The Conjuration That Brought Its Wizards
The 2008 Financial Crisis has established itself as one of the most significant phenomena to have befallen the human race in recorded history. Not since the Second World Was had the entire globe shared the bitter-sweet broth of calamity and even the Great War had not consequences as far reaching, as damning as those that shall result from the actions of the past two years. Never since had the entire world bore the brunt of the actions of the few who almost brought our world and our reality to its knees! And who were these few? Yes, they included the politicians, whose lack of regulation and foresight allowed the world's economy to overheat and implode; Yes, they included the public in the Western world, whose rabid desire and demand for cheaper credit to fuel higher living standards fuelled the credit markets into a drunken and dangerous marauding ogre of greed; And yes, it included people like you and I- Engineering students- who went on to pursue careers in Finance. They are the Financial Engineers- masters of the Financial Universe, Money Magicians who have used their exceptional intellect to manipulate the Financial Universe using Spells of valuation, oracles of prediction and conjurations of debt to enrich their personal coffers and build fiefdoms of the Financial Galaxies! And these Money Magicians have built their universe upon the new face of money- a face that is unlike the worth of a coin or the weight of a note. This report shall reveal this new face and explore the great debacle that was the 2008 Financial Crisis, and these in addition to introductory exploration of the financial sector, should provide an education to aspiring Financial Engineers, in the hope that they do not repeat the mistakes of yesteryear! The approach to these explorations shall be quite detailed but within the grasp of an average 2nd Year Electrical and Electronic Engineering Student.
We have collected data and insights from sources as diverse as Academic Papers and newspaper articles to conversations and contributions by current Investment Bankers at the world's greatest financial institutions such as UBS? Investment Bank, so as to generate a report that caters for both the academic rigour and the aesthetic realities of the Financial Universe!
This Report is written in the hope that it shall open the eyes of its readers to the great mysteries of money, the 2008 Financial Crisis and the manipulations utilised by Money-Magicians to create exorbitant wealth. It is also hoped that it shall inspire the aspiring Financial Engineers through its exploration of Mathematical themes in Finance and past Financial Engineers who have made their mark in the Financial Universe- from Louis Bachelier, the father of Financial Wizardry to Robert Merton, the Newton of modern economics!
This report shall draw conclusions as to: the true meaning of money; the true cause of the Financial Crisis and how it could have been predicted; the effects of the crisis on the technology sector including a surprising effect on innovation; the single valuation technique that does not inflate the worth of a company; and as to whether the perfect language of science, mathematics, can perfectly model financial phenomena.
We hope this report offers as good reading to you as the writing did for us. And remember: it's not all about the money!
The True Face of Money and How This Contributed To the Financial Crisis of 2008
A Forbes article in early 2009 had a sub-title "Last year the world had 1,125 billionaires. Today there are 793. How did $1.4 trillion vanish".  This question lies in the root of the topic "What is Money?"
Many are aware that the credit crunch which hit the Global economy in late 2008 had detrimental effects on all levels of society - from the billionaire Money-Magicians of London, Wall street and Shanghai to factory workers in Vietnam.Before delving deep into the problem and its repercussions, this section will attempt to trail back to the root of the credit crunch of 2008.
On the 12th of September 2001, Alan Greenspan, the then Chairman of the Federal Reserve (Fed) of the United States was afraid that the country's economy would have come to a standstill after the terrorist attacks on the previous day shocked the nation and the world. To encourage public spending Mr. Greenspan cut interest rates to about a half of its value before September 11 2001 to 1.75% by December 2001. #p#分页标题#e#
But Greenspan's interest rate cuts began long before the September 11 attacks. To avoid an economic crisis after the dot-com bust in early 2001, the Fed cut interest rates from 6.5 % in late 2000 down to 3.5% by August 2001.  By cutting interest rates, there was an incentive for the public to borrow more money from the banks to finance a variety of things. One of such things is mortgages for homes. The past has seen several governments engineer methods to encourage home-ownership. In America, the Congress formed 2 banks, the first being the Federal National Mortgage Association, nick named Fannie Mae, in 1938 as the US was recovering from The Great Depression.  In 1976, Freddie Mac or the Federal Home Loan Mortgage Corporation was formed to increase competition in the field.
When the bank lends money to a person, he or she gives the bank a promise to pay it all back with interest. But this "promise" also carries some risk with it as the debtor might not be able to repay the mortgage loan. The banks then found a way to increase revenues and get some risk out of their balance sheets by pooling together these promises, through a method called securitization. In the financial universe, a security is a contract that can be assigned value and traded. Examples of securities may include bank notes, company stocks, government bonds or any other financial asset.
The value of any loan including a mortgage loan is essentially the value of money that is to be paid back multiplied by the probability of that debtor to pay that amount. When these loans get pooled together, the risk of losing a large sum of money reduces since the risk of a small number of defaulters can be compensated by the majority who pay those loans. The result of this modelling is that these large groups of loans which have now been put together seem like a lucrative investment tool. So, the banks started selling this security in pieces to other financial institutions.
This security was called a Mortgage Backed Security (MBS) because the underlying asset of this financial instrument was a mortgage loan. When an MBS issuing bank sells these products to other institutions, they automatically transfer their risk to the buyers of these securities. As a consequence, the banks were not required by the regulators to have the amount of capital in reserves needed to protect them if these risks were to occur.
The sales of Mortgage Backed Securities were so lucrative that the banks were willing to issue more and more loans to people wanting to own houses and from people who wanted to refinance their existing mortgages in order to borrow more money from the bank. The push for more loans caused a huge sub-prime loan market to thrive. A sub-prime loan is a loan issued to someone who does not have a good credit history. In other words, a sub-prime borrower is more likely to default on his loan compared to a prime borrower.
The Credit Ratings agency, which rates different debt-related financial instruments based on their risk, had at first rated the CDOs whose underlying assets were MBSs as extremely high-risk investments. But some Money-Magicians found loopholes in the rating system and structured the CDOs in such a way that they received the highest credit rating: AAA.
Investors from all around the world rushed to buy these CDOs as they assumed that the credit ratings would ensure that their investment was not extremely risky. Since the CDOs were selling like hot cakes, the banks would ask more financial institutions to issue more mortgage loans to as many people as possible.
