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Fire sales, endogenous risk and price-mediated contagion

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Automatisierte Medienanalyse

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change he planned to do so I ever and have come so thank you very much
for in inviting this lets me thinking and thank you especially fish found so I've most events was a PhD student and somehow we always end up working on the same topic so he this so the work done they are attracting agent bundles which was the topic is interesting in that time many started work on risk measure than I was interested in that and now these little system this so I can only very happy that here so around but today I would like to talk about a project that we've been working on with the PC student of mine Eric scanning so that's not the uh title uses 2 days and 2 engine Maggie's from book somewhere and this is a project related
to the modeling of systemic risks through price mediated contagions I'll explain what I mean by this why it's important when I present a simple model for a price mediated contagion and then you know and show how it applies to European banking data obtained from the European Banking Authority what is so is the outline of my talk was the very discussing the B channels of contagion which lead to systemic risk and that will focus on 1 particular channel which is fire cells were out of prison more OK so L. well systemic risk is a very important topic that has been studied a lot in the recent years in response partially to the crisis that we witnessed and uh when we talk about systemic risk in the financial system we uh we we are
referring to scenarios in which many financial institutions simultaneously undergo large losses so the question from the theoretical side modeling side has been what's what are the mechanisms underlying systemic risk in the financial system so here's some mechanisms which have been identified in the previous price as important and so we could quickly go through them so 1 is obviously common exposures to are too risky assets if many financial institutions are exposed to the same source of waste say for example the housing market well the following the heart in housing prices will lead to simultaneous losses across these institutions mainly to insolvency of some institutions and so on so that's kind of obvious and this is uh this can be tracked by looking at the notion of exposures to different so that's fairly easy to track although it's not the has been tracked but is fairly easy to understand then a sound so this the it is that we're the only source of systemic risk then the year losses in the banking system would be of the same order of magnitude as the losses triggering uh that uh the shops that come from the outset of the banking system triggering these as of losses and this was not the case in the recent crises that that was not the case that in the previous large financial crises so this has led to recognize that the mechanisms of amplification and contagion within the financial system which may actually amplify an initial lost coming from outside the the housing sector and uh lead to a larger total so what are these because of contagion amplification well 1 mechanism which is fairly easy to understand its balance sheet contagion to the assets so this is true counterpart units so if far if y counterparty defaults then I lose light exposure to the counterparty this creates a loss in my balance sheet and if this loss of large I can in not in turn become insolvent and this can trigger a cascade of of coat of contagion through counterpart elections so this is 1 mechanism which has been studied in the literature and this is this the density is monitored through exposures and through the some exposures and collateral and so on and this is uh this has been the focus of a lot of regulation and the central clearing collateral requirements and so that's something that is is pretty well understood the 2nd mechanism of contagion can be to the library the sites refunding solely from my if I'm unable to renew my funding because i there there is a because the institutions that's funny withdraw the funding because they have difficulties or they perceive that I might have difficulties that can lead to a the institution because you liquid although it may be some solvent it they lack the liquidity to go on and this happened to me man this happened to Bear Stearns and this happened to energy so this is not uh a small and uh the small issue and this has been the focus of a lot of recent studies and a lot of the things in Basel 3 like than the greedy coverage ratio try to focus on this the could eat your funding channel and try to the but to mitigate now uh this uh this withdrawal of funding that can occur either through the through genuine prior problems in in in credit quality or through a bank run which may or may not be related to the actual the actual credit worthiness of institution to these backgrounds either through depositors or by institutions and there's have also been a mechanism in the recent and to reason I since this is a channel that has been studied a lot in the literature so here in this talk I would like to focus on a different channel uh so all of these these previous chapters of contagion the a are based on relations between at financial institutions other counterparty relations the limit relation when these relations break down through the foul 2 of the of the withdrawal of funding or bank runs that's when the system fails and there's a system but there's another channel of convergence which I think is much more difficult to control and that's what we call price mediated contagion that situation in which there can be a destabilizing feedback that a mechanism which generates risk in the system this is what we call an endogenous race and you will see that this mechanism uh is the contagion here takes place through the act of artists the descending and the price of the pressure which moves the prices as a result of spelling and we see that this began as a means much more progress because it it does not even require direct relations across institutions for contagion talk so
that's words and I want to talk about it only knows that 1 1 so the starting point of this uh in this approach is that the other mechanisms of contagion I refer to which uh are based on finding or counterparty relations between institutions cannot possibly explain the extent of losses we observed in the recent crisis because if you look at what happened in 2007 2008 those initial last which was large 500 million roughly in US sub-prime mortgages uh and then we had a worldwide financial crisis is much broader than the initial sector I was exposed to these sub-prime and the magnitude of the talk about his after was was in trillions and what support is that affected all other classes nearly and across multiple countries even institutions with little or no initial exposure to subprime were heavily effect OK now balance sheet contagion others through counterparty risk of funny cannot explain the law the magnitude and breadth of this contagion especially across that's classes no end that and many studies which I will quickly review it in the sequel have identified as a key factor in the transmission of these classes to other address class that's a that's a prime is a key factor was the leverage in large scale the leveraging of bank portfolios uh so what happened was that a large number of banks which had some exposure to sub-prime when they were hit by subprime about busses exactly for the same reason that was referred to in the introduction because these instruments work in liquid during that period they could not offer these instruments in the back are unless it took a huge loss future you realize last so they prefer to uh dilemmas the by certain other assets they held in the portfolio of the more liquid assets this is known as the leveraging and this leveraging that to a large scale sale of different assets that banks hold the during that period and a short period that was the end of 2008 and the sale was led to a a depreciation of the prices of these assets is if you have a large amount is being sold than it kills the mountains in supply and demand and it pushes the price is that now and this this this started the feedback loop which
a can be shown in this phase there's an initial mass uh the that the bad start the leveraging these 2 numbers and has an impact on the price and the use and this will lead to uh the the the values of the assets being so being pushed out and then other personal spending the same masses will then have mark-to-market bosses and this may in turn put pressure on them to do leveraging internet and so on so this is the feedback that we're going to study
