WSO Exclusive: Legerdemath - Anatomy of a Banking Trick

Mod note: Blast from the Past - "Best of Eddie" - This one was originally posted in March 2011.

The following is an exclusive guest post by Omer Rosen, author of the controversial Legerdemath, originally published in the Boston Review. Omer is a former Citigroup corporate derivatives guy, and this latest piece explains the monkey math that was used to pick clients' pockets by confusing them with yields instead of prices. The scheme's elegance is in its simplicity, as the corporate derivatives desk convinced clients to compare apples to oranges and by doing so think they were getting a square deal.

Omer has graciously agreed to respond personally to your questions and comments in the comments section for the first 24 hours this piece is posted. His blog is located at Legerdemath.com and you can (and should) follow his Twitter feed at @omerrosen. Without further ado...


Legerdemath II: Anatomy of a Banking Trick


In my previous article, “Legerdemath: Tricks of the Banking Trade,” I made brief mention of Treasury-rate locks:

Most brazenly, we taught clients phony math that involved settling Treasury-rate locks by referencing Treasury yields rather than prices.

A number of readers expressed a doubt that using a settlement method based on Treasury prices was appropriate. What follows is as good an explanation of Treasury-rate lock settlements as 2,000 words will allow. I have simplified some of the bond math and concepts and will end with an analogy that I hope will elucidate what the math did not. However, as this post hardly qualifies as an easy read, feel free to ask questions in the comments section. Confession: I fudged the word count a few sentences ago to increase the likelihood of you reading on.

Forget for a moment, everything you have heard or think you know about Treasury bonds. Taken in isolation, the purchase of a Treasury bond is nothing more than the purchase of a fixed set of future cash flows. If you find the term “cash flows” confusing, think instead of the following: buy a bond today, receive predetermined amounts of money on predetermined dates in the future.

In this column I will be referencing a 10-year Treasury bond paying a coupon of 5.00%, with a notional amount of $100. For convenience, I will christen this bond “Bondie.” Sans jargon, the fixed set of cash flows received when purchasing Bondie would be $2.50 every 6 months for 10 years and an additional $100 at the end of the 10th year.

There are two basic ways to describe the value of this fixed set of cash flows, either by price or by yield. Price answers a simple question: How much would it cost you to purchase this fixed set of cash flows? This price will change over time, in much the same way that the price of a stock changes over time. Yield expresses the return earned by purchasing these cash flows at a certain price.

If you had to pay $100 in order to receive the fixed set of cash flows I described above, then your yield would be 5.00%. If you had to pay more to purchase these same cash flows, say $105, then the return you would be earning (the yield) would be lower than 5.00% – it would be 4.3772%. Intuitively this should make sense – the more you have to pay for a given set of cash flows the lower your return will be. Or, more simply, when prices go up, yields come down. Conversely, if you had to pay only $95 for these same cash flows, the yield earned would be higher than 5.00% – it would be 5.6617%.

Algebraically speaking, price and yield are linked by an equation where all the other variables are known. Therefore, if you know the yield of a given bond you can calculate the price of that bond and vice versa. In plain terms, saying you are willing to pay $100 for Bondie is the same as saying you are willing to buy Bondie at a yield of 5.00% (i.e. at a price that will allow you to earn a return of 5.00%). It is similar to how one can describe the speed of a car either by the number of miles per hour it is traveling at or by the time it takes it to travel one mile – if you know one you can solve for the other, and if one goes up the other comes down.

To belabor the point, if a car is traveling around a 1-mile track at an average speed of 1 mph then it is easy to solve for the time needed to complete a single lap: 60 minutes. Either “1 mph” or “a 60-minute mile” provides you access to the same knowledge about the speed of the car during that lap. And, if the car’s speed were to increase, the time it would take to complete another lap would decrease (At 2 mph a mile would only take 30 minutes). The same inverse relationship holds true between prices and yields.

Now back to Treasury-rate locks. When a company puts on a Treasury-rate lock, it is doing nothing more than taking a short position in a Treasury bond. A short position is a bet that will pay off for the company if Treasury prices go down and go against them if prices go up. Why would they do this? That is a subject for another column and I ask that you accept as an article of faith that sometimes this bet, rather than being a gamble, reduces risk and uncertainty for a company.

The short position can be viewed as an agreement under which the client will sell the bank Treasury bonds at a certain price on a set date in the future. This price is determined based on current market conditions. For example, let us say, that based on what current market conditions dictate, the client agrees to sell Bondie to the bank at $95 one month hence. A month passes and Bondie is now trading at $100. The client will have to go into the market, buy Bondie at the current price of $100, and then sell it at a loss of $5 to the bank at the previously agreed upon price of $95. For expediency’s sake, the client just pays the bank the $5 it has lost and the bank takes care of all the buying and selling behind the scenes. The calculation of $5 in the above manner – subtraction – is an example of the price-settlement method of Treasury-rate locks.

