, has announced a new defined benefit pension scheme – Atal Pension Yojanai (APY, henceforth) – for unorganised sector workers who are not covered under any statutory social security scheme. It has been proposed that the existing subscribers of National Pension System-Swavalamban (NPS-S), the extant pension scheme for the unorganised sector, be automatically migrated to the APY unless they voluntarily opt out. Under the NPS-S, launched in September 2010, the Government of India currently contributes Rs. 1000 per year to every subscriber who makes a minimum contribution of Rs. 1000 per year towards building a post-retirement corpus.

The proposed APY differs from the NPS-S in two significant ways. First, the NPS-S is a defined contribution scheme where the subscriber’s contribution is invested in government securities, corporate bonds, and equity instruments-the scheme does not guarantee fixed returns to subscribers. In contrast, the APY is a defined benefit scheme that will provide the subscriber with fixed monthly incomes between Rs.1000 and Rs.5000 based on the respective monthly contribution amounts (which varies by age and saving potential of the subscriber; refer Table 2 below). Second, under the APY, the government will match either 50 per cent of the subscriber’s contribution or Rs. 1000, whichever is lower (initially for a five year period till 2019-20). This paves the way for the creation of a graded matching scheme where subscribers who contribute below Rs. 1000 also receive a (less than equal) matching contribution. For availing the same amount of co-contribution as under the NPS-S, a subscriber will need to contribute Rs. 2000 into APY (Rs. 1000 under NPS-S).

Adequacy of benefit

In order to judge the adequacy of the defined benefit proposed under APY, we compare the proposed benefit to the average monthly expenditure incurred by individuals in the lowest income quintile. Table 1 below presents the average monthly expenditure of an individual in each income quintileii. As the Table shows, the average monthly expenditure of an individual in the first income quintile is Rs. 628. As the APY is designed as a pension scheme for a household, we assume the average monthly expenditure for two people in our analysis.


Table 2 and Table 3 (below) present the defined pension amount (nominal and real) that will be paid to the subscriber and his spouse based on two sets of indicative monthly contributions so as to get nominal defined benefit pay-outs of Rs. 1,000 per month and Rs. 5,000 per month respectively. For example, in order to receive a nominal defined benefit of Rs. 1000 per month at the time of retirement at 60 years (Table 2, Column 4), an 18-year old needs to contribute Rs. 42 per month while a 40-year old needs to contribute Rs. 291 per month. Similarly, in order to receive a nominal defined benefit of Rs. 5000 per month (Table 3, Column 4), an 18-year old and a 40-year old need to contribute Rs. 210 per month and Rs. 902 per month respectively.


Source: http://pib.nic.in/newsite/PrintRelease.aspx?relid=116208 and author’s own calculations.

Table 2 and Table 3 also provide, in Columns 5 and 6, the real monthly pensions that households would receive and the shortfall in pension compared to their expenditure needs, which is a more realistic representation of the actual value of money households will actually be able to get. In order to calculate the real value of the pension we present value the cash flows at a discount rate of 5%, which is one per cent higher than the long-term inflation target, set by the Reserve Bank of India. According to the indicative tables, an 18-year old who contributes Rs. 42 per month will result in a real monthly pension of of Rs. 129 for the household. Assuming that the 18-year old’s income falls within the first income quintile, the defined benefit will cover 10.3% of her monthly expenditure. However, even if the 18-year is able to contribute Rs. 210 per month towards pensions, the defined benefit at retirement will yield a real monthly amount of Rs. 644 for the household (equivalent to a nominal monthly pension of Rs. 5,000) and will be sufficient to cover only 51.2% of her monthly expenditure.

Thus, an 18-year old in the first income quintile can hope to cover between 10% and 51% of her monthly expenditure upon retirement by contributing to the scheme. Tables 2 and 3 also make clear that there is a real risk of significant shortfalls for all age-groups, whether they contribute into the nominal defined benefit of Rs. 1,000 or Rs. 5,000.