and is not specific to the recent the witness it's there has been largely documented that institutional investors Our systematically led to unwind lot positions during the market crisis scenario is not specific to bias it has also been observed that the in studies on asset managers and so on and there are no and the recent empirical studies comeback of identified the piece the channel of Sokal 5 sells it as a key contagion challenges so what specific here is that when you do managing a crisis scenario in response to a constant on your portfolio uh this is very different from portfolio rebalancing in normal types because you have a small time window during which you need to deliver to raise the quality for example and you do not have a chart that the choice to to to to to the leverage a portfolio over a long time period order fashion the circles 5 cells look faster leveraging of a portfolio may not be orderly and may entail sizeable market impact you may actually push the price away from you as you sell and that's what's a starts to feedback loop because yourself can move the price is against you so this will actually under fire bosses and create losses in another parts of the so that's the the the the main ingredient of this evidence in the back so what to but to look at is the model to understand how large this impact can be what factors does it depend on the final regulator overview of the banking system what are the things I have to look for it to be able to quantify this effect and why does it have still so however them at the an undefined effect in a market crisis scenario and how large is amplified
it OK so the they structure of the of this of the feedback mechanism is the is the following 1st initially what we will have as a shock to us at values this can be an external shock which has nothing to do with the banking system of the financial system can be found in housing prices for instance something that comes from the outside economy now uh if the portfolios were completely free from constraints they could just buy and hold it hold the instruments for ever and they take the shock and they have a buffer and that that they just wait but never going see that the key a key role is played by political constant so uh by controllers for example are not constrained free they have constraints on capital requirements leverage so Stevan last which represents the capital requirements to fall below a certain special because just sit there and wait to have 2 D leverage some something the portfolio to adjust the which assumes the the person who constraints and typically here the constraints are defined by the regulation in the examples in the cave that's what triggers a for the leveraging in this model and then demanded that the leveraging if it's that if the volume of the division is large enough it had an impact on market prices what we call market impact here and the market impact has the effect of of of pushing down the prices and if you start up the several assets simultaneously you push down the prices simultaneously this leads to correlate the policies in these assets yourself and then that's the phase which we call parts needed a condition now other course follows holding the same assets will have a mark-to-market loss because it pushed on the prices of the as assets and the the the and the constant here they're going to define shortly is because of the overlapping portfolio if you sell a and I don't own a maybe I don't care but if you sell a and B and I only and the well then I have a loss in my portfolio due to the fact that a whole the same mass so if the portfolios of overlaps in terms of us a class that's when this this contagion approaches and these portals will have again constant was so this could have before OK so here what be is this this feedback on how it can be modeled how how we can the quantitative model for this now
what makes this feedback loop important is that so this this feedback that we call price mediated come contagion but unlike balance sheet contagion in effect of institutions holding the asset that is being sold so even if I have no counterpart in relation with you know finding relation to you as long as you have the same assets as I not certain in proportions of my uh the fact that under leveraging will affect performance so that moves rows sensing there and things like that will totally ineffective to contain this channel and that's a very important thing to to keep in mind yeah then in the 2nd thing which makes this the importance that the fire cells uh so that last leveraging can lead to contagion of busses even in the absence of default I don't want to have a actual default for for something from back to happen in this because of them or and I don't even need a downgrade to happen no no breaking no default doesn't mean there's nothing bad here as long as there's a Musketeer leveraging this this this this channeled contagion will have so that means that it's also has the largest scale of contagion and the other 2 kinds of the image but uh the 3rd thing which would going to discuss the data the talk is that isolated contagion complicates the task of the risk manager reckoned because as we will see this is not the kind of use we will see why this the case and the this set of contagion has the consequence of that the consequence is that and that I cannot actually quantify properly the risk of my portfolio and just by looking at my part 4 so we see that the presence of this chair of contagion in implies that actually the risk of my portfolio my exposure to these scenarios of could of the contagion can depend on things that I don't know that regulators could possibly collected no but I cannot know it but also this this creates a need for global systemic risk indicators and markup additional things which cannot be simply calculated at the level of 1 1 and 5 5 and what makes it also very difficult to control and that uh instruments used by the recognizer to to contain other channels of contagion numbers go shows liquidity requirement kept ratios and so on they actually play a triggering role for this chapter OK so if you have absolutely no constant on your favorite capital and so on you would actually just so what I think the last and weight but that's not the case and this is what actually the 1st is been institutions to to deliver so this is very perverse because it means that things that you designed for containing other channels connected pay triggering here it's it should be considered a globally and not in isolation and finally yeah that's something that pension it defies institutional to refer that of so that is always the
provides on the suggest that understanding completed this general provision is not solely so the objective of this of the model that would only 2 per cent are to have to be able to quantify the system-wide exposure in financial system to this channel of contagion wanted the system exposure to 5 sales what does it depend on only members have level of diversification how these things affect uh the uh the the the contagion due to this channel and what does this imply for the risk of the individual institution a finalist manager so however users and if I may aid regulator highlight the monitored is how the quantified is and what could I do so these are the questions were going to ask and will
try to give quantitative OK so let me start with the model and then come back to work so of course this general for of feedbacks that 2 2 5 so this is not new and has been studied a lot in the economic literature they're not they're not at all the papers that study the impact of feedback effects due to fire cells most of these studies focus on 1 institution and 1 efforts so they say OK the institution has to that the numbers the assembly acid this so that best push the price down and we want to quantify how much the price is pushed down so the focus on the price effect the fires now here we're interested in so this is this stupid described bank and 1 but here we are interested in the contagion aspect so we have to look at a model with multiple institutions and enterprises because we want to understand how this leads to a contagion across Aceh classes and across institutions so going to look at something which is much larger scale multiple institutions and multiple assets and this is what distinguishes our study from the previous theoretical studies um and the so on this planet some cities in the rest of the tree show so those 2 purposes by Greenwood out and worked and has about so the the the empirical papers that study a model of ourselves based on what's called the Leverage targeting of come come back to this in a few slides and then the other studies that have have looked at this issue on these mentioned here and I think there will be a topic I was the components that OK so that every
