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 Customer Reviews
Tilting at windmills, 02 Jun 2007
In this tome Mr Mandelbrot lambasts the previous century's inadequate financial models but seems unwilling to admit that the field has moved on somewhat, and unable to offer a practical model of his own.
Mr Mandelbrot shows how Bachelierian models fail to account for disastrous market drops which ruined many investors. He rubbishes two conventional assumptions: that each price move is independent of another and that their magnitude follows a Normal distribution. Skillfully constructed charts make plain the reality that a large market move is likely to be followed by another. More charts show just how badly market data fits to a Normal distribution: by this measure dozens of trading days in the 20th century were so unlikely not even one should have occurred in the lifetime of the universe.
The author suggests we discard such woefully unrealistic theory and start again, taking fractals as our base. In a display humility atypical of the rest of the book Mr Mandelbrot admits to having no way to calculate price and risk in his proposed model, or even calibrate its parameters "Alpha" and "H" to the real world.
The tragedy of this foray into fractal finance is in its pointlessness. What made 1960s financial models so unrealistic was the assumption of unchanging volatility. By late 90s anyone with sufficient computing power could drop this assumption and include real "volatile volatility" in their models. In modern theory, October 1987 was not a 22-sigma "not in the lifetime of the universe" event. It was a spike in the volatility process, as the models predict will happen from time to time.
In fairness, the book offers many insights into what drives the markets, the trouble with fundamental valuation, rationality of market agents, flow of information, and more. I could recommend reading it for those insights alone.
...with tangerine trees and marmalade skies..., 08 Jul 2006
Orthodox economics is very formal using complex models to predict future behaviour. Most economists, like meteorologists, are not held accountable for their predictions.
Within the very wide field of economics there are many conflicting views about the nature of economics and there is much in the way of interesting work going on out there and I would cite the contributions of the Austrian school and the evolutionary school and especially point to the very accessible work of Paul Ormerod who give somewhat different views to those of the standard model.
This book is not aimed at those practitioners of economics or indeed the professionals of the City of London or Wall Street. To my mind, as an interested observer, Mandelbrot and Hudson are doing all of us a service in illuminating the gaps in economic theory that underpins the financial industry. John Maynard Keynes, who's General Theory of Employment, Interest and Money (1936)can be said to lie at the heart of much of contemporary economic theory, once famously compared the financial services industry to gambling, also made his fortune on the stock market.
The book methodically disects each of the pillars of contemporary financial theory and exposes it's weakness then introduces some basic fractal geometry ideas to exhibit their apparent ly better predictive use. As someone who favours the approach of ideas of chaos theory into the economics brew I tend to be more open to the approach that Mandelbrot uses but the proof of the pudding, as we say in England, lies in the eating and this populist text is certainly not the place for complex technical proofs or highly mathematical analysis. It is a difficult path to take but for the purposes for which this book is intended, which I believe is aimed at the educated investor or someone without an economics or financial background, it is about right.
I found the book both accessible and lucid. There are areas with which I would have wished for a more techical exposition but this is something that I will take up when I delve further into this subject matter.
There are many interesting ideas here and I suspect that there are many in the financial services community who are looking into these in greater detail or even have already absorbed them into their toolkit. Given the competitive nature of the financial markets I suspect that this knowledge will quickly be dispesed throughout the community.
All in all this is a nice easy read which will prompt further thought and study upon it's contents. My only, minor reservation, which prevents me awarding five stars is that I think a non-technical appendix, in keeping with the rest of the book, about the basic precepts of fractal geometry would have been helpful for the lay reader.
Well worth a look.
Necessary evil, 16 May 2006
If you invited Benoit Mandelbrot to your party, he'd be the geeky guy dissing people's illogical clothing, drinking too much punch, testing the aerodynamics of different canapes, and pouring food colouring in the pool. In other words, he's a risk and he won't get any girls, but on a balance of probabilities, the party Mandelbrot was at will be the one people will wish they'd been at.
This book is a rant, reflecting the death of editing in favour of celebrity authorship. So it's repetitive. It's also light on theory, and it repeats itself. But that doesn't mean it's wrong. Mandelbrot makes the case early on that the behaviour of market prices, or of any variable not constrained by physics, are not normally distributed. He then goes on to claim that artificial systems are non-Gaussian, putting them outside the reach of statistics - and by extension, outside the reach of CAPM, Black-Scholes, VAR, and GARCH. He proposes power law distributions as an alternative. He's probably right, but he never demonstrates this claim, and the alternative he suggests - multifractals - is, by his own admission, not very useful.
He comprehensively demolishes the random walk model, claiming to have demonstrated that volatility clusters, and that there is memory in all markets. This may be true, but it will have the effect of encouraging snake oil salesmen (see below).
More pertinent and scary is that Mandelbrot does show that the exponents needed to model power law distributions for different markets or instruments are so diverse and intractable as to make general market models meaningless. He does not explain how multifractals address this. He also points to the simple arithmetic inadequacy of using closing prices in hindcasting exercises, which is equally scary for anyone who actually tests their models. He spits on technical analysts, who don't. For this he gets an extra star.
Nassim Taleb is probably more eloquent on the subject of wild randomness, but he's too urbane to punk your party. Mandelbrot is trouble, and if you're in finance, he's coming your way.
A solid critique to Modern Finance Theory, 21 Oct 2005
Benoit Mandelbrot may sometimes write too much about himself, but his critique of the Modern Finance Theory is very sharp. After exposing why some basic assumptions underlying the Modern Finance Theory and, more importantly, its applications in financial products, are totally nonscientific, Mandelbrot explores his way out of the chaos. Some parts of the book may be redundant, but the insights are bright indeed. After reading the book, one wonders why so much money is invested using evidently mistaken theories. Even many insiders might have an interesting read, as the financial world is well known for its herdfollowers. Mandelbrot does not offer a new Theory and those looking for chaos theory to so solve the problems may be disappointed. However, his final suggestions need a follow-up from the financial world. Very recomendable for people in the money business.
Best finance layman's book Iýve ever read!!, 12 Jul 2005
Mandelbrot, much like Mr. Howard, "say it as it is". Modern finance theory simply does not fit the facts. This is a grave accusation but Mandelbrot makes such a good case against modern finance that one is left wondering upon completing the book how the workhorses of academic ink are still standing! A truly fascinating book that at best will lead you into seriously questioning what you have learned at uni and at worst will enhance your historical understanding of financial theory. Written in eloquent, "user-friendly" manner, this book advocates a completely fresh look at the financial world through the lenses of fractal geometry. This means that the reader will encounter terms like "fractional Brownian motion set in multifractal time", which may sound more like rocket science to some than finance, but Mandelbrot and Hudson do a magnificent job in explaining tough terms in everyday English (not to mention the pictorial essays). In a nutshell, this book is thought-provoking, well-written and personally, i think that for the price that it is selling a true bargain.
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Customer Reviews
Tilting at windmills, 02 Jun 2007
In this tome Mr Mandelbrot lambasts the previous century's inadequate financial models but seems unwilling to admit that the field has moved on somewhat, and unable to offer a practical model of his own.
Mr Mandelbrot shows how Bachelierian models fail to account for disastrous market drops which ruined many investors. He rubbishes two conventional assumptions: that each price move is independent of another and that their magnitude follows a Normal distribution. Skillfully constructed charts make plain the reality that a large market move is likely to be followed by another. More charts show just how badly market data fits to a Normal distribution: by this measure dozens of trading days in the 20th century were so unlikely not even one should have occurred in the lifetime of the universe.
The author suggests we discard such woefully unrealistic theory and start again, taking fractals as our base. In a display humility atypical of the rest of the book Mr Mandelbrot admits to having no way to calculate price and risk in his proposed model, or even calibrate its parameters "Alpha" and "H" to the real world.
The tragedy of this foray into fractal finance is in its pointlessness. What made 1960s financial models so unrealistic was the assumption of unchanging volatility. By late 90s anyone with sufficient computing power could drop this assumption and include real "volatile volatility" in their models. In modern theory, October 1987 was not a 22-sigma "not in the lifetime of the universe" event. It was a spike in the volatility process, as the models predict will happen from time to time.
In fairness, the book offers many insights into what drives the markets, the trouble with fundamental valuation, rationality of market agents, flow of information, and more. I could recommend reading it for those insights alone.
...with tangerine trees and marmalade skies..., 08 Jul 2006
Orthodox economics is very formal using complex models to predict future behaviour. Most economists, like meteorologists, are not held accountable for their predictions.