It should also be noted that if inflation continues to hover around historical inflation of 8%, the defined benefit would cover a much lesser percentage of an individual’s expenditure per annum. For instance, for an 18-year old who contributes Rs. 42 a month, the monthly defined benefit would be sufficient to cover a mere 3.1% of her monthly expenditure upon retirement.

The need for inflation indexation and a more optimal investment mix

If we assume that the government contribution will be discontinued at the end of five years, the annualised rate of return required to guarantee Rs.1000 per month (or Rs.1.7 lakh corpus) for an 18-year old contributing Rs. 42 a month is 7.58%. If we relax the assumption that government contribution will be discontinued and that the matching contribution from the government will continue in perpetuity, the annualised rate of return required to guarantee the defined benefit drops to 6.68%. Depending on the evolution of inflation rates over time, these nominal rates of return could end up resulting in very low real return or even the risk of erosion in capital due to inflation. The APY could benefit from addressing two key design limitations of the NPS-S:

  1. Lack of inflation indexation: In order to ensure that the pension corpus of low-income customers is not eroded over time, the government needs to index both the subscriber contribution and the matching contribution to inflation. Assuming that the matching contribution continues in perpetuity and that the government invests the corpus in the current NPS-S investment mix (upto 85% in government bonds and upto 15% in equity), indexing both the subscriber and government contributions to inflation on an annual basis could provide the subscriber with a substantially higher corpus (as much as 4 times higher than the guaranteed amount). Indexing social security benefits to inflation would also be in line with international best practices. For instance, the US Social Security Administration makes an annual cost of living adjustment by linking social security benefits to the Consumer Price Index.
  2. Conservative investment mix: The current NPS-S investment mix invests upto 85% of the corpus in bonds and upto 15% in equity, the remaining comprising of corporate bonds. In contrast, the NPS-Main follows a life-cycle investment mix which invests 50% of a 20-year old subscriber’s corpus in equity, 30% in corporate bonds, and 20% in government bonds. As the subscriber ages, the share of equity and corporate bonds is reduced and transferred to the less-volatile government bonds. According to our calculations, investing in the life cycle fund mix could provide returns that are 49% higher than the returns on the current NPS-S mix. While guaranteeing a minimum amount through investments in approved fixed income instruments, the government could ensure that subscribers can accumulate corpuses that vastly exceed the guaranteed benefit by shifting to a more equity-heavy investment mix depending on age of the subscriber.

It is indeed heartening that there is a lot of policy attention on these very important questions of old age income security, and the emergence of the NPS and now the APY are testament to this. If some of the design limitations of the NPS-S were to be addressed in the APY, it would mean that the most vulnerable households would be able to build pension corpuses that could meaningfully provide them with old age income security.


i – http://pib.nic.in/newsite/PrintRelease.aspx?relid=116208
ii – This analysis has been performed on data from a financial services firm that is operational across rural districts in three states of India for a sample of over 200,000 households.


District selection and estimating the potential of the KGFS entity through GDP Mapping

By Surabhi Mall, IFMR Rural Finance

This is the first blog post in the KGFS (Kshetriya Gramin Financial Services) Model Incubation series. The objective of the series is to methodically conceptualize an approach to build the branch network while incubating a new KGFS entity or expanding to contiguous districts. The posts focus on themes that range from district selection to identification of branch locations and optimization of the distribution network.

In this post we start with a brief discussion on the choice of a district and later discuss geography-specific questions that influence the economics of the model. Finally, the post stresses on GDP mapping as a heuristic solution to those questions.

Among the early steps of setting up a KGFS model is identifying a district. District selection is mostly a matter of organisational strategy and choice. The choice may be based on parameters such as district’s rural population, its population density, credit to GDP ratio, forest cover, road density, among others. Reviewing these attributes prior to finalising the district provides an elementary sense of the KGFS’s business potential, composition of the product basket in the branches as well as the degree of customisation that may be required to set up the model. Following this, reconnaissance (Recce) of the district provides insights to questions such as – Does the model need any fundamental changes or customisation in the given geography? What is the degree of competition it is likely to face? What is the current status of customers – i.e. their access to credit, income earning potential, and savings or repayment behaviour. This step serves as a final validation to the district selection strategy.