talking about so let's consider now a system composed of a certain number of institutional portfolios so each of these parts fellows I would look at it uh in this way so there's the acids on 1 side and then later it is on the other side and the blue here is the capital of the equity of of this institution OK so if you access not divided schematically into in liquid assets so these are methods that cannot be sold in the practice scenario that you just hold them but you cannot really seldom cannot hope to some of the price and then the process which can be solved by OK so and the liquid assets out I also consider that the many asset classes here so the liquid assets so this and the addresses of institutions j j denotes the institution I will I will assume that there's approach family of interconnected so piety eyes is the is the number of shares and as I held by station OK so this is the value of the quot assets and the family motion this portfolio has to which is the total assets over the capital and we assume that this leverage is subject to a constraint so those of maximum allowed divergent a system which is typically fixed by the regulator of social so this can be was but with the assets so total assets in euros so this can be interpreted as the Basel 2 constant of the bottom 3 considers this depends on what to to focus so there's a members country now what we have is a is a stressor nuzzled was a shock there's a loss in the in the good assets for instance I can also play shop with the but there's a really big difference let's consider for simplicity the shock of that is applied to in in the that's so there is at a loss of epsilon per cent in the in the the so we have to do is to study the response of the system to this shot I'm not going to assume anything about the statistical distribution of epsilon I don't really care I want to consider the scenario of epsilon % loss and then see what now so now what happens is that well when there is a shocker those a loss so the leverage will change because of the acid value changes and the underside the equity to changes so the equity and the and the value in the classes will because by the same amount so now I have this new value of the leverage of the portfolio so if this value is is a map but the leverage them the map that the highest amount of leverage system then that's fine but if it goes about this and this is entirely possible a and this happens as soon as a shop is greater than this threshold then uh we have to deliver the institution has to do something they have to sell some of their assets to pay some of the debt and and reduce the size of the poor no no we notice that the leveraging is estimated respect NASA game so if I have doing I don't need to do leverage I can be balanced but I can do it you know commonly I don't need to do it in a hurry but if I have a large mass which exceeds this amount then I have to do level because of cost constraint I got a call from the borders minds of you know what's going on so this means that this is the response of the portfolio to a shop is a symmetric with respect to the loss of
and so now this the leveraging the smaller occurs as soon as the shock size is greater than this threshold and if you look at the threshold what what you see is the distance of the initial leverage to the maximum so if I'm very close to the maximum of advertisement shock and make me leverage you find very fancy the matter marriage at 25 I'm at 15 then you know that I can take a large shock and still not be forced to show that reflects the banks of the mass absorption capacity and no another way to see leveraging this is the models I suspected earlier but uh group but the size of of the Greenwood Alan Eisenbarth and and coauthors they look at the model which is called lemmas targeting so they assumed that the bank has a given that leverage and then maintain this leverage in time so if they they're if they yeah doing if that is going on in the actually increase the leverage and the other news involving the delivers but they don't do this continues to be even if the game is point 0 1 per cent they still uh of increase or decrease the numbers In this model suppression long model uh so uh you believe leverage if the mass is greater than the special so uh in that matter the retarded no associate threshold is you you you always want to any shop and that does not and the size does not matter so this is the big difference in in between 2 models and what I show you the empirical results and compare the results with these OK
now so so we said that the shock is greater than special institution with the leverage well how much is it the leverage well at least as much as needed to restore the the uh the lover's back to the constant it didn't average more but we will assume that cannot reduce the minimum amount so that's a conservative assumption of the a so uh OK so now how does it the leverage that so that that's a different question well so it can be leverage in many ways especially the portfolios complex it can so 1 simple assumption we're going to use in this in the calculations is then the leveraging disproportionately just sounds a proportion gamma J of its portfolio self everything proportionally such that to restore its leverage to the required another possibility which we do it from the paper by local talk about it here because it's more complicated is to be the you instead of having to stand for the liquid you have liquidity classes the most eloquent them the 2nd most of it and so on and start at the bottom you start so the most quickly than the 2nd most difficult and so on that's another scheme it does make use of more complicated but all of the also look at this OK so here I just assume that they will send a proportion of the holdings to restore the members to the more the proportion you can write it a very simple calculation it's is 0 if the shock is grounded on the threshold if the shop is above the threshold is it's the media the shots at of course you can so that more than 100 % at this point you and for OK now every
situation is subject to this shop and so every institution will do the same thing but some of them don't hold it in liquid assets on the whole the lot illiquid acid so the amount they will the leverage will depend on the size the leverage and how much of the image that the whole so we just sum this across the institution so the asset class I uh this is the volume of the leveraging of the class I waste ution JI some across all institutions this gives me the aggregate amount of 5 so that's i in response to a shock to the image now if you look at is what what you see is that these are so called low you all of these are uh hockey sticks out functions like call option pale would strike that some J and these are positive coefficients so few some things you get a convex function so this convex function is 0 if epsilon is smaller than the smallest of the thresholds epsilon j and so on until at least 1 bank started leveraging the leverage is trivial so it initially for small epsilon this function is 0 and what as you increase epsilon it's a convex function is that the near because this means that as you that when you multiply the shop by c well for small shops you went multiplied by 2 the response but for a lot of you gonna multiplied by number larger than 2 and is going to keep increasing the shot so it means the margin of response is increasing talks OK so that's that's what we call the multiplier effect so there's an amplification the response is not linear it grows faster than here and this is the different from deliberate targeting was in which a response is linear and shocks that's an essential which now
if you calculate the stock to complete this
response function you just need to know the leverages of the banks their their holdings them in a liquid and the good assets and that's it and and we got this data from
