Model explains market movements
By Eric Smalley and Kimberly Patch, Technology Research News
Researchers from the Massachusetts Institute of Technology and Boston University have developed a mathematical model that explains some well-known fluctuation patterns in the stock market.
The model shows that the trading choices of the largest 500 or so players are responsible for big up and down movements, including extreme swings like the crashes of 1929 and 1987, said Xavier Gabaix, an assistant professor of economics at MIT.
The model also shows that the same forces underlie all types and sizes of markets, including stock markets in different countries, said Gabaix.
It has long been known that stock market fluctuations follow mathematical patterns, known as power laws, that are similar to those of earthquakes, business sizes, city sizes, and Web site popularity.
In all cases there are a few very large examples of this type of activity or entity and many smaller occurrences or examples, said Gabaix. There are only a few very large earthquakes, businesses, cities and very popular Web sites, and there are many more small earthquakes, businesses, cities and less popular Web sites. This relationship follows a precise mathematical graph.
Numbers that describe the relationship between large fluctuations in stock market prices, trading volume and number of trades also follow the same power-law mathematics, Gabaix said.
For example, the number of days a particular stock price moves by one percent will be eight times the number of days it moves by two percent, and the number of days it moves by two percent will be eight times the number of days it moves by four percent, and so on.
A similar power law characterizes the number of daily trades, said Gabaix. "For instance, if 100,000 shares of Apple stock were traded on 512 days during a certain period, then you can predict that there would be 64 days when 400,000 shares of Apple stock were traded, and eight days when 1,600,000 shares of Apple stock were traded, and one day when 6,400,000 shares of Apple stock were traded," he said.
Past postulations about power laws in the stock market have looked at the effects of large collective movements arising when, for example, some type of anxiety snowballs. What has been difficult to explain with this hypothesis, however, are the specific numbers shown by the empirical evidence, said Gabaix. The power law exponents for return and volume in the stock market remain steady at 3 and 1.5 respectively.
The researchers model showed that the behavior of big players is responsible for these numbers.
Certain power laws arise when market participants trade optimally, meaning they carefully trade off the time to execution and the cost of execution, said Gabaix. "If you want to trade a large trade quickly, you'll have a very big price impact, which traders want to avoid. This leaves them to trade more slowly when they have to make a big trade. But they don't want to trade too slowly either, because the opportunity for a good trade may go away," he said.
Big trades beget more trades, and those additional trades are usually in the same direction as the initial trades, according to the model.
When traders follow the optimal strategy, "they appear to generate exactly the power laws we observe empirically -- an exponent of 3 for returns and an exponent of 1.5 for volumes," said Gabaix. "Being smart about how to trade in the short term is part of the basic knowledge that professional traders must have, so we think... optimal execution of trade is a good approximation for the traders' behavior," he said.
The model can help predict the probability of a stock market crash occurring in a given period of time based on past returns and trading activity, said Gabaix. A 30-percent crash, for example, is likely to happen every century, he said.
The model probably won't help much in preventing crashes, however, said Gabaix. This is because preventing crashes would require drastic regulations or taxes to make the market much less liquid. Such drastic measures are "probably not desirable, because it's good to have a liquid market for a host of other reasons," he said.
The model could be used to hedge against large risks or to make money on stock market derivatives, but will not help investors gain better returns on direct stock trades, said Gabaix.
The researchers are currently working on identifying the origin of extreme movements in the stock market, Gabaix said. This may allow for a model that could help in mitigating the extremes, he said.
Gabaix' research colleagues were Parameswaran Gopikrishnan, Vasiliki Plerou, and H. Eugene Stanley of Boston University. The work appeared in the May 15, 2003 issue of Nature. The research was funded by the National Science Foundation and the Russell Sage Foundation.
汗!!! 能不能不给鸟语的呀! 原帖由 liza012 于 2010-8-5 21:43 发表 http://bbs.macd.cn/static/image/common/back.gif
汗!!! 能不能不给鸟语的呀!
如果以每日回报波动1%的天数为基数，每日波动2%的天数是1%的 1/2^3, 即1/8；而每日波动4%的天数是2%的1/8；
对于交易量，天数关系是1/2^1.5 .