Within the very wide field of economics there are many conflicting views about the nature of economics and there is much in the way of interesting work going on out there and I would cite the contributions of the Austrian school and the evolutionary school and especially point to the very accessible work of Paul Ormerod who give somewhat different views to those of the standard model.
This book is not aimed at those practitioners of economics or indeed the professionals of the City of London or Wall Street. To my mind, as an interested observer, Mandelbrot and Hudson are doing all of us a service in illuminating the gaps in economic theory that underpins the financial industry. John Maynard Keynes, who's General Theory of Employment, Interest and Money (1936)can be said to lie at the heart of much of contemporary economic theory, once famously compared the financial services industry to gambling, also made his fortune on the stock market.
The book methodically disects each of the pillars of contemporary financial theory and exposes it's weakness then introduces some basic fractal geometry ideas to exhibit their apparent ly better predictive use. As someone who favours the approach of ideas of chaos theory into the economics brew I tend to be more open to the approach that Mandelbrot uses but the proof of the pudding, as we say in England, lies in the eating and this populist text is certainly not the place for complex technical proofs or highly mathematical analysis. It is a difficult path to take but for the purposes for which this book is intended, which I believe is aimed at the educated investor or someone without an economics or financial background, it is about right.
I found the book both accessible and lucid. There are areas with which I would have wished for a more techical exposition but this is something that I will take up when I delve further into this subject matter.
There are many interesting ideas here and I suspect that there are many in the financial services community who are looking into these in greater detail or even have already absorbed them into their toolkit. Given the competitive nature of the financial markets I suspect that this knowledge will quickly be dispesed throughout the community.
All in all this is a nice easy read which will prompt further thought and study upon it's contents. My only, minor reservation, which prevents me awarding five stars is that I think a non-technical appendix, in keeping with the rest of the book, about the basic precepts of fractal geometry would have been helpful for the lay reader.
Well worth a look.
Necessary evil, 16 May 2006
If you invited Benoit Mandelbrot to your party, he'd be the geeky guy dissing people's illogical clothing, drinking too much punch, testing the aerodynamics of different canapes, and pouring food colouring in the pool. In other words, he's a risk and he won't get any girls, but on a balance of probabilities, the party Mandelbrot was at will be the one people will wish they'd been at.
This book is a rant, reflecting the death of editing in favour of celebrity authorship. So it's repetitive. It's also light on theory, and it repeats itself. But that doesn't mean it's wrong. Mandelbrot makes the case early on that the behaviour of market prices, or of any variable not constrained by physics, are not normally distributed. He then goes on to claim that artificial systems are non-Gaussian, putting them outside the reach of statistics - and by extension, outside the reach of CAPM, Black-Scholes, VAR, and GARCH. He proposes power law distributions as an alternative. He's probably right, but he never demonstrates this claim, and the alternative he suggests - multifractals - is, by his own admission, not very useful.
He comprehensively demolishes the random walk model, claiming to have demonstrated that volatility clusters, and that there is memory in all markets. This may be true, but it will have the effect of encouraging snake oil salesmen (see below).
More pertinent and scary is that Mandelbrot does show that the exponents needed to model power law distributions for different markets or instruments are so diverse and intractable as to make general market models meaningless. He does not explain how multifractals address this. He also points to the simple arithmetic inadequacy of using closing prices in hindcasting exercises, which is equally scary for anyone who actually tests their models. He spits on technical analysts, who don't. For this he gets an extra star.
Nassim Taleb is probably more eloquent on the subject of wild randomness, but he's too urbane to punk your party. Mandelbrot is trouble, and if you're in finance, he's coming your way.
A solid critique to Modern Finance Theory, 21 Oct 2005
Benoit Mandelbrot may sometimes write too much about himself, but his critique of the Modern Finance Theory is very sharp. After exposing why some basic assumptions underlying the Modern Finance Theory and, more importantly, its applications in financial products, are totally nonscientific, Mandelbrot explores his way out of the chaos. Some parts of the book may be redundant, but the insights are bright indeed. After reading the book, one wonders why so much money is invested using evidently mistaken theories. Even many insiders might have an interesting read, as the financial world is well known for its herdfollowers. Mandelbrot does not offer a new Theory and those looking for chaos theory to so solve the problems may be disappointed. However, his final suggestions need a follow-up from the financial world. Very recomendable for people in the money business.
Best finance layman's book Iýve ever read!!, 12 Jul 2005
Mandelbrot, much like Mr. Howard, "say it as it is". Modern finance theory simply does not fit the facts. This is a grave accusation but Mandelbrot makes such a good case against modern finance that one is left wondering upon completing the book how the workhorses of academic ink are still standing! A truly fascinating book that at best will lead you into seriously questioning what you have learned at uni and at worst will enhance your historical understanding of financial theory. Written in eloquent, "user-friendly" manner, this book advocates a completely fresh look at the financial world through the lenses of fractal geometry. This means that the reader will encounter terms like "fractional Brownian motion set in multifractal time", which may sound more like rocket science to some than finance, but Mandelbrot and Hudson do a magnificent job in explaining tough terms in everyday English (not to mention the pictorial essays). In a nutshell, this book is thought-provoking, well-written and personally, i think that for the price that it is selling a true bargain.
A WORK OF SPECTACULAR INSIGHT, 08 May 2008
Shapes and Forms' paper and Qabalistic based Hermetic design against this work, there is no comparison. Daud Sutton is a born scholar who manages to introduce the dazzling complexity and subtlety of Islamic lineal shapes and forms with consummate ease. One of my favourite source works. --Steven Ashe
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Customer Reviews
Tilting at windmills, 02 Jun 2007
In this tome Mr Mandelbrot lambasts the previous century's inadequate financial models but seems unwilling to admit that the field has moved on somewhat, and unable to offer a practical model of his own.
Mr Mandelbrot shows how Bachelierian models fail to account for disastrous market drops which ruined many investors. He rubbishes two conventional assumptions: that each price move is independent of another and that their magnitude follows a Normal distribution. Skillfully constructed charts make plain the reality that a large market move is likely to be followed by another. More charts show just how badly market data fits to a Normal distribution: by this measure dozens of trading days in the 20th century were so unlikely not even one should have occurred in the lifetime of the universe.
The author suggests we discard such woefully unrealistic theory and start again, taking fractals as our base. In a display humility atypical of the rest of the book Mr Mandelbrot admits to having no way to calculate price and risk in his proposed model, or even calibrate its parameters "Alpha" and "H" to the real world.
The tragedy of this foray into fractal finance is in its pointlessness. What made 1960s financial models so unrealistic was the assumption of unchanging volatility. By late 90s anyone with sufficient computing power could drop this assumption and include real "volatile volatility" in their models. In modern theory, October 1987 was not a 22-sigma "not in the lifetime of the universe" event. It was a spike in the volatility process, as the models predict will happen from time to time.
In fairness, the book offers many insights into what drives the markets, the trouble with fundamental valuation, rationality of market agents, flow of information, and more. I could recommend reading it for those insights alone.
...with tangerine trees and marmalade skies..., 08 Jul 2006
Orthodox economics is very formal using complex models to predict future behaviour. Most economists, like meteorologists, are not held accountable for their predictions.
Within the very wide field of economics there are many conflicting views about the nature of economics and there is much in the way of interesting work going on out there and I would cite the contributions of the Austrian school and the evolutionary school and especially point to the very accessible work of Paul Ormerod who give somewhat different views to those of the standard model.
This book is not aimed at those practitioners of economics or indeed the professionals of the City of London or Wall Street. To my mind, as an interested observer, Mandelbrot and Hudson are doing all of us a service in illuminating the gaps in economic theory that underpins the financial industry. John Maynard Keynes, who's General Theory of Employment, Interest and Money (1936)can be said to lie at the heart of much of contemporary economic theory, once famously compared the financial services industry to gambling, also made his fortune on the stock market.
The book methodically disects each of the pillars of contemporary financial theory and exposes it's weakness then introduces some basic fractal geometry ideas to exhibit their apparent ly better predictive use. As someone who favours the approach of ideas of chaos theory into the economics brew I tend to be more open to the approach that Mandelbrot uses but the proof of the pudding, as we say in England, lies in the eating and this populist text is certainly not the place for complex technical proofs or highly mathematical analysis. It is a difficult path to take but for the purposes for which this book is intended, which I believe is aimed at the educated investor or someone without an economics or financial background, it is about right.
