Lehman Brothers was a planetary fiscal services house. It was the 4th largest investing bank in the US before declaring bankruptcy in 2008. The purpose of this short paper is to give a better apprehension of the grounds that led this large fiscal establishment to bankruptcy. We will seek to understand why hazard direction policy did non work efficaciously for Lehman Brothers. After that, utilizing fiscal informations obtained from DataStream, we will seek to measure two recognition hazard step: the Merton theoretical account for the computation of the chance of default and the KMV. We will use these two steps to our specific instance of involvement and so discourse the consequences, besides supplying remarks about the advantages and drawbacks of these two steps. Before continuing with the analysis relation to our specific instance we will give an overview about the causes that led to the well known fiscal crisis, from a planetary point of position and from a hazard direction point of position.

## THE RISE OF OTC DERIVATIVES AND THE SUBPRIME CRISIS

In June 1998 OTC derived functions value over the universe was less than 100 millions dollars. It sounds like a large figure, but it is still a little sum if compared to the 650 millions dollars over the counter derived functions go arounding ten old ages subsequently. When an OTC contract is concluded trading is done straight between two parties, without any supervising of an exchange, there is no glade house and therefore it is a hazardous dealing. As these minutess around the Earth have reached an sum worth more than 600 millions dollars, it is clear how high is the hazard embedded in this sort of vague market. Derived functions are fiscal instrument that are truly utile when it comes to pull off certain sort of hazards that would be otherwise truly hard to pull off, but they could besides stand for a strong danger if they are non regulated. To cite what Warren Buffet said in 2002 “ Derived functions are fiscal arms of mass devastation, carry dangers that, while now latent, are potentially deadly ” . However his warnings were wholly disregarded. Alan Greenspan, former Federal Reserve Chairman was a strong booster of the deregulating policy, he was a strong guardian of the free market political orientation, and this political orientation played a large function in the planetary fiscal crisis that exploded in 2008.

Furthermore in the U.S. after twelvemonth 2000-2001 another phenomenon was taking topographic point. A phenomenon that would hold exploded in what we know as the “ lodging bubble ” . Monetary values were so increasing a batch after 2001 and this was particularly due to the fact that about everyone could purchase a house. When person wanted to purchase a house and had no warrants that he would hold been able to pay back the loan, Bankss used to give him money anyhow. These are the so called subprime mortgages. Therefore house demand started to increase and monetary values were lifting at a really fast gait, up to a certain point. In the meanwhile Bankss were securitizing their assets, that is pooling together assorted types of contractual debt such as mortgages and selling them to assorted investors, that should hold received the principal and the involvement of debt. Equally far as the borrower would hold been able to pay the mortgage no job would hold risen, and anyhow there was the warrant of the house, a valuable plus that could hold been sold to pay back the mortgage anyhow. But something went incorrect. At a certain point house monetary values were so high that people started gaining that the monetary values possibly did non reflect the true value of the plus itself, and this was merely the start of a crisp bead in the value of houses, the bubble exploded. After the bubble exploded many borrower were unable to pay back the debt, since they owed a batch of money to Bankss, and what was even worse is that their houses were non deserving much any longer, therefore even the warrants represented by the fix assets, could non be considerate a existent warrant any longer as they did non cover the value of the debt. The securitized mortgage were already spread all over the universe and about every fiscal establishments hold them, and since they were chiefly traded over the counter it was impossible to cognize who had a batch of these toxic assets with certainty. Cipher trusted cipher any longer, and this was merely the start of a large and profound planetary crisis.

In a 24 hours period Lehman went belly-up, Merrill merged with Bank of America, the Reserve Fund broke the vaulting horse and AIG required a bail-out. And why were Bankss non able to contrast this scenario efficaciously? What was losing in their hazard direction policies? What is the ground that forced a fiscal giant like Lehman Brothers to travel bankrupt? Two of the chief grounds have been an inconsiderate usage of purchase and a deficiency to sing worst instance scenarios seeking to forestall episodes, that even if are improbable, still can happen in an economic system that is ever capable to strong fluctuations.

