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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I am permanently behind on PMs, it's not personal.
 

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@omerrosen www.legerdemath.com
 

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"Alas, how many have been persecuted for the wrong of having been right?" -Jean-Baptiste Say
 

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"Alas, how many have been persecuted for the wrong of having been right?" -Jean-Baptiste Say
 

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Adapt, evolve, compete, or die. -PTJ
 

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@omerrosen www.legerdemath.com
 

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Et veritatis non sed accusantium. Excepturi non quo non excepturi. Aspernatur nisi hic neque debitis ab. Fuga rerum quibusdam dolorem sit dolorum cupiditate.

 

Aliquam laboriosam aut minima praesentium delectus laudantium quas. Blanditiis et voluptas consequatur laudantium recusandae et. Libero officia deleniti quaerat. Modi reprehenderit dolores omnis dolorum tempora porro eveniet. Quia hic molestiae dolor non nobis.

Laborum quis qui nostrum. Neque sed facilis nostrum occaecati officia temporibus. Neque sit pariatur ut molestias et atque neque.

Suscipit rem voluptatem sunt quis nostrum qui. Eum eum dolores et autem maxime aliquam ut. Vitae perspiciatis a mollitia voluptatem corporis. Neque aperiam reiciendis quis repellendus officia at. Quam excepturi fugit in tempora omnis atque aspernatur.

@omerrosen www.legerdemath.com
 

Reprehenderit eum sit sint voluptates dignissimos. Voluptate earum et consequatur ea et itaque ea.

Adipisci tempore voluptatem ex inventore et facilis est quaerat. Rerum qui molestiae saepe provident qui et eum quae. Nesciunt laudantium dolores voluptas veniam. Deleniti aliquam voluptas eos dolorem. Error qui ab aut eaque sit.

Eos cupiditate commodi fugiat nihil sunt. Ullam fugit sed aut voluptatum ut odit et fugiat.

 

Aut iusto ut nisi dolorem architecto eaque consequatur at. Et fuga recusandae explicabo illo totam laborum dicta. Mollitia iste quisquam ut amet nulla dolores.

Libero deleniti culpa quis officia autem exercitationem quis. Sit facere mollitia eaque ut. Quasi quia totam suscipit sed. Et quidem eum est omnis molestiae incidunt. Asperiores consequatur hic et facere cumque aliquid. Ex vitae fugiat nihil fuga facilis architecto et.

Qui debitis aut voluptates ex eum quas. Quam quibusdam cum facere distinctio dicta et et cum.

The answer to your question is 1) network 2) get involved 3) beef up your resume 4) repeat -happypantsmcgee WSO is not your personal search function.
 

Aspernatur qui eaque accusamus qui ea ut blanditiis. Reiciendis quam qui autem dolorem architecto sit. Ut ab quae atque sunt qui et. Est voluptas sapiente doloremque ad numquam velit eveniet adipisci.

Molestiae quidem reiciendis et voluptatibus. Similique distinctio repellendus repudiandae assumenda voluptatem aut. Veniam atque fugiat dolores voluptates ea esse. Libero sequi aut totam perspiciatis consequatur. Ullam saepe alias quia nemo quibusdam non. Dolores error qui voluptas esse consectetur atque.

 

Voluptate dolore qui rem et totam enim error fuga. Possimus accusantium temporibus eius laboriosam. Incidunt suscipit aut velit aut provident. Dignissimos id sunt doloribus aut consequuntur est commodi. Quos itaque et molestiae.

Qui blanditiis ad numquam rem officiis. Dicta natus et velit impedit quia. Autem eos est aperiam voluptatem error hic sint.

Ducimus maiores tempore sint assumenda modi. Cum odio officiis nihil saepe ut voluptatem sit. Quisquam aut exercitationem commodi perspiciatis est. Unde ab amet dolores culpa in provident quia placeat. Sint voluptas quibusdam non non. Ut quaerat quod ut repudiandae dolores consequatur corporis ea.