Recce gives field-level insights on the geography and competition in the district while secondary data helps understand the demography and infrastructure availability. Since geography, demography and the availability of credit in a place have significant influence on how the local economy develops, this should provide reasonable understanding of village-level economics and perhaps its influence on the branch’s business. It may even be leveraged to formulate the entity’s business plan, its competitive strategy and the network of branches. However, is this sufficient to understand the requirements and provide suitable comprehensive financial services? Is this information adequate for each branch to realise and achieve its potential volume of business at every life-stage? In fact, how does one quantify potential of a typical service branch in the chosen district? Finally, can the impact that the branch or the entity would have in the economic well-being of people in the long-run be measured? Estimating the branch service area’s Gross Domestic Product (GDP) provides powerful insights in unpacking such questions.

Figure 1: Three steps prior to setting up a new KGFS branch

Why the GDP?

To start with, what do we mean by estimating the GDP of a branch service area? GDP of an area is essentially the summation of different economic activities that thrive and contribute to the economy of that area.

Now, a KGFS stands to ensure the financial well-being of ‘every’ customer and enterprise in the area. This dictates that each customer’s needs be identified, acknowledged and serviced. In this context, the GDP exercise provides valuable insights on the composition of different sectors that thrive in the area. This can then be used to segment customers, identify their respective needs, customise the product basket at the branch and design an apt pricing as well as marketing strategy for them. A deep dive into the village economics through this exercise enables the branch to identify and prioritize customers from occupations with high degree of cash-flow mismatches, i.e. customers who are most likely to benefit from financial services. In effect, all this reinforces the KGFS’ geographic commitment by accounting for all possible households and economic drivers in the area.

The exercise gives insights on the share of existing financial players (from the interest income generated in the area), the median profile of a customer’s household and her debt servicing capacity. At the very outset, these can serve as a filter (post the Recce) to re-assert the choice of the district and the working estimates of the business plan. These estimates can then be built into the annual and monthly business targets for the branch. The activity can also be designed to give a rich sense of actual business that the branch is expected to do, i.e. its market share1. By capturing the share of other formal and informal financial institutions in the area, one can assess the volume of competition. This can then be netted off from the estimated demand for credit, thereby giving the potential market share of the branch.

From an operational point of view, data from GDP can be used to add greater granularities to the branch’s customer management database. It also enables scope for new business development2. For the product development team, it helps estimate occupation-based credit requirement and decisions regarding risk-exposure limits.

More generally, the GDP map helps visualise what kind of financial services are required to increase the size of the pie in the first place. It is a quantifiable measure that may be used as baseline for a ‘village profile’ in order to assess the financial viability and/or impact of a branch.

When – Ex-ante or ex-post?

While the above arguments advocate executing this prior to branch opening, this may not be a binding proposition. One can customize the scope of the exercise based on the objective sought at different life stages of a branch. For example, for an existing, low-performing branch where the enrolled database isn’t representative of the area’s population, the study’s objective can be to capture the economic drivers, re-estimate the branch’s potential and identify untapped business avenues. It may also aid to gauge the share of competition of other players’ vis-à-vis that of the KGFS branch.

However, the maximum utility of the exercise would lie in leveraging it as a diagnostic tool to acclimatize with the new geography of business. Such information, when captured at the very inception stage of branch set-up can greatly aid in understanding the branch’s gross potential and scale of operations, relevant needs of potential customer and perhaps even insights into strategies to thwart current or budding competition. If the GDP study in a branch is conducted at the proposed stage of branch, re-estimation and scoping for new business development through primary studies may then become redundant. Another added advantage of doing this prior is that this can be a part of the branch staff’s training track aimed at familiarizing them to the landscape of the area.

In the long run, a time-series GDP exercise process– prior to branch opening and ‘x years’ post branch opening is perhaps going to be the only real indicator of branch performance. Branch performance in this case will not mean the business at the branch but perhaps the change in (composition of) GDP of the service area and the impact of the KGFS branch on the lives of the people3.