Easy credit for owning a home then created a huge investment bubble in the property market. Consumers and businesses in the real estate sector were making hefty profits through trading in the property market. A surge in demand here caused the prices of the properties to sky-rocket, which made the banks extremely happy until near mid-2007.
As the price of houses increased faster than the average household income, the number of people who couldn't afford to pay their mortgages increased. As the banks planned, they repossessed the houses from the defaulters. This in turn caused the house prices to plummet. When the asset which backed all these derivates became sour or toxic, this financial instrument broke down.
Like all economic cycles, this led to a domino effect. Since, the banks sold so many CDOs and MBSs around the world; they affected the stakeholders on those countries as well. Moreover, the banks did not have capital to bail themselves out after they reduced the amount in reserves under the assumption that they had removed the majority of the risk when they sold the structured-products with mortgages as their assets.
The psychological effect of the sub-prime mortgage crisis could be seen when investors started selling other derivates which caused even the CDOs which did not have mortgages as their base to plummet in value. Financial institutions did not want to lend money to other institutions which were suffering a slump as they feared bankruptcies as well. The only way the governments thought they could stop a bigger financial catastrophe was by pumping in taxpayers money into the bank to increase liquidity- a procedure known as quantitative easing. And the rest is history.
Although money remained as the centerpiece of trade, it gave birth to a new concept that would revolutionize the world - Credit. This theory allowed people to borrow money and repay it at a later date. The impact ithad on the economic history of the world is beyond the scope of human imagination.
Today, money is created by two institutions. The first of these is the central bank of a country. It increases the base supply which the commercial banks expand, these being the second institution.  To obtain a firm grasp of the mechanics of this system, a few concepts should be learned. These are: the origins of bank notes, Fractional Reserve Banking and the functions of the Central Bank.
Precious metals (e.g. Gold) were used as a medium of exchange a long time ago. Since these metals were valuable, banks were created to store them in a safe place. As a proof of the deposit the banks gave the depositors a receipt which said how much gold that person had deposited and that the person with that receipt can give it to the bank to redeem the deposited gold. Since the number of people using banks increased, people started exchanging this receipt as a medium of exchange with the trust that this receipt can be converted to gold anytime. This was how the bank note was born, a receipt denominated by a specific amount of precious metal, mainly gold.
Fractional Reserve Banking——部分准备金银行制度
As the public were comfortable with using receipts or bank notes, the people who owned the bank noticed that people were largely unaware of the total amount of gold stored in the bank. This inspired the banks to lend money in a different way. Now banks formulate a method to lend out more money than they actually had. This system is referred to as fractional reserve banking because a fraction of the money deposited is kept in reserves while the rest lent out. 
Theoretically, the banks could lend out all the money they had but this would pose as a problem: if a few depositors came to the bank to withdraw their deposits, a 'bank run' would ensue!
Let us say that a person, Jack, has ￡1000.00 that he deposits into Bank A. For the moment we shall merely accept its existence. We shall assess where exactly this 'money' comes from in the coming sections. To simplify this example, we assert another assumption that interests on these transactions do not exist. Now the bank keeps 10 % of this amount in reserves and makes loans of the rest. In other words, it keeps ￡100.00 and lends out ￡900 to one Lisa. Lisa then uses her ￡900 to pay her lawyer who deposits this payment in his bank, Bank B. Bank B repeats this process and lends out 90 % of ￡900 which is ￡810 to a person who buys a bike and holds ￡90 in its reserves. The bike seller deposits his earnings in Bank A.
This process can continue up to a point. But we'll stop here by asking a question: How much money is there in the system?#p#分页标题#e#
To do this we need to first define how we value money. The most basic definition would be the total amount of money in the Bank, . 
But if you now ask the groups of people how much money they think they have, the answer will come out to be something spectacular. Let's call this new definition of money the . Jack will say he has ￡1000, the lawyer will say that he has ￡900 and finally the bike salesman will say he has ￡810. The total shall be:
This shows that the original 'money' has expanded almost three-fold although there is only ￡1000 in actual cash in the banks at this point in time! So how can the newly expanded money supply represent tangible wealth? The new value does represent real wealth if the investments or loans made by the Bank A and B are solid investments i.e. the investments can provide future returns at least equal to the amount loaned from the bank. Moreover, if the investments result in an increase in production of the economy, the expanded money does turn into true wealth.
With this reserve rate, there will be a limit where the original ￡1000.00 can expand to. This limit is called the money multiplier, .  , where R is the reserve ratio. With the reserve rate at 10%,. So, the money supply, can expand up to 10 times its initial amount.
Functions of The Central Bank——中央银行的职能
As aforementioned, the Central Bank controls the supply of money by increasing the base money using Open Market Operations (OMO). To increase the money supply, the central bank buys top quality bonds like UK Treasury Gilts in the open market using the money they "created" out of thin air. By doing so the central bank has effectively increased the money supply in an economy. To reduce the money supply, the central bank sells the bonds they own in the open market.
To know how much money the central bank would want to create, they use a yardstick called "interest-rates"!
In simple terms, the interest rate in a country represents the rate at which private banks in the country would lend each other money for. For example Bank A wants to borrow some money from Bank B to increase its reserves. The rate at which Bank B will lend to Bank A will depend on the supply and demand of money. If a government buys bonds in an open market operation, they have given this amount of money to someone or a group of people. This group will then deposit the money into their bank account. For simplicity, let's say one group deposits it in Bank A and another group deposits it in Bank B.
Now, Bank A needs less money and Bank B has more money to lend out, so Bank B will lend it out at a lower interest rate. Hence governments set a specific target for the interest rate and through OMOs, they control the base money supply and hence change interest rates, until their target is met.
But how does the amount of money affect the economy of the whole world? To answer this, we shall examine 'monetary policy.'
Monetary Policies: The Constraints of National Economies upon the Financial Universe
Monetary policy in a country affects all kinds of economic and financial decisions people make - from getting a loan to buying a new house to starting up a company. This in turn will influence the performance of the economy as reflected in factors like inflation, economic output and unemployment. Moreover, these policies affect how people in the country invest their money in. As we saw in recent years, weak monetary policies around the world have led more and more people into speculation, which has caused various asset bubbles.
