KNR外汇的出入金有手续费吗？出入金时间是多久？_百度知道
KNR外汇的出入金有手续费吗？出入金时间是多久？
我有更好的答案
我一直做得KNR，出入金手续费都没有手续费，入金工作日基本就十几分钟，出金两个工作日，比如今天出金明天到账。
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我们会通过消息、邮箱等方式尽快将举报结果通知您。&figure&&img src=&https://pic2.zhimg.com/v2-12b7ffd9d6a6eb76b41e6e_b.jpg& data-rawwidth=&600& data-rawheight=&337& class=&origin_image zh-lightbox-thumb& width=&600& data-original=&https://pic2.zhimg.com/v2-12b7ffd9d6a6eb76b41e6e_r.jpg&&&/figure&&p&本文主要介绍盈透证券（电汇）出入金的具体步骤，前提是你已办好境外银行卡。电汇（wire）是目前盈透个人交易者使用最频繁的出入金方式，手续费各家银行不同，具体请咨询银行。若有疑问，欢迎私信。参考官网：&a href=&http://link.zhihu.com/?target=https%3A//www.interactivebrokers.com.hk/cn/index.php%3Ff%3Dfunding%26p%3Dcash& class=& wrap external& target=&_blank& rel=&nofollow noreferrer&&注资参考 | Interactive Brokers&/a&&/p&&p&一、入金时间和费用&/p&&p&（以招行为例，其他银行可能手续费略有不同，请咨询各家银行）&/p&&p&&b&美元&/b&：&/p&&p&时间：一般2-3个工作日&/p&&p&手续费：招行入金到盈透（花旗银行纽约分行），招行收20美元，中间行收30美金。&/p&&p&&b&港币&/b&：（推荐入金方式）&/p&&p& 时间：一般1-2个工作日&/p&&p&手续费：招行入金到盈透（花旗银行香港分行），招行收50港币。&/p&&p&推荐港币入金的原因是，盈透自己也是外汇交易商，它结合了全球14家最大的外汇报价商（占全球银行间市场份额的70%），并且直接进入银行间报价体系，10万美元等值货币兑换只收2美金手续费（银行收费跟它比，简直就是在抢劫！）。链接：&a href=&http://link.zhihu.com/?target=https%3A//www.interactivebrokers.com.hk/cn/index.php%3Ff%3D3106%26ns%3DT& class=& wrap external& target=&_blank& rel=&nofollow noreferrer&&外汇产品亮点 | Interactive Brokers&/a&&br&&/p&&p&&i&注意：招行境内卡汇至香港招行一卡通，香港一卡通不收取手续费，但是境内招行会收取电报费150元/笔，另按金额收取境外汇出汇款手续费，普卡千一，金卡万五，金葵花卡（黑卡）免收。&/i&&/p&&br&&br&&br&&h2&&b&美元入金&/b&（在盈透操作）&br&&/h2&&p&1.账户申请完后，登录官网，选则“资金”-“资金转账”，发起注资申请&br&&/p&&figure&&img src=&http://pic1.zhimg.com/v2-00f056a82cac68acf648_b.png& data-rawwidth=&1100& data-rawheight=&316& class=&origin_image zh-lightbox-thumb& width=&1100& data-original=&http://pic1.zhimg.com/v2-00f056a82cac68acf648_r.png&&&/figure&&p&2.保存入金设置（第一次入金可以不填）&/p&&figure&&img src=&http://pic4.zhimg.com/v2-e188cfe9ff09c7c97d68a475e3db1193_b.jpg& data-rawwidth=&972& data-rawheight=&718& class=&origin_image zh-lightbox-thumb& width=&972& data-original=&http://pic4.zhimg.com/v2-e188cfe9ff09c7c97d68a475e3db1193_r.jpg&&&/figure&&p&3.盈透收款行信息（需截图或复制）&/p&&figure&&img src=&http://pic2.zhimg.com/v2-5a74b5d9fb52d3db8605_b.jpg& data-rawwidth=&969& data-rawheight=&826& class=&origin_image zh-lightbox-thumb& width=&969& data-original=&http://pic2.zhimg.com/v2-5a74b5d9fb52d3db8605_r.jpg&&&/figure&&p&4.银行汇款页面（以招行为例）&/p&&p&登陆招行的“个人银行香港专业版”网银，进入后点击“转账汇款”，选择“国外汇款”&/p&&p&&figure&&img src=&http://pic3.zhimg.com/v2-24df2bb35e42f91dc56062_b.jpg& data-rawwidth=&854& data-rawheight=&521& class=&origin_image zh-lightbox-thumb& width=&854& data-original=&http://pic3.zhimg.com/v2-24df2bb35e42f91dc56062_r.jpg&&&/figure&最后等待银行处理。&br&&br&&br&&/p&&h2&&b&港币入金&/b&（在盈透操作）&/h2&&p&1.发起注资申请&br&&figure&&img src=&http://pic1.zhimg.com/v2-73e49d6f206b726d52e38_b.png& data-rawwidth=&1116& data-rawheight=&318& class=&origin_image zh-lightbox-thumb& width=&1116& data-original=&http://pic1.zhimg.com/v2-73e49d6f206b726d52e38_r.png&&&/figure&2.盈透收款行信息（需截图或复制）&/p&&p&&figure&&img src=&http://pic3.zhimg.com/v2-0c651bf6dd293e0e0f9cfe7834f5eeb6_b.png& data-rawwidth=&1091& data-rawheight=&656& class=&origin_image zh-lightbox-thumb& width=&1091& data-original=&http://pic3.zhimg.com/v2-0c651bf6dd293e0e0f9cfe7834f5eeb6_r.png&&&/figure&3.银行汇款页面（以招行为例）&br&登录招行“个人银行香港专业版”网银，进入后点击“转账汇款”，选择“香港本地转账”&/p&&p&&figure&&img src=&http://pic1.zhimg.com/v2-c6f69d28ee579a8acaaeba29a7940dd0_b.jpg& data-rawwidth=&897& data-rawheight=&558& class=&origin_image zh-lightbox-thumb& width=&897& data-original=&http://pic1.zhimg.com/v2-c6f69d28ee579a8acaaeba29a7940dd0_r.jpg&&&/figure&最后等待银行处理&/p&&br&&br&&h2&&b&取款（出金）&/b&&br&&/h2&&p&登录官网，选择“资金转账”-“取款”&/p&&figure&&img src=&http://pic4.zhimg.com/v2-306d6d10adeb_b.png& data-rawwidth=&935& data-rawheight=&797& class=&origin_image zh-lightbox-thumb& width=&935& data-original=&http://pic4.zhimg.com/v2-306d6d10adeb_r.png&&&/figure&&p&最后确认身份，即可转出。&/p&&p&&i&注意：由于一些产品当日平仓不一定马上现金到账，所以一般按照可取款现金取款，如果提前多取了，可能会被盈透征收一些利息。&/i&&/p&&p&&i&盈透每月首次取款免费，之后按10美元/&/i&&i&&i&95港币&/i&/8欧元收取费用，详情见：&a href=&http://link.zhihu.com/?target=https%3A//www.interactivebrokers.com/cn/index.php%3Ff%3D14779%26ns%3DT& class=& wrap external& target=&_blank& rel=&nofollow noreferrer&&其它费用 | Interactive Brokers&/a& &取款&&br&&/i&&/p&&p&&i&出于安全考虑，不同安全设备（密保卡），有不同的取款限制，如下图：&/i&&/p&&p&&figure&&img src=&http://pic4.zhimg.com/v2-5a82fbf40be03e766f15c87c_b.png& data-rawwidth=&1498& data-rawheight=&281& class=&origin_image zh-lightbox-thumb& width=&1498& data-original=&http://pic4.zhimg.com/v2-5a82fbf40be03e766f15c87c_r.png&&&/figure&详情见：&a href=&http://link.zhihu.com/?target=https%3A//www.interactivebrokers.com.hk/cn/index.php%3Ff%3DDlog%23limit& class=& wrap external& target=&_blank& rel=&nofollow noreferrer&&盈透证券集团实力和安全 | Interactive Brokers&/a& &取消限制&&br&&/p&&p&关于安全设备的资料，可以参考另一篇文章：&a href=&https://zhuanlan.zhihu.com/p/& class=&internal&&知乎专栏&/a&&/p&&br&&br&&br&&h2&&b&内部转账&/b&&br&&/h2&&p&一般适用于个人多个账户之间内部转账，或机构账户（如顾问/经纪商账户）内部转款。如：从本人名下A账户转移至名下B账户&/p&&p&&figure&&img src=&http://pic3.zhimg.com/v2-7ce520e661b48f8e4a2fe_b.png& data-rawwidth=&934& data-rawheight=&684& class=&origin_image zh-lightbox-thumb& width=&934& data-original=&http://pic3.zhimg.com/v2-7ce520e661b48f8e4a2fe_r.png&&&/figure&&i&注意：A账户和B账户的账户名、证件号码、地址等信息必须保持一致，否则有可能无法转账，如出现无法转账，请咨询盈透上海客服进行协助（021-）。 &/i&&/p&&br&&br&&h2&&b&第三方取款&/b&&/h2&&p&从客户A账户出金到B先生账户&br&&figure&&img src=&http://pic4.zhimg.com/v2-e075eb2fa7_b.png& data-rawwidth=&828& data-rawheight=&786& class=&origin_image zh-lightbox-thumb& width=&828& data-original=&http://pic4.zhimg.com/v2-e075eb2fa7_r.png&&&/figure&&/p&&p&流程：&br&1.客户A在盈透官网发起“第三方取款”申请指令。&br&2.客户A致电给盈透，身份确认后，需确认这笔出金。&br&3.盈透收到“第三方取款”指令，进行审核。主要审核第三方（B先生）与客户A之间的关系，如不能提供合理的关系解释，盈透有权拒绝此笔出金申请，即使客户A同意出金，最后也无法成功。&br&&br&关于合理的关系的解释案例：&br&如某机构账户出于某些原因被关闭，而A先生100%全资拥有该公司，则A先生想要出金到自己银行账户，盈透认为该解释合理。假如A先生拥有99%的股权，盈透有权拒绝出金，因为不是100%拥有。&br&PS.盈透不鼓励第三方出入金，有可能是担心出现各种纠纷，或涉及洗钱风险，于是对每笔“第三方取款”（除联名账户之外）都会进行审核。&/p&&p&以上就是盈透出入金的主要方式与流程，笔者竭尽全力把以上流程全部操作了一遍，但仍然有一些不能100%实现，结合了朋友、客户的一些经验之后，总结出来。如您发现差错，请及时与笔者联系，非常感谢！&/p&&p&版权所有，转载请注明出处！&/p&
本文主要介绍盈透证券（电汇）出入金的具体步骤，前提是你已办好境外银行卡。电汇（wire）是目前盈透个人交易者使用最频繁的出入金方式，手续费各家银行不同，具体请咨询银行。若有疑问，欢迎私信。参考官网：一、入金时间和…