the European Banking Authority this is basically the data that was composed instead was composing this uh the the during the the 2013 bank stress tests by the European Banking Authority so this is exactly the information that we need here and and we can compute this this response function so for example if you look at a scenario where you look at them the the shot quantum users and but for instance in this scenario I undergoes a scenario which is defined as of a shock to put to sovereign debt and then look at the aggregate amount of viruses in Portuguese bonds in that in so we clearly see that from the empirical data by contemplar this function is going up the near it starts off linearly and then it accelerates in this acceleration is an amplification picture which is all of these things at this level it's in the response OK I'm not even said what the response does the price already in the response to this oxygen picture now when this when the institutions but the leverage through this mechanism this the leveraging it and they sell something they sell as the sales move the price of assets they push the price of assets I down if there's something and here we're going to assume this the simple metaphor for market impact of the sales so revenge assume the minimum level so it means that if I said a quantity Q the end if the market gets or price elasticities delta I I push down the price by proportion q over them all so this this constant is a market that is the market that is within its being impact is 0 the market that is finite if I sell something which is 10 % of upon like that I will have to push down right OK and now this this happens in all that the subject cells and this change in the price needs to a mark-to-market loss which affect everybody holding this as so if I'm holding a quantity high GI units that I and if the price moves down right this amount I have mark-to-market losses which which is equal to the amount I hope time to change the price and how to sum over all their if OK but now the change in the price is due to the 5 of the 5 thousand was due to the year that the leverage
and the holdings of the property values so again this depends on type G so that's where the
interesting thing happens is that if we don't put together explicitly this when this price change came from but also came from the who resulted from the holdings of the bag so now I have that the total mass institution J. the mark-to-market last is is a function is an expression where do brings the the matrix of portfolio holdings appears twice OK and so it's a positive form of the portfolio holdings and so when we see that it can be in the mood expression for the mass of the bagged J last class we have conventional exposures of bank j that's normal its last time so uh exposure but we also have the the notional exposures of banking so this is my last in this in this duration will depend not only on my holding but on somebody else's holding because they're selling the things that are so that's not very good and we see that this is at the root of all these complications of so this means that there is an interaction in between these 2 portfolios to this optimal here and this interaction is what leads to contagion and feedback as well OK now if we now if you have a look at the influence of family OK what's the influence of the leveraging of K on-demand message of J that influence comes from all the coefficients where J and K appear together and if we collect them together in this expression we see that well it takes this form here it's takes the form of of this expression so it's a sum over all aspects of the but holding of j times holding of K and adjusted by the that the depth of the uh the instrument so this is what we call them the quantity weighted overlap with the between put foraging so if we have a lot in common then up in all the terms in the sum either this is 0 this is 0 so the sum is so if you are if I'm a pure commodity trading fund and you're only dealing in that interval the sub-prime then we don't have anything in common and there's no overlap but if we have something in common of failure of this leads to a non-zero overlap OK so that's what that's what this means that the interest seam EB overlap is weighted by the quantities so it means if we have a saying in liquid assets there is a much bigger contribution to this song benefit homeless and liquid at the end of the OK so OK so what we see that these the greedy weighted overlaps are the main determinants of contagion if somebody the leveraging the I'm unaffected not depends on my equally weighted overlap with that you should that's a very simple function OK now this is the
model so it's fairly easy to describe noun this simple model because of this quadratic term because of the fact that the the professional and enjoying K. appear in the same expression for the loss of J this leads to very troubling speech so 1st thing that you can see immediately even if you have only 2 banks and a model is that this leads to the notion of indirect exposure so what indirect exposure in that's what it means of all the when you say expenditure what what's what's your exposure to to uh uh say the Greek uh the bank and well and look at the National sizes of Greek bonds in my portfolio as a hundred million OK busses and in fact in this model this is not correct because it eat even if I have no uh durational holdings in in an instrument if I have it there's somebody else in the pocket which has some common holdings would need to presented the uh I I've it's just that i've between assets in illiquid and liquid at Bank on holds the acid bank to dozen in the holy in liquid at most supplemented by 2 by 1 vote now uh both banks hold the same liquid acts OK so what happens is that bank to thinks that he's not exposed to the it in aggressive because doesn't hold in the portfolio what happens is that when there is a shock to the assets the bank 1 will be exposed to about 1 if the shoppers imagine a bank 1 was started but the leveraging of the leveraging we will start selling the liquid acts so then that 1 starts selling the liquid assets the other bank which person in the class it takes about market loss is the mark to market and is pumped about the last and what does it come from a convex set the market you know looks at dojo books that the Financial Times what happened and there's nothing going on in the market right did I think about my well because there was a shop on the acid you don't hold and you're the bank is the selling the liquid acid that's what so this means that in every scenario here where there's a magic last on the in the graph large not small there'd be a 5 cells and devices will result mechanically in a mark-to-market lost in the process always the people who don't even all really so this means that if you plot the yeah uh OK 1st then the the temperature varies in this example is very easy to calculated from the back of an envelope in that institution here is indirectly exposed to losses in an acid it doesn't even so actually not good because it means that all you think you know if you know if you think you know your exposures well know because the exposure like indirect so that we not but now this has
important implications for class because it means that well even if I don't hold and as it can be exposed to it indirectly and head and for after that I do so I my exposure is not necessarily commensurate with the notional exposure it can be much bigger much point depends on the concentration of other people holding and this is well known to fund managers called crowded trade and this is 1 of the 4 majors they know knowledge that the contrary to do the same trend as everybody else there was very much higher than the volatility of the asset holding because everyone will try to make is the the same so this is a well-known phenomenon here this value can be quantified in various principle at now this is very uh problematic because it means that large punishers tutions may be underestimating systematically the received engage in a common on like this so this is information that only originated in and so this is really this this this requires some dissemination of information uh on the indirect exposures to risk for that outcome of our collective is that in the last part now we did
this so we ran this model on the European banking systems holding data and we try to estimate the year as the difference between the act and exposure so the notion of exposure and the effective exposure of which is the upper plus the indirect exposure to the virus so in a very simple way you apply shot but to the image that the class so so true 1 in a quadratic as you apply shot to this and to accentuate the exposure is the ratio of your last to the shop you apply to the universe that exposure now if you don't want to be 0 all but it's not because of the indirect effect so we will this racial and at the end of the phone and i to spare you the look at the the table if you look at the answer is not at the extreme cases which can be 2 on the floor on average in the in the banks that we looked at in the European banking system if we look at the best scenario which is the Spanish housing market so we consider that the Spanish foragers we apply such as part of this question is what's the what's the ratio of your exposure versus your apparent exposures notion of holding In the Spanish well on average is 25 per cent and that's an average of for some cases for the conference something that was put to 100 per cent so this means you know only it's not a small small among the largest I was almost 27 so there was 1 bank in the temple is it's apparent exported so effective exposures 27 times higher than this so this notion of exposure that's because it has links with other it had it then it it had been too many common holdings with the banks which have substantial Spanish probabilities on the balance sheet although we didn't have much they want to OK so this