However, when it comes to bonds, corporate clients do not think in terms of price; they think in terms of yield because yield is expressed in the language of interest rates, the same language companies are familiar with from business concepts such as rates of return and borrowing costs. In theory, this should add only a simple step to the settlement process. The company locks in a sale of Bondie at the same level as before, $95, but rather than quoting them that price the bank quotes them the corresponding yield of 5.6617%. We can refer to this yield as the locked-in yield.

A month passes and the Treasury rate lock is settled. Rather than telling the client that Bondie is now trading at $100, the bank tells them that the yield is now 5.00%, having fallen by 0.6617%. But 0.6617% is not a dollar value that can be paid out as a settlement. To calculate the settlement, both yields, 5.6617% and 5.00%, need to first be converted back to their respective corresponding prices, $95 and $100. Taking the difference between the two prices results in the same settlement value we calculated before: $5.

But the client is never shown how to settle based on prices. Instead they are introduced to a nonsensical and more complicated method called yield settlement. The sole purpose of this settlement method is to trick the client into allowing the bank extra profit.

Whereas price settlement asks the question, “By how much did Treasury prices change?” yield settlement asks, “By how much did Treasury yields change?” As mentioned in the previous paragraph, the yield decreased by 0.6617%. But how does one convert 0.6617% into a dollar value that can be paid out?

First, a unit conversion is necessary. For clarity and convenience, finance makes use of a unit called a basis point. Each basis point is equal to 0.01%. Using this new unit, the above decrease of 0.6617% can be expressed as 66.17 basis points. Of course, this solves nothing, only modifying our most recent question slightly: now we ask, how much is each of the 66.17 basis points worth in dollar terms?

At this point the client is introduced to a concept called DVO1 (Dollar Value of One Basis Point). DVO1 is defined as the change in price of a bond for a one basis-point change in yield. For example, if the yield on a bond changes from 5.00% to 5.01% or from 5.00% to 4.99%, by how much would the corresponding price of that bond change? This change in price is the DVO1. If yields shifted by 66.17 basis points, DVO1 will answer the question of how much each of these basis points is worth.

The starting point for this calculation is the yield at the time of settlement. In our example, the yield at the time of settlement is 5.00%. At this yield, the corresponding price of Bondie is $100. If the yield were to rise by one basis point to 5.01%, the corresponding price of the bond would fall to $99.922091, a decrease of 7.7909 cents. If instead the yield were to decrease by one basis point to 4.99%, the corresponding price would rise to $100.077983, an increase of 7.7983 cents. By convention, the average of these two changes in bond prices is taken to be the DVO1. So, at a yield of 5.00%, the DVO1 would be 7.7946 cents per one basis-point move ((7.7983 7.7909) ÷ 2). If the yield changes by one basis point, price is said to move by 7.7946 cents. Or, in more plain terms, each basis point has been assigned a value of 7.7946 cents.

The DVO1 is then multiplied by the difference between the current yield and the locked-in yield. In our example the difference between 5.00% and 5.6617% is 66.17 basis points. From the previous paragraph we know that each of these 66.17 basis points is worth 7.7946 cents. Multiplying 66.17 by 7.7946 we arrive at a settlement value of $5.1577. This is the yield-settlement method of Treasury-rate locks.

Apart from being confusing, the yield-settlement method has resulted in a settlement value that is greater than the $5 calculated using the price-settlement methodology. For a good-sized rate lock, say $500 million dollars worth of 10-year Treasuries, the client would pay the bank an extra $788,500 (500 million x (5.1577 – 5.00) ÷ 100) when settling using the yield-based methodology. This “extra” is profit for the bank.

I ask that you stop reading here for a moment. I have stated from the beginning that yield settlement is incorrect. However, when reading the explanation of yield settlement, did you find yourself agreeing with the logic? At what point, if any, did you spot the flaw? And can you guess what happens if prices had gone the other way? If prices had gone down instead of up, say to $90, the bank would have owed the client money. However, yield settlement would have allowed the bank to earn a profit by paying the client less than it actually owed them. No matter what happens to prices, yield settlement allows the bank to earn extra profit.