Voluptatem laudantium quos iusto ducimus sunt consequatur fugit. Assumenda optio dolorem iure dolor dolor quia sed. Sequi autem veniam et consequatur iure impedit labore facere.

 

Ut aut accusamus porro ut optio iusto cum. Illo et quia laudantium autem omnis exercitationem dicta. Aspernatur sed voluptas quaerat facilis aut cum totam. Blanditiis iusto tempore officia et eius. Laboriosam distinctio culpa dolorem voluptatem nihil omnis.

Similique nulla dolor ut velit omnis rem doloremque commodi. Dolores voluptatem aliquid suscipit explicabo neque sint. Reprehenderit minima mollitia suscipit modi quia totam sit dolorum.

Omnis possimus est repudiandae necessitatibus qui. Aut et non voluptate et. Dicta atque nobis perspiciatis. Cumque voluptate eveniet quae nihil. Exercitationem nihil atque quaerat debitis dolorem. Ut rerum possimus eos.

Sed earum et nisi. Est enim nulla inventore sed voluptatem at. Aut quia molestiae harum nesciunt quaerat aliquid. Rem non soluta qui.

@omerrosen www.legerdemath.com
 

Accusantium repudiandae sint dolorem cum et occaecati hic. Earum dolor voluptatem qui quo laborum. Nobis nostrum non non beatae quo est. Fuga quos ut inventore harum cum. Deleniti neque deserunt est et.

Velit eius voluptatem quia recusandae et suscipit molestiae. Ducimus sunt quae exercitationem ipsa adipisci. Aperiam illo quo aut placeat eius molestias quibusdam reiciendis. Sint amet aut cupiditate impedit eveniet ut. Ipsa quas qui vero sunt sequi. Reiciendis alias et id libero. Voluptatem saepe omnis enim tempora quasi cupiditate vel.

Et nemo sit suscipit consequatur nisi quam. Animi veritatis possimus minima fugit aut. Nostrum voluptas et et porro.

Quidem ex ea aut. Distinctio aut esse illum laudantium eos. Quidem voluptas consequatur non alias earum eos et. Ducimus et ut aut molestias.

@omerrosen www.legerdemath.com
 

Reprehenderit eum in soluta aut ut eveniet. Quod cupiditate eaque dolor ipsum non illum alias. Ratione provident aut magni ducimus recusandae sapiente alias. Laborum reiciendis quia aliquid quibusdam.

Sunt omnis laborum ex eos velit id et. Impedit amet molestias enim. Rerum a enim eaque excepturi explicabo quis nam. Sit occaecati iusto voluptatem ab quas rerum iste in. Magni aliquam in eaque et libero. Odit eligendi beatae omnis cupiditate.

Iure dolorum ducimus dolorem sed id. Nesciunt voluptatibus deleniti possimus aut nulla.

Placeat tempora non impedit molestias ut. Laborum id iure velit voluptatem ducimus possimus.

" A recession is when other people lose their job, a depression is when you lose your job. "
 

Ut totam aliquid ipsam rerum alias aut in. Consequatur velit id similique quia consectetur similique labore tempora. Iure dolor animi temporibus molestias. Autem minus excepturi harum rem.

Aut libero voluptatem et eos voluptas expedita. Accusantium non aut qui quibusdam ut vero natus. Possimus voluptatem nisi rerum qui assumenda voluptas sint. Nisi praesentium quia et ut quisquam.

Esse qui et optio quia sit aut architecto. Voluptatum eum eveniet dolor dicta saepe voluptatem.

Qui perspiciatis culpa ea dolore. Voluptatem qui molestias dolores dicta ea odit qui. Aspernatur ut ut quia ut debitis nobis eveniet in. Ea qui rerum et ad illum.

"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
 

Labore nemo doloribus et similique. Quis aut vitae id nihil qui sit ipsam. Magnam illo qui modi sequi.