&p&盈透专栏：&a href=&https://zhuanlan.zhihu.com/IB-trader-Club& class=&internal&&IB盈透交易者俱乐部&/a&&/p&&p&&br&&/p&&p&一、盈透介绍&/p&&p&1.&a href=&https://zhuanlan.zhihu.com/p/& class=&internal&&盈透证券系列（一）---盈透证券介绍&/a&&/p&&p&&br&&/p&&p&二、开户&/p&&p&1.&a href=&https://zhuanlan.zhihu.com/p/& class=&internal&&盈透证券系列（二）---开户前准备&/a&&/p&&p&2.&a href=&https://zhuanlan.zhihu.com/p/& class=&internal&&盈透证券系列（三）---常见开户疑问&/a&&/p&&p&3.&a href=&https://zhuanlan.zhihu.com/p/& class=&internal&&盈透证券系列（四）---开立普通账户&/a&&/p&&p&&br&&/p&&p&三、入金&/p&&p&1.&a href=&https://zhuanlan.zhihu.com/p/& class=&internal&&盈透证券系列（五）---为什么要换汇&/a&&/p&&p&2.&a href=&https://zhuanlan.zhihu.com/p/& class=&internal&&盈透证券系列（六）---国内银行卡购汇&/a&&/p&&p&3.&a href=&https://zhuanlan.zhihu.com/p/& class=&internal&&盈透证券系列（六）---国内银行卡购汇&/a&&/p&&p&4.&a href=&https://zhuanlan.zhihu.com/p/& class=&internal&&盈透证券系列（七）---国内银行卡入金&/a&&/p&&p&5.&a href=&https://zhuanlan.zhihu.com/p/& class=&internal&&盈透证券系列（八）---办理境外银行卡&/a&&/p&&p&6.&a href=&https://zhuanlan.zhihu.com/p/& class=&internal&&盈透证券系列（九）---境外银行卡入金&/a&&/p&&p&&br&&/p&&p&四、出金&/p&&p&1.出金至国内银行（待制作）&/p&&p&2.出金至境外银行（待制作）&/p&&p&&br&&/p&&p&五、交易软件培训&/p&&p&1.&a href=&https://zhuanlan.zhihu.com/p/& class=&internal&&盈透证券系列（交易篇1）---交易权限、市场数据&/a&&/p&&p&2.&a href=&https://zhuanlan.zhihu.com/p/& class=&internal&&盈透证券系列（交易篇2）---交易软件下载、调试&/a&&/p&&p&3.&a href=&https://zhuanlan.zhihu.com/p/& class=&internal&&盈透证券系列（交易篇3）---货币兑换（记账货币、外汇兑换、现货外汇）&/a&&/p&&p&4.&a href=&https://zhuanlan.zhihu.com/p/& class=&internal&&盈透证券系列（交易篇4）---修改行情图参数（增加盘前盘后行情、修改涨跌颜色）&/a&&/p&&p&5.&a href=&https://zhuanlan.zhihu.com/p/& class=&internal&&盈透证券系列（交易篇5）---选择交易产品（查询产品代码、市场扫描仪）&/a&&/p&&p&6.&a href=&https://zhuanlan.zhihu.com/p/& class=&internal&&盈透证券系列（交易篇6）---常用定单类型（市价单、限价单、止损单等）&/a&&/p&&p&7.&a href=&https://zhuanlan.zhihu.com/p/& class=&internal&&盈透证券系列（交易篇7）---盘前盘后交易（DAY/GTC、常规交易时间之外）&/a&&/p&&p&8.&a href=&https://zhuanlan.zhihu.com/p/& class=&internal&&盈透证券系列（交易篇8）---杠杆/保证金交易简介（账户类型介绍）&/a&&/p&&p&&i&（因近期出差，时间紧张，预计月底前完成剩下50%部分，敬请期待）&/i&&/p&&p&&br&&/p&&p&================分================割=================线=============&/p&&p&因为太多人咨询开户问题，所以做了个知乎问答和专栏，后续会陆续更新，敬请关注！&/p&&p&&br&&/p&&h2&《盈透证券(Interactive brokers)开户流程》&/h2&&figure&&img src=&https://pic2.zhimg.com/v2-87df830d75944d21dca9fccbb7e831a1_b.jpg& data-caption=&& data-size=&normal& data-rawwidth=&1503& data-rawheight=&656& class=&origin_image zh-lightbox-thumb& width=&1503& data-original=&https://pic2.zhimg.com/v2-87df830d75944d21dca9fccbb7e831a1_r.jpg&&&/figure&&h2&第一步、准备“银行账户”&/h2&&p&目前盈透不支持人民币直接入金，必须购汇成外币（美元或港币）再入金。盈透也不接受现金入金。没有境外银行卡的朋友，直接用国内一般的建行卡入金，有条件的尽量去办理境外银行卡，比如香港招行卡、工银亚洲、香港民生等，国内因为近期外汇管制问题，在国内网点开境外账户有些限制，因为银行政策变化，具体请咨询银行。&/p&&p&&br&&/p&&p&总的来说，如果入金规模不超过外管局规定的每人5万美金/年的额度话，国内建行卡完全够用。如果超过则需要自己想办法了，在此不便展开。&/p&&p&&br&&/p&&blockquote&1.没有境外银行账户能不能做盈透？&br&答：可以的，境内少数几家银行（强烈建议选择建行）的普通账户也能入金，但是收款人不能直接写盈透证券等带有证券、金融投资等字眼，可以缩写成Inter Br等，这样盈透也能收到并认可。&br&&br&2.境内银行能入金多少？&br&答：根据外管局规定，每人每年5万美元额度。所以如果用境内账户入金的话，不得超过5万美金/年。&br&&br&3.超过5万美金怎么办？&br&答：根据国家相关规定和券商合规要求，在此不便展开，请自行解决。&br&&br&4.出金到境内银行卡可以吗？&br&答：可以的，没问题。&br&&br&5.为什么要办境外银行卡？&br&答：主要是担心境内银行受国内监管机构影响太大，封锁了汇出通道，导致出入金不畅，办一张境外卡则可以避免这个问题，因为境内卡转本人境外卡不会被卡主，境外卡受国内监管机构影响比较小，转盈透也不会被卡。&br&&br&6.听说现在国内办境外卡特别麻烦？&br&答：是的，基本上都有一些限制条件或要求，具体可以咨询当地银行网点。因银行政策常常变化，本人对国内办卡不甚了解，每日盈透咨询量很多，故无法提供境内银行办卡的相关建议，请见谅！&/blockquote&&p&&br&&/p&&p&&br&&/p&&h2&第二步、盈透证券开户&/h2&&p&1.开户&b&门槛&/b&&/p&&blockquote&1.年龄＞18周岁&br&2.最低入金：&br&
1.年龄25岁以下：最低入金3,000美金 &br&
2.一般客户注册：最低入金10,000美元 &br&
3.顾问/经纪商邀请开户：最低入金5,000美金 &/blockquote&&p&2.开户&b&流程&/b&&/p&&blockquote&1.准备好身份证明（&u&&b&身份证&/b&&/u&、护照等）、地址证明（&u&&b&驾照&/b&&/u&、信用卡账单(近6个月)等）&br&2.网上填写开户资料，约15分钟-2小时（盈透申请资料比较多，第一次申请会比较困惑，如果需要&u&&b&开户指南(免费)&/b&&/u&，请给我留言）&br&3.注意事项：&br&
1.住宅地址：建议填写地址证明（驾照、信用卡账单）上的地址，再选择“邮寄地址与住宅地址不同”，此时填写的邮寄地址，是以后盈透给你寄东西的地址，而且以后还可随时修改。
2.身份证明：记得身份证上传正反面&br&
3.地址证明：一般建议用驾照、近6个月信用卡账单&/blockquote&&p&&i&（注：最近盈透好像与国内机构联网了，你输入身份证后不需要再上传身份证，可以直接检查到你本人信息....）&/i&&/p&&p&&br&&/p&&p&3.开户&b&渠道&/b&&/p&&p&下面两种都是在盈透开户，前者是普通个人开户，后者是通过机构渠道开户，功能是一致的。&/p&&blockquote&1.自己去官网申请。&br&2.通过介绍人邀请开户（提供开户、软件指导、费用减免、专业投资社区）&br&
1.最低入金只需要5,000美元（个人开户是10,000美元）&br&
2.提供在线开户指导（个人开户需要自己摸索）&br&
3.减免每个月账户管理费（个人账户＜10万美元，收10美元/月）&br&
4.提供盈透TWS软件简单培训（制作中）&br&
5.有专门的盈透交流社区，交易者累计资产近1000万美元&/blockquote&&p&&br&&/p&&h2&《盈透证券介绍人系统介绍》&/h2&&p&“经纪商”类似于国内证券公司“证券经纪人”角色，介绍开户、合并名下客户交易量，客户账户还是开在证券公司(盈透证券)，不是开在&经纪商(经纪人)&名下。&/p&&figure&&img src=&https://pic1.zhimg.com/v2-b7e8ba99cda194f6d2eda0_b.jpg& data-caption=&& data-size=&normal& data-rawwidth=&1465& data-rawheight=&744& class=&origin_image zh-lightbox-thumb& width=&1465& data-original=&https://pic1.zhimg.com/v2-b7e8ba99cda194f6d2eda0_r.jpg&&&/figure&&p&&br&&/p&&p&结束语：&/p&&p&盈透证券作为全美最大、世界知名的网络券商，已是国内多家知名美股、港股、外盘证券期货公司的“底层交易通道”，技术实力全球领先、软件功能极其强大、交易佣金、融资利率非常之低，真正的让普通投资者享受到“职业投资人”的专业服务，性价比极高。这也是为什么我们原意和盈透合作的原因，我司早在2012年开始在盈透交易期货产品，对盈透较为熟悉，去年年底拿下“全披露经纪商”资格。资质截图如下：&/p&&p&&br&&/p&&p&&br&&/p&&figure&&img src=&https://pic4.zhimg.com/v2-ff7edfe21c6b8db02fefd360f051bd0f_b.jpg& data-caption=&& data-size=&normal& data-rawwidth=&720& data-rawheight=&782& class=&origin_image zh-lightbox-thumb& width=&720& data-original=&https://pic4.zhimg.com/v2-ff7edfe21c6b8db02fefd360f051bd0f_r.jpg&&&/figure&&p&&br&&/p&&p&&br&&/p&&p&利益相关：盈透证券(interactive brokers)全披露经纪商(Fully Disclosed Broker)运营人员&/p&&p&&br&&/p&&p&欢迎对盈透感兴趣的朋友，可以添加我个人微信号：&b&&u&qow008&/u&&/b&&/p&
盈透专栏： 一、盈透介绍1. 二、开户1.2.3. 三、入金1.2.
&figure&&img src=&https://pic4.zhimg.com/ad3e2cac2fcfcb515d12b_b.jpg& data-rawwidth=&584& data-rawheight=&306& class=&origin_image zh-lightbox-thumb& width=&584& data-original=&https://pic4.zhimg.com/ad3e2cac2fcfcb515d12b_r.jpg&&&/figure&&p&&em&今天我们介绍一个神奇的人，和他神奇的公式。目前网络上传播较广的一篇讲凯利公式前世今生的文章，个人认为深度不够，而且思路是有问题的。大家不要看多了走偏路。最近也花了一些力气做梳理，把这篇分享出来，尽量做到讲对，讲透，也是提醒各位，低头挖矿，不要搞错了挖矿的初衷。&/em&&/p&&br&&br&&br&&blockquote&&h3&&strong&一、故事背景&/strong&&/h3&&/blockquote&&p&市场不好的时候，我们总是会犹豫，满仓？半仓？还是空仓？有没有一个科学的办法给出一个标准答案呢？下面来看看&strong&仓位管理神器——凯利公式&/strong&。&/p&&p&投资（ji）就是一场赌博。像索普、香农等很多投资大师早期都对研究赌博业的秘密情有独钟，科学家们总是希望从理论上找到赌博游戏的必胜策略，使得一场游戏中赢的概率远远高过输的概率。&/p&&p&凯利就是这样一个大师。他是香农（信息论创始人）在贝尔实验室的同事，这个来自德克萨斯州、爱摆弄手枪、喜欢一根接一根抽烟的狂野硬汉，干过很多恶作剧，特别喜欢将填满塑料的子弹射进他客厅的墙壁里来戏弄家里暂住的客人。他的研究领域从量子物理学到电视信号解码，发明了能够准确模拟人类声音的电脑设备。最广为人知的研究贡献，便是将香农的信息论运用到了赛马赌博中。&/p&&p&凯利用这样一个精巧简洁的公式，将信息论与赌博之间的本质联系揭露出来，告诉我们在有限了解的信息下，如何下注能使得资本增值的速度最大化。&/p&&br&&br&&blockquote&&h3&&strong&二、赌博怎么用凯利公式？&/strong&&/h3&&/blockquote&&p&最早的凯利公式是运用在赌博游戏中的，我们先看看赌博情形下凯利公式的特殊形式：&/p&&br&&figure&&img src=&https://pic1.zhimg.com/22dd110ff_b.jpg& data-rawwidth=&239& data-rawheight=&84& class=&content_image& width=&239&&&/figure&&p&&strong&f&/strong&：下注比例&br&&strong&Pwin：&/strong&赌赢的概率&br&&strong&Ploss&/strong&：赌输的概率（=1-Pwin）&br&&strong&b&/strong&：赔率，押1赔b（这个赌球的朋友们是不陌生啦）&/p&&br&&br&&blockquote&&b&特殊形式凯利公式的证明过程（此处感谢&a href=&https://www.zhihu.com/people/850b6a38f141c& data-hash=&850b6a38f141c& class=&member_mention& data-editable=&true& data-title=&@程峰& data-hovercard=&p$b$850b6a38f141c&&@程峰&/a&的建议）&/b&&/blockquote&&p&我们可以做一个简单的证明。资金曲线asset对f求导，就可以得到特殊形式下的凯利公式。&/p&&p&&b&In[0]:&/b&&/p&&div class=&highlight&&&pre&&code class=&language-python&&&span&&/span&&span class=&kn&&from&/span& &span class=&nn&&sympy&/span& &span class=&kn&&import&/span& &span class=&o&&*&/span&