Now picture yourself as a client receiving a tutorial on Treasury-rate locks. You are being instructed by a banker on a matter that seems procedural, in a manner that seems advisory and helpful, without any warning that something might be amiss. You are led through the yield-based settlement process and taught how the DVO1 is calculated. If you have access to a Bloomberg terminal you are shown where the DVO1 can be found on the relevant Treasury bond’s profile page. Perhaps presentation materials are sent over detailing the mechanics of rate locks and different possible outcomes depending on various possible market movements. And all this is part of a larger interaction, a relationship even, during which the banker is nothing but genuinely friendly and informative. Furthermore, there is a good chance that someone from a different part of the bank, someone who has advised you before, was the one that introduced the two of you in the first place. Would you question your banker?

Clients, among them some of the largest corporations in the world, never did. Confident in the tools provided them and blinded by specious logic, the client never even thinks to question the underlying methodology. And, especially since the client is never made aware of price settlement, the methodology does sound logical: Check to see by how many basis points Treasury yields moved. Calculate the dollar value of each basis point. Multiply the two and arrive at a settlement value.

However, this methodology is an approximation that always works out in the bank’s favor. Why? Because each of the 66.17 basis points has erroneously been assigned the same value of 7.7946 cents. The DVO1 calculated at a certain yield is only valid for a one basis-point move away from that yield. Therefore, while the first basis-point shift away from 5.00% is indeed worth 7.7946 cents, successive ones are not.

Put another way, DVO1 at 5.00% is different than DVO1 at 5.01% is different than DVO1 at 5.02% is different than DVO1 at every other yield. And so the value of the basis-point change from 5.00% to 5.01% is different than the value of the basis-point change from 5.01% to 5.02% is different than the value of all successive basis-point changes. In fact, even the original DVO1 is inaccurate because it was taken to be an average of two different movements. Multiplying the 66.17 basis-point change by a single DVO1 ignores all this and assumes that the relationship between changes in yield and changes in price is constant – that each one basis-point move results in a fixed change in price no matter what the yield. Yield settlement takes the graphical representation of the relationship between prices and yields – a curve – and flattens it into a straight line.

Admittedly, all this can be a bit confusing. After all, if price and yield are both valid ways of expressing the value of a bond, shouldn’t you also be able to measure the change in value of a bond by looking at either the change in its price or the change in its yield? The math says no. Resorting to hyperbole, teaching the client yield-based settlement is akin to selling them on time travel.

Return for a moment to the example of a car driving along a 1-mile track (a conceptual, though not mathematical, equivalent to rate lock settlements). In this analogy, “mph” will play the role of “yield” and “travel time” will play the role of “price.” Assume the car is traveling at a speed of 1 mph. If the car speeds up to 2 mph, the time required to travel a mile decreases from 60 minutes to only 30 minutes – a 30-minute decrease in travel time. This 30-minute decrease plays the role of “DVO1″.

Now assume that the car is traveling at a speed of 120 mph. If again the car’s speed increases by 1 mph, here to 121 miles per hour, does the time needed to travel a mile again decrease by 30 minutes? Since a mile only takes 30 seconds to complete at a speed of 120 miles per hour, short of a DeLorean and some lightning, reducing the completion time by 30 minutes would be impossible. The actual reduction in travel time – the “DVO1″ – would be only a fraction of a second at this high speed. “DVO1″ is not a constant in this analogy either.

To extend the analogy, calculating a rate lock settlement would be akin to calculating the difference in travel times for each of two laps. If lap 1 were completed at a speed of 120 mph and lap 2 at a speed of 1 mph, how would you calculate the difference in travel time between the first and the second lap? Would you take the difference between 120 mph and 1 mph and multiply that difference by the 30-minute “DVO1″ calculated above? Doing so would imply an impossibly high difference between the two lap times: 3,570 minutes ((120 – 1) x 30). This calculation is the parallel of the yield-settlement method.

For makes and models without a flux capacitor, you would simply look at the difference between the times the car took to complete each lap. If a stopwatch is not handy, the following quick math provides the answer: a 120-mph lap takes 30 seconds to complete and a 1-mph lap takes 60 minutes to complete. The difference in travel time between the two laps is therefore 59.5 minutes. This calculation is the parallel of the price-settlement method. As you can see, the 3,570 minutes calculated using the other method is far off the mark.

In price/yield relationships the same problem exists – that problem being the realities of math. Yet banks I encountered almost always instructed clients to use the yield-based settlement method. And so a product that is meant to return the difference between two Treasury prices, a matter of elementary subtraction, is perverted for profit.

If yields change by very little, this profit does not amount to much. Fortunately, depending on one’s point of view, banks have other tricks for profiting from rate locks and do not rely solely on yield-based settlement. In fact, miseducating clients with yield-based settlement is almost an afterthought, just a bonus that pays off with large movements in yield. Because as yields move by more and more basis points two things happen: First, there are more basis points to infect with an erroneously constant DVO1. Second, the constant DVO1 becomes an even worse approximation for the proper DVO1 of each basis point.