In most countries, central banks are responsible for steering the monetary policies of the country. In the US and UK, the central banks, being the Federal Reserve Bank and the Bank of England respectively, have inflation-targeting Monetary policies. As the name suggests, the banks aim to keep the inflation in the countries at a specific rate to ensure stable economic growth and low levels of unemployment as opposed to rapid growth. The most notable part of the Monetary Policy in these countries is that, they allow the markets to regulate themselves. For example, Spanish banks like Santander and BBVA were hardly affected by the recession because they were well capitalized due to strict regulations by the Spanish government.
On the other hand, China- the fastest growing economy in the world- undertakes a different approach in their policies since they are more focused on rapid industrialization and growth. The People's Bank of China emphasizes targeting the rate of exchange between the Chinese Renminbi and a basket of other currencies. The problem with this approach is that inflation has been relatively high in China with the rate lying in the region of 6% to 8 %. Besides that, China has the largest reserve in foreign currencies because it has had a positive trade balance, i.e. where its exports have exceeded its imports.
From the examples in the previous section, different countries have different monetary policies depending on the goals of the government, the state of development in that country, and whether the government focuses more on controlling inflation or promoting growth. However, despite the various monetary policies used, in light of the current financial crisis, central banks around the world have loosened monetary policies and injected money into the markets to provide liquidity. Furthermore they have kept interest rates low so as to reduce the cost of credit, which would encourage business kick start the global economy. These actions have come under harsh criticism though, for example from the opposition Conservative Party in the UK and from the German Government, as they shall cause an inflation explosion and greatly increase the public deficit in the generation to come.
The previous sections were aimed at explaining the basics of modern money mechanics. This section, on the other hand, will try to investigate the consequences of our current monetary system. We have seen that the money supply is expanded mainly through commercial banks as they grant more loans. This has been done by fractional reserve banking where the banks only keep a fraction of the deposits and lend the rest out.
But, the reserve ratio requirement has long been abandoned and it has been replaced by a few other ratios like the Capital Adequacy Ratio (CAR) which is just the ratio of a bank's capital to the risks in its investments. CAR can be used to regulate banks because regulators are able to see whether the bank has some of its own capital to protect itself from bankruptcies and bank runs.
On the flipside, since the definition of CAR is wider than that of the Reserve Ratio, banks have found numerous ways how to manipulate their CAR in order to create more loans. For example, these banks invest in short term government bonds where risk is considered low to boost their CAR. In the early 1990s, a new financial instrument, the Credit Default Swap (CDS) was invented to further boost a bank's CAR. With a CDS it is possible to insure against a debt default by selling a CDS for a particular debt instrument. By selling a CDS for a loan for example would reduce its risk and hence the bank could still issue debt and still have a CAR within the required limit.
In reality, with the abandonment of the reserve ratio requirement, banks can now expand the money supply with more loans. This brings us to a powerful conclusion that almost every pound in the economy is someone else's debt to the bank. Money and debt have virtually become tied together. To comprehend this phenomenon, consider this thought experiment. Let us assume that bank grants a loan. This in turn expands the money supply. Then at a later date the loan is repaid with interest. Now the bank has removed more money from the economy than it introduced. With the multiplier effect taken into account, when the bank grants a loan, the initial money introduced to the economy multiplies into more money (and debt) and later if the debt is repaid with interest, even more is taken out of the system.
To go even deeper, let us assume that all money is created through debt. This is not a far fletched assumption since about 95% of money is created as such.  Refer to Graph 1.1 to see how the debt and Stock (i.e. money supply) obey this relationship.
If this is the case, then how does the world pay interest on the principal for these loans? The simple answer is that there isn't enough money to pay the interest. Since not everyone is paying off all the debt simultaneously, this is not an obvious problem. Being unobvious doesn't reduce the severity of the issue.
In another perspective, one could argue that if some loans are paid fully, defaults on some of the others are inevitable. Thus, bankruptcies and continued refinancing of loans are needed to keep up with the interest payments. This is shown by the growing corporate, government and individual debt through the years in the UK. The graph on Graph 1.2 shows the ten year growth in the average total household debt to income ratio. The appalling fact is that in recent years; people have more debt than their income as illustrated below where the household debt to income reaches 140%!
Besides the soaring individual debt, corporations are also spending more and more money into debt repayments. Data which is presented below in Graph 1.3 shows that throughout the years, larger proportions of incomes from businesses are used for debt repayments. To catch up with the interest payments corporations are forced to increase the prices of their products and/or produce products which are of low quality such that consumers are forced to buy those products more frequently.
One of the consequences of this system of supplying money is that it imposes the need for rapid growth in output. In the end of section 2.2, it was said that the expansion of money supply is only justified if output of the economy is increased. Besides that, since money is created through debt, money has two separate demands associated with it. Not only is money needed as a medium of exchange for services and goods, but almost every pound is also needed to be repaid by some party who has borrowed that money into existence. This causes an extra demand for money which leads in excessive competition for money.
Also, the creation of money by private banks has allowed spending to be focused on a few areas which banks think are important. This has led to many asset bubbles like the NASDAQ bubble of 2000 and the recent real estate bubble. The methods of valuation that led to this overpricing of assets shall be explored in Chapter 3.
The Sorcery of the Money-Magicians unleashed the Tempest that was the recent Financial Crisis, which rained fire and brimstone upon the Financial Industry and infected us mortals with a most potent fear of Armageddon. But what effect did it have on the technology sector- an industry that is ever the more central to humanity and one that is of central interest to us as Engineers in training? This section provides the answers!
The 4 Great Winds of the Tempest——4大风暴的风
The enormous scale of the recent financial crisis has been found to be its most outrageous characteristic. Unlike the Wall Street Crash of 1930 or the Asian Crisis of the 1990's whose effects were mainly restricted to USA and Japan respectively, the Financial Crisis of 2008 has affected every continent and every nation on the planet, and it has done so because this great tempest attacked with the 4 financial winds:#p#分页标题#e#
A Banking crisis——银行业危机
A Banking Crisis is the first wind through which the tempest that is the recent Financial Crisis attacked the globe. A Bank has to lend out the cash it receives in deposits so as to make a profit, whilst keeping some in reserve for withdrawal by its depositors. The problem arises when the deposits are abruptly demanded, and the bank finds it is difficult to pay back all the deposits. Consequentially, the bank would be stuck in bankruptcy and to make it worse, the depositors would lose their money if they were not covered by deposit insurance.