&span class=&n&&f&/span&&span class=&p&&,&/span&&span class=&n&&b&/span&&span class=&p&&,&/span&&span class=&n&&pwin&/span& &span class=&o&&=&/span& &span class=&n&&symbols&/span&&span class=&p&&(&/span&&span class=&s1&&'f b pwin'&/span&&span class=&p&&)&/span&
&span class=&c1&&#资金曲线asset&/span&
&span class=&n&&asset&/span& &span class=&o&&=&/span& &span class=&n&&pwin&/span&&span class=&o&&*&/span&&span class=&n&&log&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span& &span class=&o&&+&/span& &span class=&n&&b&/span&&span class=&o&&*&/span&&span class=&n&&f&/span&&span class=&p&&)&/span& &span class=&o&&+&/span& &span class=&p&&(&/span&&span class=&mi&&1&/span& &span class=&o&&-&/span& &span class=&n&&pwin&/span&&span class=&p&&)&/span&&span class=&o&&*&/span&&span class=&n&&log&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&o&&-&/span&&span class=&n&&f&/span&&span class=&p&&)&/span&
&span class=&c1&&#资金曲线增长最大，即asset对f求导=0时f的值&/span&
&span class=&n&&solve&/span&&span class=&p&&(&/span&&span class=&n&&diff&/span&&span class=&p&&(&/span&&span class=&n&&asset&/span&&span class=&p&&,&/span&&span class=&n&&f&/span&&span class=&p&&),&/span&&span class=&n&&f&/span&&span class=&p&&)&/span&
&/code&&/pre&&/div&&p&&strong&Out[0]:&/strong&&/p&&div class=&highlight&&&pre&&code class=&language-python&&&span&&/span&&span class=&p&&[(&/span&&span class=&n&&b&/span&&span class=&o&&*&/span&&span class=&n&&pwin&/span& &span class=&o&&+&/span& &span class=&n&&pwin&/span& &span class=&o&&-&/span& &span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&/&/span&&span class=&n&&b&/span&&span class=&p&&]&/span&
&/code&&/pre&&/div&&br&&p&&strong&举个简单的例子&/strong&&/p&&p&假想一个游戏。赢的概率是60%，输的概率40%。入场费随意交。如果赢了获得2倍的入场费金额（1赔1），输则输掉入场费。小米有100元做本金，请问小米每次给多少入场费，理论上4次游戏后几何期望收益能最大？&/p&&p&然后我拿凯利公式算了一下，最佳的策略是每次投剩余本金的20%。&/p&&p& f = （1×0.6-0.4）/1 = 0.2。&/p&&p&基于上述的例子，做个简单的蒙特卡洛模拟实验（进行200次游戏）：&/p&&br&&p&&strong&In[1]:&/strong&&/p&&div class=&highlight&&&pre&&code class=&language-python&&&span&&/span&&span class=&kn&&from&/span& &span class=&nn&&pandas&/span& &span class=&kn&&import&/span& &span class=&n&&DataFrame&/span&
&span class=&n&&base&/span& &span class=&o&&=&/span& &span class=&mi&&100&/span&
&span class=&n&&pwin&/span& &span class=&o&&=&/span& &span class=&mf&&0.6&/span&
&span class=&n&&ploss&/span& &span class=&o&&=&/span& &span class=&mi&&1&/span&&span class=&o&&-&/span&&span class=&n&&pwin&/span&
&span class=&n&&b&/span& &span class=&o&&=&/span& &span class=&mi&&1&/span&
&span class=&n&&c&/span& &span class=&o&&=&/span& &span class=&mi&&1&/span&
&span class=&n&&rnd_position&/span& &span class=&o&&=&/span& &span class=&mf&&0.25&/span&
&span class=&n&&rnd_position2&/span& &span class=&o&&=&/span& &span class=&mf&&0.15&/span&
&span class=&n&&kelly_position&/span& &span class=&o&&=&/span& &span class=&p&&(&/span&&span class=&n&&pwin&/span&&span class=&o&&*&/span&&span class=&n&&b&/span& &span class=&o&&-&/span& &span class=&n&&ploss&/span&&span class=&p&&)&/span&&span class=&o&&/&/span&&span class=&n&&b&/span&
&span class=&n&&stopline&/span& &span class=&o&&=&/span& &span class=&mi&&1&/span&
&span class=&k&&print&/span& &span class=&s1&&'kelly position is &/span&&span class=&si&&%s&/span&&span class=&s1&&'&/span&&span class=&o&&%&/span&&span class=&n&&kelly_position&/span&
&span class=&n&&port_A&/span& &span class=&o&&=&/span& &span class=&n&&DataFrame&/span&&span class=&p&&()&/span&
&span class=&n&&port_B&/span& &span class=&o&&=&/span& &span class=&n&&DataFrame&/span&&span class=&p&&()&/span&
&span class=&n&&port_C&/span& &span class=&o&&=&/span& &span class=&n&&DataFrame&/span&&span class=&p&&()&/span&
&span class=&n&&port_D&/span& &span class=&o&&=&/span& &span class=&n&&DataFrame&/span&&span class=&p&&()&/span&
&span class=&c1&&#重复模拟次数&/span&
&span class=&k&&for&/span& &span class=&n&&i&/span& &span class=&ow&&in&/span& &span class=&nb&&range&/span&&span class=&p&&(&/span&&span class=&mi&&1000&/span&&span class=&p&&):&/span&
&span class=&n&&port1&/span& &span class=&o&&=&/span& &span class=&p&&[&/span&&span class=&n&&base&/span&&span class=&p&&]&/span&
&span class=&n&&port2&/span& &span class=&o&&=&/span& &span class=&p&&[&/span&&span class=&n&&base&/span&&span class=&p&&]&/span&
&span class=&n&&port3&/span& &span class=&o&&=&/span& &span class=&p&&[&/span&&span class=&n&&base&/span&&span class=&p&&]&/span&
&span class=&n&&port4&/span& &span class=&o&&=&/span& &span class=&p&&[&/span&&span class=&n&&base&/span&&span class=&p&&]&/span&
&span class=&c1&&#游戏进行次数&/span&
&span class=&k&&for&/span& &span class=&n&&step&/span& &span class=&ow&&in&/span& &span class=&nb&&range&/span&&span class=&p&&(&/span&&span class=&mi&&200&/span&&span class=&p&&):&/span&
&span class=&n&&rnd&/span& &span class=&o&&=&/span& &span class=&n&&random&/span&&span class=&o&&.&/span&&span class=&n&&random&/span&&span class=&p&&()&/span&
&span class=&k&&if&/span& &span class=&n&&rnd&/span& &span class=&o&&&&/span& &span class=&n&&pwin&/span&&span class=&p&&:&/span&
&span class=&n&&next_step&/span& &span class=&o&&=&/span& &span class=&n&&b&/span&
&span class=&k&&else&/span&&span class=&p&&:&/span&
&span class=&n&&next_step&/span& &span class=&o&&=&/span& &span class=&o&&-&/span&&span class=&n&&c&/span&
&span class=&k&&if&/span& &span class=&n&&port1&/span&&span class=&p&&[&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&]&/span& &span class=&o&&&&/span& &span class=&n&&base&/span&&span class=&o&&*&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&o&&-&/span&&span class=&n&&stopline&/span&&span class=&p&&):&/span&
&span class=&n&&port1&/span&&span class=&o&&.&/span&&span class=&n&&append&/span&&span class=&p&&(&/span&&span class=&n&&port1&/span&&span class=&p&&[&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&]&/span&&span class=&o&&*&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&o&&+&/span&&span class=&n&&next_step&/span&&span class=&p&&))&/span&
&span class=&k&&else&/span&&span class=&p&&:&/span&
&span class=&n&&port1&/span&&span class=&o&&.&/span&&span class=&n&&append&/span&&span class=&p&&(&/span&&span class=&n&&port1&/span&&span class=&p&&[&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&])&/span&