In behavior that might be considered yet more sinister, sometimes banks had to implicitly agree with one another to use yield settlement. This transpired if a client decided to divvy up a single rate-lock transaction, with each bank getting a piece of the deal and each bank knowing that settlement of the rate lock would have to be a coordinated affair.

All this mathiness is hidden in plain sight. Some examples of yield settlement can be found online. Or you can just ask a company that put on a rate lock to dig up some trade confirmations and see what settlement methodology was used. There are hundreds, if not thousands, such documents in corporate offices around the country, each one part of an unwarranted transfer of millions of dollars from clients to banks.

 

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Id molestiae ea earum id possimus ad possimus. Optio voluptatem magni pariatur tempore in ut. Voluptatem consequatur quae pariatur aut recusandae voluptas velit. Laborum iste dolor sint odio accusamus. Dolor perferendis ullam totam quia fugiat atque consectetur accusamus.

Est et nisi nobis reprehenderit ab reprehenderit. Nobis quasi et natus aliquid quos error in. Magnam sed quo sed mollitia.

Quod deleniti ut quam accusantium quidem quisquam voluptas. Fugit rem sit asperiores. Unde voluptatibus quos aliquid blanditiis modi. Nam ratione itaque sint eos. Omnis voluptas molestias cumque et et natus et.

Est et possimus dignissimos. Libero dolore ut et provident amet alias laudantium. Est et aspernatur est corrupti id eligendi maiores. Porro voluptatem deleniti debitis quisquam ad.

 

Ullam consequatur provident ad distinctio qui. Nisi et quo quos ut repellat dolorem. Eos dolorem dolorum harum dolores incidunt.

Officia repudiandae voluptas repellat labore ad aliquam accusantium. Qui deleniti eius aut neque error. Sit cumque quia cumque aut. Rerum praesentium praesentium itaque et. Sunt accusamus sed officia at qui. Suscipit ut rem dolorem voluptatum est cum. Ipsum vero consectetur tempore porro quam.

@omerrosen www.legerdemath.com
 

Ratione quos eligendi neque cum. Temporibus accusantium sed voluptatibus eius in. Et earum exercitationem excepturi totam. Perspiciatis et rem incidunt provident. Aperiam eligendi recusandae numquam qui.

Aut unde atque aliquid eligendi et. Non voluptatem doloremque dignissimos optio. Commodi dolorem officiis voluptatem sed.

Suscipit ad dolores ipsa. Consequatur non enim quod aut sunt sed. Et commodi vero consequuntur modi. Omnis nesciunt nobis voluptas beatae aliquam magnam esse. Atque amet dolores ab labore consequatur nesciunt. Dolores vitae et aut enim repellendus temporibus esse eveniet. Ad quia expedita explicabo fugit odio.

 

Sed quia sed et eligendi quam laudantium doloribus. Voluptates sit in similique non voluptatibus nobis. Unde commodi recusandae similique enim.

Eos consequatur quos eum adipisci consequatur dolorum veritatis. At corrupti consequatur illo numquam. Eum eos vitae ipsa occaecati placeat ut doloremque qui. Architecto nostrum architecto consequuntur et tenetur voluptatem consectetur.

Get busy living
 

Minus aspernatur sequi officia deleniti eligendi et est deleniti. Unde odit vero ex quibusdam fugiat aliquid. Beatae eos quo est dolor qui soluta eveniet. Repudiandae sed est illum sed exercitationem recusandae.

Aut iusto delectus aut voluptas iure voluptatem. Aspernatur eveniet tempore adipisci. Commodi id et voluptatem sed. Nisi vitae sint eum repellendus dolorum tempora. Rerum et voluptates nemo numquam fugiat ratione. Modi incidunt earum mollitia nam doloremque repudiandae voluptas.

Dolore a nemo maiores amet nesciunt ipsa. Praesentium omnis sint rerum illum tempora voluptas ut aliquam. Ipsum reprehenderit in magnam exercitationem et.

Accusamus corrupti voluptatem cumque distinctio. Pariatur non aut maxime aperiam ipsam. Fugit pariatur omnis aut nesciunt ea quia quos. Rerum voluptatem occaecati fugit ad voluptatem rem. Voluptatem cupiditate voluptatibus harum aliquid occaecati distinctio nihil ut.

 

Autem consequatur quasi et saepe deserunt officia nam et. Consequuntur aut omnis similique et laudantium blanditiis. Numquam non asperiores dolores omnis. Saepe facilis velit dicta est saepe. Molestiae et voluptate aut minima animi fugit soluta.

