hello everyone in this session we are going to talk about uh the classifications and the key concepts of credit risk as a part of this session we would be uh looking at uh the different kinds of classification of credit risk what are the different kinds of risks that typically go as a part of credit risk two broad classifications is what we would be talking of the next slide I will highlight those various classifications of credit risk then whenever we use the word credit risk the first thing that should come to our mind is the probability of default so we need to have different mechanisms to understand what is meant by probability of default how do we really compute the probability of default so we'll spend some time understanding that aspect then comes recovery when a default occurs it may be possible that uh it may be possible that some amount can be recovered from the borrower so only some amount will be at risk so that is what we are talking about the recovery risk what is the possibility of recovery and how much amount cannot be recovered from the borrow lower in case of default so we'll spend some time to understand the recovery risk then exposure risk exposure is typically the amount that uh one party needs to pay to the other party so is it possible that the exposure increases or decreases in the case of default in which cases the exposure increases and how can exposure itself could be an additional risk is something that we are going to look at here then once we have a good understanding of these different kinds of credit risks we'll have a mechanism to compute the expected loss and what is meant by expected loss and how should I treat the expected loss in the financial statements then moving on to the unexpected loss how do we really compute the unexpected loss and based on that how do we move forward towards the assessment of value at risk for this particular uh credit portfolio and what do I really mean by concentration risk in the context of credit risk when does the concentration risk typically arise how does it arise and when we have talk talking about the portfolios unexpected loss how do I really assess the contributions of each and every individual asset class or the asset to the overall portfolios unexpected loss so that is what we are calling as a marginal contribution we'll talk about a formula for computing the same and finally we will move towards our computation of risk adjusted pricing we'll use a couple of mechanisms there called risk adjusted return on Capital and risk adjusted written on risk adjusted capital r r r a so these are some of the mechanisms along with the understanding of economic capital is something that we would be discussing as a part of this particular aspect now let's move on to the first one classification of the credit risk on a broad note the credit risk can be classified into two major headings the default based credit risk and the value based credit risk the default so different kinds of credit risk that are associated with the defaulting of account counterparty one party not paying the loan on time the borrower not not paying on time uh the the the amount that needs to be paid either in the form of Interest or in the form of principle so they are all the occasions of default Associated so there is a pure default risk where the party has actually uh defaulted on the commitment that needs to be made both in time in terms of time as well as value then there is a recovery risk so when the default has actually occurred whatever the amount that I am able to recover from the borrower is much lesser than the full amount that the borrower has to pay so that is the recovery risk means I'm getting only a part of the amount as a part of the recovery from the borrower so that is what is how much of that money is at risk with respect to the recovery in some cases I have taken a collateral under the assumption that this collateral would typically offset the possibility of loss that that might crop up because of the default of the counterparty but that collateral value may be so low may have gone so low that its value now is nowhere sufficient to cover the amount that is due by the borrower to the lender so all these are examples where recovery risk comes into picture so that's one more category of default based credit risk and we also have exposure risk there is some possibility that at the time of default when the person has defaulted during that particular period the overall amount that may have to be paid by the borrower to the seller by the to the lender is much higher than in the normal scenarios at the time when the borrower has defaulted at that point in time the amount that needs to be paid appears to be much higher than the amount that needs to be paid under normal circumstances so these are the three different kinds of credit risk that are associated with the default and one point we need to understand is these default PR they have very very low correlation they are almost not much correlated with the pure Financial Risk when I talk about the pure Financial Risk it is an interest rate risk the losses coming because of the fluctuations in the interest rates exchange rates or even the inflation so when when I look at the default risk or the recovery risk or exposure risk we see that they don't carry much of a correlation with respect to the pure Financial Risk then the next category of the credit risk is a value based which we generally find are highly correlated with the pure Financial Risk whether it is interest risk or exchange rate risk or even the inflation based risk within this we see again three different kinds of risks one the migration risk here the party is not defaulting but there is a change in the credit quality let's say a AAA rated uh issuer now has got a credit rating of eight which means there is a dow gradation of the credit rating now that itself can impact the market value of this particular company there is no default