&span class=&k&&if&/span& &span class=&n&&port2&/span&&span class=&p&&[&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&]&/span& &span class=&o&&&&/span& &span class=&n&&base&/span&&span class=&o&&*&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&o&&-&/span&&span class=&n&&stopline&/span&&span class=&p&&):&/span&
&span class=&n&&port2&/span&&span class=&o&&.&/span&&span class=&n&&append&/span&&span class=&p&&(&/span&&span class=&n&&port2&/span&&span class=&p&&[&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&]&/span&&span class=&o&&*&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&o&&+&/span&&span class=&n&&next_step&/span&&span class=&o&&*&/span&&span class=&n&&kelly_position&/span&&span class=&p&&))&/span&
&span class=&k&&else&/span&&span class=&p&&:&/span&
&span class=&n&&port2&/span&&span class=&o&&.&/span&&span class=&n&&append&/span&&span class=&p&&(&/span&&span class=&n&&port2&/span&&span class=&p&&[&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&])&/span&
&span class=&k&&if&/span& &span class=&n&&port3&/span&&span class=&p&&[&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&]&/span& &span class=&o&&&&/span& &span class=&n&&base&/span&&span class=&o&&*&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&o&&-&/span&&span class=&n&&stopline&/span&&span class=&p&&):&/span&
&span class=&n&&port3&/span&&span class=&o&&.&/span&&span class=&n&&append&/span&&span class=&p&&(&/span&&span class=&n&&port3&/span&&span class=&p&&[&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&]&/span&&span class=&o&&*&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&o&&+&/span&&span class=&n&&next_step&/span&&span class=&o&&*&/span&&span class=&n&&rnd_position&/span&&span class=&p&&))&/span&
&span class=&k&&else&/span&&span class=&p&&:&/span&
&span class=&n&&port3&/span&&span class=&o&&.&/span&&span class=&n&&append&/span&&span class=&p&&(&/span&&span class=&n&&port3&/span&&span class=&p&&[&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&])&/span&
&span class=&k&&if&/span& &span class=&n&&port4&/span&&span class=&p&&[&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&]&/span& &span class=&o&&&&/span& &span class=&n&&base&/span&&span class=&o&&*&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&o&&-&/span&&span class=&n&&stopline&/span&&span class=&p&&):&/span&
&span class=&n&&port4&/span&&span class=&o&&.&/span&&span class=&n&&append&/span&&span class=&p&&(&/span&&span class=&n&&port4&/span&&span class=&p&&[&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&]&/span&&span class=&o&&*&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&o&&+&/span&&span class=&n&&next_step&/span&&span class=&o&&*&/span&&span class=&n&&rnd_position2&/span&&span class=&p&&))&/span&
&span class=&k&&else&/span&&span class=&p&&:&/span&
&span class=&n&&port4&/span&&span class=&o&&.&/span&&span class=&n&&append&/span&&span class=&p&&(&/span&&span class=&n&&port4&/span&&span class=&p&&[&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&])&/span&
&span class=&n&&port_A&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&]&/span& &span class=&o&&=&/span& &span class=&n&&port1&/span&
&span class=&n&&port_B&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&]&/span& &span class=&o&&=&/span& &span class=&n&&port2&/span&
&span class=&n&&port_C&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&]&/span& &span class=&o&&=&/span& &span class=&n&&port3&/span&
&span class=&n&&port_D&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&]&/span& &span class=&o&&=&/span& &span class=&n&&port4&/span&
&span class=&n&&plt&/span&&span class=&o&&.&/span&&span class=&n&&figure&/span&&span class=&p&&(&/span&&span class=&n&&figsize&/span& &span class=&o&&=&/span& &span class=&p&&(&/span&&span class=&mi&&8&/span&&span class=&p&&,&/span&&span class=&mi&&5&/span&&span class=&p&&))&/span&
&span class=&n&&plt&/span&&span class=&o&&.&/span&&span class=&n&&plot&/span&&span class=&p&&(&/span&&span class=&n&&exp&/span&&span class=&p&&(&/span&&span class=&n&&log&/span&&span class=&p&&(&/span&&span class=&n&&port_A&/span&&span class=&o&&.&/span&&span class=&n&&T&/span&&span class=&p&&)&/span&&span class=&o&&.&/span&&span class=&n&&sum&/span&&span class=&p&&()&/span&&span class=&o&&/&/span&&span class=&mi&&1000&/span&&span class=&p&&),&/span&&span class=&n&&label&/span& &span class=&o&&=&/span& &span class=&s1&&'port1:full'&/span&&span class=&p&&)&/span&
&span class=&n&&plt&/span&&span class=&o&&.&/span&&span class=&n&&plot&/span&&span class=&p&&(&/span&&span class=&n&&exp&/span&&span class=&p&&(&/span&&span class=&n&&log&/span&&span class=&p&&(&/span&&span class=&n&&port_B&/span&&span class=&o&&.&/span&&span class=&n&&T&/span&&span class=&p&&)&/span&&span class=&o&&.&/span&&span class=&n&&sum&/span&&span class=&p&&()&/span&&span class=&o&&/&/span&&span class=&mi&&1000&/span&&span class=&p&&),&/span&&span class=&s1&&'*'&/span&&span class=&p&&,&/span&&span class=&n&&label&/span& &span class=&o&&=&/span& &span class=&s1&&'port2:kelly'&/span&&span class=&p&&)&/span&
&span class=&n&&plt&/span&&span class=&o&&.&/span&&span class=&n&&plot&/span&&span class=&p&&(&/span&&span class=&n&&exp&/span&&span class=&p&&(&/span&&span class=&n&&log&/span&&span class=&p&&(&/span&&span class=&n&&port_C&/span&&span class=&o&&.&/span&&span class=&n&&T&/span&&span class=&p&&)&/span&&span class=&o&&.&/span&&span class=&n&&sum&/span&&span class=&p&&()&/span&&span class=&o&&/&/span&&span class=&mi&&1000&/span&&span class=&p&&),&/span&&span class=&n&&label&/span& &span class=&o&&=&/span& &span class=&s1&&'port3:0.25'&/span&&span class=&p&&)&/span&
&span class=&n&&plt&/span&&span class=&o&&.&/span&&span class=&n&&plot&/span&&span class=&p&&(&/span&&span class=&n&&exp&/span&&span class=&p&&(&/span&&span class=&n&&log&/span&&span class=&p&&(&/span&&span class=&n&&port_D&/span&&span class=&o&&.&/span&&span class=&n&&T&/span&&span class=&p&&)&/span&&span class=&o&&.&/span&&span class=&n&&sum&/span&&span class=&p&&()&/span&&span class=&o&&/&/span&&span class=&mi&&1000&/span&&span class=&p&&),&/span&&span class=&n&&label&/span& &span class=&o&&=&/span& &span class=&s1&&'port4:0.15'&/span&&span class=&p&&)&/span&
&span class=&n&&plt&/span&&span class=&o&&.&/span&&span class=&n&&legend&/span&&span class=&p&&(&/span&&span class=&n&&loc&/span& &span class=&o&&=&/span& &span class=&mi&&0&/span&&span class=&p&&)&/span&