I found the book both accessible and lucid. There are areas with which I would have wished for a more techical exposition but this is something that I will take up when I delve further into this subject matter.
There are many interesting ideas here and I suspect that there are many in the financial services community who are looking into these in greater detail or even have already absorbed them into their toolkit. Given the competitive nature of the financial markets I suspect that this knowledge will quickly be dispesed throughout the community.
All in all this is a nice easy read which will prompt further thought and study upon it's contents. My only, minor reservation, which prevents me awarding five stars is that I think a non-technical appendix, in keeping with the rest of the book, about the basic precepts of fractal geometry would have been helpful for the lay reader.
Well worth a look.
Necessary evil, 16 May 2006
If you invited Benoit Mandelbrot to your party, he'd be the geeky guy dissing people's illogical clothing, drinking too much punch, testing the aerodynamics of different canapes, and pouring food colouring in the pool. In other words, he's a risk and he won't get any girls, but on a balance of probabilities, the party Mandelbrot was at will be the one people will wish they'd been at.
This book is a rant, reflecting the death of editing in favour of celebrity authorship. So it's repetitive. It's also light on theory, and it repeats itself. But that doesn't mean it's wrong. Mandelbrot makes the case early on that the behaviour of market prices, or of any variable not constrained by physics, are not normally distributed. He then goes on to claim that artificial systems are non-Gaussian, putting them outside the reach of statistics - and by extension, outside the reach of CAPM, Black-Scholes, VAR, and GARCH. He proposes power law distributions as an alternative. He's probably right, but he never demonstrates this claim, and the alternative he suggests - multifractals - is, by his own admission, not very useful.
He comprehensively demolishes the random walk model, claiming to have demonstrated that volatility clusters, and that there is memory in all markets. This may be true, but it will have the effect of encouraging snake oil salesmen (see below).
More pertinent and scary is that Mandelbrot does show that the exponents needed to model power law distributions for different markets or instruments are so diverse and intractable as to make general market models meaningless. He does not explain how multifractals address this. He also points to the simple arithmetic inadequacy of using closing prices in hindcasting exercises, which is equally scary for anyone who actually tests their models. He spits on technical analysts, who don't. For this he gets an extra star.
Nassim Taleb is probably more eloquent on the subject of wild randomness, but he's too urbane to punk your party. Mandelbrot is trouble, and if you're in finance, he's coming your way.
A solid critique to Modern Finance Theory, 21 Oct 2005
Benoit Mandelbrot may sometimes write too much about himself, but his critique of the Modern Finance Theory is very sharp. After exposing why some basic assumptions underlying the Modern Finance Theory and, more importantly, its applications in financial products, are totally nonscientific, Mandelbrot explores his way out of the chaos. Some parts of the book may be redundant, but the insights are bright indeed. After reading the book, one wonders why so much money is invested using evidently mistaken theories. Even many insiders might have an interesting read, as the financial world is well known for its herdfollowers. Mandelbrot does not offer a new Theory and those looking for chaos theory to so solve the problems may be disappointed. However, his final suggestions need a follow-up from the financial world. Very recomendable for people in the money business.
Best finance layman's book Iýve ever read!!, 12 Jul 2005
Mandelbrot, much like Mr. Howard, "say it as it is". Modern finance theory simply does not fit the facts. This is a grave accusation but Mandelbrot makes such a good case against modern finance that one is left wondering upon completing the book how the workhorses of academic ink are still standing! A truly fascinating book that at best will lead you into seriously questioning what you have learned at uni and at worst will enhance your historical understanding of financial theory. Written in eloquent, "user-friendly" manner, this book advocates a completely fresh look at the financial world through the lenses of fractal geometry. This means that the reader will encounter terms like "fractional Brownian motion set in multifractal time", which may sound more like rocket science to some than finance, but Mandelbrot and Hudson do a magnificent job in explaining tough terms in everyday English (not to mention the pictorial essays). In a nutshell, this book is thought-provoking, well-written and personally, i think that for the price that it is selling a true bargain.
A WORK OF SPECTACULAR INSIGHT, 08 May 2008
Shapes and Forms' paper and Qabalistic based Hermetic design against this work, there is no comparison. Daud Sutton is a born scholar who manages to introduce the dazzling complexity and subtlety of Islamic lineal shapes and forms with consummate ease. One of my favourite source works. --Steven Ashe
Ian Stewart has done it again!, 29 Nov 2008
What more can I say?
Ian Stewart takes us on a journey through group theory to places you probably never considered, but in a completely fun and accessible manner. The historical tone of the book works really well, this book has inspired me to study galois theory in far greater depth.
A MUST for anybody with an interest in mathematics.
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Customer Reviews
Tilting at windmills, 02 Jun 2007
In this tome Mr Mandelbrot lambasts the previous century's inadequate financial models but seems unwilling to admit that the field has moved on somewhat, and unable to offer a practical model of his own.
Mr Mandelbrot shows how Bachelierian models fail to account for disastrous market drops which ruined many investors. He rubbishes two conventional assumptions: that each price move is independent of another and that their magnitude follows a Normal distribution. Skillfully constructed charts make plain the reality that a large market move is likely to be followed by another. More charts show just how badly market data fits to a Normal distribution: by this measure dozens of trading days in the 20th century were so unlikely not even one should have occurred in the lifetime of the universe.
The author suggests we discard such woefully unrealistic theory and start again, taking fractals as our base. In a display humility atypical of the rest of the book Mr Mandelbrot admits to having no way to calculate price and risk in his proposed model, or even calibrate its parameters "Alpha" and "H" to the real world.
The tragedy of this foray into fractal finance is in its pointlessness. What made 1960s financial models so unrealistic was the assumption of unchanging volatility. By late 90s anyone with sufficient computing power could drop this assumption and include real "volatile volatility" in their models. In modern theory, October 1987 was not a 22-sigma "not in the lifetime of the universe" event. It was a spike in the volatility process, as the models predict will happen from time to time.
In fairness, the book offers many insights into what drives the markets, the trouble with fundamental valuation, rationality of market agents, flow of information, and more. I could recommend reading it for those insights alone.
...with tangerine trees and marmalade skies..., 08 Jul 2006
Orthodox economics is very formal using complex models to predict future behaviour. Most economists, like meteorologists, are not held accountable for their predictions.
Within the very wide field of economics there are many conflicting views about the nature of economics and there is much in the way of interesting work going on out there and I would cite the contributions of the Austrian school and the evolutionary school and especially point to the very accessible work of Paul Ormerod who give somewhat different views to those of the standard model.
This book is not aimed at those practitioners of economics or indeed the professionals of the City of London or Wall Street. To my mind, as an interested observer, Mandelbrot and Hudson are doing all of us a service in illuminating the gaps in economic theory that underpins the financial industry. John Maynard Keynes, who's General Theory of Employment, Interest and Money (1936)can be said to lie at the heart of much of contemporary economic theory, once famously compared the financial services industry to gambling, also made his fortune on the stock market.
The book methodically disects each of the pillars of contemporary financial theory and exposes it's weakness then introduces some basic fractal geometry ideas to exhibit their apparent ly better predictive use. As someone who favours the approach of ideas of chaos theory into the economics brew I tend to be more open to the approach that Mandelbrot uses but the proof of the pudding, as we say in England, lies in the eating and this populist text is certainly not the place for complex technical proofs or highly mathematical analysis. It is a difficult path to take but for the purposes for which this book is intended, which I believe is aimed at the educated investor or someone without an economics or financial background, it is about right.
I found the book both accessible and lucid. There are areas with which I would have wished for a more techical exposition but this is something that I will take up when I delve further into this subject matter.
There are many interesting ideas here and I suspect that there are many in the financial services community who are looking into these in greater detail or even have already absorbed them into their toolkit. Given the competitive nature of the financial markets I suspect that this knowledge will quickly be dispesed throughout the community.
All in all this is a nice easy read which will prompt further thought and study upon it's contents. My only, minor reservation, which prevents me awarding five stars is that I think a non-technical appendix, in keeping with the rest of the book, about the basic precepts of fractal geometry would have been helpful for the lay reader.
Well worth a look.
Necessary evil, 16 May 2006
If you invited Benoit Mandelbrot to your party, he'd be the geeky guy dissing people's illogical clothing, drinking too much punch, testing the aerodynamics of different canapes, and pouring food colouring in the pool. In other words, he's a risk and he won't get any girls, but on a balance of probabilities, the party Mandelbrot was at will be the one people will wish they'd been at.
