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Anyways, one of the recent nobel prizes in economics went to two of the 3 people behind the so-called Black-Scholes equation. It is a partial differential equation that deals with the values of options, a type of equity.
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<p>A minor objection - options are not a ‘type’ of equity. Not at all. They are actually a derivative security that allows you to speculate on the movements of certain financial data and derive their value from that data. </p>
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The kicker: The reason the equation is so powerful is because the inventors of the equation came up with a specific substitution that transforms the PDE into the famous heat equation studied by mathematicians and physicists for quite some time.</p>
<p>You can interpret that story however you wish, I am just pointing the potential usefulness of a scientific mind in economics.
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<p>You guys are clearly talking about Myron Scholes and Robert Cox Merton, the infamous architects of the LTCM hedge fund that, a decade ago, not only lost a ridiculous $4.6 billion, but also required a government-organized bailout. So, I guess you’re right; these models are indeed extremely powerful in that they can destroy huge amounts of wealth in a tiny amount of time, and hence truly are financial ‘weapons of mass destruction’. </p>
<p>[Long-Term</a> Capital Management - Wikipedia, the free encyclopedia](<a href=“http://en.wikipedia.org/wiki/Long-Term_Capital_Management]Long-Term ”>Long-Term Capital Management - Wikipedia )</p>
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<p>It is indeed an excellent example…of financial engineering models that resulted in the destruction of a catastrophic amount of wealth and placed the world’s economy at risk. The LTCM catastrophe was simply a preview to today’s troubles in the financial system when you rely too heavily on mathematical models.</p>
<p>Look guys, I don’t have any objection to financial mathematical models themselves. Obviously they have their uses. However, clearly, the banking sector has relied far too heavily on these models without understanding their limitations. If these models were truly perfect, we wouldn’t be seeing the entire world’s economy being placed in jeopardy, and we certainly wouldn’t need governments to be bailing out millionaire bankers. It is now widely recognized that financiers were relying on models that they didn’t fully understand. For example, when the ratings agencies were stamping AAA ratings on CDO’s and CDO-squareds that only later turned out to be dodgy, when Ibanks were gearing up by 30x in buying MBS’s under the historical assumption that it was “impossible” for housing prices nationwide to decline, when banks were relying on short-term (in some cases 6-hour rollover) funding under the assumption that markets will always be liquid, when the financial system interlocks itself with up to $100 trillion worth of opaque over-the-counter CDS’s supposedly as ‘financial insurance’ without properly accounting for counterparty risk, such that nobody even knows how total CDS’s are out there, who holds them, and what they’re worth (hence they’ve been likened to “dark matter”, we’ve clearly hit a world where financial models have hit their limits. </p>
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It turns out that what Brown discovered — called Brownian motion — is useful in studying all sorts of random phenomena, including financial risk. It’s useful — but not foolproof.</p>
<p>Richard Lindsay is the author of How I Became a Quant, about financial engineers. He says financial models built on Brownian motion have done a great deal of good. These models have been so helpful in managing risk — at least some of the time — that they have made the world far richer. But that doesn’t mean they always work — they’re not perfect. But they’re “the best thing that we have,” Lindsay says.
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<p>[Why</a> Risk Models Failed to Spot the Credit Crisis : NPR](<a href=“http://www.npr.org/templates/story/story.php?storyId=89507530]Why ”>Why Risk Models Failed to Spot the Credit Crisis : NPR )</p>
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…market-sensitive risk models used by thousands of market participants work on the assumption that each user is the only person using them. This was not a bad approximation in 1952, when the intellectual underpinnings of these models were being developed at the Rand Corporation by Harry Markovitz and George Dantzig. This was a time of capital controls between countries, the segmentation of domestic financial markets and to get the historical frame right, it was the time of the Morris Minor with its top speed of 59mph.</p>
<p>In today’s flat world, market participants from Argentina to New Zealand have the same data on the risk, returns and correlation of financial instruments and use standard optimization models, which throw up the same portfolios to be favoured and those not to be. Market participants don’t stare helplessly at these results. They move into the favoured markets and out of the unfavoured. Enormous cross-border capital flows are unleashed. But under the weight of the herd, favoured instruments cannot remain undervalued, uncorrelated and low risk. They are transformed into the precise opposite.</p>
<p>When a market participant’s risk model detects a rise in risk in his portfolio, perhaps because of some random rise in volatility, and he tries to reduce his exposure, many others are trying to do the same thing at the same time with the same assets. A vicious cycle ensues of vertical price falls prompting further selling. Liquidity vanishes down a black hole. The degree to which this occurs is less to do with the precise financial instruments, but more with the depth of diversity of investor behaviour. Paradoxically, the observation of areas of safety in risk models, creates risks and the observation of risk, creates safety.</p>
<p>Quantum physicists will note a parallel with Heisenberg’s uncertainty principle.</p>
<p>Policy makers cannot claim to be surprised by all of this. The observation that market-sensitive risk models, increasingly integrated into financial supervision in a prescriptive manner, was going to send the herd off the cliff edge was made soon after the last round of crises*. Many policy officials in charge today, responded then that these warnings were too extreme to be considered realistic.</p>
<p>This brings us to the philosophical problem of the reliance of supervisors on bank risk models. The reason we regulate markets over and above normal corporate law is that from time to time markets fail and these failings have devastating consequences. If the purpose of regulation is to avoid market failures, we cannot use as the instruments of financial regulation, risk-models that rely on market prices, or any other instrument derived from market prices such as mark-to-market accounting. Market prices cannot save us from market failures. Yet, this is the thrust of modern financial regulation, which calls for more transparency on prices, more price-sensitive risk models and more price-sensitive prudential controls. These tools are like seat belts that stop working whenever you press hard on the accelerator.