&span class=&k&&print&/span& &span class=&s1&&'&/span&&span class=&se&&\n&/span&&span class=&s1&&不同组合的几何期望收益'&/span&
&span class=&k&&print&/span& &span class=&s1&&'full position &/span&&span class=&si&&%s&/span&&span class=&s1&&'&/span&&span class=&o&&%&/span&&span class=&n&&exp&/span&&span class=&p&&(&/span&&span class=&n&&log&/span&&span class=&p&&(&/span&&span class=&n&&port_A&/span&&span class=&o&&.&/span&&span class=&n&&T&/span&&span class=&p&&)&/span&&span class=&o&&.&/span&&span class=&n&&sum&/span&&span class=&p&&()&/span&&span class=&o&&/&/span&&span class=&mi&&1000&/span&&span class=&p&&)&/span&&span class=&o&&.&/span&&span class=&n&&iloc&/span&&span class=&p&&[&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&]&/span&
&span class=&k&&print&/span& &span class=&s1&&'kelly position &/span&&span class=&si&&%s&/span&&span class=&s1&&'&/span&&span class=&o&&%&/span&&span class=&n&&exp&/span&&span class=&p&&(&/span&&span class=&n&&log&/span&&span class=&p&&(&/span&&span class=&n&&port_B&/span&&span class=&o&&.&/span&&span class=&n&&T&/span&&span class=&p&&)&/span&&span class=&o&&.&/span&&span class=&n&&sum&/span&&span class=&p&&()&/span&&span class=&o&&/&/span&&span class=&mi&&1000&/span&&span class=&p&&)&/span&&span class=&o&&.&/span&&span class=&n&&iloc&/span&&span class=&p&&[&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&]&/span&
&span class=&k&&print&/span& &span class=&s1&&'position = 0.25 &/span&&span class=&si&&%s&/span&&span class=&s1&&'&/span&&span class=&o&&%&/span&&span class=&n&&exp&/span&&span class=&p&&(&/span&&span class=&n&&log&/span&&span class=&p&&(&/span&&span class=&n&&port_C&/span&&span class=&o&&.&/span&&span class=&n&&T&/span&&span class=&p&&)&/span&&span class=&o&&.&/span&&span class=&n&&sum&/span&&span class=&p&&()&/span&&span class=&o&&/&/span&&span class=&mi&&1000&/span&&span class=&p&&)&/span&&span class=&o&&.&/span&&span class=&n&&iloc&/span&&span class=&p&&[&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&]&/span&
&span class=&k&&print&/span& &span class=&s1&&'position = 0.15 &/span&&span class=&si&&%s&/span&&span class=&s1&&'&/span&&span class=&o&&%&/span&&span class=&n&&exp&/span&&span class=&p&&(&/span&&span class=&n&&log&/span&&span class=&p&&(&/span&&span class=&n&&port_D&/span&&span class=&o&&.&/span&&span class=&n&&T&/span&&span class=&p&&)&/span&&span class=&o&&.&/span&&span class=&n&&sum&/span&&span class=&p&&()&/span&&span class=&o&&/&/span&&span class=&mi&&1000&/span&&span class=&p&&)&/span&&span class=&o&&.&/span&&span class=&n&&iloc&/span&&span class=&p&&[&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&]&/span&
&/code&&/pre&&/div&&p&&strong&Out[1]:&/strong&&/p&&figure&&img src=&https://pic3.zhimg.com/bf82b420ae82ffc154f74_b.jpg& data-rawwidth=&511& data-rawheight=&448& class=&origin_image zh-lightbox-thumb& width=&511& data-original=&https://pic3.zhimg.com/bf82b420ae82ffc154f74_r.jpg&&&/figure&&p&观察四种操作方式：满仓下注、按凯利公式下注20%、按25%下注、按15%下注 &/p&&p&图为进行200次游戏之后几何期望资金曲线的情况 &/p&&br&&br&&p&&strong&凯利无疑是增长最快的！&/strong&&/p&&br&&br&&blockquote&&h4&&strong&从另一个角度，我们来理解一下&/strong&&/h4&&/blockquote&&p&不同赔率下，赢的概率多大我们会选择入场参与游戏？&/p&&br&&p&还是上面的游戏，如果赢的概率40%，输的概率60%，那么，期望净收益就是（1×0.4-0.6）& 0；从概率的角度说，一个期望净收益为负的游戏是不值得参与的，求得的f小于0，也就是不下注。&/p&&br&&p&下面看一下&strong&不同赔率下一个游戏赌赢的概率为多少才值得参加？&/strong&&/p&&br&&p&同样，用实验来观察：&/p&&br&&p&&strong&In[2]:&/strong&&/p&&div class=&highlight&&&pre&&code class=&language-python&&&span&&/span&&span class=&kn&&import&/span& &span class=&nn&&numpy&/span& &span class=&kn&&as&/span& &span class=&nn&&np&/span&
&span class=&kn&&from&/span& &span class=&nn&&mpl_toolkits.mplot3d&/span& &span class=&kn&&import&/span& &span class=&n&&Axes3D&/span&
&span class=&n&&b&/span& &span class=&o&&=&/span& &span class=&n&&np&/span&&span class=&o&&.&/span&&span class=&n&&linspace&/span&&span class=&p&&(&/span&&span class=&mi&&20&/span&&span class=&p&&,&/span&&span class=&mi&&1&/span&&span class=&p&&,&/span&&span class=&mi&&20&/span&&span class=&p&&)&/span&
&span class=&n&&pwin&/span& &span class=&o&&=&/span& &span class=&n&&np&/span&&span class=&o&&.&/span&&span class=&n&&linspace&/span&&span class=&p&&(&/span&&span class=&mi&&0&/span&&span class=&p&&,&/span&&span class=&mi&&1&/span&&span class=&p&&,&/span&&span class=&mi&&20&/span&&span class=&p&&)&/span&
&span class=&n&&b&/span&&span class=&p&&,&/span&&span class=&n&&pwin&/span& &span class=&o&&=&/span& &span class=&n&&np&/span&&span class=&o&&.&/span&&span class=&n&&meshgrid&/span&&span class=&p&&(&/span&&span class=&n&&b&/span&&span class=&p&&,&/span&&span class=&n&&pwin&/span&&span class=&p&&)&/span&
&span class=&n&&kelly&/span& &span class=&o&&=&/span& &span class=&p&&(&/span&&span class=&n&&b&/span&&span class=&o&&*&/span&&span class=&n&&pwin&/span&&span class=&o&&-&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&o&&-&/span&&span class=&n&&pwin&/span&&span class=&p&&))&/span&&span class=&o&&/&/span&&span class=&n&&b&/span&&span class=&o&&*&/span&&span class=&p&&(&/span&&span class=&n&&b&/span&&span class=&o&&*&/span&&span class=&n&&pwin&/span&&span class=&o&&-&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&o&&-&/span&&span class=&n&&pwin&/span&&span class=&p&&)&/span&&span class=&o&&&=&/span&&span class=&mi&&0&/span&&span class=&p&&)&/span&
&span class=&n&&zero&/span& &span class=&o&&=&/span& &span class=&mi&&0&/span&
&span class=&n&&fig&/span& &span class=&o&&=&/span& &span class=&n&&plt&/span&&span class=&o&&.&/span&&span class=&n&&figure&/span&&span class=&p&&(&/span&&span class=&n&&figsize&/span& &span class=&o&&=&/span& &span class=&p&&(&/span&&span class=&mi&&10&/span&&span class=&p&&,&/span&&span class=&mi&&6&/span&&span class=&p&&))&/span&
&span class=&n&&ax&/span& &span class=&o&&=&/span& &span class=&n&&fig&/span&&span class=&o&&.&/span&&span class=&n&&gca&/span&&span class=&p&&(&/span&&span class=&n&&projection&/span& &span class=&o&&=&/span& &span class=&s1&&'3d'&/span&&span class=&p&&)&/span&
&span class=&n&&surf&/span& &span class=&o&&=&/span& &span class=&n&&ax&/span&&span class=&o&&.&/span&&span class=&n&&plot_surface&/span&&span class=&p&&(&/span&&span class=&n&&b&/span&&span class=&p&&,&/span&&span class=&n&&pwin&/span&&span class=&p&&,&/span&&span class=&n&&kelly&/span&&span class=&p&&,&/span&&span class=&n&&rstride&/span&&span class=&o&&=&/span&&span class=&mi&&1&/span&&span class=&p&&,&/span& &span class=&n&&cstride&/span&&span class=&o&&=&/span&&span class=&mi&&1&/span&&span class=&p&&,&/span&&span class=&n&&cmap&/span& &span class=&o&&=&/span& &span class=&n&&plt&/span&&span class=&o&&.&/span&&span class=&n&&cm&/span&&span class=&o&&.&/span&&span class=&n&&coolwarm&/span&&span class=&p&&)&/span&