This book is a rant, reflecting the death of editing in favour of celebrity authorship. So it's repetitive. It's also light on theory, and it repeats itself. But that doesn't mean it's wrong. Mandelbrot makes the case early on that the behaviour of market prices, or of any variable not constrained by physics, are not normally distributed. He then goes on to claim that artificial systems are non-Gaussian, putting them outside the reach of statistics - and by extension, outside the reach of CAPM, Black-Scholes, VAR, and GARCH. He proposes power law distributions as an alternative. He's probably right, but he never demonstrates this claim, and the alternative he suggests - multifractals - is, by his own admission, not very useful.
He comprehensively demolishes the random walk model, claiming to have demonstrated that volatility clusters, and that there is memory in all markets. This may be true, but it will have the effect of encouraging snake oil salesmen (see below).
More pertinent and scary is that Mandelbrot does show that the exponents needed to model power law distributions for different markets or instruments are so diverse and intractable as to make general market models meaningless. He does not explain how multifractals address this. He also points to the simple arithmetic inadequacy of using closing prices in hindcasting exercises, which is equally scary for anyone who actually tests their models. He spits on technical analysts, who don't. For this he gets an extra star.
Nassim Taleb is probably more eloquent on the subject of wild randomness, but he's too urbane to punk your party. Mandelbrot is trouble, and if you're in finance, he's coming your way.
A solid critique to Modern Finance Theory, 21 Oct 2005
Benoit Mandelbrot may sometimes write too much about himself, but his critique of the Modern Finance Theory is very sharp. After exposing why some basic assumptions underlying the Modern Finance Theory and, more importantly, its applications in financial products, are totally nonscientific, Mandelbrot explores his way out of the chaos. Some parts of the book may be redundant, but the insights are bright indeed. After reading the book, one wonders why so much money is invested using evidently mistaken theories. Even many insiders might have an interesting read, as the financial world is well known for its herdfollowers. Mandelbrot does not offer a new Theory and those looking for chaos theory to so solve the problems may be disappointed. However, his final suggestions need a follow-up from the financial world. Very recomendable for people in the money business.
Best finance layman's book Iýve ever read!!, 12 Jul 2005
Mandelbrot, much like Mr. Howard, "say it as it is". Modern finance theory simply does not fit the facts. This is a grave accusation but Mandelbrot makes such a good case against modern finance that one is left wondering upon completing the book how the workhorses of academic ink are still standing! A truly fascinating book that at best will lead you into seriously questioning what you have learned at uni and at worst will enhance your historical understanding of financial theory. Written in eloquent, "user-friendly" manner, this book advocates a completely fresh look at the financial world through the lenses of fractal geometry. This means that the reader will encounter terms like "fractional Brownian motion set in multifractal time", which may sound more like rocket science to some than finance, but Mandelbrot and Hudson do a magnificent job in explaining tough terms in everyday English (not to mention the pictorial essays). In a nutshell, this book is thought-provoking, well-written and personally, i think that for the price that it is selling a true bargain.
A WORK OF SPECTACULAR INSIGHT, 08 May 2008
Shapes and Forms' paper and Qabalistic based Hermetic design against this work, there is no comparison. Daud Sutton is a born scholar who manages to introduce the dazzling complexity and subtlety of Islamic lineal shapes and forms with consummate ease. One of my favourite source works. --Steven Ashe
Ian Stewart has done it again!, 29 Nov 2008
What more can I say?
Ian Stewart takes us on a journey through group theory to places you probably never considered, but in a completely fun and accessible manner. The historical tone of the book works really well, this book has inspired me to study galois theory in far greater depth.
A MUST for anybody with an interest in mathematics.
A little gem, 10 Dec 2007
Clear and fascinating explanations about a subject I didn't know I was interested in until I came across this book. I recommend this book to all with or without a prior interest. Beautiful illustrations complete this delightful work.
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Customer Reviews
Tilting at windmills, 02 Jun 2007
In this tome Mr Mandelbrot lambasts the previous century's inadequate financial models but seems unwilling to admit that the field has moved on somewhat, and unable to offer a practical model of his own.
Mr Mandelbrot shows how Bachelierian models fail to account for disastrous market drops which ruined many investors. He rubbishes two conventional assumptions: that each price move is independent of another and that their magnitude follows a Normal distribution. Skillfully constructed charts make plain the reality that a large market move is likely to be followed by another. More charts show just how badly market data fits to a Normal distribution: by this measure dozens of trading days in the 20th century were so unlikely not even one should have occurred in the lifetime of the universe.
The author suggests we discard such woefully unrealistic theory and start again, taking fractals as our base. In a display humility atypical of the rest of the book Mr Mandelbrot admits to having no way to calculate price and risk in his proposed model, or even calibrate its parameters "Alpha" and "H" to the real world.
The tragedy of this foray into fractal finance is in its pointlessness. What made 1960s financial models so unrealistic was the assumption of unchanging volatility. By late 90s anyone with sufficient computing power could drop this assumption and include real "volatile volatility" in their models. In modern theory, October 1987 was not a 22-sigma "not in the lifetime of the universe" event. It was a spike in the volatility process, as the models predict will happen from time to time.
In fairness, the book offers many insights into what drives the markets, the trouble with fundamental valuation, rationality of market agents, flow of information, and more. I could recommend reading it for those insights alone. ...with tangerine trees and marmalade skies..., 08 Jul 2006
Orthodox economics is very formal using complex models to predict future behaviour. Most economists, like meteorologists, are not held accountable for their predictions.
Within the very wide field of economics there are many conflicting views about the nature of economics and there is much in the way of interesting work going on out there and I would cite the contributions of the Austrian school and the evolutionary school and especially point to the very accessible work of Paul Ormerod who give somewhat different views to those of the standard model.
This book is not aimed at those practitioners of economics or indeed the professionals of the City of London or Wall Street. To my mind, as an interested observer, Mandelbrot and Hudson are doing all of us a service in illuminating the gaps in economic theory that underpins the financial industry. John Maynard Keynes, who's General Theory of Employment, Interest and Money (1936)can be said to lie at the heart of much of contemporary economic theory, once famously compared the financial services industry to gambling, also made his fortune on the stock market.
The book methodically disects each of the pillars of contemporary financial theory and exposes it's weakness then introduces some basic fractal geometry ideas to exhibit their apparent ly better predictive use. As someone who favours the approach of ideas of chaos theory into the economics brew I tend to be more open to the approach that Mandelbrot uses but the proof of the pudding, as we say in England, lies in the eating and this populist text is certainly not the place for complex technical proofs or highly mathematical analysis. It is a difficult path to take but for the purposes for which this book is intended, which I believe is aimed at the educated investor or someone without an economics or financial background, it is about right.
I found the book both accessible and lucid. There are areas with which I would have wished for a more techical exposition but this is something that I will take up when I delve further into this subject matter.
There are many interesting ideas here and I suspect that there are many in the financial services community who are looking into these in greater detail or even have already absorbed them into their toolkit. Given the competitive nature of the financial markets I suspect that this knowledge will quickly be dispesed throughout the community.
All in all this is a nice easy read which will prompt further thought and study upon it's contents. My only, minor reservation, which prevents me awarding five stars is that I think a non-technical appendix, in keeping with the rest of the book, about the basic precepts of fractal geometry would have been helpful for the lay reader.
Well worth a look.
Necessary evil, 16 May 2006
If you invited Benoit Mandelbrot to your party, he'd be the geeky guy dissing people's illogical clothing, drinking too much punch, testing the aerodynamics of different canapes, and pouring food colouring in the pool. In other words, he's a risk and he won't get any girls, but on a balance of probabilities, the party Mandelbrot was at will be the one people will wish they'd been at.
This book is a rant, reflecting the death of editing in favour of celebrity authorship. So it's repetitive. It's also light on theory, and it repeats itself. But that doesn't mean it's wrong. Mandelbrot makes the case early on that the behaviour of market prices, or of any variable not constrained by physics, are not normally distributed. He then goes on to claim that artificial systems are non-Gaussian, putting them outside the reach of statistics - and by extension, outside the reach of CAPM, Black-Scholes, VAR, and GARCH. He proposes power law distributions as an alternative. He's probably right, but he never demonstrates this claim, and the alternative he suggests - multifractals - is, by his own admission, not very useful.
He comprehensively demolishes the random walk model, claiming to have demonstrated that volatility clusters, and that there is memory in all markets. This may be true, but it will have the effect of encouraging snake oil salesmen (see below).