that has occurred but there is a change in the market value of that particular entity and this decrease in market value is also another resemblance of credit risk so when we are talking about the credit risk we are focusing not just on the default side but even a reduction in the value because of the downg radation of the ratings then the other aspect that is coming up is the spread risk see sometimes when the economy is in uh a recession right when the economy is in a recession it is very much possible that the investors would charge a more premium for the Investments that they have done compared to when the economy is in an expansionary phase so due to different market conditions the investors are typically a looking for different kinds of returns because they are perceiving the Investments the same investment as uh as different levels of risk during the different Market scenarios so even because of that the overall exposure can be either revalued or devalued even that is a part of the credit risk and in some cases just like the way we have experienced the 20089 financial crisis where the markets have become very less liquid so because of that all the kinds of exposures to the credit risk all the kinds of collaterals which the parties have maintained the values of the collaterals have gone down quite drastically all the exposures they had to be sold at much much lesser prices than the market prices than the expected prices resulting in a loss to the parties so the loss occurring because of the credit liquidity risk is also a kind of value based credit risk which we really need to understand so whenever we are talking about the credit risk we have to appreciate the fact that it can come from any of these six different dimensions three from the default based categories and three from the value based category and uh the ratings the rating agencies really play a very very important role in analyzing and measuring all the above credit RIS that I have discussed that's the major role of any credit rating agency when they are offering or providing the credit rating to a particular issue or to a particular issuer they have to consider all the aspects that we have mentioned above then moving on to the next topic where the intention is to find the probability of default generally the probability of default is computed for a specific time Horizon it could be for a one-ear period or a multi-year kind of a period so we are Computing the probability of default for a particular period and it's very very important to assess the cumulative probabilities especially when the exposure years are for more than one year we should be able to compute the cumulative probabilities because we don't know uh let's say after a particular point in time this particular firm can go default or this particular firm can get a much better credit rating or any of these aspects what we need to understand is if the time Horizon is very very short for that small time Horizon the probability of default may be very very low though I cannot completely say that it will be zero but definitely it would be very very low and as the time Horizon is increasing the probability of default also typically increases now there are different approaches to compute the probability of default one based on the historical default frequencies I observe the default frequencies of various firms historically so I'm I'm first of all grouping all my borrowers into homogeneous classes right based on various profiles so there are different uh techniques to identify the profiles of the customers group them probably uh there is something called cluster analysis which actually groups uh all the similar similar datas together into different clusters so these are the homogeneous classes I'm trying to observe the historical default frequencies of the different borrowers homogeneous classes so one there could be a the way we are creating the classes it could be based on a subjective analysis or it could be through a kind of uh statistical mechanism called cluster analysis now if it is more and more subjective the analytical competencies of the skilled credit officers are very much tested in the process but this is an expost rating class per rating class because once we have class once we have grouped the observations for each of them we have tried finding out the historical default frequency and based on that we are trying to say that for this particular class of uh customers or borrowers this is the probability of default so this is purely based on the historical mechanic whereas we have another mechanism right so this is most like Expos so after the data is derived we are simply uh trying to find out what is the proportion of those borrowers in each of the classes who have defaulted we also have a mathematical and statistical tools which we can apply on the large databases so various types of information that is collected regarding the Borrowers is taken in the form of a score so historically the various defaults and the various attributes are taken together some kind of mathematical or statistical models are being built linking the default of the customers with the various attributes find coming up with a kind of a scoring process and uh uh based on that for new customers when I input in that particular score I'm getting whether this party was going to default or not default so this is an exanti measure so it can facilitate the monitoring over time this this formula can keep changing over time and based on that the assessment of the probability of default for each of the customers or for each of the classes at each of the time intervals can very well be computed and in some cases it could be a combination of both judgmental and mechanical so there is a mathematical and a statistical approach as well as a judgmental approach so when we are talking about the classification it is automatic probably I can use a cluster analysis or some such kind of mechanisms