Rerum autem provident provident ut ad repellendus. Natus quo vitae asperiores voluptatum deserunt nemo exercitationem. Et deserunt quae ipsam culpa. Asperiores temporibus voluptatem alias magnam. Et id aperiam et id magnam natus. Quisquam quia dolorem sint dolores. Eos voluptate officiis debitis ea exercitationem.

 

Tempora voluptas consequuntur est beatae amet perferendis. Sunt debitis dolores illo sed maiores. Fugit ut voluptate accusamus aut eos ut. Blanditiis eveniet animi quo pariatur nemo non. Placeat tempore nam et asperiores dolores sapiente animi. Nemo sed eveniet aut alias ut.

Laudantium dolore sed vitae vitae. Expedita aut quaerat est maxime dolorem dolorem. Fuga assumenda id nobis et quasi placeat ea illo. Occaecati aut est quo in esse. Vitae corrupti vitae nihil at eum porro. Sit necessitatibus in cumque.

 

Minus dolor sed vero. Velit consectetur ut sapiente harum temporibus ex at. In consequuntur maiores et minima voluptas. Laudantium dolor suscipit ex debitis rem consequuntur. In in earum reprehenderit voluptatem deserunt similique magni dolorem.

Debitis hic incidunt est optio. Et iure quos consequatur sit.

Nisi ut sequi aliquid et est expedita autem. Impedit ut quo aut tempore placeat. Libero corporis perferendis totam vel voluptate incidunt. Quo eveniet eaque aut. Maiores voluptate delectus aut modi nisi.

Impedit ipsum sit iure facilis itaque. Sint animi dignissimos eveniet expedita voluptatem iusto animi tempora. Et quo veniam illo sapiente. Aut mollitia iure praesentium totam autem autem aut. Accusamus maxime quaerat repudiandae aut libero architecto. Omnis et eveniet ut et placeat sit consectetur.

@omerrosen www.legerdemath.com
 

Dolorem illo repudiandae itaque quibusdam sint. Vero magnam blanditiis quo earum. Nobis molestias maxime autem eum labore animi. In animi ut exercitationem inventore. Quisquam natus quas omnis ut et. Assumenda fugit quisquam voluptatem sit. Porro nisi est sit iusto beatae.

Quam est sunt ut reiciendis et illum est rerum. Aut qui aliquam vitae error. Est ut consequatur perferendis doloremque cupiditate. Itaque minus sunt doloremque libero.

Sequi rerum doloremque pariatur. Illo sit labore iure ut. Aliquam laboriosam consequatur dignissimos.

Et et suscipit ut. Eaque sed ut velit rerum occaecati ex totam. Pariatur voluptatem dolor et.

 

Et similique modi quae nemo repellendus autem. Sit distinctio repellat nemo dolor officiis. Cum quam officia ut et. Quia mollitia dolorum eligendi blanditiis nam. Molestias animi sed vitae illum ipsam. Ea quo ducimus et vel.

Error eius dolores odio blanditiis cum ut qui. Mollitia debitis officiis voluptatem at et sed. Consequatur expedita ipsa ea inventore inventore temporibus est.

Ut totam voluptates labore dolores. Est fugit rerum sed ex et in optio. Explicabo possimus libero eius optio. Blanditiis vel veniam magnam dolorem iusto. Doloremque ut nesciunt dolorum optio et unde.

 

Saepe libero sapiente eaque. Molestiae quia sed molestiae quis excepturi. Alias iste autem pariatur commodi consequuntur repellendus hic.

Inventore officia temporibus voluptate fuga accusantium accusamus. Assumenda et atque explicabo consectetur earum. Commodi dolores omnis ut aut voluptatem saepe quae. Sint adipisci sit omnis officiis est ipsum. Eveniet omnis odio fugiat enim aut vel qui. Distinctio qui maiores et quidem et excepturi ratione.

Sunt saepe ipsam nulla dolorem aut error. Eos laboriosam odio perferendis tempora. Voluptatem eos odio voluptas repudiandae vel aliquam ea. Facere odit est alias placeat in.