More pertinent and scary is that Mandelbrot does show that the exponents needed to model power law distributions for different markets or instruments are so diverse and intractable as to make general market models meaningless. He does not explain how multifractals address this. He also points to the simple arithmetic inadequacy of using closing prices in hindcasting exercises, which is equally scary for anyone who actually tests their models. He spits on technical analysts, who don't. For this he gets an extra star.
Nassim Taleb is probably more eloquent on the subject of wild randomness, but he's too urbane to punk your party. Mandelbrot is trouble, and if you're in finance, he's coming your way. A solid critique to Modern Finance Theory, 21 Oct 2005
Benoit Mandelbrot may sometimes write too much about himself, but his critique of the Modern Finance Theory is very sharp. After exposing why some basic assumptions underlying the Modern Finance Theory and, more importantly, its applications in financial products, are totally nonscientific, Mandelbrot explores his way out of the chaos. Some parts of the book may be redundant, but the insights are bright indeed. After reading the book, one wonders why so much money is invested using evidently mistaken theories. Even many insiders might have an interesting read, as the financial world is well known for its herdfollowers. Mandelbrot does not offer a new Theory and those looking for chaos theory to so solve the problems may be disappointed. However, his final suggestions need a follow-up from the financial world. Very recomendable for people in the money business. Best finance layman's book Iýve ever read!!, 12 Jul 2005
Mandelbrot, much like Mr. Howard, "say it as it is". Modern finance theory simply does not fit the facts. This is a grave accusation but Mandelbrot makes such a good case against modern finance that one is left wondering upon completing the book how the workhorses of academic ink are still standing! A truly fascinating book that at best will lead you into seriously questioning what you have learned at uni and at worst will enhance your historical understanding of financial theory. Written in eloquent, "user-friendly" manner, this book advocates a completely fresh look at the financial world through the lenses of fractal geometry. This means that the reader will encounter terms like "fractional Brownian motion set in multifractal time", which may sound more like rocket science to some than finance, but Mandelbrot and Hudson do a magnificent job in explaining tough terms in everyday English (not to mention the pictorial essays). In a nutshell, this book is thought-provoking, well-written and personally, i think that for the price that it is selling a true bargain. A WORK OF SPECTACULAR INSIGHT, 08 May 2008
Shapes and Forms' paper and Qabalistic based Hermetic design against this work, there is no comparison. Daud Sutton is a born scholar who manages to introduce the dazzling complexity and subtlety of Islamic lineal shapes and forms with consummate ease. One of my favourite source works. --Steven Ashe Ian Stewart has done it again!, 29 Nov 2008
What more can I say?
Ian Stewart takes us on a journey through group theory to places you probably never considered, but in a completely fun and accessible manner. The historical tone of the book works really well, this book has inspired me to study galois theory in far greater depth.
A MUST for anybody with an interest in mathematics. A little gem, 10 Dec 2007
Clear and fascinating explanations about a subject I didn't know I was interested in until I came across this book. I recommend this book to all with or without a prior interest. Beautiful illustrations complete this delightful work. Well done.., 22 Jul 1999
Bold has a gem of a book here. It's only a little bit over a hundred pages, but it's packed full of the great geometry problems that occupied the minds of the world's greatest thinkers for the past 2000 years. The title describes the book perfectly. These really are "Famous Problems from Geometry" and he does indeed explain how to solve them. The book has four major sections/chapters. He discusses in detail the three problems from antiquity (one section each): squaring a circle, doubling a cube, and trisecting an angle. Furthermore, he spends significant time with constructions of regular polygons (the fourth section) - which ones can be constructed and why. He also discusses which ones cannot be constructed and why. The reader will be expected to understand concepts from Modern Algebra, particularly the concept of a Field. While Bold does spend time explaining what a Field is, his definition is quick and is assumed to be more of a refresher for someone who has already learned about them. Bold also has a section on Complex Numbers where he derives one of the formulas used later in the book. Again - this section is assumed to be a refresher on Complex Numbers. High School Geometry or Algebra students would have significant trouble understanding his explanations and proofs. Bold provides problems for the reader to work along the way. These are problems that logically lead to the proof of the problem being studied. The problems are good. As a third year college student majoring in mathematics, I found the explanations/solutions to be sometimes hard to follow. He assumes a great deal about the reader's level of proficiency in math and in geometry. As a result, he liberally skips steps in proofs that are assumed to be "obvious." If you're expecting simple proofs to these problems, you're not going to find them. If they were simple, they wouldn't have taken 2000 years to solve. But they are explained clearly here in terms that anyone with a college degree should be able to understand. Overall, a superb book. A must have for anyone interested in the famous problems from the history of Geometry.
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Customer Reviews
Tilting at windmills, 02 Jun 2007
In this tome Mr Mandelbrot lambasts the previous century's inadequate financial models but seems unwilling to admit that the field has moved on somewhat, and unable to offer a practical model of his own.
Mr Mandelbrot shows how Bachelierian models fail to account for disastrous market drops which ruined many investors. He rubbishes two conventional assumptions: that each price move is independent of another and that their magnitude follows a Normal distribution. Skillfully constructed charts make plain the reality that a large market move is likely to be followed by another. More charts show just how badly market data fits to a Normal distribution: by this measure dozens of trading days in the 20th century were so unlikely not even one should have occurred in the lifetime of the universe.
The author suggests we discard such woefully unrealistic theory and start again, taking fractals as our base. In a display humility atypical of the rest of the book Mr Mandelbrot admits to having no way to calculate price and risk in his proposed model, or even calibrate its parameters "Alpha" and "H" to the real world.
The tragedy of this foray into fractal finance is in its pointlessness. What made 1960s financial models so unrealistic was the assumption of unchanging volatility. By late 90s anyone with sufficient computing power could drop this assumption and include real "volatile volatility" in their models. In modern theory, October 1987 was not a 22-sigma "not in the lifetime of the universe" event. It was a spike in the volatility process, as the models predict will happen from time to time.
In fairness, the book offers many insights into what drives the markets, the trouble with fundamental valuation, rationality of market agents, flow of information, and more. I could recommend reading it for those insights alone. ...with tangerine trees and marmalade skies..., 08 Jul 2006
Orthodox economics is very formal using complex models to predict future behaviour. Most economists, like meteorologists, are not held accountable for their predictions.
Within the very wide field of economics there are many conflicting views about the nature of economics and there is much in the way of interesting work going on out there and I would cite the contributions of the Austrian school and the evolutionary school and especially point to the very accessible work of Paul Ormerod who give somewhat different views to those of the standard model.
This book is not aimed at those practitioners of economics or indeed the professionals of the City of London or Wall Street. To my mind, as an interested observer, Mandelbrot and Hudson are doing all of us a service in illuminating the gaps in economic theory that underpins the financial industry. John Maynard Keynes, who's General Theory of Employment, Interest and Money (1936)can be said to lie at the heart of much of contemporary economic theory, once famously compared the financial services industry to gambling, also made his fortune on the stock market.
The book methodically disects each of the pillars of contemporary financial theory and exposes it's weakness then introduces some basic fractal geometry ideas to exhibit their apparent ly better predictive use. As someone who favours the approach of ideas of chaos theory into the economics brew I tend to be more open to the approach that Mandelbrot uses but the proof of the pudding, as we say in England, lies in the eating and this populist text is certainly not the place for complex technical proofs or highly mathematical analysis. It is a difficult path to take but for the purposes for which this book is intended, which I believe is aimed at the educated investor or someone without an economics or financial background, it is about right.
I found the book both accessible and lucid. There are areas with which I would have wished for a more techical exposition but this is something that I will take up when I delve further into this subject matter.
There are many interesting ideas here and I suspect that there are many in the financial services community who are looking into these in greater detail or even have already absorbed them into their toolkit. Given the competitive nature of the financial markets I suspect that this knowledge will quickly be dispesed throughout the community.
All in all this is a nice easy read which will prompt further thought and study upon it's contents. My only, minor reservation, which prevents me awarding five stars is that I think a non-technical appendix, in keeping with the rest of the book, about the basic precepts of fractal geometry would have been helpful for the lay reader.
Well worth a look.
Necessary evil, 16 May 2006
If you invited Benoit Mandelbrot to your party, he'd be the geeky guy dissing people's illogical clothing, drinking too much punch, testing the aerodynamics of different canapes, and pouring food colouring in the pool. In other words, he's a risk and he won't get any girls, but on a balance of probabilities, the party Mandelbrot was at will be the one people will wish they'd been at.