means that it's not really something that is
easy to of understand as you have the a system-wide view of not all of another interesting of question in this model is the impact of diversification so typically if you look at this stand-alone investor the typical advises you should diversify your investments because because it's a it's a good part of 4 for finishing with so here can think about how price media contagion operates actually the safest system from the point of view of ourselves contagion is a system where portfolios are totally segmented so they're not diverse all if you have some item is the only commodity some only in this only in some some initial the gray market on in some categories of long and nothing else if you have things mandated institutions they they engage in fire so they will only affect institution similar to themselves and not the other way so segmented so opposite of diversified portfolios uh stop this kind of on the other hand if everybody is diversified in the same way so if I variables have holdings in every asset class and the guy was by the same mommy they all the same and it's basically then contagion is maximal because we have portfolios are also aligned properly place in the world all that's the worst case scenario is overlaps some maximum overlap just across so you see the divers gages but this a good in this scenario what is important here is dying versus the rather than diversification diversity meaning if a liar diversified well that's good for us but from for systemic risk in this sense what's important is i we diversified in the same way or in a different way OK well for example uh if you look at hedge funds for example uh there then we have the results of 2 rooms in the hedge fund market market well a lot of fiction in the same uh strategy class suffered large losses together at examples of 2007 for instance the but in the same that is owned by a lot of mutual funds didn't have any loss that's because they were both diversify but in different ways you would be the resident in different directions and performed so what matters here is is actually used to look at these portfolios are the aligned on the part of the cooling your ability now 1 way to look at this is
to say OK I look at the portfolio holdings of all these institutions I do a cross-sectional analysis in terms of principle because component and if there aren't coming here the means that the 1 in lakes and they're all proportional to the same in the the active more if they're totally different this means that many different directions i'm going to do a principal component analysis and look at the co-variance of these portfolios then holdings of the returns just the holdings and again a holding the samples from some of some random airline tried to compute the covariance structure and what we're interested in is not the covariance structure where we multiply holdings and average them because as you saw what's important is really weighted overlap so the co-variance in the sense that the inner product where I'm going the physicians by the quality of the corresponding path focus so this can be done you have to look at the matrix of portfolio overlaps of all institutions and this is the matrix which looks like core matrix is a covariance matrix but the properties and when you
look at the yeah it's the yeah the eigenvectors and I'll use so what you see that well indeed if you look at the European banking portfolios well there are common features and where they are if you decompose these these these these you can froze as the linear combination of factors think of these factors of as the indices that really trading but the in the thing that you can think of here then in the 1st in the 1st factor that explains a large proportion of the holdings and so on so so few portfolios to you you could actually model the cross-sectional uh um uh structure of the bank qualities in Europe and the low-dimensional factor model obtained and we'll see that it has a very important consequences
for for what the so this means that for example if
we have only 1 factor here is the opposite of diversity so this 1st is actually diversified portfolio it's a for for the spread of all aspects if everybody's concentrating this direction means that you have 0 diversity is maximal complete theory that so lucky they're not because the these other attitude the drops very quickly so it's very so means this is said
this is not something which is small effect in this of so many so it so many students because it gets go introduce here but the but the basic message here is that the uh the diversification in the banking system can has a non-monotonic effect on the magnitude of this that have the system-wide contagious a little bit of diversification is good because it diminishes concentration in the last class of the prior I suspect would leverage but if you diversify it uh on a large scale everybody the rest of us in the similar way this has an offices so this this can studied more more more detail and the
object now uh course directly and by showing you need show now the results of the empirical study on the European Banking Authority data so this is this is taken from the stress system that you can buy authority 2013 so what we have in the data is the capital and the holding of the bank by country and after class for the for the set of large European
banks so in this dataset the leveraging of the portfolio of services widely in all spread across the spectrum so we have never do in the thing that we have moved leverage 65 and we invite the level you know through with the lot vector of leverage facials and we did this analysis will using risk-weighted capital so because the ratio constraint and the members countries of the findings of presently with no no risk local not this fear of gaining we do a casual of legal analysis of this and we see that a large banks and other higher this increases the complexity of the multiplier effect of the year of the response function which gives you the volume of the leveraging as a as a function of the shot and now some not some
number so if you under stress there so what we do is we choose another class the 1 of the the the categories of loans amount of so much of what it is held on by portfolios we give a shot to this at the class so the choice of the that the last part of the scenario is not real for the generic response to shop to before that the class so I think the Senator 1 is shot to the shock applied to the value of the mortgage is in Spain and Portugal and tune is use of France's 3 is used in Europe any scenario we look at uh the value of the lost in the system as a percentage of the total uh from from equity events in the system so this is a 5 means 5 % of antiquity law the and here we plot the power function of the initial shock applied to the liquid so the liquid assets by presenting value and person 15 but this is this is a small shopping and this is a lot like it from both in the 20 per cent loss which is gained it into new OK so what we see is that well and all these calculations we did them all for the threshold model so this is shown in solid here down here and the level of the target model would you assume that the react continuously to each small shop and readjust the memory to me think of that OK so what we say that in both models you have that the last is increasing with the level of shot the friendly but uh the leverage targeting model overestimates systematically in our opinion the magnitude of the loss because as you can see for small shops Our model predicts normally leveraging and I think that's a reasonable conclusion where the standard model that could that even if there's 1 % shop to the loans you already have been leveraging and of 4 % of the thing of the equity of life that doesn't seem to me a very reasonable approach so that's the that that's because in this smaller the threshold 0 you constantly have to deliver it at any point in time OK so here what we have is that well if you have like a shot of 15 % 10 % to their own liquid hormones in in in the southern Europe this gives you a year 3 or 4 per cent loss in equity in the banking system so that's the the the magnitude you're thinking about I think it's it makes sense to people actually OK so this shows the magnitude judgment it's on a small effective using trying to focus % of the bank it could be seen in the European by system is not a small because it doesn't tell you where there's lot of growth concentrated in a few OK now if you compare the memory model and uh this special model you see that the timing model always overestimates the of losses vector this model because you you assume that the banks and the continuing