回复 #10782 liza012 的帖子
机器翻译拗口 编辑#*22*#[ 本帖最后由 coco369 于 2010-8-6 03:31 编辑 ]
回复 #10784 coco369 的帖子
机器弄的一塌糊涂 #*27*#还是看禅师的那几句好点
禅师#*)*# ，【1/2^3, 即1/8】^ 这个是开方的符号吗？ 哦，禅师又发宝了。
以前看过有个家伙用分级的电子跃迁能量来拟合，也有点意思。估计是拟合了信息在人群中的扩散方式，即俗话说的一传十，十传百。
这个具体数据在不同国家可能不一样吧？还有，如文中说的，并不能确切的知道会发生在哪一天，所以直接用于交易还不行。
[ 本帖最后由 wild酱油 于 2010-8-6 00:02 编辑 ] 原帖由 野狐禅 于 2010-8-5 22:42 发表 http://bbs.macd.cn/static/image/common/back.gif
如果以每日回报波动1%的天数为基数，每日波动2%的天数是1%的 1/2^3, 即1/8；而每日波动4%的天数是2%的1/8；
对于交易量，天数关系是1/2^1.5 .
把这个模型代入中国的股市, 好象并不正确? (汗)
推下去: 每日波动8%的天数是4%的1/8；(感觉每日波动8%的天数没这么少?)
对于交易量，天数关系是1/2^1.5 .-----这句看不懂(汗) 原帖由 liza012 于 2010-8-5 23:58 发表 http://bbs.macd.cn/static/image/common/back.gif
把这个模型代入中国的股市, 好象并不正确? (汗)
推下去: 每日波动8%的天数是4%的1/8；(感觉每日波动8%的天数没这么少?)
从收盘价到收盘价，中国指数有几天是有8%的波动的？ 沙发……赚积分呵呵 原帖由 野狐禅 于 2010-8-6 01:13 发表 http://bbs.macd.cn/static/image/common/back.gif
从收盘价到收盘价，中国指数有几天是有8%的波动的？
很不幸, 和上看看2009.07.29 那天算不算? ^_^ ( 我只查看了大约一年的棒棒) 原帖由 liza012 于 2010-8-6 07:56 发表 http://bbs.macd.cn/static/image/common/back.gif
很不幸, 和上看看2009.07.29 那天算不算? ^_^ ( 我只查看了大约一年的棒棒)
一天两天的，本来就是小机率事件。 原帖由 野狐禅 于 2010-8-5 22:42 发表 http://bbs.macd.cn/static/image/common/back.gif
如果以每日回报波动1%的天数为基数，每日波动2%的天数是1%的 1/2^3, 即1/8；而每日波动4%的天数是2%的1/8；
对于交易量，天数关系是1/2^1.5 .
"对于交易量，天数关系是1/2^1.5 " 这句话是什么意思? 看不懂.(汗!)
看K线图好象在不同的位置上相同的量所起的作用不同? (比如在冲压力位和非压力位时
同样的量打升股价的幅度是不一样的.)而且连续的同向的量的堆积似乎更容易看出主力
的意图? 或是市场的情绪?
另外中国的股市现在分成几块, 创业版中小盘股也占有约1/3的量, 还有那股指期货....弄不懂?
[ 本帖最后由 liza012 于 2010-8-7 00:23 编辑 ] wild酱油: 看见你在线上, 请给说说你对量的理解. 先谢拉 (敬茶) 顶一下，必须的 Day Price Change
1 90.02 1.96%
2 88.29 -0.55%
3 88.78 0.51%
4 88.33 -1.70%
5 89.85 1.75% 感谢禅师周图! (上茶 上茶) 从图1上看, 随时都有可能下? (汗呀!)
从图2上看下周看看交易的量怎样变化...?
和上 酱油党怎么看呀? 原帖由 liza012 于 2010-8-8 20:06 发表 http://bbs.macd.cn/static/image/common/back.gif
从图1上看, 随时都有可能下? (汗呀!)
利扎沒有覺得這市場要蓬勃向上了？ 美国上次跌10%,是不是你的模型出问题乐?或者管理模型的人都睡觉去乐?