This book is a rant, reflecting the death of editing in favour of celebrity authorship. So it's repetitive. It's also light on theory, and it repeats itself. But that doesn't mean it's wrong. Mandelbrot makes the case early on that the behaviour of market prices, or of any variable not constrained by physics, are not normally distributed. He then goes on to claim that artificial systems are non-Gaussian, putting them outside the reach of statistics - and by extension, outside the reach of CAPM, Black-Scholes, VAR, and GARCH. He proposes power law distributions as an alternative. He's probably right, but he never demonstrates this claim, and the alternative he suggests - multifractals - is, by his own admission, not very useful.
He comprehensively demolishes the random walk model, claiming to have demonstrated that volatility clusters, and that there is memory in all markets. This may be true, but it will have the effect of encouraging snake oil salesmen (see below).
More pertinent and scary is that Mandelbrot does show that the exponents needed to model power law distributions for different markets or instruments are so diverse and intractable as to make general market models meaningless. He does not explain how multifractals address this. He also points to the simple arithmetic inadequacy of using closing prices in hindcasting exercises, which is equally scary for anyone who actually tests their models. He spits on technical analysts, who don't. For this he gets an extra star.
Nassim Taleb is probably more eloquent on the subject of wild randomness, but he's too urbane to punk your party. Mandelbrot is trouble, and if you're in finance, he's coming your way. A solid critique to Modern Finance Theory, 21 Oct 2005
Benoit Mandelbrot may sometimes write too much about himself, but his critique of the Modern Finance Theory is very sharp. After exposing why some basic assumptions underlying the Modern Finance Theory and, more importantly, its applications in financial products, are totally nonscientific, Mandelbrot explores his way out of the chaos. Some parts of the book may be redundant, but the insights are bright indeed. After reading the book, one wonders why so much money is invested using evidently mistaken theories. Even many insiders might have an interesting read, as the financial world is well known for its herdfollowers. Mandelbrot does not offer a new Theory and those looking for chaos theory to so solve the problems may be disappointed. However, his final suggestions need a follow-up from the financial world. Very recomendable for people in the money business. Best finance layman's book Iýve ever read!!, 12 Jul 2005
Mandelbrot, much like Mr. Howard, "say it as it is". Modern finance theory simply does not fit the facts. This is a grave accusation but Mandelbrot makes such a good case against modern finance that one is left wondering upon completing the book how the workhorses of academic ink are still standing! A truly fascinating book that at best will lead you into seriously questioning what you have learned at uni and at worst will enhance your historical understanding of financial theory. Written in eloquent, "user-friendly" manner, this book advocates a completely fresh look at the financial world through the lenses of fractal geometry. This means that the reader will encounter terms like "fractional Brownian motion set in multifractal time", which may sound more like rocket science to some than finance, but Mandelbrot and Hudson do a magnificent job in explaining tough terms in everyday English (not to mention the pictorial essays). In a nutshell, this book is thought-provoking, well-written and personally, i think that for the price that it is selling a true bargain. A WORK OF SPECTACULAR INSIGHT, 08 May 2008
Shapes and Forms' paper and Qabalistic based Hermetic design against this work, there is no comparison. Daud Sutton is a born scholar who manages to introduce the dazzling complexity and subtlety of Islamic lineal shapes and forms with consummate ease. One of my favourite source works. --Steven Ashe Ian Stewart has done it again!, 29 Nov 2008
What more can I say?
Ian Stewart takes us on a journey through group theory to places you probably never considered, but in a completely fun and accessible manner. The historical tone of the book works really well, this book has inspired me to study galois theory in far greater depth.
A MUST for anybody with an interest in mathematics. A little gem, 10 Dec 2007
Clear and fascinating explanations about a subject I didn't know I was interested in until I came across this book. I recommend this book to all with or without a prior interest. Beautiful illustrations complete this delightful work. Well done.., 22 Jul 1999
Bold has a gem of a book here. It's only a little bit over a hundred pages, but it's packed full of the great geometry problems that occupied the minds of the world's greatest thinkers for the past 2000 years. The title describes the book perfectly. These really are "Famous Problems from Geometry" and he does indeed explain how to solve them. The book has four major sections/chapters. He discusses in detail the three problems from antiquity (one section each): squaring a circle, doubling a cube, and trisecting an angle. Furthermore, he spends significant time with constructions of regular polygons (the fourth section) - which ones can be constructed and why. He also discusses which ones cannot be constructed and why. The reader will be expected to understand concepts from Modern Algebra, particularly the concept of a Field. While Bold does spend time explaining what a Field is, his definition is quick and is assumed to be more of a refresher for someone who has already learned about them. Bold also has a section on Complex Numbers where he derives one of the formulas used later in the book. Again - this section is assumed to be a refresher on Complex Numbers. High School Geometry or Algebra students would have significant trouble understanding his explanations and proofs. Bold provides problems for the reader to work along the way. These are problems that logically lead to the proof of the problem being studied. The problems are good. As a third year college student majoring in mathematics, I found the explanations/solutions to be sometimes hard to follow. He assumes a great deal about the reader's level of proficiency in math and in geometry. As a result, he liberally skips steps in proofs that are assumed to be "obvious." If you're expecting simple proofs to these problems, you're not going to find them. If they were simple, they wouldn't have taken 2000 years to solve. But they are explained clearly here in terms that anyone with a college degree should be able to understand. Overall, a superb book. A must have for anyone interested in the famous problems from the history of Geometry.
A joy, and not just for mathematicians, 08 Feb 2008
This book is amazing. It takes a very boring and dry subject and makes it accesible and interesting, without ever once 'dumbing down'. This is NOT trigonometry for dummies. This is Trigonometric Delights, and it lives up to its title.
Ranging through historic approaches to trigonometry, coupled with sections on areas that obviously delighted the author when he discovered them, the book never loses the reader, which is an amazing achievement.
If I had to think of who would buy this book, then I would say:
any parent of a child (13-18) finding maths hard/boring/impenetrable
any university student
all maths teachers (especially the part about the unit circle)
anyone who liked Simon Singh's Fermats Last Theorem, but would have
liked to see more of the subject matter and less of the story
Basically, if you are interested enough to be reading a review of this book then you should buy it. You will not be disappointed. If you are not reading reviews about this book, don't buy it.
Very good if expensive!, 18 Oct 2001
The book starts with angles and chords and a description of Plimpton 322. These chapters are good enough but the book seems to get better with each chapter. As a mathematics teacher, I found some of the chapters fantastic and others good, if a little heavy. The chapter "Two theorems from Geometry" states a few things I didn't previously know and made me think a lot!
The book is a little expensive, but like "e: The Story of a Number", the book is well written, interesting and most of all shows beauty in mathematics.
The appendix with a list of trigonometric formulae (not the basic ones you will already know) is wonderful.
If you like trig, get it, if not, you will when you read it!
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Customer Reviews
Tilting at windmills, 02 Jun 2007
In this tome Mr Mandelbrot lambasts the previous century's inadequate financial models but seems unwilling to admit that the field has moved on somewhat, and unable to offer a practical model of his own.
Mr Mandelbrot shows how Bachelierian models fail to account for disastrous market drops which ruined many investors. He rubbishes two conventional assumptions: that each price move is independent of another and that their magnitude follows a Normal distribution. Skillfully constructed charts make plain the reality that a large market move is likely to be followed by another. More charts show just how badly market data fits to a Normal distribution: by this measure dozens of trading days in the 20th century were so unlikely not even one should have occurred in the lifetime of the universe.
The author suggests we discard such woefully unrealistic theory and start again, taking fractals as our base. In a display humility atypical of the rest of the book Mr Mandelbrot admits to having no way to calculate price and risk in his proposed model, or even calibrate its parameters "Alpha" and "H" to the real world.
The tragedy of this foray into fractal finance is in its pointlessness. What made 1960s financial models so unrealistic was the assumption of unchanging volatility. By late 90s anyone with sufficient computing power could drop this assumption and include real "volatile volatility" in their models. In modern theory, October 1987 was not a 22-sigma "not in the lifetime of the universe" event. It was a spike in the volatility process, as the models predict will happen from time to time.
In fairness, the book offers many insights into what drives the markets, the trouble with fundamental valuation, rationality of market agents, flow of information, and more. I could recommend reading it for those insights alone. ...with tangerine trees and marmalade skies..., 08 Jul 2006
Orthodox economics is very formal using complex models to predict future behaviour. Most economists, like meteorologists, are not held accountable for their predictions.