demand OK now if you look at fire-sale not classes as the proportion of system not because there is the external shock to the portfolio and the ravaging occurs and there is also the path of effect so sold the proper loss is the loss caused by initial shock so that's not too far below class the inductive biases which amplifies eventually shot so the question is what's the proportion of the loss which is due to the fact that well what we see is that the enforcement shots at 0 uh because there's no for ourselves and for as soon as the price of stocks goes quickly up and at the end it's that'll somewhere around 20 so this means that the amplification due to fire cells in this uh this dataset is around 20 or so there's a 20 per cent of application of the in the limit targeting the model this number of seems to be unrealistic it's 80 % of all the time and the thing doesn't vary a lot with shocks so this tells us that if something did not natural going on but
uh so this and I would say the same thing is what to call the system a lot from multiply the publication of the the same
graph which OK so uh let me
conclude now by saying something about how can we deal with it is to look like a very
very messy situation you have indirect exposure as the things that the found on things you don't have served as the List Manager 1 of the tools that are available to us badges and I think images to monitor and and mitigate OK and the challenges you OK if I give you all the holding the very right you could build assimilation incalculable these things but you don't have everybody holes and it may be the regulated can have access to some aggregate hold take up but they can't just give you the whole somebody else them for you to do simulations the it's confidential so anything we do has to respect this confidential now the idea is very
simple to say well what is this thing called risk weights all the Basel the risk weight is a number attached to pass a class and uh you banks Template the recently enacted by summing the holding times the risk weights and then they calculate the captain of the uh the Canterbury just which of coupled to the risk would later that's not immediately they have been criticized like thing you know there's no basis for the risk which you do a real risk measure calculation 1 of these restraints and so on they're supposed to reflect the riskiness of the asset class but there's no correlation involvement of syllable so he wouldn't say well actually let's put these risk ways to use as the macro-prudential to by by doing the following we're going to estimate the contribution of as class I 2 of the systemic loss of a budget of 5 cells and we're going to modulate the risk
weights in a way that reflects their role in transmission of shocks so you you referred you talk to contagious that's that's a very interesting term question is what is a contagious that is this a computer that the well it depends on you know holding them everybody the if if if the is part of a concentrated crowded trade it will be contagious so the idea is well unless there's so I'm regulator the cross-section of informational of portfolio holdings I'm going to do the analysis initially earlier and then do a principal component analysis compute the eigenvectors eigenvalues of this holding matrix and when you look at the principal eigenvector the 1 with the highest eigenvalue this if I had to do a one-factor model portfolio holdings I was would reading this and then I'm going to adjust the risk weight of each asset class proportionally to the component of the acid in the portfolio so this is for portfolio and response OK everywhere the concentrations of holdings are and use that as a proxy for it over laughter from good to that play a role in contagion so the idea is this going to just and just the risk weights according to this so these sort this principle for follow that reflects the concentrations and then I want to calculate the the kind of requirements with these new so what does this do well what it does is that it leads to higher capital requirements for proposed exposed to the fire silicon received as computed with this concentration factor here along the principal directions for of so you don't know who your overlapping with of how you extend you sir please no I'm going to increase the risk weight for this acid because I know something you know they know questions
OK so now I'm going to just stand by showing you how this works so we did a comparative static analysis so we did the same stress this that I described earlier for the European Bank system but now we applied fictitious levels of capital propre requirements 1 is is the usual crap apart from as tool what is the capital requirements where we put your square this amounts to using unweighted numbers constant of the of the week and then what is the what I just described we use adjusted risk ways to risk-weighted assets that I been adjusted with a surcharge that is proportional to this 1st eigenvector that includes the contribution of this as a classifier to the portfolio over if this as a classified appears in many parts of the country weight the surcharges and then we do the adjusting stress that and we can calculate the level of
losses as a percentage of of of the solar system so that's the the and the result of the simulation so each each curve in what was the gives you the system-wide loss as a function of its the total capital requirements in the system for the 3 different the capital requirements schemes so this the circles are the by the Basel 2 requirements sold the risk weights of by tool that green 1 is uh is it is a couple of leverage is about the 3 requirements and the red 1 is this time risks so as you can see the targeted risk weights always over performed uh the 1 on the but it doesn't to risk weights because the respects of just the on depend on anything worse here I find to them to the current crop crowding in the performance of some the the the green 1 the leverage 1 over performs both initially because there's 1 line here which has the leverage of 65 so if you put them at constant that faculty have to massively increase capital initially but then afterward speed of the red 1 would be people that means that actually targeted risk weights do have an effect they produce systemic exposure to parts of the system without disseminating call confidential information and they are based on a centralized commission on by a regulator that can observe some level of your portfolio holdings and the data required to do this is exactly at the same time as the 1 used for this OK but if the system express this problem of them and you so that's what I want OK so the conclusion
is well I tried to explain how 1 can use a simple way of although the instabilities and feedback effects that result from 5 cells in the in the portfolios of financial institutions what I try to convince you that these 5 in generally to a non-linear pp Bacanal which can lead to instability of the system and the speed that was not well represented by models of living a life in which assume the liver targeting because there is a genuine social effect which makes this a which introduces an amplification system uh in the sky even and localized shoppers single after class lead to what's that passes across many aristocrats institutions and when you take this effect into account you to the concept of indirect exposure which has the consequence that your exposure to a class can be different from the notional exposure to the we saw that the main driver of this price data contagion is a simple quantity that's the query the way we took over a lot of institutional holdings and this can be calculated cross sectional data you can analyze the fact model for men in can use this likelihood weighted over love to build uh targeted risk or adjust the risk weights to reflect the contribution of have classes to work on overlap and we propose to use this as the macro-prudential to to to control this type of racism without revealing confidential information so be thank