for classifying the customers and uh once the automatic classification is being done that's where the experts come into picture Corrections are done by the experts so they look at the various qualitative aspects and based on that they look at both the judgmental as well as mechanical they look at the Historical as well as the statistical part do the appropriate Corrections and bring out the best possible models and one more way in which I can look at the probability of default is purely based on the market prices sometimes the market prices of the Securities are in such a way that corresponding let's say if I'm talking about a particular probability of default let's look at it in a simple way right so some PD is the probability of default 1 minus PD is the probability of no default so at the end of one period right there is a PD chance that there is a default so if uh so which means when there is a default I'm only going to get the recovery amount whereas there is a one minus probability of default chance that I'll will get my full one so obviously at the end of the period when there is a default the amount that I'm getting is PD into recovery rate + 1 - PD into 1 whereas when I'm when there is no default I'm going to get one and I'm talking about the present value 1 by E power r t or R should be same as PD into recovery rate + 1 - PD divided by E power r + Delta now based on this I should be able to calculate my Delta which is the probability of default so I could clearly see that E power R is equal to our E power R into PD into RR + 1 - PD is equal to E power R into E power Delta so now from here I'm getting E power Delta is equal to this much and from here so which means this if I look at PD so this is coming out as 1 + PD into recovery rate minus 1 or 1 minus of PD into 1 minus recovery rate so I could clearly see the value of uh Delta which is uh what is associated with the the spread the spread that is coming out because of the probability of default and based on that spread whatever is the spread I can find out what is the probability of default associated with this particular uh class so even this kind of method also can very well be engaged so there are different ways in which I can find out the probability of default then comes the next aspect which is the computation of the recovery risk right the recovery rate is nothing but one minus of loss given default given that the party has defaulted how much is the loss that is going to be there which is obviously uh based on how much can be recovered from that particular party so these two are complimentary stuff recovery rate is 1 minus of loss given default we express these things in percentage and we have to understand that the recoveries are different based on the different types of credit contracts right for different kinds of credit contracts we have different kinds of recovery methods recovery amounts recovery processes because the way the legal system is designed will talk about the efficiency of the recovery process in some cases it is dependent on the economic conditions also because when we talk about an economy in a recessionary phase probably the recovery percentages could be much much lesser people may not be able to pay during a recessionary phase the borrowers even if they are default the recovery also could be very pathetic but especially when the economy is doing well then the recoveries could be much much better so even the recovery procedures could differ based on the economic conditions and even the business sectors play an important role in some sectors the recoveries are much higher whereas in some sectors the recoveries are much lower especially associated with the asset values the volatility that is associated with the asset values in different sectors in some sectors the volatility of the assets are much much higher which means their values are going to fluctuate quite drastically overall the values could be much lesser whereas in some other economies where in some other sectors where the volatility is much much lesser the recovery values also could be much better off and even the recoveries are based on the various coant that are associated especially some kind of restrictions that are put on the borrowers by the lenders regarding the kind of actions that dos and don'ts that the borrowers can do until the settlement of of the load and they are a kind of privilege to the lenders so depending on how stringent how strong are the Covenant structured in the deal uh we would typically look at what amount could be recovered and what amount may not be recovered from the borrows so this is also a so the these are the various things that needs to be done as a part of the recovery how much is the will be the recovery rate if I have to assess it beforehand assess it x and t then that's also a very very difficult process just like assessing the propability of default uh uh uh before itself the recovery data is very very difficult to collect because majority of the times we see that the recoveries are m ised at Central locations at the counterparties position so they reference to the original contracts because of this there there reference to original contracts collaterals guarantees that have been taken at the beginning of the contract that references get lost they are managed purely at the counterparties position so even if I building very sophisticated statistical techniques to model the recovery risk still I cannot build a lot of comprehensive capabilities into the model that is what has been the observation with respect to the recovery risk then we also talk about the exposure risk which is purely associated with the amount of risk in case of default of a particular counterparty the amount that is at risk see when we are talking talking about instruments like term loans Etc where we know how much one party has to pay to the other which is a fixed kind of an amount where we have the whole reimbursement plan for both