Misbehavior of Market | 失控的市場
“Misbehavior of Markets: A Fractal View of Risk, Ruin, and Reward” is a book co-authored by Benoît Mandelbrot and Richard L. Hudson. Benoît Mandelbrot is renowned as the father of fractal theory.
This book succinctly summarizes its core argument: modern financial theory has flaws that fail to accurately reflect the complexity of markets. Mandelbrot proposes a market analysis method based on fractal theory, arguing that price changes in markets are not random but exhibit complex fractal patterns akin to coastlines or ferns. This fractal model indicates that markets exhibit long-range dependence and that price volatility can produce aggregation effects, leading to risks that are far greater than traditional theories suggest. Ultimately, Mandelbrot’s perspective challenges conventional financial theories and asserts that using fractal models can more effectively predict market volatility, construct portfolios, assess option pricing, and manage risks.
Why Market Behavior Does Not Align with Traditional Financial Theory Predictions
Traditional financial theory predicts that prices will randomly fluctuate within a “normal” range. However, price changes are not random, and the “normal” range fails to encompass all price fluctuations. This defect in traditional financial theory has resulted in severe vulnerabilities within the global financial system.
Moreover, traditional financial theory does not adequately capture the full scope of market risk. For instance, it holds that the average risk of a stock is not as high as suggested by the stock premium. However, phenomena such as scale effects and long-range dependence indicate that market risks are far greater than traditional models assume. Due to the scale effect, the probability of a stock rising from 1 to 10 units is the same as from 10 to 100 units, suggesting that stock premiums merely serve as reasonable compensation for high risk.
Additionally, traditional financial theory assumes that market time flows at the same speed for everyone. However, price movements can exhibit scale effects over time; a day’s trading chart can resemble that of a week, month, or even a decade. Thus, market time can expand and contract.
Traditional financial theory also assumes that price changes are random and unpredictable, independent of one another, and follow a normal bell curve distribution. However, price changes are neither independent nor randomly distributed. Large price fluctuations often trigger further large fluctuations, while small fluctuations lead to more small ones. In other words, volatility tends to cluster.
Ultimately, the foundations of traditional financial theory are weak, rendering it incapable of accurately predicting market behavior. It fails to consider the complexity and non-linear characteristics of the market, such as scale effects, long-range dependence, and volatility clustering.
Mandelbrot’s Views on Financial Market Operations
Mandelbrot believes that the operation of financial markets differs fundamentally from the views held by traditional financial theory. He sees the market as inherently turbulent, filled with risks and deceptive in nature.
He likens the market to a turbulent ocean, characterized by complex phenomena such as whirlpools, currents, and tides that interact with one another. Like the ocean, the market exhibits “scale invariance,” meaning that the magnitude and frequency of price fluctuations are not constant; sometimes they are dramatic, and at other times relatively calm. Additionally, the market shows long-range dependence, where past events influence present and future market conditions.
Characteristics of Price Volatility
Mandelbrot opposes the traditional financial theory that prices follow a normal distribution. He asserts that price volatility is not random and unpredictable but has the following characteristics:
- Discontinuous Price Changes: Prices often experience jump-like changes rather than slow, stable transitions.
- Volatility Clustering: Large price fluctuations tend to be followed by more large fluctuations, while small fluctuations lead to more small fluctuations.
- Long-Range Dependence: Past price movements affect future price movements.
Universal Market Patterns
Mandelbrot posits that all markets, regardless of time or location, follow the same rules. He employs fractal geometry to study these patterns, which remain consistent even when spatial or temporal scales change.
The Deceptiveness of Markets
Mandelbrot points out that people tend to seek patterns in the market, and market analysts often cater to this demand by attempting to explain these patterns. However, these patterns are frequently products of randomness, and attributing excessive meaning to them is baseless.
The Inevitability of Market Bubbles
Due to price scale invariance, market bubbles are an inevitable phenomenon. Once significant price volatility occurs, it is likely to trigger even greater volatility, leading to the formation of bubbles.
In conclude,
Mandelbrot views the financial market as a complex, turbulent, and deceptive system. Traditional financial theory oversimplifies market complexity and fails to accurately describe how markets operate. He advocates for the use of fractal geometry and multifractal models for market analysis, as these methods better capture the non-linear and irregular characteristics of the market.
Predictable Characteristics of Financial Markets: Volatility
While Mandelbrot believes that price itself is difficult to predict, he asserts that price volatility can be forecasted. Traditional financial theory holds that price fluctuations are random and unpredictable, but Mandelbrot notes that large price changes are typically followed by more large fluctuations, while small fluctuations lead to more small fluctuations. In other words, volatility clusters.
Mandelbrot suggests that predicting market volatility is a more feasible approach than attempting to predict prices. He argues that we can emulate meteorologists who predict weather patterns to forecast market volatility.
Summary
Mandelbrot’s fractal theory offers us a new perspective for reconsidering the essence of market behavior. As the limitations of traditional financial theory become increasingly evident, a deeper understanding of market complexity, non-linear characteristics, and risk management becomes crucial. The price volatility characteristics revealed by Mandelbrot, such as discontinuity, volatility clustering, and long-range dependence, challenge previous assumptions.