&span class=&n&&ax&/span&&span class=&o&&.&/span&&span class=&n&&plot_surface&/span&&span class=&p&&((&/span&&span class=&mi&&1&/span&&span class=&o&&-&/span&&span class=&n&&pwin&/span&&span class=&p&&)&/span&&span class=&o&&/&/span&&span class=&n&&pwin&/span&&span class=&p&&,&/span&&span class=&n&&pwin&/span&&span class=&p&&,&/span&&span class=&mi&&0&/span&&span class=&p&&)&/span&
&span class=&n&&ax&/span&&span class=&o&&.&/span&&span class=&n&&set_xlabel&/span&&span class=&p&&(&/span&&span class=&s1&&'b 赔率'&/span&&span class=&p&&)&/span&
&span class=&n&&ax&/span&&span class=&o&&.&/span&&span class=&n&&set_ylabel&/span&&span class=&p&&(&/span&&span class=&s1&&'pwin 赢概率'&/span&&span class=&p&&)&/span&
&span class=&n&&ax&/span&&span class=&o&&.&/span&&span class=&n&&set_zlabel&/span&&span class=&p&&(&/span&&span class=&s1&&'kelly 下注比例'&/span&&span class=&p&&)&/span&
&span class=&n&&fig&/span&&span class=&o&&.&/span&&span class=&n&&colorbar&/span&&span class=&p&&(&/span&&span class=&n&&surf&/span&&span class=&p&&,&/span&&span class=&n&&shrink&/span& &span class=&o&&=&/span& &span class=&mf&&0.6&/span&&span class=&p&&,&/span&&span class=&n&&aspect&/span& &span class=&o&&=&/span& &span class=&mi&&10&/span&&span class=&p&&)&/span&
&/code&&/pre&&/div&&p&&strong&Out[2]:&/strong&&/p&&br&&figure&&img src=&https://pic1.zhimg.com/70bfae0ed7fa88add89c2c_b.jpg& data-rawwidth=&551& data-rawheight=&354& class=&origin_image zh-lightbox-thumb& width=&551& data-original=&https://pic1.zhimg.com/70bfae0ed7fa88add89c2c_r.jpg&&&/figure&&p&上图说明两个问题：&/p&&br&&p&1. 如果一次赌博赔率越大，在赢的概率较小的情况下，凯利公式就开始提示要下注啦。（如图赔率为20时，只需要10%的赢率就可以入场玩啦）&/p&&br&&p&2. 同一赔率下，凯利公式只有在稳赢（赢概率=100%）时才会支持押下全部本金，否则都是本金的一定比例。也即永远不会输完所有的钱。&/p&&br&&br&&blockquote&&h3&&strong&三、炒股怎么用凯利公式？&/strong&&/h3&&/blockquote&&p&凯利的论文给出的押注策略，神奇之处就在于，当你总是遵循这一准则进行操作，你就能预测接下来发生的事情，你也能清楚的知道你的财富增长速度是在控制住风险情况下最优的结果。&/p&&br&&p&来看看凯利运用他的财富公式，专门成立的hedge fund 的performance~20年15倍，就是辣么厉害。&/p&&p&&figure&&img src=&https://pic2.zhimg.com/f_b.jpg& data-rawwidth=&707& data-rawheight=&543& class=&origin_image zh-lightbox-thumb& width=&707& data-original=&https://pic2.zhimg.com/f_r.jpg&&&/figure&数据：《财富公式：玩转拉斯维加斯和华尔街的故事》&/p&&br&&p&那么问题来了，我们&strong&量化炒股如何引入这么神奇的仓位管理神器？&/strong&&/p&&br&&p&因为股市的涨跌我们不会一次性赔光本金，所以引入损失率对凯利公式做微调，即更一般性的凯利公式：&/p&&figure&&img src=&https://pic2.zhimg.com/ac633b194d9eb77ff51fc68_b.jpg& data-rawwidth=&263& data-rawheight=&73& class=&content_image& width=&263&&&/figure&&p&&strong&f&/strong&：仓位比例 &/p&&p&&strong&Pwin&/strong&：赌赢的概率—股市上涨概率 &/p&&p&&strong&Ploss&/strong&：赌输的概率—股市下跌概率 &/p&&p&&strong&b&/strong&：赢钱率（资产从1增加到1+b） &/p&&p&&strong&c&/strong&：损失率（资产从1减少到1-c）&/p&&br&&br&&blockquote&&b&一般性凯利公式的证明过程（再次感谢&a href=&https://www.zhihu.com/people/850b6a38f141c& data-hash=&850b6a38f141c& class=&member_mention& data-title=&@程峰& data-editable=&true& data-hovercard=&p$b$850b6a38f141c&&@程峰&/a&的提议，在此加上证明过程）&br&&/b&&/blockquote&&p&一次投资过程，压上总资本（A）的一定比例：f*A。有pwin的概率赢，赢了财富为A*（1+fb），ploss的概率会输，输了资本变为A*（1-fc）。N次投资后，总资本函数为：&/p&&br&&p&凯利公式要做的是使得总资本曲线的几何收益最大，也就是log(An)/N最大。即log(AN)/N对f求导=0时f的值就是凯利公式了~&/p&&br&&figure&&img src=&https://pic4.zhimg.com/2f72fa918f61ffb28d2b9eaa0d528de7_b.jpg& data-rawwidth=&514& data-rawheight=&249& class=&origin_image zh-lightbox-thumb& width=&514& data-original=&https://pic4.zhimg.com/2f72fa918f61ffb28d2b9eaa0d528de7_r.jpg&&&/figure&&br&&br&&blockquote&&p&&strong&仔细想一个问题（挖矿秘籍）&/strong&&br&&/p&&/blockquote&&p&赌博和买股票，赢概率Pwin和输概率Ploss究竟是什么？&/p&&br&&p&赌博的时候，Pwin和Ploss是根据游戏规则算出的概率而定。比如投硬币（Pwin=Ploss=0.5），或者转轮盘，扑克等更为复杂的游戏。&/p&&br&&p&而买股票的过程，是n次离散赌博的过程。当你找到一个有效信号之后进行一次操作（比如有效信号是价格突破5日均线，财务数据好，成交量放大，或者各种金叉死叉等等。。）&/p&&br&&p&假设我们找到了一个有效信号，信号发生时，股价为S。我们提前给定价格S（1+b）和S（1-c）作为信号发生后止盈和止损的边界，这个时候的Pwin和Ploss应该是基于历史这个信号的收益情况做数据统计分析胜率（赢概率）和败率（输概率）来给出，也即价格触碰到S（1+b）止盈的概率是Pwin，触碰到S（1-c）止损的概率是Ploss。&/p&&p&关于信号这部分的可视化的理解，可参见&a href=&https://link.zhihu.com/?target=https%3A//www.joinquant.com/post/1311& class=& wrap external& target=&_blank& rel=&nofollow noreferrer&&好多凯利公式的文章，但好像没有说透彻的……&/a&。这篇是与JoinQuant的小编讨论后发布在JQ社区的一篇文章。&/p&&br&&br&&p&&strong&又举一个简单例子&/strong&&/p&&br&&p&&strong&有效信号&/strong&：当前价突破5日均线 &/p&&p&&strong&统计样本&/strong&：100只相似股票，过去三年有效信号发生了1000次&/p&&p&&strong&统计包含&/strong&：假定上涨20%止盈，下跌20%止损。止盈赢钱的次数57次，止损输钱的次数43次&/p&&br&&p&对应公式的&strong&参数&/strong&：Pwin=0.57，Ploss=0.43，b=0.20，c=0.20&/p&&br&&p&此时f=Pwin/c – Ploss/b = 0.57/0.20 – 0.43/0.20= 70%&/p&&br&&p&按照我们对某一个有效信号做历史统计定出来的Pwin，Ploss，b和c来进行模拟的投资组合看看看效果：&/p&&br&&p&&strong&In[3]:&/strong&&/p&&div class=&highlight&&&pre&&code class=&language-python&&&span&&/span&&span class=&kn&&from&/span& &span class=&nn&&pandas&/span& &span class=&kn&&import&/span& &span class=&n&&DataFrame&/span&
&span class=&n&&base&/span& &span class=&o&&=&/span& &span class=&mi&&100&/span&
&span class=&n&&pwin&/span& &span class=&o&&=&/span& &span class=&mf&&0.57&/span&
&span class=&n&&ploss&/span& &span class=&o&&=&/span& &span class=&mi&&1&/span&&span class=&o&&-&/span&&span class=&n&&pwin&/span&
&span class=&n&&b&/span& &span class=&o&&=&/span& &span class=&mf&&0.2&/span&
&span class=&n&&c&/span& &span class=&o&&=&/span& &span class=&mf&&0.2&/span&
&span class=&c1&&# stopline后文会介绍&/span&
&span class=&n&&stopline&/span& &span class=&o&&=&/span& &span class=&mi&&1&/span&
&span class=&n&&rnd_position&/span& &span class=&o&&=&/span& &span class=&mf&&0.6&/span&
&span class=&n&&rnd_position2&/span& &span class=&o&&=&/span& &span class=&mf&&0.9&/span&
&span class=&n&&kelly_position&/span& &span class=&o&&=&/span& &span class=&p&&(&/span&&span class=&n&&pwin&/span&&span class=&o&&/&/span&&span class=&n&&c&/span& &span class=&o&&-&/span& &span class=&n&&ploss&/span&&span class=&o&&/&/span&&span class=&n&&b&/span&&span class=&p&&)&/span&&span class=&o&&*&/span&&span class=&n&&stopline&/span&
&span class=&k&&print&/span& &span class=&s1&&'kelly position is &/span&&span class=&si&&%s&/span&&span class=&s1&&'&/span&&span class=&o&&%&/span&&span class=&n&&kelly_position&/span&
&span class=&n&&port_A&/span& &span class=&o&&=&/span& &span class=&n&&DataFrame&/span&&span class=&p&&()&/span&
&span class=&n&&port_B&/span& &span class=&o&&=&/span& &span class=&n&&DataFrame&/span&&span class=&p&&()&/span&
&span class=&n&&port_C&/span& &span class=&o&&=&/span& &span class=&n&&DataFrame&/span&&span class=&p&&()&/span&
&span class=&n&&port_D&/span& &span class=&o&&=&/span& &span class=&n&&DataFrame&/span&&span class=&p&&()&/span&