the interest as well as PL principle is fully planned out fully mentioned as a part of the contract how much to be paid at what point in time so in this case finding out the exposure the amount that is at risk is a very straight for process but when we are talking about revolving credit lines kind of stuff where the balance how much amount needs to be paid keeps changing at regular intervals of time there are lot of external events borrowers behaviors which would influence them modeling this particular aspect of the exposure risk becomes more and more complicated so if I have to really do a quick computing ation of the exposure at default we talk about okay how much of the loan the that the borrower has already taken amount that he has currently uh withdrawn or used as a part of the loan plus whatever is the amount that is totally granted by the bank to the borrower which is more like already discussed that he would be entitled to a credit limit of this much out of this he has already used some portion of the credit limit so let's say the the bank has granted him a credit limit of 1 million let's say 200,000 has already been used by the borrower so the remaining 800,000 he has uh the bank has already granted but he has not used now when I'm talking about the exposure at default we are talking about 200k which is already used Plus on the remaining 800k we will multiply it with the loan equivalency Factor so we are talking about what is the rate of usage of this entire 800k especially when the when the counterparty is very close to default in near default scenarios what is the kind of rate of usage of this excess limit that is what we are calling as a loan equivalency factors so this number would typically be used to finally arrive at the exposure at default for various revolving credit lines kind of mechanisms and when it comes to deriva is so the due value in the event of default when the default occurs how much needs to be paid by one party to the other is purely based on the market conditions of the under lying asset so the exposure at default keeps changing at different intervals it is purely it is based on market conditions and various other aspects so we need to really uh focus on what are the various uh ways in which the exposure risk can be determined for different kinds of asset classes so there is an assessment assumption regarding a probabilistic nature where the amount is a forecast of the future events how much amount is at risk it's a forecast of the future events with an intrinsically stochastic approach we build some kind of a stochastic model to typically U model the amount uh for the future events and various kinds of exposure at default models are used to measure the EAD risk right now once we know different kinds of risks now that we have already uh looked at what is default risk what is uh exposure risk and what is recovery risk now based on that we would be Computing the expected losses so as a definition it's an average loss that is generated in the long run which is typically expressed as a percentage of exposure at default there are two major approaches to compute the expected loss one is a financial approach where we are talking about the loss in terms of decrease in the market values resulting from any of the six different forms of credit risk which is the default risk the exposure risk or even the recovery risk or even from the other aspects like uh the migration risk the spread risk or even the liquidity risk so when we are using a financial approach the expected loss is computed based on all these different kinds of risks their probability of occurrence as well as the loss that is going to occur given that uh given that scenario has occurred and the exposure that is at default in each of the cases so these are the three things that are taken for each of the scenarios multiplied to obtain the expected loss the second approach is an actorial approach where the losses only associated with the default which means the first three categories are only considered while for computing the expected losses through the acturial approach and coming to the banks from the banks perspective expected loss is a kind of an industrial cause that the lender has to face which means this has to be taken into the financial statements of the bank it has to be as a part of the losses that are already known so it has to be embedded it's a kind of a cost that they have to embed as a part of the banking business business and the credit decision so that much of loss is expected so whatever is the portion of the loss that is expected it has to be embedded into the overall the banking business as well as the various credit decisions that are typically taken whereas when it comes to unexpected losses see in many cases when we talk about short time Horizons a smaller time periods the expected losses may not match with actuals there could be a huge deviation between what is the actual loss that has occurred versus the expected so when we are talking about short-term uh losses versus longterm average there could be a big deviation between them in short term there could be a huge amount of volatility in terms of the expected losses based on market conditions and various other aspects which we have already discussed so there might be a lot of deviation between the shortterm loss versus long-term average it could be because of credit Cycles it could be uh because of economic scenarios or various other aspects Associated so in some cases the actual losses may be much much higher than expected and in that case the capability of the bank to continue on a going concern basis will be challenged quite seriously so that is where the unexpected is coming into picture now I that unexpected loss or to mitigate that unexpected loss or a compensation against the unexpected loss the banks have to hold enough equity capital in case the losses have occurred at that particular point in time in case the actual