《市場的失控行為：風險、毀滅與報酬的分形觀》一書是由Benoît Mandelbrot 和 Richard L. Hudson 合著，Benoît Mandelbrot是當代著名的分形理論之父，想了解更多關於分形可以到這個連結。
這本書以簡潔的概括，介紹了核心論點： 現代金融理論存在缺陷，無法真實反映市場的複雜性。 Mandelbrot 提出了一種基於分形理論的市場分析方法，認為市場的價格變化並非隨機的，而是呈現出類似海岸線或蕨類植物的複雜分形圖案。 這種分形模式顯示出市場存在著長期依賴性，價格波動會產生聚合效應，因此風險程度遠高於傳統理論的估計。 最終Mandelbrot 的觀點挑戰了傳統金融理論，並指出採用分形模型能夠更有效地預測市場波動，建立投資組合，評估期權價格和管理風險。
金融市場行為為何不符合傳統金融理論的預測？
傳統金融理論預測，價格會在「常態」範圍內隨機變動。但價格變動並非隨機，而且「常態」範圍也不足以涵蓋所有價格波動。傳統金融理論的這個缺陷，導致全球金融體系存在嚴重的弱點。
傳統金融理論未能充分掌握市場風險的全貌。例如，傳統金融理論認為，股票的平均風險並不如股票溢價所暗示的那麼高。然而，規模效應和長期依存性這兩種現象，使得市場的風險遠高於傳統模型的假設。由於市場的規模效應，股票從 1 元漲到 10 元，和從 10 元漲到 100 元的機率是相同的。因此，股票溢價只是對高風險的合理補償。
傳統金融理論認為市場時間對每個人來說都以相同速度流逝。然而，價格會隨著時間推移而產生規模效應。一天的交易圖表看起來就像一週、一個月或十年的圖表。 因此，市場時間會擴張和收縮。
傳統金融理論認為價格變動是隨機且不可預測的，彼此獨立且呈常態鐘形分佈。然而，價格變動並非彼此獨立，也不呈隨機分佈。大型價格波動往往會引發其他大型波動，而小型波動則會引發其他小型波動。換句話說，波動性會聚集。
最終，傳統金融理論的基礎薄弱，無法準確預測市場行為。 傳統金融理論沒有考慮到市場的複雜性和非線性特徵，例如規模效應、長期依存性和波動性聚集等現象。
Mandelbrot對金融市場運作的看法
Mandelbrot認為金融市場的運作方式與傳統金融理論的觀點截然不同。他認為市場本質上是動盪不安、充滿風險且具有欺騙性的。
市場如同波濤洶湧的大海：
Mandelbrot將市場比喻為大海，具有湍流、渦流、水流、河道、順流和逆流等複雜現象，彼此相互影響。 市場也像海洋一樣具有「尺度不變性」，價格波動的幅度和頻率並不恆定，有時波動劇烈，有時則相對平靜。 此外，市場也存在長期依存性，過去的事件會對現在和未來的市場產生影響。
價格波動的特性：
Mandelbrot反對傳統金融理論認為價格呈常態分佈的觀點，他認為價格波動並非隨機且不可預測，而是具有以下特性 :
- 價格變動不連續： 價格經常會出現跳躍式的變動，而非緩慢而穩定的變化。
- 波動性聚集： 大型價格波動容易引發其他大型波動，而小型波動則容易引發其他小型波動。
- 長期依存性： 過去的價格變動會影響未來的價格變動。
市場的普遍規律：
Mandelbrot認為所有市場，不論時間或地點，都遵循著相同的規律。他利用碎形幾何來研究這些規律，這些規律即使在空間或時間尺度發生變化時也保持不變。
市場的欺騙性：
Mandelbrot指出，人們傾向於在市場中尋找模式，而市場分析師也經常迎合這種需求，試圖解釋這些模式。 然而，這些模式往往只是隨機現象的產物，賦予它們過多意義是沒有根據的。
市場泡沫的必然性：
由於價格的尺度不變性，市場泡沫是不可避免的現象。一旦出現大幅度的價格波動，就很有可能引發更大的波動，從而形成泡沫。
總而言之，Mandelbrot認為金融市場是一個複雜、動盪且具有欺騙性的系統。 傳統金融理論過於簡化市場的複雜性，無法準確描述市場的運作方式。 他主張使用碎形幾何和多重碎形模型來分析市場，因為這些方法更能捕捉市場的非線性和不規則特性。
Mandelbrot認為可以用來預測金融市場的特性：波動性
雖然Mandelbrot認為價格本身難以預測，但他認為 價格的波動性是可以預測。 傳統金融理論認為價格波動是隨機且不可預測的，但Mandelbrot現大型價格波動後通常伴隨著更多大型波動，而小型波動後也會有更多小型波動。 換句話說，波動性會聚集。
Mandelbrot認為，與試圖預測價格相比，預測市場波動性是更為可行的做法。他主張可以仿效氣象學家預測天氣的方式來預測市場波動性。
小結
Mandelbrot的分形理論為我們提供了一種新的視角，讓我們重新思考市場行為的本質。隨著傳統金融理論的局限性日益顯現，對於市場複雜性、非線性特徵及風險管理的深入理解變得尤為重要。Mandelbrot所揭示的價格波動特性，如不連續性、波動性聚集和長期依存性，挑戰了過去的假設。