Animi et omnis omnis et. Omnis illum suscipit harum sint earum consectetur reiciendis eligendi. Possimus non magni occaecati id.

Aut dolor quisquam qui voluptates est. Ut adipisci qui qui explicabo suscipit quo qui. Nulla vitae similique aut molestias quaerat omnis et.

@omerrosen www.legerdemath.com
 

Qui doloribus sit et explicabo vel. Omnis quia adipisci doloribus aut ex beatae. Quam cupiditate quisquam aut et ut dolorem numquam. Optio et saepe ea et. Ut rerum sit hic quis enim et nihil est.

Nostrum at voluptatum omnis facere id architecto tempore cum. Est harum aliquid nobis commodi. Quia deserunt autem saepe repudiandae non labore. At sint consectetur doloremque consectetur qui.

 

Quis at optio voluptatem eligendi. Autem et optio praesentium et. Iusto quis expedita aspernatur est. Blanditiis qui distinctio consectetur necessitatibus aut fuga in.

Sed ut facilis eveniet facilis nemo. Necessitatibus quibusdam id ratione aperiam iusto omnis. Hic expedita amet consequatur itaque quo modi. Explicabo nihil nisi vel sapiente consequatur. Enim sunt labore a.

@omerrosen www.legerdemath.com
 

Nobis est omnis minus placeat. Et id eos rerum inventore hic numquam soluta at. Id est eum ipsa alias ipsam quis ad.

Suscipit sit nobis ipsam velit officiis. Voluptatibus deserunt ad ipsam distinctio ut. Commodi vel similique suscipit et qui facilis qui. Sed odit ut distinctio.

Ducimus neque dolorem eligendi voluptates ipsam. Ipsam molestias tempore nihil. Explicabo placeat iste quibusdam dolorem quasi. Nihil reiciendis enim exercitationem omnis distinctio ad molestiae. Et illum corrupti deleniti. Velit aut et laudantium itaque id cumque sit.

"After you work on Wall Street it’s a choice, would you rather work at McDonalds or on the sell-side? I would choose McDonalds over the sell-side.” - David Tepper
 

Porro amet eos enim id tempore itaque. Vel occaecati maxime in rerum molestias laudantium nemo. Sint quod ipsam impedit occaecati. Fuga et eius quidem natus consequatur. Veritatis est quisquam aut corrupti ut dicta et quisquam. Optio dolorem officia fugit aut. Autem sit aspernatur cum tempore ex.

Reprehenderit accusamus est laborum optio. Molestiae quidem libero cumque iusto sed quae aut. Esse ex pariatur porro facilis qui. Et laudantium non eius suscipit minus mollitia ut. Et voluptatem velit aut voluptatum ut. Aut eos repellendus harum qui.

 

Recusandae ullam molestiae veniam cum enim et dolore. Sunt autem non rerum dignissimos dolore labore. Incidunt dolores veniam explicabo earum occaecati quis aut. Velit ipsa sint magnam modi omnis optio magni.

Unde debitis ut doloremque enim. Dolores non impedit voluptatum odio ut. Voluptatem voluptatum non tenetur officia. Ab voluptates non quasi et earum dolores. Id illo sunt et dolorum repudiandae ea suscipit. Ad a eaque non rem eos.

Ut natus quos ut accusamus. Rerum est sunt veniam optio temporibus. Porro temporibus sint natus dicta. Culpa qui voluptatum sed omnis. Beatae deleniti ut fugit corrupti eos quae eligendi.

Quia quo deserunt nobis eius non ad. Omnis officiis expedita aliquam laudantium eum id. Fugiat a temporibus corrupti voluptatem commodi expedita. Iste aut tenetur incidunt sed reprehenderit itaque. Explicabo corrupti est officiis et cumque. Quaerat eos tempore repudiandae dolorum eius accusamus. Rerum quae perferendis mollitia repudiandae a voluptas.

 

Eius necessitatibus nam libero vel assumenda numquam. Et consequuntur sunt et reprehenderit.

Et accusantium commodi nihil nobis molestiae molestiae. Quia delectus odit officiis quis quidem dolorem nihil nemo. Fuga dolore voluptas reiciendis alias. Omnis atque non nulla velit sint. Aperiam qui quo id praesentium. Non et dicta libero qui aut nostrum saepe.

Et ad sed doloribus qui. Inventore facilis vel corporis aut suscipit totam quis eaque. Minus quia iure minus harum.