&span class=&c1&&#重复模拟次数&/span&
&span class=&k&&for&/span& &span class=&n&&i&/span& &span class=&ow&&in&/span& &span class=&nb&&range&/span&&span class=&p&&(&/span&&span class=&mi&&1000&/span&&span class=&p&&):&/span&
&span class=&n&&port1&/span& &span class=&o&&=&/span& &span class=&p&&[&/span&&span class=&n&&base&/span&&span class=&p&&]&/span&
&span class=&n&&port2&/span& &span class=&o&&=&/span& &span class=&p&&[&/span&&span class=&n&&base&/span&&span class=&p&&]&/span&
&span class=&n&&port3&/span& &span class=&o&&=&/span& &span class=&p&&[&/span&&span class=&n&&base&/span&&span class=&p&&]&/span&
&span class=&n&&port4&/span& &span class=&o&&=&/span& &span class=&p&&[&/span&&span class=&n&&base&/span&&span class=&p&&]&/span&
&span class=&c1&&#投资次数步长&/span&
&span class=&k&&for&/span& &span class=&n&&step&/span& &span class=&ow&&in&/span& &span class=&nb&&range&/span&&span class=&p&&(&/span&&span class=&mi&&500&/span&&span class=&p&&):&/span&
&span class=&n&&rnd&/span& &span class=&o&&=&/span& &span class=&n&&random&/span&&span class=&o&&.&/span&&span class=&n&&random&/span&&span class=&p&&()&/span&
&span class=&k&&if&/span& &span class=&n&&rnd&/span& &span class=&o&&&&/span& &span class=&n&&pwin&/span&&span class=&p&&:&/span&
&span class=&n&&next_step&/span& &span class=&o&&=&/span& &span class=&n&&b&/span&
&span class=&k&&else&/span&&span class=&p&&:&/span&
&span class=&n&&next_step&/span& &span class=&o&&=&/span& &span class=&o&&-&/span&&span class=&n&&c&/span&
&span class=&k&&if&/span& &span class=&n&&port1&/span&&span class=&p&&[&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&]&/span& &span class=&o&&&&/span& &span class=&n&&base&/span&&span class=&o&&*&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&o&&-&/span&&span class=&n&&stopline&/span&&span class=&p&&):&/span&
&span class=&n&&port1&/span&&span class=&o&&.&/span&&span class=&n&&append&/span&&span class=&p&&(&/span&&span class=&n&&port1&/span&&span class=&p&&[&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&]&/span&&span class=&o&&*&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&o&&+&/span&&span class=&n&&next_step&/span&&span class=&p&&))&/span&
&span class=&k&&else&/span&&span class=&p&&:&/span&
&span class=&n&&port1&/span&&span class=&o&&.&/span&&span class=&n&&append&/span&&span class=&p&&(&/span&&span class=&n&&port1&/span&&span class=&p&&[&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&])&/span&
&span class=&k&&if&/span& &span class=&n&&port2&/span&&span class=&p&&[&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&]&/span& &span class=&o&&&&/span& &span class=&n&&base&/span&&span class=&o&&*&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&o&&-&/span&&span class=&n&&stopline&/span&&span class=&p&&):&/span&
&span class=&n&&port2&/span&&span class=&o&&.&/span&&span class=&n&&append&/span&&span class=&p&&(&/span&&span class=&n&&port2&/span&&span class=&p&&[&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&]&/span&&span class=&o&&*&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&o&&+&/span&&span class=&n&&next_step&/span&&span class=&o&&*&/span&&span class=&n&&kelly_position&/span&&span class=&p&&))&/span&
&span class=&k&&else&/span&&span class=&p&&:&/span&
&span class=&n&&port2&/span&&span class=&o&&.&/span&&span class=&n&&append&/span&&span class=&p&&(&/span&&span class=&n&&port2&/span&&span class=&p&&[&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&])&/span&
&span class=&k&&if&/span& &span class=&n&&port3&/span&&span class=&p&&[&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&]&/span& &span class=&o&&&&/span& &span class=&n&&base&/span&&span class=&o&&*&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&o&&-&/span&&span class=&n&&stopline&/span&&span class=&p&&):&/span&
&span class=&n&&port3&/span&&span class=&o&&.&/span&&span class=&n&&append&/span&&span class=&p&&(&/span&&span class=&n&&port3&/span&&span class=&p&&[&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&]&/span&&span class=&o&&*&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&o&&+&/span&&span class=&n&&next_step&/span&&span class=&o&&*&/span&&span class=&n&&rnd_position&/span&&span class=&p&&))&/span&
&span class=&k&&else&/span&&span class=&p&&:&/span&
&span class=&n&&port3&/span&&span class=&o&&.&/span&&span class=&n&&append&/span&&span class=&p&&(&/span&&span class=&n&&port3&/span&&span class=&p&&[&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&])&/span&
&span class=&k&&if&/span& &span class=&n&&port4&/span&&span class=&p&&[&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&]&/span& &span class=&o&&&&/span& &span class=&n&&base&/span&&span class=&o&&*&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&o&&-&/span&&span class=&n&&stopline&/span&&span class=&p&&):&/span&
&span class=&n&&port4&/span&&span class=&o&&.&/span&&span class=&n&&append&/span&&span class=&p&&(&/span&&span class=&n&&port4&/span&&span class=&p&&[&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&]&/span&&span class=&o&&*&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&o&&+&/span&&span class=&n&&next_step&/span&&span class=&o&&*&/span&&span class=&n&&rnd_position2&/span&&span class=&p&&))&/span&
&span class=&k&&else&/span&&span class=&p&&:&/span&
&span class=&n&&port4&/span&&span class=&o&&.&/span&&span class=&n&&append&/span&&span class=&p&&(&/span&&span class=&n&&port4&/span&&span class=&p&&[&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&])&/span&
&span class=&n&&port_A&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&]&/span& &span class=&o&&=&/span& &span class=&n&&port1&/span&
&span class=&n&&port_B&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&]&/span& &span class=&o&&=&/span& &span class=&n&&port2&/span&
&span class=&n&&port_C&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&]&/span& &span class=&o&&=&/span& &span class=&n&&port3&/span&
&span class=&n&&port_D&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&]&/span& &span class=&o&&=&/span& &span class=&n&&port4&/span&
&span class=&n&&plt&/span&&span class=&o&&.&/span&&span class=&n&&figure&/span&&span class=&p&&(&/span&&span class=&n&&figsize&/span& &span class=&o&&=&/span& &span class=&p&&(&/span&&span class=&mi&&8&/span&&span class=&p&&,&/span&&span class=&mi&&5&/span&&span class=&p&&))&/span&