KGFS Impact Long Run = f (actual business and type of customers served by the branch, increase in GDP share contributed by those served in the area that can be exclusively attributed to KGFS’ operations between KGFS0 & KGFS1).
[KGFS0 – is the GDP estimate from the study in time period 0 (prior to branch opening) & KGFS1 – Is the GDP estimate from the study in time period 1 (post x years of operation)]

The next blog in the series is on the Activity-based Costing of the GDP exercise. Through the lens of GDP studies done in the past, it will attempt to provide indicative answers to questions such as time and resource costs of the exercise.


  1. Market share of a branch estimates the actual served market/sales of a branch. This addresses concerns such as market cannibalization.
  2. Based on forward and backward linkage of value chains in the area, loan purpose and occupation type, unexplored segments, etc,.
  3. This estimation needs to account for fixed effects.

We recently hosted a series of knowledge management sessions (Spark Spring Edition 2015), as part of which Surabhi presented on this topic. In her session titled “Gross Domestic Product Mapping”, she spoke on how GDP Mapping can provide an intensive diagnosis of a defined location and how it can be used in a research process aimed at providing richer, robust and relevant information about markets, variables and potential.

View the presentation from her session below:


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, C_i, with corresponding proportions, c_i, where i = 1 to 3. Then the degree of diversification for P across counterparties can be measured using HHI, where HHI is:

HHI =\sum\limits_{i=1}^3 c_i^2

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 \rho_{ij} can be written as:

GHHI= {\sum\limits_{i=1}^n} c_i^2 + \sum\limits_{i}^n \sum\limits_{j\neq i}^n 2c_ic_j\rho_{ij}

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.


Selection of Research Proposals for the NSE-IFF Financial Deepening and Household Finance Research Initiative

By Dr Santadarshan Sadhu, Coordinator, NSE-IFF Financial Deepening and Household Finance Research Initiative

The NSE-IFF Financial Deepening and Household Finance Research Initiative is very pleased to announce its final set of proposals selected for funding in this round. We expect, through this initiative, to catalyse a body of high quality research pertaining to critical questions of household finance, financial inclusion and financial deepening. We would like to thank all the researchers who applied to this initiative, making it extremely competitive and setting a high benchmark for future rounds. We would like to congratulate all the researchers whose proposals have been selected for funding and wish them the very best. Here are the selected proposals with a short description of each:

1. Getting our priorities right: Targeted agricultural credit and technology adoption in India 

Access to agricultural credit directly influences production through two main channels: Primarily, credit can raise investment in input use and hence productivity; Secondly, credit provides farmers with the opportunity to smooth consumption and thereby increase the willingness to take risks and engage in productive agricultural investments. However, existing evidence on agricultural lending through formal institutions has questioned the effectiveness of priority sector lending as a pathway from poverty. India’s progressive financial inclusion agenda, including the promotion of a wide network of rural bank branches as well as encouraging priority sector lending, provides a unique setting in which to examine the constraints of these hypotheses. We will build on existing research and methods to determine if and how credit influences production decisions and investment, and ultimately productivity. The specific questions we consider are:

i. Does reducing liquidity constraints through formal credit flows encourage farmers to adopt widely available technologies? Does adoption of these improved technologies increase aggregate productivity of major crops?
ii. What is the impact of credit on farmers’ production decisions? Specifically, does credit enable farmers to cultivate more high-risk-high-return cash crops?
iii. Does formal credit allow farmers to make more long-term investments?

2. Quality of investment advice in retail banking in India: An assessment 

Understanding that opening of the bank account is but the first step in a much longer journey to financial inclusion, this paper seeks to analyse the efficacy of banks as vendors of retail financial products. The study aims to evaluate if bank based relationship managers sell financial products that are high fee generating regardless of the products that may be more suitable for the customer. The theoretical literature on financial distribution makes a distinction between sophisticated and naive customers and considers naive customers to be particularly susceptible to mis-selling. In this study, we evaluate if even informed customers, i.e. those that understand their financial requirements, and the gaps in their portfolio, are vulnerable to mis-selling in the absence of a regulatory framework that recognises specific customer rights, or requires basic suitability checks in advice and sale of financial products. The study proposes to evaluate the extent and pervasiveness of mis-selling in the banking channel in India. This allows us to measure advisers response when we exogenously vary the types of clients, especially in their financial sophistication in the form of knowledge of and demand for specific products.