Stock market crash——股市行情暴跌
This happens when stock prices drop severely across a generous cross-section of a stock market. It is often associated with a bubble- the overpricing of stock due to overly expectant investment- which inflates due to crowd behaviour of free markets, before it bursts on realisation of its superficial nature when large portions of investors sell their stakes almost simultaneously, plunging the share prices.
Localized National Financial Crises——本地化的国家金融危机
Mainly influenced by the currency crises, this problem occurs when a nation with normally predetermined exchange rate is strained to undervalue its currency, due to speculative attack.
Recession and economic depression——经济衰退和经济萧条
Recession happens when there is a negative GDP growth which lasts for two or more quarters. When it occurs consistently for a considerably longer time, it is referred to as an economic depression. One notable example is the Great Depression in the 1930s which was originally caused by the stock market crash in the United States.
In the emergence of a crisis, a lack of immediately accessible credit and an increase in commercial interest rates ensues i.e. the expense of borrowing increases. In the aftermath of the Credit-Crunch firms, many firms were faced with a lack of funding which led to the coining of the term. Lack of available credit causes several problems to businesses, and in the following section its impact on certain technology firms shall be analysed.
The impact of the 2008 Financial Crisis on semiconductor-production and ICT firms——2008年金融危机的影响在半导体生产和ICT公司
The past two decades have seen the ascension of the importance of Information and Communication Technologies (ICT) to economic development and job creation. ICT is a sector with intensive Research and Development (R&D) which contributes to innovations across the technology field. The semiconductor industry forms a central cog in the machinery of the ICT sector, as they form a key substance to most electronic equipment. With customer needs evolving annually- from using a CD Walkman? one year to living off an i-pod? the next- the semiconductor industry too has been forced to match this dynamicity through innovation.#p#分页标题#e#
Unfortunately, the 2008 Financial Crisis impacted this industry greatly resulting in the 4 major consequences detailed below. But the effect of this crisis on innovation is mind-bogglingly counter-intuitive and shall be divulged in the conclusion that follows the detailed consequences!
Recently, Research from by the Organisation for Economic Co-operation and Development (OECD) showed that the semiconductor industry has been severely impacted by the 2008 Financial Crisis. In fact, it was the first to be stricken by the downturn of economy. The production of semiconductors declined steeply from the end of 2008 till the first quarter of 2009 in immediate consequence to the recent financial crisis and is not expected to recover by the end of 2009 or early 2010. This is shown in the graph of quarterly revenue growth of the top ten semiconductor firms. Notice the plunging figures for the 2008-2009 period.
In terms of internal cash accessibility, most of these firms had lower net cash at the end of 2007, 2008 and in the beginning 2009 compared with seven years ago. For example, Intel? reduced their capital spending from Q408 (fourth quarter of 2008) levels $1.8 billion to $944 million in Q309, while Texas Instruments? reduced theirs form Q408 levels of $763 million to $226 million in Q309.
Reduced Global Demand for ICT-related Products——减少全球对有关产品的需求
The 2008 Financial Crisis caused a significant decrease in demand for ICT-related products. The impact has been most apparent in regions whose R&D scale differs greatly from their production scale, such as China and East Asia. Asian countries felt a huge impact from the economic downturn with a massive downscaling of once sprawling production. For example, production in Taipei and Japan declined by 40% in early 2009, and the crisis among integrated Asian manufacturing networks caused Asian ICT trade fall by 25%-40%. 
During the final quarter of 2008, worldwide PC distribution declined for the first time since 2002; it later accelerated in early 2009. Although there are new expanding areas, such as the introduction of Netbooks in the market, they still can't compensate the loss in 2009. Moreover, cheaper Netbooks would be preferable to substitute more-expensive laptops and this will cause a temporary decline in total revenues from PC Sales.
Other micro-sectors were struck by the failing worldwide trade as well, particularly in the electronic sector. The demand for consumer electronic devices, such as LCD screens for notebook computers and handheld devices, as well as other associated products fell between 2008 and 2009. In contrary, the growth of environmental friendly electronics and related technologies are expected to increase. For example, despite the decline of overall revenues by 20% in the last quarter of 2008, one of the major Japanese electronics manufacturers Sharp? saw an increase in revenues by 18% from its solar cell division.#p#分页标题#e#
Spending towards Research & Development (R&D)——支出对研究与开发(R&D)
The growth in spending towards R&D in the IT equipment sector declined throughout the period and follows the trend that occurred in revenue growth shown previously in Graph 2.1. The significant decrease on revenue and R&D growth mirrors the sloping demand and declivity ICT usage by corporate, public-sector and domestic consumers.
Despite the fact that R&D activity in ICT sector declined throughout the year, it achieved better results than revenues and production. R&D investment was more robust due to harsh competitiveness and the need for progress through innovation, since the importance of stressing on advancements in new growth regions is easily seen.
Changing trends in outsourcing——外包的变化趋势
The 2008 Financial Crisis exerted pressure on ICT service costs and increased internal cost-cutting measures used in a firm. One of the measures that these firms became more likely to utilise was outsourcing, a process where a firm hires out part of its functions to an external third party for a considerable period of time. Good management of outsourcing can help an organisation to reduce its production and management costs, hence gain more profit over time. The success relies completely on the third party since it controls the whole function of that particular operation. The Financial Crisis also caused firms to reduce the amount of outsourcing they already carried out in a bid to reduce general production and management costs.
Since external sourcing of IT services is more reliable and flexible, it is one proven method to slightly recover cash flow and lessen internal costs. A survey done by Info-Tech Research shows that 60% of the correspondences from more than 150 IT companies are considering focussing on offshore outsourcing to reduce overall costs. It can be seen that the trends in IT outsourcing have changed over the year due to the instability of market.
The tempest of the global Financial Crisis of 2008 that was created and perpetuated by Money-Magicians rained an inferno of instability and financial loss upon a broad range of sectors of which technology formed part. Through its 4 winds of a Banking Crisis, a Stock market crash, localized national financial crises and economic recessions, it affected each and every nation in the world as well. This leads us to the conclusion that although this great tempest has ravaged the economic landscape, it is important for firms, especially those in the technology sector, to recover so as to maintain stability and rejuvenate confidence in the market.