you all the yeah I get in this thing on the the I think the thing that is the problem in the rest of it on the you want to place on the basis that the but they have the right to and I will come come up with the of the the result last 1 of the things that you need that we have a lot of times you look at these huge you know it are the time here is this the say it is what is in on we all long it the same about you the technologies and we use the in our the mediator has information on where we have the it is different as us by the the where is it just pass it on you know so I mean there's in your present 2 things 1 is if you uh you can remove the source of fire sale by by allowing more time for the institutions affected by loss to the leveraged you have to the leverage in 1 in 1 week so OK we're not understand that you have a temporary office OK you should be leveraged future should bring down your lab required we give you as weeks to do that so if you and the this is what plays a role because what plays a role here is the is the speed at which a generative view if you generate a set amount infinitely so there's absolutely no effect on the bottom so that's 1 thing that the president of the school of OK this is this depend many other things so I'm not sure that the parts of the only concern there will be other concerns the depositors little on the other thing is that of course if you uh the risk weights the the effect is what you said if I increase the risk weights for some other class people that after class well that's the goal here because here I can tell you you know you you have a small portfolio would you not use the same portfolio as the guy and head neck storable and coming in and you know you so I'm going to do so I say the acid class for this for for this as a class the respect has increased you draw the conclusion that you want to hold less but that's exactly what I want this stands of reducing your indirect exposure so this is what I want so this change is this shift away the portfolios from the direction of constantly so in that sense in this case it's it's not an unintended consequence it's intended of course the rest of you you so the the overall plays in the cost in of the model priced right from the start I mean and use there is the kind of course and I think that this is the this is something I will also offer you deal with the highest rate is in idiot this we really so that all the last in this 1st I have to say something like this that then I the or explain it and he is using the time RIS ways right all of you know what it is that contribution on which as outside 1 view is that they are out of the way right if I understood correctly he was asked to somehow and it was just a how will ask to teach sorry this race you get on the right the role of the guys get out of the last days did that's the yeah so that's the difficult part in the implementation so in the other study that thank the assumed that the learned instruments across all of the everything has the same could be the using universal somebody something like price of lots of something like that so this is so this is because it's at the very difficult to get numbers for now here we are doing like because that's enough for the Norwegian centralized so we have detailed the data on as holdings we're going to market data to estimate the daily volume and so on but uh yeah it's it's it's the part which takes the most time in the publication how you actually
attach a liquidity facility to the test applies to the mean the same thing for nouns and for staff so on so that the whole part but if you don't if you but you have to do it because if you don't have even a rough approximation of the liquidity you can even stop talking about in practical so this is an essential part what we saw in the comparisons i showed here we use the same convention as in the other papers to compare with the number of the model but in the actual implementation we do for the state in the region they would a much more information we do estimates for each instrument based on the volumes and the list so basically it's a great regression all the returns on the trading volume and that's the and the coefficient is that of but you need some data yeah absolutely so that when we have no data on this side we classify them as in that might not be a good classification for practical of yeah and and was and the the so you can always use human voluntary the motivation of this and this and you use of the size the what you you the expected know on the moon then when I asked us to come to a halt when we're not to do the same as the size with the state of the same thing well this is a rather rich so this is the head movements and a new and I think or set of Finley that is actually data to the 1st question in a gene this life something that's your of it will be this model will not only in the last part was just a static comparative statics the entitled comparative statics I didn't say we're describing the actual impact of changes respects but I want to do definitely is moving away from the concentration in the direction that you know when you're going to create a new 1 that's this and here you the only thing I can you would so this is where the updates you we what is the value of as it was you there and you all this out in the in the in the in the the if you want you this as with the other 1 what about you OK so this is the university to offer is especially given 1 1 the there is the data collection issue but at the time the targeted risk weight that doesn't mean you specify everything in detail for example you increase the respectful Jonathan probably 20 categories or as you increase 1 of them before the median invited people also that specific OK well it but that's what you want because you see a concentration that you want to you want some investors to go away from that OK you can make a lot of that doesn't mean that there are many ways to off often the mass and you can put it in in various other directions a started me whether they will put them in the same where people it so that the given example that give an example you have a government bonds sovereign dead weight is 0 OK so this OK so some some somebody estimated that there's no risk of what it knows it well there's something funny going on in Greece maybe I shouldn't say that the Greek debt has 0 it's maybe it's not such a great formal recommendation maybe I should increase 0 2 5 % OK this has an impact as you said that people will start holding the Greek that because they see that the there is some capital charge no OK is that by the the good well that's what you want that's why you what they will invest with they all invested in German bonds or they will invest in the UK gilts are you not imposing there are many ways to go away so I'm not true so group so that you all go to the same what said the few
and in the and
Risikomessung
Mathematik
t-Test
Projektive Ebene
Physikalisches System
Faserbündel
Ereignishorizont
Resultante
Zentralisator
Einfügungsdämpfung
Total <Mathematik>
Summengleichung
Gerichteter Graph
Physikalische Theorie
Einheit <Mathematik>
Arithmetische Folge
Endogene Variable
Inverser Limes
Regulator <Mathematik>
Beobachtungsstudie
Grothendieck-Topologie
Relativitätstheorie
Auflösbare Gruppe
Physikalisches System
Flüssiger Zustand
Fokalpunkt
Mechanismus-Design-Theorie
Dichte <Physik>
Arithmetisches Mittel
Summengleichung
Gefangenendilemma
Energiedichte
Druckverlauf
Größenordnung
Mechanismus-Design-Theorie
Numerisches Modell
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Klasse <Mathematik>
Länge
Einfügungsdämpfung
Subtraktion
Punkt
Gruppenoperation
Klasse <Mathematik>
Nebenbedingung
Relation <Mathematik>
Summengleichung
Zahlenbereich
Fortsetzung <Mathematik>
Gesetz <Physik>
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Phasenumwandlung
Beobachtungsstudie
Zentrische Streckung
Erweiterung
Teilbarkeit
Relativitätstheorie
Flüssiger Zustand
Länge
Ruhmasse
Frequenz
Teilbarkeit
Summengleichung
Druckverlauf
Reduktionsverfahren
Größenordnung
Mechanismus-Design-Theorie
Einfügungsdämpfung
Größenordnung
Nebenbedingung
Einfügungsdämpfung
Ortsoperator
Gruppenoperation
Klasse <Mathematik>
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Term
Division
Algebraische Struktur
Korrelation
Endogene Variable
Spezifisches Volumen
Regulator <Mathematik>
Auswahlaxiom
Phasenumwandlung
Umwandlungsenthalpie
Beobachtungsstudie
Kreisfläche
Flüssiger Zustand
Ruhmasse
Physikalisches System
Frequenz
Teilbarkeit
Loop
Konditionszahl
Mereologie
Normalvektor
Ordnung <Mathematik>
Einfügungsdämpfung
Beobachtungsstudie
Normalspannung
Numerisches Modell
Größenordnung
