Материал готовится,

пожалуйста, возвращайтесь позднее

пожалуйста, возвращайтесь позднее

Ever since mathematics came to Wall Street, mainly in the 1980s, “quants” have been blamed for many things: dangerous innovations, overcomplexity, opacity, and using ivory-tower ideas to overrule common sense. Broadly speaking, there is truth to these accusations.

Most of the change in the financial system over the last 30 years has been driven by mathematical theory. Of course, we would have had plenty of financial disasters without mathematicians to help. They might have been less harmful than the disasters we had, or more harmful. But they definitely would have been different. I think the tremendous good wrought by the quantification of finance far outweighs any possible harm, but I do not deny that there was harm.

In recent years, more specific allegations have become popular. To cite some examples at random, Felix Salmon made a splash claiming the Gaussian Copula model was "the formula that killed Wall Street." Ian Stewart argued instead that the Black-Scholes model was “the mathematical justification for the trading that plunged the world's banks into catastrophe." Pablo Triana wrote a book blaming value-at-risk — The Number That Killed Us: A Story of Modern Banking, Flawed Mathematics, and a Big Financial Crisis. Scott Patterson wrote two books — The Quants: How a New Breed of Math Whizzes Conquered Wall Street and Nearly Destroyed It pointing the finger at systematic trading algorithms and Dark Pools: High-Speed Traders, A.I. Bandits, and the Threat to the Global Financial System blaming computerized execution systems.

If I had to pick a mathematical error that was responsible for the global financial crisis, I’d name a different candidate. It was confusion among mathematicians and economists over the meaning of the word “capital” a quarter century ago that encouraged the creation of huge global institutions with business models guaranteed to blow up.

To understand how this happened, we have to go back to the early 1980s. The first “rocket scientists” arrived on Wall Street and began to trade using mathematical models. Unlike qualitative traders, we quants had a good idea of the probability distribution of our results. For example, suppose a trading system generated a +10% return on 51% of days, and a -10% return the other 49% of days. This is a toy example; real trading systems generate a range of potential returns and you have to worry about things like valuations, liquidity, and funding as well as accounting profit and loss. But the complexities do not change the basic mathematical point.

At first glance, this looks like a profitable trading system. On average it makes 0.2% per day which compounds to 68% per year. But despite having a positive expected return every day, this strategy is certain to blow up (in trader’s jargon, to “blow up” is to lose so much money you give back your accumulated profits and more, and have to stop trading).

The problem is something called “volatility drag.” Every time the strategy has a gain followed by a loss (or a loss followed by a gain) it loses 1%. A gain turns $1.00 into $1.10, a 10% loss from there means you end up with $0.99. A loss turns $1.00 into $0.90, a 10% gain from there means you end up with $0.99. The net loss from a gain and a loss is equal to the gain squared, 10% squared is 1% (10% is really 0.1, 0.12 is 0.01 or 1%).

Suppose after 100 days you have the expected 51 gains and 49 losses. That means you have 49 pairs of gains and losses, each of which costs you 1%, reducing $1.00 to $0.61.

Most of the change in the financial system over the last 30 years has been driven by mathematical theory. Of course, we would have had plenty of financial disasters without mathematicians to help. They might have been less harmful than the disasters we had, or more harmful. But they definitely would have been different. I think the tremendous good wrought by the quantification of finance far outweighs any possible harm, but I do not deny that there was harm.

In recent years, more specific allegations have become popular. To cite some examples at random, Felix Salmon made a splash claiming the Gaussian Copula model was "the formula that killed Wall Street." Ian Stewart argued instead that the Black-Scholes model was “the mathematical justification for the trading that plunged the world's banks into catastrophe." Pablo Triana wrote a book blaming value-at-risk — The Number That Killed Us: A Story of Modern Banking, Flawed Mathematics, and a Big Financial Crisis. Scott Patterson wrote two books — The Quants: How a New Breed of Math Whizzes Conquered Wall Street and Nearly Destroyed It pointing the finger at systematic trading algorithms and Dark Pools: High-Speed Traders, A.I. Bandits, and the Threat to the Global Financial System blaming computerized execution systems.

If I had to pick a mathematical error that was responsible for the global financial crisis, I’d name a different candidate. It was confusion among mathematicians and economists over the meaning of the word “capital” a quarter century ago that encouraged the creation of huge global institutions with business models guaranteed to blow up.

To understand how this happened, we have to go back to the early 1980s. The first “rocket scientists” arrived on Wall Street and began to trade using mathematical models. Unlike qualitative traders, we quants had a good idea of the probability distribution of our results. For example, suppose a trading system generated a +10% return on 51% of days, and a -10% return the other 49% of days. This is a toy example; real trading systems generate a range of potential returns and you have to worry about things like valuations, liquidity, and funding as well as accounting profit and loss. But the complexities do not change the basic mathematical point.

At first glance, this looks like a profitable trading system. On average it makes 0.2% per day which compounds to 68% per year. But despite having a positive expected return every day, this strategy is certain to blow up (in trader’s jargon, to “blow up” is to lose so much money you give back your accumulated profits and more, and have to stop trading).

The problem is something called “volatility drag.” Every time the strategy has a gain followed by a loss (or a loss followed by a gain) it loses 1%. A gain turns $1.00 into $1.10, a 10% loss from there means you end up with $0.99. A loss turns $1.00 into $0.90, a 10% gain from there means you end up with $0.99. The net loss from a gain and a loss is equal to the gain squared, 10% squared is 1% (10% is really 0.1, 0.12 is 0.01 or 1%).

Suppose after 100 days you have the expected 51 gains and 49 losses. That means you have 49 pairs of gains and losses, each of which costs you 1%, reducing $1.00 to $0.61.

Загрузка...

Выбрать следующее задание

Ты добавил

Выбрать следующее задание

Ты добавил