Fischer Sheffey Black (January 11, 1938 - August 30, 1995)
Awarded a PhD in Applied Mathematics, he also studied computers and Artificial Intelligence at Harvard and went on to work in A.I. consultancy before focussing on financial-engineering, and on Monetary Policy in particular. In 1973, he and Myron Scholes published the paper 'The Pricing of Options and Corporate Liabilities' which introduced the world to a financial model which is still in use today- The Black-Scholes Equation- which models the market for an equity, in which its price is a Stochastic process. The Black-Scholes-Merton Model, born of this work, was awarded the 1997 Nobel Prize in Economics. Unfortunately, he had passed away 2 years earlier. 
Robert C. Merton (born 31 July 1944)
Earning a BSc. in Engineering Mathematics from Columbia University and an MSci. from California Institute of Technology, he went on to earn a doctorate in Economics from the Massachusetts Institute of Technology under the guidance of Paul Samuelson- the father of modern economic theory- who described him as the Newton of modern economics. In 1970, he introduced the Merton Model which broke new ground with its treatment of equity as an option on the firm's assets. He derived a Merton model for European options- a more elegant derivation of the Black-Scholes Model- for which he too was awarded the Nobel Prize in 1997 for the Black-Scholes-Merton Model. In 1973 he introduced the Intertemporal Capital Asset Pricing Model- a construction which uses explicit investors' hedges to litigate the risk from savings shortfalls. 
Business Valuation: The Spell of Estimation, "Guess-timation" and "Gigantisation"
What is Valuation? As any Money-Magician learned of the ways of the dark-arts will tell you, Valuation is much more than meets the eye. More than finding the true value of a Business, it is also finding the best value of a business from the perspective of either the buyer, the investor or the seller.
Why is it done and by whom? The three individuals mentioned above reveal the answer to this:#p#分页标题#e#
Valuation is necessary before a Takeover. This is when a company takes control of another by acquiring a majority stake. The Acquirer wants the Company to be cheap without being outbid; The Seller wants a profit from the sale without detering potential buyers with a high price. This aspect of valuation forms important business for Investment Banks through their Mergers and Acquisitions Departments. As an apprentice Money-Magician in this department, your first role would be as an analyst.
Valuation may also necessary before an investor buys a large share of a company, as an aspect of a long term investment
Valuation is also necessary for Regulatory purposes. Anti-Trust and Anti-Competition bodies will frequently refer to a business' valuation during their analyses of market fairness
How did it contribute to recent and past Financial Crises? This question shall be answered by this section through elaboration on how specific Valuation methods can produce inflated asset and company prices as opposed to others. It is these inflationary methods that played a part in stirring the dark-clouds that unleashed the tempest of the recent and past Financial Crises and Bubbles unto an unknowing world.
The Business Valuation Process in Detail:——详细业务估值过程
Step 1: Breakup Procedure
This is carried out if the Firm being valued comprises several distinct Business lines as opposed to a single one. Consider a Firm such as General Electric?, whose businesses include the manufacture of appliances, selling homes, providing financial advice and power generation. A method to value one business will very likely not apply to another whose variables and concerns greatly differ.
Step2: Fundamental Valuation Methods
Figure &1 shows the 5 main Fundamental Valuation methods. Figure &2 illustrates the vastness of the sea of recipes used to conjure the Spell of Estimation, Guess-timation and Gigantisation that is valuation. It shows the frequency of the use of certain valuation methods by Analysts at Morgan Stanley-Dean Witter, a leading American Investment Bank, during the gestation of the Financial Crisis. Due to the scope of this report, we shall go on concentrate on only 3 main valuation techniques: P/E multiple, EV/EBITDA multiple and the DCF model.
Earnings are a primary driver, hence this ratio provides a fair estimation especially of a growing company 
P/E seems to dominate all other multiples in terms of its accuracy 
Unlike EV/EBITDA, this ratio does not take debt into account and so is not a good multiple on which to base a Takeover
Cannot be used if a company has negative or zero earnings
Not reliable if a company has volatile earnings
In Accounting, the measure of Earnings is susceptible to manipulation, thus the multiple is only as good as the quality of the extraction of the Earnings value
The significance of this multiple to a company depends heavily on effective comparisons to its peers and less on comparisons to the wider market. Hence, this valuation may cause a bubble within a sector.
Relationship to the Financial Crisis and Sector Bubbles——与金融危机的关系和行业泡沫
As previously stated, P/E values in excess of 25 may signify the existence of a speculative bubble within the sector within which the company exists. As potential Engineers, note that most financial bubbles of the past were due to technological advancements, such as the advent of radios and automobiles that led to the 1920s Bubble and the revolution of the world-wide-web that led to the .com crash of the late 1990s. It is thus of note to potential entrants of pioneering engineering fields such as Green-Tech to keep track of one's company's and one's sector's P/E multiple.
In several instances, a company may be in recovery from a slump, such as that during the recession that occurred as a result of the recent Financial Crisis. A recession holds the advantage of forcing an increase in innovation, and innovation increases earnings across a sector. Below is a graph showing the number of patents filed. Notice the contrast between their frequency during financially-stressful (1987 Wall Street Crash, 1989 Asian Crisis which mainly affected Japan- a great innovator,2000-02 dotcom crash) and optimal-growth periods:
Company Value Multiples——企业价值倍数
EV to EBITDA multiple
Enterprise Value= Market Capitalisation + Debt + Minority Interest + Preferred Shares - Total Cash
Market Capitalisation = (Number of Shares Outstanding) x (Price per Share Outstanding)
EBITDA = Earnings Before Interest, Tax, Depreciation and Amortization
The EV to EBITDA multiple, commonly referred to as the EBITDA multiple, is one of the more widely used multiples while casting the Spell of Estimation, Guess-timation and Gigantisation that is valuation. It is unlike the capitalization multiples for it takes debt into account, through the Enterprise Value term. For this reason, the Enterprise Value is commonly referred to as the theoretical take-over price.