Klasse <Mathematik>
Multiplikation
Gewicht <Mathematik>
Gruppenoperation
Nebenbedingung
Zahlenbereich
Übergang
Physikalisches System
Numerisches Modell
Charakteristisches Polynom
Kommunalität
Indexberechnung
Regulator <Mathematik>
Addition
Zentrische Streckung
Gerichtete Menge
Relativitätstheorie
p-V-Diagramm
Physikalisches System
Flüssiger Zustand
Regulator <Mathematik>
Mechanismus-Design-Theorie
Endogene Variable
Summengleichung
Arithmetisches Mittel
Objekt <Kategorie>
Menge
Verschlingung
Mereologie
Einfügungsdämpfung
Numerisches Modell
Größenordnung
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Klasse <Mathematik>
Einfügungsdämpfung
Subtraktion
Prozess <Physik>
Extrempunkt
Gruppenoperation
Klasse <Mathematik>
Relation <Mathematik>
Nebenbedingung
Familie <Mathematik>
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Topologie
Übergang
Stetige Abbildung
Multiplikation
Numerisches Modell
Spieltheorie
Endogene Variable
Petersen-Graph
Zusammenhängender Graph
Beobachtungsstudie
Diskrete Wahrscheinlichkeitsverteilung
Distributionstheorie
Zentrische Streckung
Mathematik
Güte der Anpassung
Flüssiger Zustand
ANSYS
Ruhmasse
Übergang
Physikalisches System
Stichprobenumfang
Fokalpunkt
Rechenschieber
Mereologie
Beobachtungsstudie
Normalspannung
Numerisches Modell
Grenzwertberechnung
Resultante
Punkt
Extrempunkt
Klasse <Mathematik>
Nebenbedingung
Flüssiger Zustand
Stellenring
Gruppenkeim
Ruhmasse
Zahlenbereich
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Flüssiger Zustand
Rechnen
Numerisches Modell
Mittelwert
Spieltheorie
Minimum
Lemma <Logik>
Abstand
Gammafunktion
Numerisches Modell
Randverteilung
Lineares Funktional
Lineare Abbildung
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Klasse <Mathematik>
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Konvexer Körper
Konkave Funktion
Endogene Variable
Numerisches Modell
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Endogene Variable
Nichtunterscheidbarkeit
Spezifisches Volumen
Grenzwertberechnung
Elastische Deformation
Lineare Abbildung
Lineares Funktional
Einfügungsdämpfung
Mathematik
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Numerisches Modell
Einheit <Mathematik>
Funktion <Mathematik>
Exakter Test
Endogene Variable
Quantisierung <Physik>
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Normalspannung
Einfügungsdämpfung
Mechanismus-Design-Theorie
Größenordnung
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Lineare Abbildung
Lineares Funktional
Matrizenrechnung
Total <Mathematik>
Gewichtete Summe
Mathematik
Determinante
Minimierung
Klasse <Mathematik>
Familie <Mathematik>
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Konvexer Körper
Bilinearform
Flüssiger Zustand
Term
Endogene Variable
Arithmetischer Ausdruck
Numerisches Modell
Funktion <Mathematik>
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Nichtunterscheidbarkeit
Wurzel <Mathematik>
Einfügungsdämpfung
Einfügungsdämpfung
Abstimmung <Frequenz>
Punkt
Prozess <Physik>
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Konfigurationsraum
Klasse <Mathematik>
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Flüssiger Zustand
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Flüssiger Zustand
Regulator <Mathematik>
Physikalisches System
Konzentrizität
Statistischer Test
Arithmetischer Ausdruck
Rechter Winkel
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Mereologie
Einfügungsdämpfung
Normalspannung
Numerisches Modell
Subtraktion
Teilbarkeit
Tabelle
Gruppenoperation
Klasse <Mathematik>
Physikalisches System
Summengleichung
Arithmetisches Mittel
Mittelwert
Mereologie
Phasenumwandlung
Tabelle
Messprozess
Grundraum
Numerisches Modell
Arithmetisches Mittel
Größenordnung
Resultante
Matrizenrechnung
Klasse <Mathematik>
Einfügungsdämpfung
Subtraktion
Kovarianzfunktion
Gerichteter Graph
Punkt
Extrempunkt
Kovarianzmatrix
Klasse <Mathematik>
Term
Richtung
Physikalisches System
Karhunen-Loève-Transformation
Algebraische Struktur
Variable
Gewicht <Mathematik>
Standardabweichung
Stichprobenumfang
Zusammenhängender Graph
Funktor
Multifunktion
Teilbarkeit
Kategorie <Mathematik>
Indexberechnung
Physikalisches System
Skalarproduktraum
Fokalpunkt
Mechanismus-Design-Theorie
Querschnittsanalyse
Arithmetisches Mittel
Mereologie
Strategisches Spiel
Hill-Differentialgleichung
Term
Einfügungsdämpfung
Numerisches Modell
Größenordnung
Perspektive
Paradoxon
Indexberechnung
Kombinator
Teilbarkeit
Regulator <Mathematik>
Linearisierung
Algebraische Struktur
Puffer <Netzplantechnik>
Eigenwert
Phasenumwandlung
Hauptkomponentenanalyse
Indexberechnung
Einfügungsdämpfung
Numerisches Modell
Größenordnung
Zentrische Streckung
Perspektive
Paradoxon
Gruppenoperation
Klasse <Mathematik>
t-Test
Indexberechnung
Euler-Winkel
Physikalisches System
Regulator <Mathematik>
Physikalische Theorie
Teilbarkeit
Richtung
Konzentrizität
Puffer <Netzplantechnik>
Phasenumwandlung
Hauptkomponentenanalyse
Größenordnung
Tropfen
Einfügungsdämpfung
Beobachtungsstudie
Resultante
Distributionstheorie
Nebenbedingung
Lineares Funktional
Klasse <Mathematik>
Gruppenoperation
Flüssiger Zustand
Vektorraum
Physikalisches System
Komplex <Algebra>
Punktspektrum
Übergang
Objekt <Kategorie>
Frequenzgang
Derivation <Algebra>
Gewichtung
Spezifisches Volumen
Normalspannung
Analysis
Größenordnung
Einfügungsdämpfung
Punkt
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Klasse <Mathematik>
Zahlenbereich
Kartesische Koordinaten
Gesetz <Physik>
Übergang
Physikalisches System
Numerisches Modell
Endogene Variable
Inverser Limes
Auswahlaxiom
Leistung <Physik>
Lineares Funktional
Kategorie <Mathematik>
Standardmodell <Elementarteilchenphysik>
Übergang
Physikalisches System
Vektorraum
Flüssiger Zustand
Schätzung
Rechnen
Ereignishorizont
Einheit <Mathematik>
Mereologie
Größenordnung
Normalspannung
Einfügungsdämpfung
Normalspannung
Numerisches Modell
Graph
Lagrange-Multiplikator
Exakter Test
Übergang
Physikalisches System
Mechanismus-Design-Theorie
Regulator <Mathematik>
Unendlichkeit
Physikalisches System
Numerisches Modell
Iteration
Gewicht <Mathematik>
Einfügungsdämpfung
Normalspannung
Eigenwertproblem
Risikomessung
Matrizenrechnung
Einfügungsdämpfung
Gewicht <Mathematik>
Fisher-Information
Klasse <Mathematik>
Matrizenrechnung
Zahlenbereich
Singulärwertzerlegung
Term
Rechenbuch
Streuquerschnitt
Karhunen-Loève-Transformation
Gewicht <Mathematik>
Eigenwert
Reelle Zahl
Endogene Variable
Gewichtung
Zusammenhängender Graph
Korrelationsfunktion
Regulator <Mathematik>
Analysis
Hauptideal
Teilbarkeit
Stichprobenfehler
Rechnen
Teilbarkeit
Konzentrizität
Eigenwert
Sortierte Logik
Reduktionsverfahren
Basisvektor
Mereologie
Innerer Punkt
Numerisches Modell
Resultante
Größenordnung
Einfügungsdämpfung
Gewicht <Mathematik>
Total <Mathematik>
Gruppenoperation
Fakultät <Mathematik>
Gewichtete Summe
Nebenbedingung
Übergang
Physikalisches System
Statistischer Test
Gewicht <Mathematik>
Eigenwert
Gleichmäßige Konvergenz
Gerade
Regulator <Mathematik>
Analysis
Lineares Funktional
Äquivalenzklasse
Kreisfläche
Kurve
Konfigurationsraum
Übergang
Strömungsrichtung
Physikalisches System
Konstante
Quadratzahl
Mereologie
Surjektivität
Normalspannung
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Größenordnung
Resultante
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Klasse <Mathematik>
Einfügungsdämpfung
Gewicht <Mathematik>
Sterbeziffer
Gruppenoperation
Klasse <Mathematik>
Toter Winkel
Zahlenbereich
Gerichteter Graph
Richtung
Numerisches Modell
Gewicht <Mathematik>
Minimum
Schätzung
Gewichtung
Spezifisches Volumen
Grundraum
Verschiebungsoperator
Beobachtungsstudie
Mathematik
Likelihood-Funktion
Physikalisches System
Endogene Variable
Menge
Loop
Rechter Winkel
Basisvektor
Mereologie
Randverteilung
Einfügungsdämpfung
Numerisches Modell
Schätzwert
Gewicht <Mathematik>
Approximation
Mathematik
Stab
Güte der Anpassung
Gruppenkeim
Zahlenbereich
Ruhmasse
Paarvergleich
Flüssiger Zustand
Medianwert
Richtung
Hydrostatik
Arithmetisches Mittel
Konzentrizität
Exakter Test
Koeffizient
Lineare Regression
Mereologie
Spezifisches Volumen
Grundraum
Numerisches Modell
Aggregatzustand

Metadaten

Formale Metadaten

Titel Fire sales, endogenous risk and price-mediated contagion
Serientitel LUH-Kolloquium Versicherungs- und Finanzmathematik 2015
Teil 2
Anzahl der Teile 4
Autor Cont, Rama
Lizenz Keine Open-Access-Lizenz:
Es gilt deutsches Urheberrecht. Der Film darf zum eigenen Gebrauch kostenfrei genutzt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.
DOI 10.5446/34047
Herausgeber Leibniz Universität Hannover (LUH), ZQS/elsa
Erscheinungsjahr 2015
Sprache Englisch
Produzent ZQS/elsa
Produktionsjahr 2015

Inhaltliche Metadaten

Fachgebiet Mathematik, Wirtschafts- und Sozialwissenschaft

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