losses are much much higher and in case the bank survival is getting questioned so that is against that unexpected loss the banks are expected to hold enough Capital to absorb the losses that are going to crop up during the bad times and during good times when they are generating higher than expected amount of profits this is typically replenished and when we are to talk about how much of capital do they really require as a backup now this is where we are talking about the robust analytical risk models because obviously whatever they have lent they may not lose the whole amount which might be possible only once in a once in a blue moon kind of scenario and there's no point in having that much of capital as a backup so this is where how much of capital should really be required as a part of the backup needs robust analytical risk models and measures but again these models they should not be restricted purely based on the credit risk alone they have to look at the complete Enterprise wise risk and the the amount that needs to be uh set aside the amount that needs to be used as a compensation should follow an Enterprise risk perspective rather than a silo approach so there should be an integrated view of the risk not just the credit risk and when we talk about the ratings here they become the core how much of the credit risk is playing to what extent credit risk is contributing to the overall risk of the bank the credit rating play an important role in explaining this particular aspect though I have to look at the overall integrated view of the risk the credit rat becomes a very very important uh aspect in the process and the credit ratings given by the rating agencies they become very very essential measures in determining to what extent credit contri credit risk is typically contributing to the overall Bank risk and we also know that for different kinds of credit ratings let's say AAA versus a a versus B Etc the variability of the losses is very very different for a AAA rated security the losses variability could be much much lesser whereas for a b-rated Securities the variability of the losses could be significantly higher now what we need to understand here is though as a measure of risk we generally use the word standard deviation in many aspects as a measure of risk for various kinds of risks to measure the risk effectively we talk about the usage of standard deviation but generally in the credit risk world we don't talk about standard deviation that effectively the reason being if you try to recollect some of the limitations of standard deviation standard deviation will not be a reliable thing if the data is having too many outliers in it or if the data is very much skewed so nonnormal kind of a data or non symmetric kind of the data if the data is not symmetric standard deviation as a measure of risk will will will not have of a reliability and what we see in credit risk is uh every aspect of credit R whether you talk about the losses the distribution of the losses they are very much asymmetric the distribution of the default rates is very much asymmetric loss given defaults are asymmetric so because majority of the credit risk related uh elements are are asymmetric we cannot use standard deviation as a measure of credit risk now this is where we are uh talking about using value at risk which is expressed as a percentage of exposure at default being a better measure of variability compared to the credit uh compared to the standard deviation and in case of value address we talk about the difference between what is the maximum loss the bank can have at a particular confidence level so let me uh quickly draw out a diagram now if this is this is how the distribution of the losses could be right very skewed kind of stuff so if this is my mean which is my expected loss so this could be my 99% area this is the 1% area associated with this distribution so when I'm talking about the 99% area this is the one so this is the maximum loss that the bank can have at 99% level of confidence and this is my expected loss and what we are saying is the difference between the two will for my unexpected loss right and this much is the value of value at risk for me so uh against this particular value at risk we are talking about that much of capital is very much needed by the bank to really protect itself from the possibility of default and this capital is what we are calling as economic capital the amount of capital that is needed by the bank to protect itself from the failure at this level of confidence at a particular level of confidence is what we are calling as the economic capital so which means now if the the bank has actually set aside this much of capital based on the value at risk now the insolvency is coming out only in the small proportion which means if there is some catastrophe some some extreme loss that is coming up whose probability is 1 minus the confidence interval only when such kind of a percentage is going to in that kind of a percentage where the loss is going to be a a low frequency High severity kind of a loss only in those cases the bank is going to lose very badly in all other cases the bank is being protected by a capital that is the economic capital which is being used as a backup for production purpose so we we have already discussed the probability distributions are a symmetric the loss given defaults are asymmetric right even even we could see that uh the default rates are also highly asymmetric so the Adverse Events they are low frequency but High severity kind of events they have a very very small probability of occurrence but when they occur the sity could be much much higher they can affect the overall profit and loss account of the bank very drastically so when we are trying to go ahead in terms of computation of the econom IC capital I need to have a good understanding on the distribution of the return otherwise that 1% could be a a very very bad decision that I