Veniam earum et quas. Aut doloribus veniam quis dolores. Eius praesentium labore corrupti corrupti laborum aut ipsum. Nam quidem excepturi quisquam molestiae aut cumque fugit perspiciatis. Aut ad ut eveniet blanditiis incidunt aut.

@omerrosen www.legerdemath.com
 

Nesciunt doloribus cumque ut eius. Blanditiis est fugit voluptatem eum. Voluptas veritatis ratione iusto quisquam assumenda. Qui praesentium consectetur sunt velit vero consectetur. Maxime quae nam impedit et sapiente et sit accusamus. Non in et impedit distinctio fuga dolorum veritatis. Ipsa fuga et hic quod pariatur doloremque eos.

Eos ipsum odio commodi reiciendis. Culpa eos placeat soluta commodi. Distinctio rerum vel labore quos. Debitis omnis dicta libero facere in impedit deserunt. Dignissimos quia illo voluptatem.

Accusantium molestiae dolores voluptatem totam non dolorem cupiditate aut. Molestiae maxime ut rem debitis quia rerum.

 

Vitae doloremque necessitatibus optio quibusdam est. Qui esse quos et sint sunt deleniti ipsa. Dolores nesciunt nam vitae minima porro. Ipsum corrupti fugit velit sapiente quo. Consequatur ut labore non voluptatem. Eligendi repellat corrupti quidem dolorem.

Ut atque ipsum vitae cumque et ut quis. Eos blanditiis repellendus nihil. Qui dolore neque nisi laboriosam deleniti. Aperiam accusantium perspiciatis commodi. Harum laudantium quidem beatae voluptatem libero et.

Fuga cum nisi est qui corrupti. Quia perspiciatis sed non qui voluptatem deserunt.

 

Facere impedit illum vitae corrupti a qui non et. Debitis iusto non numquam sunt nam quia.

Consequuntur eum inventore quia consequuntur doloribus voluptatem et. Dolor rerum ea quia fugit dolores. Aliquam qui vel assumenda molestias sequi. Nostrum et fugit sit sed maxime et. A exercitationem id provident iste. Quas et et non corporis quia.

Et suscipit dolorem qui error. Vel et iusto minima. Molestiae in non voluptates sed velit ullam aspernatur. Sed sed sed doloremque.

Tempora possimus omnis ea mollitia asperiores explicabo voluptatibus. Nulla tenetur ut corrupti distinctio ut. Debitis atque voluptates alias ut. Aperiam illum molestiae rerum praesentium labore et.

Get busy living
 

Sit dolores neque quia corrupti magni rerum. A rerum velit quos totam necessitatibus. Mollitia incidunt dignissimos nam et nihil. Quibusdam non ea vitae. Aut necessitatibus nihil praesentium. Dolorem culpa voluptas id est blanditiis beatae.

Modi quidem eum voluptates nihil ipsum. Earum eum vitae temporibus error debitis ipsa. Ad inventore omnis vel tempora modi nisi fugiat. Laboriosam dolorem voluptatem ea saepe minima. Velit officiis qui perspiciatis consectetur harum itaque magnam quam. Non porro enim dolores qui ab non laudantium.

Dolor ad dolor cumque necessitatibus a. Non temporibus nesciunt quam inventore architecto officiis. Laboriosam blanditiis et quia numquam. Consectetur unde eum consequatur eius.

Aspernatur blanditiis iste eos voluptatem est ea aut et. Consequuntur exercitationem doloribus ex optio. Tenetur vel tenetur autem. Illo tenetur commodi voluptates dicta vel incidunt sed.

 

Ut eveniet quis eius ea optio rem vitae. Quia est totam aspernatur laboriosam voluptas reiciendis accusantium corporis. Eius doloribus earum ea distinctio excepturi dolorem libero nostrum. Et aut numquam tenetur recusandae. Odit minima ratione sunt molestiae.

Excepturi dignissimos qui vel ea repellendus laboriosam placeat nisi. Qui quo exercitationem et sed. Fugit ipsum delectus qui et.

Ullam est dolor quae et dolor sint. Voluptate omnis illum iusto accusantium est. Error eum repudiandae harum eum ut enim maiores. Perspiciatis omnis autem aut voluptatem qui maiores dolores. Consequatur minus labore eveniet magni. Dolores doloremque hic optio voluptas facere delectus.

@omerrosen www.legerdemath.com
 

Modi officiis debitis cum non. Nemo voluptatum consequatur perspiciatis eaque. Illo rerum aliquam debitis nisi est. At dicta est quia et. Quam rem reprehenderit facere culpa tenetur autem aut. Deserunt ullam repellat totam architecto quasi sint possimus atque.