## THE REASONS OF THE INEFFECTIVENESS OF THE RISK MANAGEMENT POLICY USED BY LEHMAN BROTHERS

In twelvemonth 2006 Lehman Brothers made the determination to ship upon an aggressive growing scheme and in order to prosecute this scheme it took a great sum of hazard by increasing well the sum of purchase on its capital. In 2007 the sub-prime residential mortgage concern degenerated and the job led to a large fiscal crisis. Lehman instead than draw back made the witting determination to seek to increase their net income from a counter-cyclical scheme. By making so Lehman significantly and repeatedly exceeded its ain internal hazard bounds and controls. Bankers normally like purchase because by commanding a bigger sum of assets you can besides do more money, and hence fillips will be higher, but this is a double-edged blade. In the same manner that you can increase net incomes when things go good, you risk to incur in a great sum of losingss when things does non travel in the manner that was expected. And this is what happened to Lehman.

In its last one-year study Lehman boasted of holding “ a civilization of hazard direction at every degree of the house ” . But if there efficaciously was this civilization of hazard direction, so person could oppugn why to raise a batch the purchase ratio in the troubled market of November 2007. Indeed bankers were let to acquire on with the concern of doing existent money without worrying excessively much about the hazards that they were taking.

The job, that is embedded in the VAR technique of hazard direction, is that people cares merely about the maximal expected loss that they could incur within a 99 % ( sometimes even lower ) assurance interval, and do their determination harmonizing to this step. Lehman in this instance wholly disregarded what could hold happened in that 1 % left. Investing bankers and bargainers believed that this 1 % did n’t affair. Since it is merely 1 % chance they were certain that it would non hold been unsafe. However since the step of VAR was calculated from day-to-day monetary value motions, that 1 % really should hold been taken into consideration and his importance non disregarded. Another issue to which we have to pay attending is the fact that VAR measures depend on an rating of the volatility of the stock concerned. However the volatility is low by definition in periods when the market is quiet, whilst it increases a batch in disruptive markets. Hence the system ‘s appraisal of hazard is low when markets are quiet, and therefore bargainers will take a batch of hazard stacking on places like lunatics, and so when things go incorrect, these places can non be unwound. If a bank is utilizing prosodies such as VAR to mensurate hazard, without trusting on other system to do hazard direction policies more accurate, and at the same is increasing purchase in turbulent markets ( we can see in the undermentioned graph the addition in entire liabilities compared to common equity for Lehman up to November 2007 ) , saying at the same clip to “ hold a civilization of hazard direction at every degree ” , there is a spot of incompatibility in these words. Lehman Brothers bankruptcy clearly show us that increasing purchase in disruptive market period is inconsiderate and that extra measuring of hazard direction must be taken. Now we will present the construct of chance of default, depicting the Merton and the KMV theoretical account, and using them to the specific instance of involvement, that is Lehman Brothers failure.

## MERTON MODEL

The theoretical account of Merton describes the fiscal construction of the adoption house in a simplified mode. It assumes that a company has merely one individual liability, i.e. a zero voucher bond debt that calls for refund of the principal in a ball upon adulthood at clip T. If the value of debt is equal to F and the value of the houses plus is equal to Vt, than the chance of default can be expressed as the chance that Vt is less than F when the dept calls for refund. The market ‘s value of the company ‘s assets fluctuates following a geometric Brownian gesture, that can be described in the undermentioned manner: = I?dt + I?vdz = I?dt + I?vIµ

Where I? is the deterministic constituent, besides known as impetus, whilst I?v is the stochastic constituent that implies a random perturbation, and the higher the volatility the higher will be the consequence of this perturbation. Imitating many times the procedure we can measure the chance that at clip T the value of Vt will fall under a given threshold, that in our instance correspond to the value of debt that calls for refund. In our analysis clip will be one twelvemonth.