might have taken the number that I'm considering for 1% could be a very very pessimistic or very very optimistic so I really uh need to uh look at the calculation of the economic capital requires a good identification of the most appropriate probability density function so that can be a pure closed form distribution going with the various parameters I can do that way or I can get into completely numerical simulations like Monte Carlo simulation use Monte Carlo simulation to typically identify those extreme events and the kind of City they have on the profit and loss account or I can have kind of discrete probability Solutions like scenarios for each of the aspects and based on them I can go ahead in terms of working out uh working out with the unexpected loss and the V aspects a few things that we have to understand in this context neither the expected loss nor the war they consider they do not consider the portfolio concentration in what sector majority of the uh asset classes are like because the sum of individual risk is not equal to the portfolio risk there is some level of diversification that is coming out because of the portfolio so more and more loans increasing the more and more loans decreasing the impact of uh very few category loans on the overall more and more diversification obviously will reduce the the portfolio risk this is purely based on uh less than perfect correlation the correlation between the various exposures the Lesser and lesser it is the more and more uh it is adding to the concept of diversification so just defining the concentration risk so especially in a case of a credit portfolio when I'm talking about the borrowers they are all exposed to Common risk factors so all borrowers are impacted by interest rates all borrowers impacted by currencies technological shes so where there are common factors which are driving the borrow all the borrowers defaulting behaviors this is what we are calling as a concentration risk so common factors among all the borrowers which is leading to either all of them defaulting at the same time or all of them not defaulting so there is diversification especially with respect to these factors so to what extent the concentration is existing with respect to these factors talks about the concentration risk so when the concentration risk is very very high both the willingness to pay as well as the ability to repay the loan willingness as well as the ability to repay the interest and the principle will typically go and that means large number of counterparties are either unwilling to pay or they don't have the ability to pay thus resulting in a huge increase in the number of defaults and uh especially with respect to some adverse external event this risk is going to increase more and more so while assessing even the concentration risk also needs to be taken into consideration so one way to overcome this concentration risk first look at large number of borrowers so whatever the splitting don't focus on one single customer or very few sing few customers with huge exposures to each one of them so try to diversify to whatever extent is possible with respect to number of borrowers with respect to each borrower limit the exposure in terms of amount that is being Lent to each of the borrowers and excessive market shares on the individual customers should typically be uh reduced so that each customer's exposure is very very limited and portfolio should be as much granular as possible as much Diversified as possible so that the risk of the overall portfolio can be reduced this whole uh diversification should should be carried out based on a thorough correlation analysis of the various events of default and based on that the selection of the various customers and the various uh asset classes need to be considered and also the change in the credit exposures due to various external events and factors need to be con uh need to be considered thoroughly and if I have to take all these things into consideration I have to build full port folio credit risk models they measure how much concentration is provided by the individual borrowers to what extent the individual borrowers are contributing to the overall risk of uh uh risk of the party so by each counterparty I need to estimate the concentration risk that is brought by each counterparty to the bank by each transaction to the bank by each market type to the bank by each facility type so I really need to see to what extent the concentration risk is increasing for the bank from each of the counterparties from each of the transactions Etc so I'm looking at modeling the codependencies across all these areas and there are different ways one I can directly measure the default correlation by looking at the Historical correlations of the data trying to understand the homogeneous group of borrowers and based on that try to understand what is the level of default correlation between the various groups and there is an other way where I'm going purely based on the asset value correlations so where I'm looking at the probability that the asset values of the two borrowers both of them taken together for both of them what is the probability that their value is falling below their respective outstanding debt so I'm talking about two borrowers A and B normally what is the probability of a defaulting what is the probability of B defaulting if I'm finding out independently that's fine but at a particular Point what is the probability that a is defaulting as well as B is defaulting or what is the probability that the value of the assets of a uh probability of value of the assets of a are less than the debt of a and or intersection value of assets of B are less than the debt of B what is the probability of this situation occurring that is what we are calling as based on the asset value correlation we are trying to model the default codependencies so the effect of diversification lies in the possibility that the counter