Within the very wide field of economics there are many conflicting views about the nature of economics and there is much in the way of interesting work going on out there and I would cite the contributions of the Austrian school and the evolutionary school and especially point to the very accessible work of Paul Ormerod who give somewhat different views to those of the standard model.
This book is not aimed at those practitioners of economics or indeed the professionals of the City of London or Wall Street. To my mind, as an interested observer, Mandelbrot and Hudson are doing all of us a service in illuminating the gaps in economic theory that underpins the financial industry. John Maynard Keynes, who's General Theory of Employment, Interest and Money (1936)can be said to lie at the heart of much of contemporary economic theory, once famously compared the financial services industry to gambling, also made his fortune on the stock market.
The book methodically disects each of the pillars of contemporary financial theory and exposes it's weakness then introduces some basic fractal geometry ideas to exhibit their apparent ly better predictive use. As someone who favours the approach of ideas of chaos theory into the economics brew I tend to be more open to the approach that Mandelbrot uses but the proof of the pudding, as we say in England, lies in the eating and this populist text is certainly not the place for complex technical proofs or highly mathematical analysis. It is a difficult path to take but for the purposes for which this book is intended, which I believe is aimed at the educated investor or someone without an economics or financial background, it is about right.
I found the book both accessible and lucid. There are areas with which I would have wished for a more techical exposition but this is something that I will take up when I delve further into this subject matter.
There are many interesting ideas here and I suspect that there are many in the financial services community who are looking into these in greater detail or even have already absorbed them into their toolkit. Given the competitive nature of the financial markets I suspect that this knowledge will quickly be dispesed throughout the community.
All in all this is a nice easy read which will prompt further thought and study upon it's contents. My only, minor reservation, which prevents me awarding five stars is that I think a non-technical appendix, in keeping with the rest of the book, about the basic precepts of fractal geometry would have been helpful for the lay reader.
Well worth a look.
Necessary evil, 16 May 2006
If you invited Benoit Mandelbrot to your party, he'd be the geeky guy dissing people's illogical clothing, drinking too much punch, testing the aerodynamics of different canapes, and pouring food colouring in the pool. In other words, he's a risk and he won't get any girls, but on a balance of probabilities, the party Mandelbrot was at will be the one people will wish they'd been at.
This book is a rant, reflecting the death of editing in favour of celebrity authorship. So it's repetitive. It's also light on theory, and it repeats itself. But that doesn't mean it's wrong. Mandelbrot makes the case early on that the behaviour of market prices, or of any variable not constrained by physics, are not normally distributed. He then goes on to claim that artificial systems are non-Gaussian, putting them outside the reach of statistics - and by extension, outside the reach of CAPM, Black-Scholes, VAR, and GARCH. He proposes power law distributions as an alternative. He's probably right, but he never demonstrates this claim, and the alternative he suggests - multifractals - is, by his own admission, not very useful.
He comprehensively demolishes the random walk model, claiming to have demonstrated that volatility clusters, and that there is memory in all markets. This may be true, but it will have the effect of encouraging snake oil salesmen (see below).
More pertinent and scary is that Mandelbrot does show that the exponents needed to model power law distributions for different markets or instruments are so diverse and intractable as to make general market models meaningless. He does not explain how multifractals address this. He also points to the simple arithmetic inadequacy of using closing prices in hindcasting exercises, which is equally scary for anyone who actually tests their models. He spits on technical analysts, who don't. For this he gets an extra star.
Nassim Taleb is probably more eloquent on the subject of wild randomness, but he's too urbane to punk your party. Mandelbrot is trouble, and if you're in finance, he's coming your way. A solid critique to Modern Finance Theory, 21 Oct 2005
Benoit Mandelbrot may sometimes write too much about himself, but his critique of the Modern Finance Theory is very sharp. After exposing why some basic assumptions underlying the Modern Finance Theory and, more importantly, its applications in financial products, are totally nonscientific, Mandelbrot explores his way out of the chaos. Some parts of the book may be redundant, but the insights are bright indeed. After reading the book, one wonders why so much money is invested using evidently mistaken theories. Even many insiders might have an interesting read, as the financial world is well known for its herdfollowers. Mandelbrot does not offer a new Theory and those looking for chaos theory to so solve the problems may be disappointed. However, his final suggestions need a follow-up from the financial world. Very recomendable for people in the money business. Best finance layman's book Iýve ever read!!, 12 Jul 2005
Mandelbrot, much like Mr. Howard, "say it as it is". Modern finance theory simply does not fit the facts. This is a grave accusation but Mandelbrot makes such a good case against modern finance that one is left wondering upon completing the book how the workhorses of academic ink are still standing! A truly fascinating book that at best will lead you into seriously questioning what you have learned at uni and at worst will enhance your historical understanding of financial theory. Written in eloquent, "user-friendly" manner, this book advocates a completely fresh look at the financial world through the lenses of fractal geometry. This means that the reader will encounter terms like "fractional Brownian motion set in multifractal time", which may sound more like rocket science to some than finance, but Mandelbrot and Hudson do a magnificent job in explaining tough terms in everyday English (not to mention the pictorial essays). In a nutshell, this book is thought-provoking, well-written and personally, i think that for the price that it is selling a true bargain. A WORK OF SPECTACULAR INSIGHT, 08 May 2008
Shapes and Forms' paper and Qabalistic based Hermetic design against this work, there is no comparison. Daud Sutton is a born scholar who manages to introduce the dazzling complexity and subtlety of Islamic lineal shapes and forms with consummate ease. One of my favourite source works. --Steven Ashe Ian Stewart has done it again!, 29 Nov 2008
What more can I say?
Ian Stewart takes us on a journey through group theory to places you probably never considered, but in a completely fun and accessible manner. The historical tone of the book works really well, this book has inspired me to study galois theory in far greater depth.
A MUST for anybody with an interest in mathematics. A little gem, 10 Dec 2007
Clear and fascinating explanations about a subject I didn't know I was interested in until I came across this book. I recommend this book to all with or without a prior interest. Beautiful illustrations complete this delightful work. Well done.., 22 Jul 1999
Bold has a gem of a book here. It's only a little bit over a hundred pages, but it's packed full of the great geometry problems that occupied the minds of the world's greatest thinkers for the past 2000 years. The title describes the book perfectly. These really are "Famous Problems from Geometry" and he does indeed explain how to solve them. The book has four major sections/chapters. He discusses in detail the three problems from antiquity (one section each): squaring a circle, doubling a cube, and trisecting an angle. Furthermore, he spends significant time with constructions of regular polygons (the fourth section) - which ones can be constructed and why. He also discusses which ones cannot be constructed and why. The reader will be expected to understand concepts from Modern Algebra, particularly the concept of a Field. While Bold does spend time explaining what a Field is, his definition is quick and is assumed to be more of a refresher for someone who has already learned about them. Bold also has a section on Complex Numbers where he derives one of the formulas used later in the book. Again - this section is assumed to be a refresher on Complex Numbers. High School Geometry or Algebra students would have significant trouble understanding his explanations and proofs. Bold provides problems for the reader to work along the way. These are problems that logically lead to the proof of the problem being studied. The problems are good. As a third year college student majoring in mathematics, I found the explanations/solutions to be sometimes hard to follow. He assumes a great deal about the reader's level of proficiency in math and in geometry. As a result, he liberally skips steps in proofs that are assumed to be "obvious." If you're expecting simple proofs to these problems, you're not going to find them. If they were simple, they wouldn't have taken 2000 years to solve. But they are explained clearly here in terms that anyone with a college degree should be able to understand. Overall, a superb book. A must have for anyone interested in the famous problems from the history of Geometry.
A joy, and not just for mathematicians, 08 Feb 2008
This book is amazing. It takes a very boring and dry subject and makes it accesible and interesting, without ever once 'dumbing down'. This is NOT trigonometry for dummies. This is Trigonometric Delights, and it lives up to its title.
Ranging through historic approaches to trigonometry, coupled with sections on areas that obviously delighted the author when he discovered them, the book never loses the reader, which is an amazing achievement.
If I had to think of who would buy this book, then I would say:
any parent of a child (13-18) finding maths hard/boring/impenetrable
any university student
all maths teachers (especially the part about the unit circle)
anyone who liked Simon Singh's Fermats Last Theorem, but would have
liked to see more of the subject matter and less of the story
Basically, if you are interested enough to be reading a review of this book then you should buy it. You will not be disappointed. If you are not reading reviews about this book, don't buy it.