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<p>[FT.com </a> | Willem Buiter’s Maverecon | Why Bank Risk Models Failed and the Implications for what Policy Makers Have to Do Now](<a href=“Financial Times ”>Financial Times )</p>
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The problem is that Wall Street and regulators relied on complex mathematical models that told financial institutions how much risk they were taking at any given time. Since the 1990s, risk management on Wall Street has been dominated by a model called “value at risk” (VaR). VaR attributes risk factors to every security and aggregates these factors across an entire portfolio, identifying those risks that cancel out. What’s left is “net” risk that is then considered in light of historical patterns. The model predicts with 99 percent probability that institutions cannot lose more than a certain amount of money. Institutions compare this “worst case” with their actual capital and, if the amount of capital is greater, sleep soundly at night. Regulators, knowing that the institutions used these models, also slept soundly. As long as capital was greater than the value at risk, institutions were considered sound – and there was no need for hands-on regulation.</p>
<p>Lurking behind the models, however, was a colossal conceptual error: the belief that risk is randomly distributed and that each event has no bearing on the next event in a sequence. This is typically explained with a coin-toss analogy. If you flip a coin and get “heads” and then do it again, the first heads has no bearing on whether the second toss will be heads or tails. It’s a common fallacy that if you get three heads in a row, there’s a better-than-even chance that the next toss will be tails. That’s simply not true. Each toss has a 50-50 chance of being heads or tails. Such systems are represented in the bell curve, which makes clear that events of the type we have witnessed lately are so statistically improbable as to be practically impossible. This is why markets are taken by surprise when they occur.</p>
<p>But what if markets are not like coin tosses? What if risk is not shaped like a bell curve? What if new events are profoundly affected by what went before?</p>
<p>Both natural and man-made systems are full of the kind of complexity in which minute changes at the start result in divergent and unpredictable outcomes. These systems are sometimes referred to as “chaotic,” but that’s a misnomer; chaos theory permits an understanding of dynamic processes. Chaotic systems can be steered toward more regular behavior by affecting a small number of variables. But beyond chaos lies complexity that truly is unpredictable and cannot be modeled with even the most powerful computers. Capital markets are an example of such complex dynamic systems…</p>
<p>The more enlightened among the value-at-risk practitioners understand that extreme events occur more frequently than their models predict. So they embellish their models with “fat tails” (upward bends on the wings of the bell curve) and model these tails on historical extremes such as the post-Sept. 11 market reaction. But complex systems are not confined to historical experience. Events of any size are possible, and limited only by the scale of the system itself. Since we have scaled the system to unprecedented size, we should expect catastrophes of unprecedented size as well. We’re in the middle of one such catastrophe, and complexity theory says it will get much worse.</p>
<p>Financial systems overall have emergent properties that are not conspicuous in their individual components and that traditional risk management does not account for. When it comes to the markets, the aggregate risk is far greater than the sum of the individual risks; this is something that Long-Term Capital Management did not understand in the 1990s and that Wall Street seems not to comprehend now. As long as Wall Street and regulators keep using the wrong paradigm, there’s no hope they will appreciate just how bad things can become. And the new paradigm of risk must be understood if we are to avoid lurching from one bank failure to the next.