prop part's value is influenced by the external economic event when I'm using simulation to model the same I will look at the various external events economic events based on that I'm looking at what is the probability that party a is defaulting what is the probability that the party B is defaulting and what is the probability that both of them are defaulting simultaneously now one we have understood the concept of under uh concepts of uh unexpected loss V and concentration risk now we are moving on to once I once I'm Computing the overall unexpected loss of the portfolio to what extent I can do an assignment or the distribution of the loss of each of the individual classes to the overall unexpected loss of the portfolio for that I want to bring in a few important notation right you take UL as the total unexpected loss of the portfolio overall portfolio this is the unexpected loss I'm looking at wi as the weight of the eighth loan on the overall portfolio so the whatever is the amount that you have invested in E Loan divided by the total loan that you have given that is what is the weight of the I and I'm also looking at the correlation between the I loan and the overall portfolio the default correlation so when the overall portfolio has fallen whether the value of the I portfolio also has fallen or has it gone up so that is what is the correlation between the I loan in the portfolio versus the overall portfolio So based on that we are trying to find out the marginal contribution of the eigh loan to the overall portfolios unexpected loss and what we are simply saying is take the overall unexpected loss of the portfolio take a partial derivative of it with respect to the weight so take a partial derivative of unexpected loss overall unexpected loss of the portfolio with respect to the weight of that loan weight of that one single Loan in in the overall portfolio so once you find out do by dowi multiply that value which is now this becomes the slope multiply this slope with wi to get what is the marginal contribution of the E Loan portfolio to the overall E Loan in the portfolio to the overall unexpected loss of the port portfolio but at the same time we are also saying if I'm using the traditional variance covariance approach then the unexpect then the contribution of the E Loan to the overall portfolio unexpected loss is taken based on the correlation between the E Loan the default correlation between the E Loan and the overall portfolio multiplied by the weight of that loan in the overall portfolio multiplied by the unexpected loss of the portfolio so here if you see this part is nothing but the proportion of the uh the proportion of the unexpected loss of the portfolio based on the weight and that we are multiplying it with the correlation between this particular security and the overall portfolios correlation now if you really see these two things in both the cases I'm talking about ulci so it's coming out that do UL of the portfolio by dowi multiplied by wi is one method then I also have the row between I and P multiplied by w i into the unlimit the unexpected loss of the portfolio when I really look at this mechanism I could see that the change in the unlimited the unexpected loss of the portfolio with respect to change in the weight is same as the correlation between the unexpected correlation between the the I loan the default correlation between the E Loan in the portfolio and the portfolio as a whole multiplied by the unexpected uh loss of the overall portfolio right so this is what we are talking of and based on this even the correlation between the two can easily be understood and based on this it's also coming out that the beta of the Ione is simply coming out as the overall uh contribution divided by the weight so this is a weight adjusted contribution divided by the unexpected loss of the overall portfolio so if you see this ulci by w i if you bring this here this is nothing but the correlation multiplied by the unexpected loss So based on that it is coming out the simplification is simply coming out as the correlation between the E Loan in the portfolio multiplied by sorry correlation between the E Loan in the portfol folio and the overall portfolio which is what we are calling as the beta of the iow and if this number is greater than one it means that the marginal risk is adding more than the average risk to the overall portfolio and if it is lesser than one we can say that the marginal risk is adding lesser than the average risk to the overall portfolio based on this the various loans can be selected so some of them could have a beta of greater than one while some of them could have a beta of less than one so once uh I I have decided on what kind of portfolios what kind of uh uh risk can be consider or what kind of loans can be considered by uh by planning on the required amount of beta then the whole amount of transactions can be identified uh B so so that the overall concentration of the portfolio what of which one of them are adding up to the concentration of the portfolio and which of the loans are uh really providing diversification benefits with respect to the portfolio we can really identify those kind of transactions and based on that the overall Balancing Act can very well be uh taken up then the next aspect that is essential in this uh uh in this uh session is the risk adjusted pricing we have already discussed that if the value at risk is much higher then obviously the amount of capital that is needed as a protection against the risk also is much higher so which is telling me that the economic capital that is typically required as a backup is much higher and once the economic capital is much higher which means the profits that the bank has to generate is going to be much much higher so there is a very much necessity of generating higher profits so if I'm typically looking like the cost of capital that is incurred for the bank and I multiply it with the value