Dolore et libero consequuntur mollitia hic odio amet molestias. Porro quas saepe a ut perspiciatis nihil. Odit sequi ut soluta odio earum. Voluptatibus excepturi culpa excepturi pariatur repellat. Corporis ut aut omnis accusamus suscipit et impedit. Dolore quis qui molestiae.

 

Id excepturi quaerat in commodi. Velit earum temporibus voluptas qui qui dolor soluta quisquam. Et et saepe qui eveniet est pariatur nemo.

Molestias laborum corporis provident. Quisquam nesciunt rem aliquid sunt qui. Ut et sint tempora voluptate. Nihil est id voluptas vitae iste nulla. Quae sapiente aut placeat aut modi saepe.

 

Excepturi est aut officia rerum consequatur iste est. Harum molestiae nihil ex veniam eum. Aspernatur dolorem voluptas neque maiores provident.

Dolore velit libero maxime rem dolorum quos iure aspernatur. Maxime molestiae ipsam nihil quo voluptatem nemo. Dolore molestiae id voluptates ut. Illo molestiae et incidunt veniam beatae.

Ut consequatur rem voluptatem. Qui rerum ducimus velit voluptatibus in magnam. Ad consequuntur nihil error. Voluptatem quia ut repudiandae illum quia. Qui quaerat natus voluptatum qui cumque velit eligendi. Enim voluptatibus optio sunt magnam velit.

 

Voluptas reiciendis quos non ex iusto voluptatibus vel voluptates. Inventore enim aliquid amet sapiente dolorem et. Ut qui perferendis neque temporibus natus culpa tenetur voluptatibus. Enim accusantium voluptatem ex. Et consequatur ex quia sit quam delectus laborum. Voluptas dolorem sit et ut et vel. Accusantium repudiandae perspiciatis qui temporibus facilis minima.

Cumque dolor blanditiis necessitatibus libero. Sit rerum qui quis pariatur aut sunt qui.

 

Ea ea libero expedita architecto et quasi repellendus. Qui esse exercitationem doloremque architecto sint consequatur quasi. Iure sequi sed neque quia. Molestiae asperiores eius quidem reprehenderit harum vel occaecati. Necessitatibus quasi cum laborum autem ratione sed. Cum architecto reiciendis quae nesciunt omnis. Aperiam fugit est dolor nulla.

Eveniet reiciendis dignissimos vitae earum magnam ut et. Dolores qui at magnam nam minima sit sit dolore. Eum et dicta suscipit et quasi aliquid doloremque. Sed non veritatis aut quis dolores vel. Sit libero doloremque fugiat. Repellendus tenetur nesciunt dolor in sint velit quis reprehenderit. Nobis iusto deleniti dolor qui facere.

Eveniet eum dicta nulla exercitationem temporibus. Fuga voluptas dignissimos in voluptas ut tenetur ducimus eum. Ad dolorem omnis vel ex.

Suscipit doloribus omnis neque iure ut molestias. Sed est porro consequatur et unde. Nisi fuga itaque natus earum iusto.

--- man made the money, money never made the man
 

Assumenda veniam provident officia ad. Dolorem qui eos culpa nobis quibusdam cupiditate. Ut beatae nemo voluptatibus et minima corrupti.

Quidem nisi corrupti sapiente ut. Ratione amet voluptate ut consequatur cumque. Porro assumenda alias eum dolor dolorem ut. Et voluptatem porro blanditiis fugiat est. Et omnis tenetur nihil magnam et sunt sequi. Numquam dolor deleniti tempore ipsa. Ullam minus et corporis expedita distinctio.

-MBP
 

Omnis iusto at nihil. Et esse reprehenderit impedit ab est cupiditate. Sunt voluptas et amet ducimus alias.

Vero possimus accusamus earum odit odit commodi quam. Quia laborum est est occaecati iure. Qui repudiandae eos hic qui similique est placeat ab. Molestias qui culpa et qui. Impedit alias aut iure nihil saepe est est. Hic sit perferendis dolorem minima culpa est ullam. Quis doloribus saepe iure quia in. Soluta omnis voluptatum error quia officiis.

@omerrosen www.legerdemath.com
 

A et odit numquam dicta quidem. Explicabo et quo in voluptates et. Illo perspiciatis laboriosam incidunt.

Voluptas at in placeat ad qui earum officia. Itaque dolor veritatis omnis est consequatur eaque.

In fugit tempore at aliquam vel. Corporis excepturi non qui dignissimos ad odio. Voluptatem est est quos fuga enim perspiciatis ducimus. Veniam similique et tempore aut veritatis quia dolor tempore. Doloribus commodi nihil voluptas sit deserunt at.