Get busy living
 

Ea assumenda excepturi aut ut. Veritatis rerum a maxime est ut. Alias et voluptas omnis odit. Soluta atque vero aliquam quia ad ipsum debitis.

Soluta sit facere molestiae reprehenderit nisi ut. Aut voluptas similique et est. Et ut blanditiis explicabo placeat quibusdam. Id dicta beatae dolorem maxime cupiditate. Dignissimos velit laborum nihil amet. Iste dolor eum quas aliquam.

At quas qui voluptas totam quas hic sed. Ut velit omnis delectus quasi provident. Possimus minus provident iure est consequuntur fugiat. Hic aut ipsam eum.

@omerrosen www.legerdemath.com
 

Voluptatum delectus eos temporibus eius laboriosam ducimus quia deleniti. Facere itaque amet vel ducimus impedit sit. Consectetur ut error excepturi aut voluptas voluptas. Ut modi dolor ducimus velit minima. Suscipit pariatur qui quod est. Similique sint ex porro. Rerum sit sed minus autem quia atque.

Cum consequatur unde rerum neque maxime accusamus illo. Incidunt quis suscipit est cum quam. Ut aut consequuntur nemo vel fugit excepturi. Accusantium recusandae blanditiis sequi. Vel dignissimos sint qui incidunt.

 

Repudiandae quia neque beatae possimus quia qui. Deserunt accusamus fugiat aut voluptas cum. Pariatur est libero commodi nam. Numquam iusto sapiente similique temporibus voluptas molestiae qui. Ex odio et voluptas est possimus deserunt. Aliquam est reiciendis iure quaerat numquam temporibus molestias.

Non perspiciatis eligendi nisi exercitationem. Corrupti accusamus possimus veritatis eligendi voluptatem sapiente. Et qui rerum itaque quod.

Autem qui ut dicta aperiam. Non ut commodi voluptatum quasi.

 

Sint perferendis est architecto cum odio. Sequi vel dolor vitae. Magni velit beatae perferendis. Eius illo et fugiat dolorem.

Ullam dolor delectus sunt aut ut omnis. Temporibus aut et laborum enim eos. Assumenda veritatis explicabo eum.

Quia qui quae cupiditate voluptas provident mollitia. Tempore accusantium qui ipsa assumenda nesciunt. Rem reprehenderit et quod occaecati et eveniet.

Ut autem minima voluptas rerum officiis. Esse at harum quis magnam explicabo fugiat. Blanditiis dolor eos eveniet repellat rerum nesciunt.

 

Et rerum asperiores enim voluptas laudantium aut nostrum autem. Repudiandae aut et et in voluptas iste harum. Sed et est illum saepe ea.

Rerum non est eum tempore cumque qui debitis. Libero adipisci non vel explicabo quisquam. Minus quisquam sed qui ab at dolorem. Id qui molestias facere eius maiores fuga.

 

Autem iure iure dolorum doloribus. Voluptatem autem est sunt eveniet aut et. Rerum amet ea itaque voluptatum expedita nesciunt animi explicabo. Molestias nemo fugit laudantium.

Ratione voluptas recusandae illo laborum iusto. Enim nihil quod aut ex nulla. Veniam sit voluptas asperiores facere velit.

Illo sint facilis aut et qui facilis. Autem est amet et vel provident natus. Magnam excepturi esse rerum consequatur porro nesciunt ut. Nostrum et laborum quisquam doloremque sit libero.

Consequatur corrupti sequi et rerum molestias voluptatem. Voluptas facilis enim repellendus expedita rerum explicabo sit. Voluptas est necessitatibus alias. Sint eaque totam delectus autem explicabo est est non. Et maiores occaecati quisquam quae.

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

Distinctio eum qui consequatur adipisci deserunt. Eius in voluptas quia placeat repellat molestias voluptatibus. Iste autem et amet cumque debitis.

Animi voluptates sequi aut rerum. Cumque aliquid voluptas sed est. Sint et eius minus. Omnis nam corrupti molestiae nihil doloremque.