at risk because that much of amount is is actually blocked so because I am blocking that much so this is the amount of capital that is uh simply getting blocked up so my profit should be much higher than this amount so it's a kind of a lending cost which has to be incorporated into credit streat and the lending policies need to be designed more and more stringently based on on this particular aspect and how much is the expected loss how much is the unexpected loss once I do the computations this the difference between these is what will decide what kind of credit strategy that needs to be followed and any amount that we are talking of as an economic capital which is the difference between the unexpected and the expected that is that needs to be uh incorporated into the loan pricing itself because uh uh we know that uh the capital has to be that much of capital needs to be a backup for the sale so the the amount needs to be a whatever is the economic capital that has to be uh considered as a part of the loan pricing policy now this is what we are calling as risk-based pricing it's a kind of a structure for active portfolio risk management it is integrating all kinds of risks credit risk Market risk operation risk and based on that we are trying to arrive at the economic capital which has to be a kind of a backup against all these risks and this particular policy will help in terms of formulating the management objectives in terms of uh the profitability at the business units level and as a part of the measure for the same one popular uh measure which is addressing the risk adjusted pricing is the risk adjusted return on capital r very common measurement it is making an assumption that the value of the different business lines that the bank is having it is purely dependent on the ability to generate the return so the return that the business line need to generate should be higher than the cost of capital that is incurred for that particular line so reward the market risk premium required by the capital corresponding to the amount of risk that it is facing so the ra is purely based on that particular aspect it is making a clear assumption that at each of the business lines level I'm looking at what is the return that that particular business line is generating is it greater than uh the amount or the return that is expected by the investors of that particular capital for that particular business line and one of the best ways to make that kind of a measurement is based on the capital asset pricing model the capm and what it says is the credit must lie on the market risk line taking into consideration the correlation with the other asset classes so how much of the credit needs to be provided it should lie on the risk to return line so the credit spread have to be in proportion with the market risk premium RM minus RF and wherein I'm taking the risk premiums associated with all the comparable investment that is what goes as a part of the raoc based pricing evaluation so as a part of the process of computing the ra we are talking about look for what is the target return that the lenders or the investors are willing to accept by investing in the risky activities of the bank so based on that the return should be much higher than the threshold of cost of capital and whatever is that Target return on Equity that is expected by the equity investors I want my risk adjusted return return on risk adjusted Capital should be greater than the target Roe so in other way if I have to put it once I know what is my cost of equity Capital If I subtract it from risk adjusted return return on risk adjusted Capital so that is my economic value act multiplying it with the economic capital which is the difference between the unexpected loss and the expected loss will give me the economic value ad if it is high and positive obviously the the the the that particular investment or that particular lending decision has done uh uh has performed better and if it is working out to be negative it's an indication that that particular decision did not yield the desired result so the whole intention of risk adjusted pricing is incorporating the various fundamental variables of the value based management approach so when we are talking about the pricing we are considering the cost of funding the expected loss so these are all the various so when we are doing the pricing we should include the cost of funding where we are talking about the fund fee as well as the spread whatever is the expected loss I'm taking out allocated economic uh economic capital and extra return required by the shareholders all of them have to be considered so when all these things are taken into consideration that is how the pricing has to happen so that is what when we are Computing the ra R we will take the spread and the fees these are the two things that are contributing to the return expected loss have to be subtracted whatever is the cost of capital which we have got uh multiplying it with multiplying it with the economic capital so the whole thing is divided by the economic capital so we are expressing it in percentage terms even the cost of operations need to be subtracted and that is what will give me the ra which is expressed as the percentage of economic capital and this economic capital can very well be used in optimizing the risk return tradeoff in the bank portfolios so that's how we have to look at the risk adjusted pricing it plays a very important role in terms of evaluating the credit decisions that have been taken up so this is what I wanted to cover as a part of this session these are the various areas which we have focused in this session I hope you got a decent amount of understanding about all these various aspects any further queries you can very well give me a call on the number that I have given below or you can send in an email at the email address provided below thanks a lot for listening to this session thank you very much