The biggest job in running this analysis is that we can happen easy the value of the day-to-day market capitalisation, but it is impossible to happen the exact market value of assets, that differs a batch from the value of equity given the fact that houses finance themselves through both equity and debt, and even their volatility will be different. One simple manner to gauge the value of assets could be to do an add-on, adding the value of debt to the value of equity. However the job persists since we have merely quarterly day of the month relating to the value of debt, there is no manner to download from portal such as Bloomberg or DataStream the day-to-day value of debt. The process applied in our analysis to gauge the day-to-day market value of assets is explained in the undermentioned paragraph.

First of all we have taken into consideration the day-to-day market capitalisation of Lehman Brothers. Than it was besides possible to obtain the information of the purchase place relation to each one-fourth. Having the informations relation to the purchase place of the company and the market capitalisation it is possible to obtain the value of assets multiplying the value of equity by a “ relative factor ” equal to the purchase ratio plus one. However whilst we have day-to-day informations for the market capitalisation we merely have quarterly observations refering the fiscal purchase. The alteration in purchase that we can detect from a one-fourth to the following 1 is sometimes rather large, but of class this alteration does non go on merely in one twenty-four hours, the purchase of the house is invariably altering during the period between the observations associating to one-fourth 1 and one-fourth 2 for case. Therefore in our analysis we tried to capture the fact that the fiscal purchase alterations every twenty-four hours by doing an insertion. We interpolated the losing informations in order to hold a different value of purchase every twenty-four hours, in this manner no crisp bead or increase in purchase will be present, so it is extremely improbable that a bank changes its purchase from 15.21 ( at the terminal of the 4th one-fourth of 2006 ) to 24.08 three month subsequently ( at the terminal of first one-fourth of 2007 ) in merely one twenty-four hours. The insertion process consists in taking the difference between the purchase of one-fourth T and one-fourth t-1 and spliting this by the figure of trading yearss between one-fourth T and one-fourth t-1. The consequence obtained can be seen as an mean day-to-day addition ( or diminish depending on the instance ) of the purchase ratio across the period considered. In such a manner we will hold the informations of the fiscal purchase altering swimmingly within quarters and the analysis will be more dependable. Of class this is still an estimate and the consequences could be biased because it is besides improbable that the fiscal purchase alterations invariably by the same sum across the period, but since we do non hold daily informations about this variable, this is a manner to better approximative fiscal purchase and have the informations required to run our analysis.

Once we have found the fiscal purchase with the insertion process we are able to gauge the value of assets, so it is sufficient to multiply the market capitalisation by the purchase value plus one ( which we call “ relative factor ” ) . In this manner we obtain a clip series with the value of assets of Lehman Brothers. The graph presented in the undermentioned page represents the plus value during the period that goes from the 15th of September 2006 to the 14th of September 2007, the values are expressed in one million millions of dollars.

The Merton theoretical account, as stated before, suggest that the theoretical account follow a geometric Brownian gesture. In order to gauge the parametric quantity of this stochastic differential equation the informations have been taken from the excel spreadsheet and imported into R package, an unfastened beginning informations analysis and statistical package. The bids used in order to run the analysis are presented in the appendix.

The value that we obtain are I?=0,020713 and I?v = 0,33715. Now that we have obtained the parametric quantity of our stochastic differential equation we can run many simulations. The start point of the simulations is 856.04, which is equal to the last value of the clip series presented above and the clip oversight considered is one twelvemonth, that is we want to understand which sort of possible scenario can take topographic point from mid September 2007 to mid September 2008 based on our theoretical account described by a geometric Brownian gesture. The pick of the period is given by the fact that we want to understand, based on Merton Model, what was the chance that the value of assets would hold been under a certain threshold at a certain day of the month. The day of the month chosen is the day of the month of the existent bankruptcy declaration of Lehman Brothers and the critical threshold is given by the value of debt that was supposed to name for refund at that day of the month, that is 824.58. This value is computed by multiplying the market capitalisation at day of the month 14/07/2007 by the purchase of that day of the month. We want to retrieve that it is still an estimate, due to the fact that the insertion process described before could be capable to prejudices. Now that we have all the relevant values needed it is possible thanks to the characteristics of R package to run many simulation and see which sort of way could follow our assets.