Very good if expensive!, 18 Oct 2001
The book starts with angles and chords and a description of Plimpton 322. These chapters are good enough but the book seems to get better with each chapter. As a mathematics teacher, I found some of the chapters fantastic and others good, if a little heavy. The chapter "Two theorems from Geometry" states a few things I didn't previously know and made me think a lot!
The book is a little expensive, but like "e: The Story of a Number", the book is well written, interesting and most of all shows beauty in mathematics.
The appendix with a list of trigonometric formulae (not the basic ones you will already know) is wonderful.
If you like trig, get it, if not, you will when you read it!
Review of The Pythagorean Theorem by Eli Maor, 02 Aug 2008
This is an excellent book on the history of the Pythagorean Theorem. I learnt a great deal of history of mathematics in relation to Pythagorasfs Theorem. This book is suitable to any student who has basic knowledge of calculus but the layperson will also find it interesting.
The book starts with the assertion that the Babylonians knew Pythagorasfs Theorem 1000 years before Pythagoras but it was the Greeks who proved the result.
There are a number of gems in the book which are not that well known in the mathematics community:
Hypotenuse is derived from the Greek words hypo meaning eunderf or edownf and teinen meaning eto stretchf. Maor points out the reason for this is that the hypotenuse of a right triangle in Euclidfs Elements was always on the bottom. (I did not know this).
There are over 400 proofs of Pythagorasfs Theorem.
It was the French lawyer eFrancois Vietef who first converted verbal algebra into symbolic algebra.
Many more of these gems crop up throughout the book.
Maor does give a number of different proofs of Pythagorasfs Theorem.
More importantly the author does not shy away from producing mathematical expressions and symbols in a popular book like this. Here are a few examples:
1. Every even perfect number is of the form 2^(n-1)*(2^n-1).
2. Vietefs Identity product which expresses 2/Î in terms of ã2.
3. Shows how the area of one arch of the cycloid is 3 times the area of the circle generating it.
4. Gives an excellent brief description of Hilbert Spaces and non Euclidean geometry.
5. Explains why Pythagorasfs Theorem is not valid in non-Euclidean geometry.
There are many more fantastic mathematical examples. The more serious mathematics is left for the appendices.
Additionally Maor has provided an excellent general history of mathematics such as:
The first woman mathematician was Hypatia (370 to 415).
The University of Gottingen was world renown for mathematics up until the Second World War.
How Edmund Landau (1877 to 1938) shunned all references to geometry. Maor points out that Landau wrote a 372 page book eDifferential and Integral Calculusf and it does not contain a single illustration.
How Euler discovered differential geometry but its modern form is due to Riemann and Gauss.
There are also non-mathematical examples of history in the book such as the first European University was Bologna founded in 1088 and why the Christians burned the Library of Alexandria.
You will learn a lot from this book because it has been thoroughly researched and shows the different fields where Pythagorasfs Theorem is used.
The author has also made excellent use of illustrations so the layperson can understand without learning all the details.
Maor has an exceptional method of writing very technical mathematics in a seamlessly way.
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Customer Reviews
Tilting at windmills, 02 Jun 2007
In this tome Mr Mandelbrot lambasts the previous century's inadequate financial models but seems unwilling to admit that the field has moved on somewhat, and unable to offer a practical model of his own.
Mr Mandelbrot shows how Bachelierian models fail to account for disastrous market drops which ruined many investors. He rubbishes two conventional assumptions: that each price move is independent of another and that their magnitude follows a Normal distribution. Skillfully constructed charts make plain the reality that a large market move is likely to be followed by another. More charts show just how badly market data fits to a Normal distribution: by this measure dozens of trading days in the 20th century were so unlikely not even one should have occurred in the lifetime of the universe.
The author suggests we discard such woefully unrealistic theory and start again, taking fractals as our base. In a display humility atypical of the rest of the book Mr Mandelbrot admits to having no way to calculate price and risk in his proposed model, or even calibrate its parameters "Alpha" and "H" to the real world.
The tragedy of this foray into fractal finance is in its pointlessness. What made 1960s financial models so unrealistic was the assumption of unchanging volatility. By late 90s anyone with sufficient computing power could drop this assumption and include real "volatile volatility" in their models. In modern theory, October 1987 was not a 22-sigma "not in the lifetime of the universe" event. It was a spike in the volatility process, as the models predict will happen from time to time.
In fairness, the book offers many insights into what drives the markets, the trouble with fundamental valuation, rationality of market agents, flow of information, and more. I could recommend reading it for those insights alone.
...with tangerine trees and marmalade skies..., 08 Jul 2006
Orthodox economics is very formal using complex models to predict future behaviour. Most economists, like meteorologists, are not held accountable for their predictions.
Within the very wide field of economics there are many conflicting views about the nature of economics and there is much in the way of interesting work going on out there and I would cite the contributions of the Austrian school and the evolutionary school and especially point to the very accessible work of Paul Ormerod who give somewhat different views to those of the standard model.
This book is not aimed at those practitioners of economics or indeed the professionals of the City of London or Wall Street. To my mind, as an interested observer, Mandelbrot and Hudson are doing all of us a service in illuminating the gaps in economic theory that underpins the financial industry. John Maynard Keynes, who's General Theory of Employment, Interest and Money (1936)can be said to lie at the heart of much of contemporary economic theory, once famously compared the financial services industry to gambling, also made his fortune on the stock market.
The book methodically disects each of the pillars of contemporary financial theory and exposes it's weakness then introduces some basic fractal geometry ideas to exhibit their apparent ly better predictive use. As someone who favours the approach of ideas of chaos theory into the economics brew I tend to be more open to the approach that Mandelbrot uses but the proof of the pudding, as we say in England, lies in the eating and this populist text is certainly not the place for complex technical proofs or highly mathematical analysis. It is a difficult path to take but for the purposes for which this book is intended, which I believe is aimed at the educated investor or someone without an economics or financial background, it is about right.
I found the book both accessible and lucid. There are areas with which I would have wished for a more techical exposition but this is something that I will take up when I delve further into this subject matter.
There are many interesting ideas here and I suspect that there are many in the financial services community who are looking into these in greater detail or even have already absorbed them into their toolkit. Given the competitive nature of the financial markets I suspect that this knowledge will quickly be dispesed throughout the community.
All in all this is a nice easy read which will prompt further thought and study upon it's contents. My only, minor reservation, which prevents me awarding five stars is that I think a non-technical appendix, in keeping with the rest of the book, about the basic precepts of fractal geometry would have been helpful for the lay reader.
Well worth a look.
Necessary evil, 16 May 2006
If you invited Benoit Mandelbrot to your party, he'd be the geeky guy dissing people's illogical clothing, drinking too much punch, testing the aerodynamics of different canapes, and pouring food colouring in the pool. In other words, he's a risk and he won't get any girls, but on a balance of probabilities, the party Mandelbrot was at will be the one people will wish they'd been at.
This book is a rant, reflecting the death of editing in favour of celebrity authorship. So it's repetitive. It's also light on theory, and it repeats itself. But that doesn't mean it's wrong. Mandelbrot makes the case early on that the behaviour of market prices, or of any variable not constrained by physics, are not normally distributed. He then goes on to claim that artificial systems are non-Gaussian, putting them outside the reach of statistics - and by extension, outside the reach of CAPM, Black-Scholes, VAR, and GARCH. He proposes power law distributions as an alternative. He's probably right, but he never demonstrates this claim, and the alternative he suggests - multifractals - is, by his own admission, not very useful.
He comprehensively demolishes the random walk model, claiming to have demonstrated that volatility clusters, and that there is memory in all markets. This may be true, but it will have the effect of encouraging snake oil salesmen (see below).
More pertinent and scary is that Mandelbrot does show that the exponents needed to model power law distributions for different markets or instruments are so diverse and intractable as to make general market models meaningless. He does not explain how multifractals address this. He also points to the simple arithmetic inadequacy of using closing prices in hindcasting exercises, which is equally scary for anyone who actually tests their models. He spits on technical analysts, who don't. For this he gets an extra star.
Nassim Taleb is probably more eloquent on the subject of wild randomness, but he's too urbane to punk your party. Mandelbrot is trouble, and if you're in finance, he's coming your way.
A solid critique to Modern Finance Theory, 21 Oct 2005
Benoit Mandelbrot may sometimes write too much about himself, but his critique of the Modern Finance Theory is very sharp. After exposing why some basic assumptions underlying the Modern Finance Theory and, more importantly, its applications in financial products, are totally nonscientific, M | | |