A low multiple represents undervaluation of the company in question, for example Apple? Inc., the American computer manufacturer, had an EV to EBITDA values of 2.61 in 2000 during its resurgence and of 18.862 in January 2009 before the extent of the success of its i-phone? had been properly reflected in its value. On January 21st 2010, it's EV to EBITDA multiple lay at 20.42.
A low multiple is also a marker of a suitable takeover candidate.
Like the Price to Earnings multiple, the EV to EBITDA multiple varies between sectors. For example, it has a higher value on high growth industries such as biotech, as compared to slow growth industries such as railways.
The EBITDA term ignores distortional effects of individual country's taxation policies and thus is useful for transnational comparisons
The Enterprise Value is a better metric than Market Capitalisation in respect to takeovers as it accounts for the company's debt that a new owner would have to assume. As such, this multiple is used to find attractive takeover candidates #p#分页标题#e#
This multiple does not depend on capital structure, hence gives fair and broadly acceptable direct comparison between companies with dissimilar capital structures
The EBITDA value faces the following limitations:
It doesn't include changes in the Working Capital requirements. Working Capital gives investors a perspective of the company's operational efficiency
It does not consider capital investments, such as purchasing new machinery
If a company has negative cash flow, EBITDA cannot be used to build this multiple
The EBITDA term is built from 1 year adjusted earnings and as such may not produce the accurate long-term value of the company.
Relationship to the Financial Crisis and Sector Bubbles——与金融危机的关系和行业泡沫
During the dotcom bubble of the late 1990s, companies promoted their stock by emphasising their EBITDA and explaining away income, which involves ignoring many one-off costs, for example, the average EBITDA value of a company on the Nasdaq Index stood at ....., compared to ...... on the Dow Index at the same time. In this way, this multiple was used as a means of over-valuation and price inflation that lent to the gestation of the Financial Crisis we face today.
Cash Flow Analyses or Cash Flow Modelling——现金流分析或现金流模型
Discounted Cash Flow
The Discounted Cash Flow model is described as an intrinsic valuation model because unlike earnings multiples, it does not assume that the rest of the stocks in a market are priced correctly. Instead, it uses a projected estimate of a company's Cash Flow over a fixed period and discounts them using the WACC to arrive at a present value.
The WACC is a calculation of a firm's cost of capital, in which each category of capital is proportionately weighted. Sources of capital include: Common Stock, Preferred Stock, Bonds and long-term debt. An increase in WACC correlates to a decrease in value of a company.
The accuracy of the DCF method is similar to that of the EV to EBITDA multiple, underlining their preference as bases for Takeovers. It is also regarded by Money-Magicians as a reliable long-term valuation tool, providing a good base for "buying a business" as opposed to "buying a stock". The target company's cash flows must be positive for this model to be used.
Since earnings do not have a constant rate while cash flows have a less volatile fluctuation, this multiple may produce a clearer picture of a company's future profitability, which makes this a preferred valuation tool for use on new companies with little financial history, such as Google, whose DCF stood in the $103-$298 range- a very healthy one- at its floatation
Makes uses of the WACC, which gives the time value of money (note the Cost of Equity term which takes into account current and past stock prices, which are both guaranteed but temporally-displaced values), which is a risk-free rate. This is preferred by investors as it stipulates the current existence of money within the business without the usual temporal risk associated with such calculations of company profitability.#p#分页标题#e#
WACC also reflects the risk premium (i.e. term), which is the extra-return an investor anticipates in reply to the risk he undertook through his initial investment
Building a Discounted Cash Flow model requires many more inputs than a P/E or EV to EBITDA multiple, and is thus a fundamentally more holistic valuation
A DCF model is based on Asset-fundamentals and is thus less exposed to market moods and exceptionalities such as sector bubbles and crises
It takes account of self correction of free-markets, which most other valuations neglect
Requires far more inputs than any other valuation method, which provides an extra work load especially to Apprentice Money-Magicians
The inputs to a DCF Model are noisy and can easily be manipulated in accounting
Valuation using a DCF model does not subscribe to the assumption that other stocks are priced correctly. As such, Equity Research Analysts- Money-Magicians whose job it is to analyse companies' stock and recommend profitable positions- who use this method compute results that are generally against the market trend and considered conservative, such as short-calling companies that are making short-term profits, hence endangering their jobs in the brutal profit-oriented financial universe.
Relationship to the Financial Crisis and Sector Bubbles
A DCF model has a unique quality of yielding contrary recommendations to capitalization multiples when markets turn unpredictable or undergo exceptional circumstances. For example, in 2007, being the period leading up to the Financial Crisis, the markets were bullish. A DCF model's valuation at this period would conclude that the company should be sold despite good earnings and high market capitalization, which indicate higher value and a desire to maintain an investment as per Capitalization multiples. This is because WACC is indirectly proportional to V which would be increasing because bull-markets resulting in higher market value of debt and shares. On the other hand, the DCF model would reach a conclusion to buy a company during periods of a bear-market, while the Capitalization multiples would conclude against investment in a company due to the low market capitalization and poor earnings at this time.
Unlike Capitalization Multiples (e.g. P/E multiple), this method of valuation is based firmly on long-term prospects of the company. The Financial Crisis and past industry bubbles were caused by imprudent trading practices by Money-Magicians who were focussed solely on the short-term gains of a company, leading them to invest greatly in untried internet business and high-risk mortgage products.
As such, this valuation method probably played the least part in fanning the current financial inferno that has engulfed the world and wreaked havoc on the Financial Universe.
Dark Spells Through an Engineer's Lens: Mathematical Modelling of Financial Phenomena——通过工程师的黑暗魔法镜头:金融现象的数学模型
The Financial Universe is filled with Magical Galaxies ruled by Money-Magicians who use their spells to conjure money out of thin air; to create value out of the nothing; to construct an empire of wealth where once a void stood! These spells are so complex, so baffling to the average mind, and this difference in financial expertise has given the Money-Magicians the power to rule over mere mortals in this universe! But it has been shown that these masters of the universe were once masters of the laboratory, and so these spells were written in the language of the laboratory, the language of science: Mathematics! And in this section, we shall labour to explore and test mathematical modelling in finance, and draw a rather bizarre conclusion as to whether the laws of the financial universe can truly be perfectly described through the language of Mathematics!