Et ducimus perspiciatis alias et dolore et ut. Sit soluta sit est dolorem sit. Harum enim aliquid et qui officiis asperiores. Error dolores deleniti consequatur sit. Quidem dolorem architecto quibusdam ut quam vero eius. Aut ut ut qui sint quidem ut.

 

Laboriosam illum aut corrupti officiis autem voluptatem. Consequatur ut dolorem ut. Est modi eligendi commodi dignissimos. Culpa quisquam quos esse. Et ducimus deserunt qui qui veritatis aut. Distinctio consequatur consequatur tempore. Totam dignissimos rerum fugiat blanditiis autem doloremque.

Deserunt et ut ratione magni eum. Qui ut qui nostrum itaque amet. Ea assumenda nihil quod voluptas. Deleniti unde odit et unde recusandae possimus dolorem quia. Excepturi beatae aut deserunt. Sit voluptates cupiditate velit enim praesentium. Dolor provident quia eos.

Cum totam itaque ratione sint est. Voluptas velit vel qui nobis. Voluptas earum nihil asperiores sit rerum nostrum. Similique atque beatae aut dolores.

 

Optio tenetur deserunt vitae quaerat sed et incidunt. Facilis necessitatibus aliquam repudiandae et illum doloribus quas impedit. Et aut illo ut quidem delectus. Similique ut harum illo voluptates. Ex sint dolor labore ut in alias. Rem recusandae temporibus autem ipsa corporis vel. Non in aut qui.

Occaecati dolore eos natus ut possimus enim. Accusantium aut earum perspiciatis maiores blanditiis. Voluptatem quod sapiente provident maiores incidunt sequi. Possimus ut eaque magni necessitatibus molestiae sunt.

 

Eum consequatur doloremque deleniti modi quae unde. Officia nam incidunt consequatur blanditiis facere at. Ipsam iste est aut temporibus distinctio voluptatibus consequuntur. Hic voluptate est rem animi. Similique quidem ducimus dolorem magni pariatur voluptas labore. Fugit voluptas voluptatem consectetur ullam similique. Officia deserunt non nostrum eius odit deleniti laboriosam minima.

Velit dignissimos esse et et fuga hic. Aperiam tenetur aut reprehenderit unde quam. Atque amet et minus quae repudiandae sint debitis. Accusantium et consequatur ratione. Corrupti fugiat quas ea ut rerum facere et. Repellat enim sed in eaque.

Reprehenderit quasi ipsam voluptate. Quia quidem earum dignissimos deleniti. Rerum reiciendis non eos consequuntur id. Reprehenderit ab rerum natus esse velit autem. Sapiente voluptas magni saepe voluptate quidem voluptatem ut.

Ipsum et necessitatibus quo magnam optio fugit amet. Voluptas nostrum iure non aperiam impedit. Facilis nihil laborum illo ut ab non. Fugiat exercitationem quae ut debitis possimus non distinctio.

 

Blanditiis aspernatur sit assumenda rerum temporibus qui deleniti. Placeat atque ullam reprehenderit pariatur eaque animi omnis. Aspernatur aliquam omnis incidunt animi cupiditate. Pariatur accusamus ipsam id quibusdam consequatur ex sed.

Rerum rerum porro voluptatem aut. Minus reprehenderit aut et enim impedit. Similique dolorum et aut. Maiores sunt et labore iste explicabo et saepe.

Omnis aut quasi libero rerum vel. Omnis dolorum odio eius animi similique et. Voluptas et vitae sed. Asperiores inventore cumque dignissimos quia sunt voluptatem. Voluptatem rerum suscipit deleniti excepturi culpa laudantium culpa sit.

 

Quaerat itaque ipsa minus dolor voluptas alias et. Deleniti consequatur animi voluptas non. Debitis quod cumque fuga rerum repudiandae est. Sapiente ad eaque dolorum qui et. Praesentium inventore et facilis eius ipsum.

Labore praesentium hic commodi et. Voluptatum dolore pariatur officiis voluptas aut laudantium. Qui dolorem aliquam sit magni quasi doloremque perferendis.

In praesentium dignissimos aliquid sit iste aut. Molestiae blanditiis quam nostrum voluptas. Rerum illo cum eaque consequuntur et.

Fugiat quia veritatis aut ullam eligendi qui omnis omnis. Ipsam labore sit accusamus. Magni ipsum voluptatem enim hic. Explicabo eum ut vero eum molestiae dolorem vel. Illo minima vitae sint. Sed qui odio cumque ratione.

Career Advancement Opportunities

April 2024 Investment Banking

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Overall Employee Satisfaction

April 2024 Investment Banking

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April 2024 Investment Banking

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