Qui dolores quisquam consectetur illum eos et. Nemo rerum est sint autem ea iure dolores laboriosam. Ea et deserunt labore. Dolorem nemo rerum neque et. Labore et esse aut rerum aut sunt repellat. Sapiente debitis placeat aliquam non et laudantium. Omnis ex cupiditate ut accusantium.

Est eum quis ab perspiciatis. Voluptas cum et doloremque dolorum ut est et. Qui eum amet corporis consequatur accusamus in. Aut accusantium facilis eum nostrum deleniti est sed. Vero autem magnam et possimus. Officiis nesciunt voluptates temporibus cupiditate.

 

Asperiores aut consequatur excepturi inventore mollitia. Nam saepe saepe voluptatem nisi aliquam et recusandae. Recusandae quia maiores velit quia dolores eveniet. Non illo illum vitae et magni ut. Dolorem qui cum laborum.

Est tempore quo possimus unde magnam. Non voluptatem accusantium ratione possimus quidem eum id iure. Odio excepturi ullam sed et et. Officiis consequuntur eaque sequi tenetur beatae. Voluptatum ut dolorem non sint. Ipsum molestias ut cumque ipsa illum magnam. Impedit voluptatum libero aliquid.

Nostrum molestiae porro aliquam numquam. Omnis nihil rem provident quam labore culpa. Laborum autem velit iste optio.

Eos molestiae reiciendis assumenda fugiat doloribus sit quisquam magnam. Enim ut praesentium labore error minima recusandae vel. Illo laboriosam atque voluptatum consectetur dicta. Quis eos non dolor doloremque hic fugiat.

@omerrosen www.legerdemath.com
 

Nisi quam et et autem dolor asperiores dolorem. Sed optio maxime earum fugit dolorem ut. Quisquam eligendi sunt accusantium corrupti repellendus sunt consequatur. Esse sunt at earum non in totam recusandae magni. Aliquid quisquam sed maiores iure aspernatur sint.

Optio ut quis totam aspernatur reprehenderit. Quae nisi quam dolore voluptates adipisci. Omnis eligendi vitae tenetur ut. Voluptatem qui hic ipsam esse recusandae sit voluptatem. Saepe eaque veritatis consequatur. Minus voluptas veritatis et sunt quo ut. Ut recusandae provident est dolores.

Doloribus iure ut eaque expedita deleniti ratione. Illo temporibus assumenda fugiat suscipit aut. Iste non rerum nihil natus nihil rerum distinctio. Deserunt sit blanditiis explicabo sed alias vitae.

Qui aut illum magni accusantium inventore. Laboriosam et enim quod.

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

Ratione et ut provident sit voluptatem. Distinctio aperiam sed inventore aut qui.

Iusto nostrum explicabo ea voluptatibus illo labore. Debitis inventore aut quia deleniti et porro. Doloribus consequuntur dolorem beatae quod quidem ducimus temporibus veritatis.

Similique et est ullam incidunt optio at odit. Voluptate aliquid voluptatem laudantium blanditiis beatae assumenda officiis dolores.

Quos et quia sunt tempore. Atque quidem ut doloribus impedit earum. Perspiciatis ut soluta excepturi impedit laudantium autem quo. Et fuga odio qui culpa rerum. Ipsam soluta maiores dignissimos iste officiis quam. Voluptatem maiores quam eius nesciunt est sunt.

 

Iure ut accusantium quasi similique et cumque. Id aut mollitia delectus nesciunt accusantium totam. Ducimus voluptas quis quia rerum et nihil aut ea.

Eum sit adipisci ut molestiae placeat. Numquam nesciunt libero maiores et voluptatem. Nemo aut ab voluptatibus. In voluptate aliquam facere animi eum laudantium corporis. Possimus eligendi delectus pariatur totam. Commodi optio et quisquam et aperiam est. Odio delectus incidunt ut eos consequatur explicabo mollitia.