As engineers, we like to simplify phenomena through the language of mathematics, which can be used to create a model that provides with a simpler view of a situation or allow us to make predictions about the future behaviour of an object. Whether it is the use of point masses to explain gravitational problems or the use of ohm's law to simplify simple electronic circuits, we can see countless examples that exemplify the need for simple mathematical models that are able to simplify a problem.#p#分页标题#e#
For example the modelling of the earth as a sphere, which then can be further modelled as a point of very high density allows us to make sufficiently accurate measurements its gravitational strength.
In our case, we wish to model the market, using the stock exchange as an indicator of the current performance of the market. We use the stock exchange as it is simply a market for financial goods, whose price and quantity supplied are determined by the supply of and demand for money. Financial goods being bonds or stocks that are purchased as they hold a possibility of a return on investment, exactly like the utility gained from a consumer product. Since the supply of money is directly linked to the amount of disposable income people have, we can use it as an indicator of how much money people have saved. Similarly, the demand for money is mainly derived from the funds required for investments. Thus the average stock prices across a variety of industries is a good indicator of the value of money and the general economic outlook of the economy,as it relates to the income of both companies and people.
Casting the First Spell: Brownian Motion as a Market Model——铸造第一个法术:布朗运动的市场模型
For example, if we look at the plot of the value of the FTSE, a stock exchange indicator used for the London Stock Exchange, as shown below, we notice the different periods of the economy that correspond to the different portions of the graph. Note that a variation in the stock price may not always be due to the actual market but due to individual manipulation. However, during the calculation of the indicator value, a whole range of stock prices are used.
As we can see from the graph above, the indicator value moves in an almost random manner, albeit with an upward average trend. The short term random motions of that we notice are much alike the motion of small particles in a medium, Brownian motion. As we can see below, the particles move in a completely random direction with a net overall effect that points in one direction, due to a force or field.
This similarity was first noticed by Louis Bachelier, the father of financial-wizardry (Pg. 15), who stated that financial markets follow a 'random walk' which can be modelled by standard probability calculus. This "random walk" is essentially a Brownian motion where the previous change in the value of a variable is unrelated to future or past changes. Bachelier offered economists a powerful way of modelling stock market fluctuations as using the formulae that define Brownian Motion, we would be able to calculate probabilities and estimate statistics very accurately.
This grouping of logarithms of prices, with respect to time, is almost analogous to a grouping of coordinates of a large number of molecules. In his analysis, he first found the price of the same random stock choices at random times and then used a probability distribution function. The result of was a steady state distribution function, which is precisely the probability distribution for a particle in Brownian motion. He was able, subsequently, to calculate a similar distribution for the value of money, using stock market indices as financial indicators.#p#分页标题#e#
Thus we have modelled a market by Brownian motion but how do we use this model practically? It may be used to model a variety of situations, with its main use being to model asset returns, by finding the price of a particular asset S (t) at a time t. The return can be represented by the ratio of the asset price in the future S (t + T) over the original price S (t). 
Bachelier made two postulates:——Bachelier的两个假设
The fair game condition: The expectation value is the same for any 2 parties that are involved in a trade and since Buy and sell orders having opposite signs, the expectation value of a trade must be zero.
At any particular trading price, financial traders do not believe that prices are rising or falling, which is to say that any change in the price is due to external factors and is independent of previous price changes.
Both these postulates can be summarized by with one hypothesis - the efficient market hypothesis. Simply put, asset prices would instantaneously reflect all the relevant information about them.
These 2 assumptions lead to the efficient market hypothesis: all available information is accounted instantaneously in asset prices, which means that every single buyer and seller knows all the information there is to know about a particular financial product. By a series of arguments, Bachelier and later researchers concluded that the statistically independent returns of an asset are drawn from a Gaussian distribution. The equation of which is shown below. 
This would mean that prices follow "geometric Brownian motion" and are drawn from a log-normal distribution. Where ? is the drift rate of the returns i.e. the growth rate of the financial product and s is the standard deviation, or volatility, of the returns. We can also find the normalized returns from the first equation by subtracting the expectation value and dividing by the standard deviation of the return series. 
Hence by measuring the volatility of a market and its current rate of return it seems we can make accurate market predictions on the profitability of investments. However as with all models we are not offered an exact view of the market as several of the assumptions required do not always hold.
A study that exemplifies the failure of Brownian motion is a one undertaken by the Department of Physics, Bayreuth University and an economics database at Karlsruhe University. The research team analysed the German market in a short period of time and found that modelling the market as Brownian motion fails terribly as the random signals occur much too frequently.
The data that the study collected is presented in the two graphs below. Graph 3.4 displays the DAX German Blue Chip Index value for the years 1999 and 2000. Graph 3.5 shows us the returns ds15?(t) on a 15-s time scale of the DAX Performance Index, normalized to their standard deviation.
From Graph 3.5 we notice signals of the order 20 to 40 s (where s is the standard deviation of the sample) are rather frequent, and there are even events up to 160 s. For comparison, the probability of a 40s event under Bachlier's second hypothesis is 1.5?10-348 and that of a 160s fluctuation is 4.3?10-5560.
However the effect of these signals is not as large as it would initially seem, the linear correlations of 15-s returns ds15?, C15?(t)=< ds15?(t)ds15?(t+t)>, are shown in the graph below.
We notice correlations (dependence of the DAX value at any time t on a previous value of the DAX) that are either positive with a short 53-s correlation time or negative (overshooting) with a longer 9.4-min correlation time. The remarkable feature of graph above, however, is the small weight of these correlations. The solid line represents a fit of the data to C 15''fit(t) = 0.89 dt,0+0.12 e-t/53?-0.01 e-t/9.4',implying that the data are uncorrelated to almost 90%, even at a 15-s time scale. Thus, we noticed that some of our assumptions hold true to a good enough extent.
The Oracle's Spell: Prediction of Investment Profitability by Mathematical Models——甲骨文的法术:投资盈利的预测数学模型
The model created by Sornette and Zhou was tested on the Shanghai Composite Index,the index that measures the average of stock prices on the Shanghai Exchange. The results of their text indicated that the model was quite accurate as the model predicted that after a 50% in just four months the market should correct itself. And as predicted in August, the index fell almost 20% in two weeks.