3. Examining the adequacy of MFI multiple lending directive by RBI: A study of slum dwellers’ loan choices

While a significant number of households in India do not have access to credit, parts of the country have already experienced crises of over borrowing. Similarly though credit is used for many purposes, it is still not taken as a signal to launch new financial products or product bundles. Though Indian financial inclusion experts in their eagerness to push credit into low-income households have received multiple setbacks, their pursuit has remained relentless. With multiple credit agencies often competing in the same geographical area, over-borrowing and even ghost borrowing has become rampant. In order to put a plug on the rising Non-Performing Assets, the Reserve Bank of India issued new directives for all Non Banking Financial Companies in December 2011 with further modifications in August 2012, restricting the borrower’s freedom in a bid to control over indebtedness. However, we reason that restraining borrowers to borrow only from two MFIs or less will create further problems for both borrowers and MFIs. In a market of illiteracy and informational asymmetries, people with a tendency to cheat can still defect, households may be denied loans at the time of need and rogue MFIs may pre-empt members from other MFIs, thus increasing their retention costs. We therefore aim to study the borrowing behaviour of slum-dwelling households in the city of Pune to gauge the adequacy of the RBI directives in containing over-borrowing and understand whether other financial products can contain their need for multiple loans other than income generation.

4. The Technology of lending: Contract design of informal credit products

The stubborn persistence of high levels of informal credit penetration, and comfortable coexistence of formal and informal credits markets, have re-emerged as important policy and research questions. Potential answers to these research questions have come from scholars in multiple fields, many of whom have focused on South Asia and India. Within economics, a vast literature has explored the causes and consequences of credit market failures, the unintended impacts of policy change, and the interaction of formal and informal credit markets. Within the field of anthropology and economic anthropology, scholars have made major advances in understanding household financial behavior, as well as the social norms embedding informal, semi-formal, and formal credit practices. Despite much excellent work, the research examining credit markets and informal practices have not yet fully explored the role of contract design in informal credit products as a cause and consequence of financial exclusion. Without such understanding, we are left with an incomplete analysis that both inhibits the opportunity for formal sector providers to learn from informal product innovations, and inhibits the clear framing of financial inclusion strategies and policy analysis. This study hopes to remedy the gap in the literature by analyzing the contract features of a clearly defined set of informal credit products in rural and urban Tamil Nadu. Through a careful analysis of the specific contract features of currently available informal credit products, I will show that in contrast to the assumption that access to formal, cheaper credit will result in households shifting away from informal credit options, the notions of access and price should be re-examined, as informal credit products rapidly adapt to changing conditions in the formal sector with a surprising set of contract innovations

5. A Framework for Financial Behaviour Modelling in a Rural, Low-Income Environment

The objective of this action research study is to create an empirically driven normative framework for business decision-making. The research design associated with this objective would be conclusive and not exploratory in nature. Additionally, given that we intend to use observational data as opposed to experimental data, this study will fit under the broad umbrella of a descriptive research design. Our research intends to use both longitudinal and cross-sectional data. Specifically, we intend to use data analysis methods to infer behaviour (defaults on loans, late-payment, cessation of service, etc.) from various attributes demographic details and past financial transactions. We intend to use a series of methods termed as ‘supervised learning’ to achieve this goal. While building credit scores from past transactional and demographic history is the bedrock of modern retail banking, a preliminary literature investigation by the researchers found little academic research in the space of developing such scores in a low-income, sparse transactional history environment. There are also problems in applying the traditional credit scoring models like FICO, CIBIL etc. to score low-income households. The major concerns are that existing prescriptive models were not built for this demographic, and existing methodologies lack the appropriate data to build a robust model. This motivates us to develop novel changes to the existing supervised learning methods, to make them more useful in this domain. The study also intends to validate the created scores with field case studies of mock implementations, and actual pilots.

The final research output upon completion of these projects will be published as working papers by March 2016.