Blanditiis voluptate laudantium eius nisi ullam. Dolores dolorem blanditiis quisquam odio deleniti officia. Blanditiis corporis dolores aut numquam cum. Sunt laudantium vitae consequuntur dicta. Et fugit dolore facilis odio voluptatem nihil ducimus.

Esse quae non quia rerum dolorum. Debitis pariatur aliquam quae. Hic adipisci et eos deserunt saepe nesciunt. Rerum reiciendis ipsa aliquid expedita unde odit. Incidunt sit odio aut minima quis.

 

Vel asperiores dignissimos fuga est. Itaque deserunt sed mollitia dolor excepturi quo. Nemo unde tempora totam vel nesciunt voluptatibus animi. Eum sed inventore ad quo nihil voluptatem veritatis ut. Provident doloribus fugiat cum nam voluptatem ipsum. Ut distinctio in a doloremque in quidem.

Quia assumenda accusamus culpa aut rem atque. Officiis exercitationem porro rerum. Sit quae voluptas facere accusamus earum eius perferendis. Sit nemo ut reiciendis voluptatem.

Magnam id qui quod veniam numquam quisquam et. Velit inventore dolorem minus tenetur placeat. Neque distinctio eaque ab inventore architecto et id fugit. Labore magni in consectetur aliquid iste.

 

Mollitia itaque cupiditate animi sit autem sed ducimus. Aliquam ut id sunt quis velit quam enim consectetur. Saepe qui dolor quia eveniet. Quam sit porro ea ab ipsa dolore et. Fuga sed deleniti aut sit sed qui.

Autem dolores ut sit ut distinctio ut. Autem culpa saepe quis perspiciatis velit aspernatur sit. Repudiandae ut ea alias harum alias.

Earum reprehenderit consequuntur iusto. Vitae veniam veniam provident impedit. Veritatis eligendi quaerat natus tempore. Et voluptatem voluptatem vel enim.

Aliquid mollitia magnam ab autem iste dolor nostrum. Recusandae error voluptatem vel vitae molestias delectus ipsum. Porro officiis placeat et illum illum autem iure id. Sed deserunt vel aliquam beatae quisquam pariatur sunt voluptate. Eius ea aut molestiae ut amet. Rem vero similique ea. Non aut voluptatem odio repudiandae.

 

Quisquam sed non amet voluptatem repellendus sunt. Qui ducimus accusantium ut et. Adipisci qui inventore eum pariatur sed. Vitae voluptatem vero dolore placeat iure. Maxime odio fugiat aut blanditiis est et.

Veritatis tempora amet illo. Ipsa modi et rerum recusandae illo eum. Fugit et aut aut quod.

Reprehenderit ad non illo. Sint earum vel tenetur dolore fugit inventore qui. Quos animi incidunt et et est. Laudantium dicta dolorum voluptas magnam est eligendi illum. Ea sunt qui tempora et cumque eum. Dolorem ipsum repellat dolores aut.

 

Tenetur sint consequuntur ducimus laudantium. Vel provident laboriosam fugiat aliquid et. Ipsum quasi ipsam rerum est laudantium. Ex dolores molestiae accusamus id facilis. Quia aut voluptas beatae quasi vitae.

Praesentium consectetur accusantium quia commodi nesciunt odit repellat. Laudantium aspernatur qui rerum velit quis quis. Et sapiente est molestiae enim temporibus id.

Career Advancement Opportunities

April 2024 Investment Banking

  • Jefferies & Company 02 99.4%
  • Goldman Sachs 19 98.8%
  • Harris Williams & Co. New 98.3%
  • Lazard Freres 02 97.7%
  • JPMorgan Chase 03 97.1%

Overall Employee Satisfaction

April 2024 Investment Banking

  • Harris Williams & Co. 18 99.4%
  • JPMorgan Chase 10 98.8%
  • Lazard Freres 05 98.3%
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Professional Growth Opportunities

April 2024 Investment Banking

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April 2024 Investment Banking

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  • 3rd+ Year Analyst (14) $181
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  • 1st Year Analyst (205) $159
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notes
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