Moreover mathematics may be employed to find a suitable sector to invest in. F. Thomson Leighton, a Mathematics Professor at the Massachusetts Institute of Technology, found that utilizing information regarding past performance, he could predict the future profitability of a financial product. Quoting the Professor: "Even if the past is not correlated with the future, the past can be combined with randomness to provide a very good prediction of future performance." Combining this intuition with randomness, Professor Leighton created an algorithm that would call for buying stocks that have paid dividends in the past. Although the model seems simple, it does not employ the dangerous strategy that produces the market crashes predicted by the technique explained earlier.
In the investment scenarios conducted, the team would have to assume that there is a stock that will pay a good dividend, and if none of the stocks paid any dividends, the model will be unable to predict the best choice. Furthermore the model is unable to advise on both buying and selling shares of stock since it does not address entities that can go down in price i.e. it is unable to provide us with the least bad option.
In order to see how the model works in practice we assume there is a finite amount of stocks available and every set amount of time, the stock you own may or may not pay a dividend. The goal is to maximize profit; hence it is important to minimize losses which can exist in the form of transaction costs due to changes in the stock chosen. After every set amount of time, you check which stock paid a dividend and each time a company pays a dividend, look at its past record. Companies that have paid more dividends in the past have better chances of coming up as heads in your coin toss. If it comes up heads, pick it on that day but if you want to switch to a different company, keep flipping coins to decide when to change.
As strange as such a method may sound its effectiveness has been proven mathematically by Professor Leighton, with the proof assuming that you are comparing your results against a worst-case scenario. Although the model is quite accurate, it does not take in to account market irregularities such as insider information that would have a much larger impact on asset choice.
Another method of modelling the market, the Capital Market Theory , is based on equilibrium systems: for example, a balance between supply and demand, risk and reward, price and quantity. Created by Alfred Marshall, the theory stems from the idea that economics is a science akin to Newtonian physics, with an identifiable link between cause and effect. The theory models the economy as an equilibrium system and if it experiences an external force it reacts as to oppose it. An example of a system that exemplifies this behaviour is an operational amplifier.
This capital market theory, largely developed over the past 50 years, rests on a few key points. These include efficient markets, random walk and rational agents. Considering each element in turn, we will outline its contribution to the theory:
Researchers theorised that stock prices should reflect all the relevant information that is known by the market traders, concerning the stock. This leads to the conclusion that a change in the price of any stock option has to occur due to some unknown or unexpected information. Hence prices will follow a random path or 'walk' that is defined by the random events that occur in time and not be affected by previous price changes. The reason Random walk is a crucial assumption is that it implies that the probability distribution of returns will be normal or near normal, which allows us to use statistics to make a large amount of financial predictions.
Stock market efficiency——股市效率
It suggests that the price of an asset incorporates all the relevant information about it, with this information being cheap and widely disseminated amongst the general public. Hence investors know exactly what they are going into, causing the stock purchase to be a 'zero net present value proposition'. This means the price reflects the risk over time, but no more. Thus Market efficiency implies that stock prices are not a result of irregularities such as insider trading.#p#分页标题#e#
This final element is an assumption that investors can assess and optimize risk/reward opportunities. Financial Scientists reasoned that risk-adverse investors would "rationally" seek the highest return for a given level of risk, leading to the use of a linear relationship between risk and return.
Sadly these assumptions do not hold true, exemplified by the case studies below:
Stock market returns are not normal, as capital market theory suggests. Rather, return distributions exhibit high kurtosis; the tails are fatter and the mean is higher than what is predicted by a normal distribution. This means that periods of relatively modest change are interspersed with higher-than predicted changes (i.e. booms and crashes). Non-normal distributions undermine the random walk and weaken the strength of the statistical tools available to evaluate market behaviour. This can be shown in the 2 graphs below.
Trading volume is higher and price changes greater than predicted. Standard economic theory predicts low trading volume and limited price volatility. In reality, trading volume is higher and the price changes come in greater size than the theory predicts.
Risk and reward are not linearly related via variance. A study conducted by Fama and French (1992) concluded that their tests do not support a positive relation between average returns and markets. However, Fama and French maintained a "rational asset-pricing framework," which means that they identified the factors associated with various returns and assumed that those returns were attributable to risk. While consistent with the theory that rational agents seek to maximize returns given risk, their conclusions are undermined if those same agents cannot, or do not, optimize the risk reward trade-off.
Investors are not rational: The case here rests on two points; the first is the growing body of evidence from decision-making theorists showing that humans make systematic judgement errors. One of the best-documented illustrations is Prospect Theory, developed by Kahneman and Tversky, which shows that individual risk preferences are influenced by how information is presented. The second point is that humans generally operate using inductive, not deductive, processes to make economic decisions. As no individual has access to all information, judgements must be based on what that person "knows" as well as what that person believes others to believe. Such decisions are often generated using rules of thumb and suggest a fundamental indeterminacy in economics. However, if enough people follow a certain path of thought based on price activity generated either consciously or randomly, the resulting price trend can be self-reinforcing, as more people follow this chain of thought simply because it is the norm.
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Afinancial instrument whose price is dependent on some otherasset,index, event, value or condition known as the'underlyingasset'
The buying and selling of government securities in the open market in order to expand or contract the amount of money in the banking system
Domestic and foreign investors selling a country's currency assets in a massive scale
A practice that limits trade such as a merger that debilitates the competitiveness of a market
Shares that are not Preferred Shares or do not have pre-determined dividend amounts. Preferred stock has a higher claim on earnings
A liability that represents a proportion of a parent-company's subsidiary that is externally owned by minority shareholders
Shares currently held by investors such as company officials and those held by the public
An expense recorded to allocate a tangible asset's cost over its full useful life
Cost of acquisition - Residual value of intangible assets e.g. patents, trademarks
Current assets - Current Liabilities. Worst case scenario of negative Working Capital is bankruptcy
Cash generated from operations of a company. OCF = Revenues - Operating Expenses
Funds used by a company to acquire or upgrade physical assets
A financial market where prices are rising or are expected to rise
A market condition where prices of stock are reducing and widespread pessimism cause the negative sentiment to be self sustaining