In the two tabular arraies presented above we can see 20 simulations. If we look carefully at those simulations, based on the stochastic differential equation estimated before, we can see that 7 of the flights ends up below the debt degree threshold equal to 824.58. Of class in order to gauge a chance of default many more simulations should be run, but we can already see that there is a good chance that the value of assets will fall below the threshold of debt that calls for refund after one twelvemonth clip, i.e. that the company will be in default. This is due, as we said earlier, to the fact that Lehman Brothers had a really high degree of purchase and this makes the company peculiarly vulnerable to disruptive market conditions. The volatility in 2007 was peculiarly high and hence the stochastic constituent of the geometric Brownian gesture have a strong impact, hence we can see running simulations big swing. Due to the high purchase pull offing those swings is peculiarly hard and Lehman failed to get by with this issue.

## THE KMV MODEL

The KMV theoretical account is another manner to cipher the chance of default. It consists foremost in calculating a hazard index called “ distance to default ” ( DD ) and so change overing it into a chance of default based on an empirical jurisprudence which is based on past grounds. The KMV makes a farther measure with regard to the Merton Model admiting that existent companies finance themselves with a combination of both short term and long term debt. In fact it is possible that assets will fall below the degree of entire debt without the company going bankrupt, since the part of long term debt will be paid back in a more distant hereafter. Therefore the KMV theoretical account considers s Default Point ( DP ) a value equal to all the short term debt plus 50 % of the long term debt. However in our analysis we will see the short term debt and current part of long term debt which we have been able to obtain from DataStream. We really do non cognize if the current part of long term debt is equal to 50 % of the long term debt, in our instance we merely take the natural information from our beginning. At the terminal of the 2nd one-fourth of 2008 this value was equal to 163148 1000000s of dollars. At the same day of the month the value of plus had been estimated to be 278709 1000000s of dollars. The standard divergence of the plus has been estimated before to be equal to 0.33715

In order to cipher the distance to default we have to utilize the undermentioned expression: DD =

V0 represents the value of assets at the terminal of one-fourth 2 of 2008, DP is the short term debt plus the current part of long term debt at the same day of the month and is the volatility of assets estimated before.

We can therefore calculate DD = = 1.23

The value of distance to default is 1.23. Now we can gauge the chance of default sing what happened in the yesteryear. In peculiar we would wish to emphasize the statistics refering houses that had a DD approximate value to 1 and 2, that are the undermentioned:

DD ( approximative value )

Number of companies

Number of defaulted companies

Default frequence

1

9000

720

8 %

2

15000

450

3 %

Since the value for Lehman Brothers is 1.23 we can gauge its chance of default as following: 0.08- ( 0.08-0.03 ) *0.23=0.0685

If we use the KMV theoretical account the chance of default of Lehman Brothers at the terminal of the 2nd one-fourth of 2008 was 6.85 % . It is evidently lower that the chance that would hold been estimated through the Merton Model since this theoretical account takes into history the difference between short and long term debt, but it still remains rather high.

## Decision

We have seen how Lehman Brothers, in a period of market convulsion, has non been able to defy to the fiscal crisis due to an inefficient hazard direction policy. An addition in purchase and the deficiency to see immediate redresss to pip instance scenarios led one of the biggest fiscal establishment of all time existed to declare bankruptcy in a short sum of clip. We have besides seen two theoretical accounts that estimated the chance of default of Lehman to be rather high. Other investings Bankss should larn from the errors in the hazard direction policy of Lehman Brothers, if they do non, even the biggest fiscal establishment in the universe is likely to default in the hereafter. Experience taught us that there is no bank that can be deemed excessively large to neglect.