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<p>[washingtonpost.com </a> - nation, world, technology and Washington area news and headlines](<a href=“http://washingtonpost.com %5Dwashingtonpost.com ”>http://washingtonpost.com )</p>
<p>I personally believe in the Black Swan principle, which holds that not only do supposedly ‘improbable’ events occur far more often than we might expect, but that these events often times have large impacts on the observed system and in ways that models cannot predict. </p>
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In the breakdown of our current financial system, which many deemed impossible or at least highly improbable, I believe we have witnessed the appearance of a black swan. The term black swan comes from the ancient Western conception that 'all swans are white.’ In that context, a black swan was a metaphor for something that could not exist. (Source: [Wikipedia](<a href=“http://www.wikipedia.org %5DWikipedia%5B/url%5D”>http://www.wikipedia.org )</a>.)</p>
<p>In Nassim Taleb’s book The Black Swan: The Impact of the Highly Improbable, he discusses how randomness and uncertainty are much more common than investors would like to admit. In our financial markets, what people perceive to be rare and improbable events do occur. Some examples of these are the stock market crash of 1987, the terrorist attacks on September 11, 2001, and the recent meltdown of our financial system. Yet investors tend to fight the acceptance of this reality. As a result, investors tend to make decisions based on certain assumptions. When markets move outside the realm of these assumptions many are confused, scared and panicked. This is because the reality of investing is much more complicated and unpredictable than many are willing to accept. Opportunities and dangers appear when we least expect them.</p>
<p>Therefore we must know and expect that any portfolio, even those considered to be the safest, will at some point experience a series of very bad returns. More importantly, we must accept that this series of bad returns is unavoidable and not a mark of failure. So with that in mind, even if you hold a portfolio of the safest assets in the world (US Treasuries, ITE) you will at some point see a loss on paper of your investment. In the last 82 years, IA US Intermediate Treasury Index has dropped as much as 6.50% in one month.</p>
<p>Most investors construct portfolios with a set of rules that hopefully allow them to achieve their investment goals under normal circumstances. However, investors must understand, study and appreciate abnormal events. Under these abnormal circumstances even passive investors must change their strategy to actively identify, avoid and adjust to game-changing events. A game-changing event is an event that would permanently change the rules that we use to manage our portfolios. The market dropping 20% in one day is not a game-changing event. In contrast, a permanent ban on short selling would be an example of a game-changing event.</p>
<p>One recent game-changing event my firm encountered was the selling of BearLinx Alerian MLP Select Index ETN (BSR). Once we identified that Bear Stearns, which backed this exchange traded note “ETN”, was at risk of going under, we sold the ETN. On March 17th Bear Stearns was acquired. Once JP Morgan Chase (JPM) announced that it would honor Bear Stearns debts we were able to buy back the ETN and continue with our strategy. We bought it to track the Alerian MLP Index. While we were willing to accept the credit risk inherent in an ETN, we were not investing in BSR to take on the credit risk of a company that might go bankrupt. As soon as we identified that this game-changing risk was present, it was time to exit the investment. While we were able to identify and manage this event, this will not always be the case.</p>
<p>It is true that over long periods of time investors have fairly accurately managed risk and return through asset allocation. I personally believe that we can effectively manage many investment risks most of the time, but not all of the time. Unfortunately and unavoidably, the asset class assumptions that we find relevant to average market situations are less relevant to irregular situations. Does this mean investors should drastically change their long-term strategy when the irregular situations occur? I believe the answer is only if the situation is deemed to be game-changing.
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<p>[System</a> down for maintenance](<a href=“http://seekingalpha.com/article/98669-current-financial-crisis-is-a-black-swan]System ”>http://seekingalpha.com/article/98669-current-financial-crisis-is-a-black-swan )</p>
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Last August, The Wall Street Journal published a statement by one Matthew Rothman, financial
<p>The theories Mr Rothman was using to produce his odds of these events were “Nobel-crowned” methods
<p>MPT produces measures such as “sigmas”, “betas”, “Sharpe ratios”, “correlation”, “value at risk”, “optimal
<p>I was a trader and risk manager for almost 20 years (before experiencing battle fatigue). There is no way
<p>Academic economists are no more self-serving than other professions. You should blame those in the real
<p>Then, in 1997, the Royal Swedish Academy of Sciences awarded the prize to Robert Merton and Myron
<p>Dynamic hedging assumes no jumps – it fails miserably in all markets and did so catastrophically in 1987
<p>Later, Robert Engle received the prize for “Arch”, a complicated method of prediction of volatility that does
<p>The environment in financial economics is reminiscent of medieval medicine, which refused to incorporate
<p>But how did financial economics take on the appearance of a science? Not by experiments (perhaps the
<p>Every time I have questioned these methods I have been abruptly countered with: “they have the Nobel”,
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<p><a href=“http://www.fooledbyrandomness.com/FT-Nobel.pdf[/url] ”>http://www.fooledbyrandomness.com/FT-Nobel.pdf</a></p> ;