&span class=&n&&plt&/span&&span class=&o&&.&/span&&span class=&n&&plot&/span&&span class=&p&&(&/span&&span class=&n&&exp&/span&&span class=&p&&(&/span&&span class=&n&&log&/span&&span class=&p&&(&/span&&span class=&n&&port_A&/span&&span class=&o&&.&/span&&span class=&n&&T&/span&&span class=&p&&)&/span&&span class=&o&&.&/span&&span class=&n&&sum&/span&&span class=&p&&()&/span&&span class=&o&&/&/span&&span class=&mi&&1000&/span&&span class=&p&&),&/span&&span class=&n&&label&/span& &span class=&o&&=&/span& &span class=&s1&&'port1:full'&/span&&span class=&p&&)&/span&
&span class=&n&&plt&/span&&span class=&o&&.&/span&&span class=&n&&plot&/span&&span class=&p&&(&/span&&span class=&n&&exp&/span&&span class=&p&&(&/span&&span class=&n&&log&/span&&span class=&p&&(&/span&&span class=&n&&port_B&/span&&span class=&o&&.&/span&&span class=&n&&T&/span&&span class=&p&&)&/span&&span class=&o&&.&/span&&span class=&n&&sum&/span&&span class=&p&&()&/span&&span class=&o&&/&/span&&span class=&mi&&1000&/span&&span class=&p&&),&/span&&span class=&n&&label&/span& &span class=&o&&=&/span& &span class=&s1&&'port2:kelly'&/span&&span class=&p&&)&/span&
&span class=&n&&plt&/span&&span class=&o&&.&/span&&span class=&n&&plot&/span&&span class=&p&&(&/span&&span class=&n&&exp&/span&&span class=&p&&(&/span&&span class=&n&&log&/span&&span class=&p&&(&/span&&span class=&n&&port_C&/span&&span class=&o&&.&/span&&span class=&n&&T&/span&&span class=&p&&)&/span&&span class=&o&&.&/span&&span class=&n&&sum&/span&&span class=&p&&()&/span&&span class=&o&&/&/span&&span class=&mi&&1000&/span&&span class=&p&&),&/span&&span class=&n&&label&/span& &span class=&o&&=&/span& &span class=&s1&&'port3:position = 0.6'&/span&&span class=&p&&)&/span&
&span class=&n&&plt&/span&&span class=&o&&.&/span&&span class=&n&&plot&/span&&span class=&p&&(&/span&&span class=&n&&exp&/span&&span class=&p&&(&/span&&span class=&n&&log&/span&&span class=&p&&(&/span&&span class=&n&&port_D&/span&&span class=&o&&.&/span&&span class=&n&&T&/span&&span class=&p&&)&/span&&span class=&o&&.&/span&&span class=&n&&sum&/span&&span class=&p&&()&/span&&span class=&o&&/&/span&&span class=&mi&&1000&/span&&span class=&p&&),&/span&&span class=&n&&label&/span& &span class=&o&&=&/span& &span class=&s1&&'port3:position = 0.9'&/span&&span class=&p&&)&/span&
&span class=&n&&plt&/span&&span class=&o&&.&/span&&span class=&n&&legend&/span&&span class=&p&&(&/span&&span class=&n&&loc&/span& &span class=&o&&=&/span& &span class=&mi&&0&/span&&span class=&p&&)&/span&
&span class=&k&&print&/span& &span class=&s1&&'&/span&&span class=&se&&\n&/span&&span class=&s1&&不同组合的几何期望收益'&/span&
&span class=&k&&print&/span& &span class=&s1&&'full position &/span&&span class=&si&&%s&/span&&span class=&s1&&'&/span&&span class=&o&&%&/span&&span class=&n&&exp&/span&&span class=&p&&(&/span&&span class=&n&&log&/span&&span class=&p&&(&/span&&span class=&n&&port_A&/span&&span class=&o&&.&/span&&span class=&n&&T&/span&&span class=&p&&)&/span&&span class=&o&&.&/span&&span class=&n&&sum&/span&&span class=&p&&()&/span&&span class=&o&&/&/span&&span class=&mi&&1000&/span&&span class=&p&&)&/span&&span class=&o&&.&/span&&span class=&n&&iloc&/span&&span class=&p&&[&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&]&/span&
&span class=&k&&print&/span& &span class=&s1&&'kelly position &/span&&span class=&si&&%s&/span&&span class=&s1&&'&/span&&span class=&o&&%&/span&&span class=&n&&exp&/span&&span class=&p&&(&/span&&span class=&n&&log&/span&&span class=&p&&(&/span&&span class=&n&&port_B&/span&&span class=&o&&.&/span&&span class=&n&&T&/span&&span class=&p&&)&/span&&span class=&o&&.&/span&&span class=&n&&sum&/span&&span class=&p&&()&/span&&span class=&o&&/&/span&&span class=&mi&&1000&/span&&span class=&p&&)&/span&&span class=&o&&.&/span&&span class=&n&&iloc&/span&&span class=&p&&[&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&]&/span&
&span class=&k&&print&/span& &span class=&s1&&'position = 0.6 &/span&&span class=&si&&%s&/span&&span class=&s1&&'&/span&&span class=&o&&%&/span&&span class=&n&&exp&/span&&span class=&p&&(&/span&&span class=&n&&log&/span&&span class=&p&&(&/span&&span class=&n&&port_C&/span&&span class=&o&&.&/span&&span class=&n&&T&/span&&span class=&p&&)&/span&&span class=&o&&.&/span&&span class=&n&&sum&/span&&span class=&p&&()&/span&&span class=&o&&/&/span&&span class=&mi&&1000&/span&&span class=&p&&)&/span&&span class=&o&&.&/span&&span class=&n&&iloc&/span&&span class=&p&&[&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&]&/span&
&span class=&k&&print&/span& &span class=&s1&&'position = 0.9 &/span&&span class=&si&&%s&/span&&span class=&s1&&'&/span&&span class=&o&&%&/span&&span class=&n&&exp&/span&&span class=&p&&(&/span&&span class=&n&&log&/span&&span class=&p&&(&/span&&span class=&n&&port_D&/span&&span class=&o&&.&/span&&span class=&n&&T&/span&&span class=&p&&)&/span&&span class=&o&&.&/span&&span class=&n&&sum&/span&&span class=&p&&()&/span&&span class=&o&&/&/span&&span class=&mi&&1000&/span&&span class=&p&&)&/span&&span class=&o&&.&/span&&span class=&n&&iloc&/span&&span class=&p&&[&/span&&span class=&o&&-&/span&&span class=&mi&&1&/span&&span class=&p&&]&/span&
&/code&&/pre&&/div&&p&&strong&Out[3]:&/strong&&/p&&br&&figure&&img src=&https://pic1.zhimg.com/ee54b294025_b.jpg& data-rawwidth=&511& data-rawheight=&446& class=&origin_image zh-lightbox-thumb& width=&511& data-original=&https://pic1.zhimg.com/ee54b294025_r.jpg&&&/figure&&p&同样四种仓位操作后的资金曲线来进行比较：&/p&&br&&p&1. 凯利公式下资金曲线增长是最快的。&/p&&p&2. 高于或低于凯利公式的比例资金曲线增长都不是最快的。&/p&&br&&br&&blockquote&&p&&strong&再思考一个问题：关于杠杆&/strong&&/p&&/blockquote&&p&&strong&再多举一个例子：f&1&/strong&&/p&&p&研究不能止步于此啊。很多知道凯利公式的朋友都有的疑问，是凯利计算出来的仓位容易过大。比如一不小心就提示几倍，几十倍了。这是什么情况呢？&/p&&br&&p&比如我们找到一个信号：Pwin=0.7，Ploss=0.3，b=0.20，c=0.20&/p&&br&&p&来看看实验结果（代码同上，只修改上述参数）&/p&&br&&p&&strong&Out[4]:&/strong&&/p&&br&&figure&&img src=&https://pic1.zhimg.com/1feaacae64389b_b.jpg& data-rawwidth=&520& data-rawheight=&445& class=&origin_image zh-lightbox-thumb& width=&520& data-original=&https://pic1.zhimg.com/1feaacae64389b_r.jpg&&&/figure&&p&f&1了，甚至等于4了，什么意思！！凯利公式在告诉你这个信号太好了，值得你做4倍的杠杆来操作~！什么，你说我多加一点好不好，看上图，加到6倍显然就挫了。。。&/p&&br&&p&（想知道凯利公式为何能做到几何期望收益最大化，证明过程戳wiki百科自行科普）&/p&&br&&br&&blockquote&&p&&strong&再思考一个止损的问题，stopline不为1&/strong&&/p&&/blockquote&&p&上面杠杆的问题引出其实说明了A股版凯利公式&strong&暗含的一个假设&/strong&：&/p&&br&&p&&strong&资金可以随意无摩擦地加杠杆操作，无借贷成本。&/strong&&/p&&br&&p&什么意思。一个好的信号，凯利会告诉你在已知风险（Pwin，Ploss，b和c）的情况下，最优的杠杆是多少。你可以毫不犹豫的就按这个杠杆去操作，最大化自己的资金曲线。&/p&&br&&p&那么真实情况下呢，我们可能不加杠杆，而且也不能承受全部本金损失掉的风险。也就是，我们stopline会小于1，甚至只到30%或者20%。那这时候凯利公式怎么用？&/p&&br&&p&这里不做实验，仅抛个引子。感兴趣的朋友可以继续深入研究，也欢迎与我探讨。&/p&&br&&br&&p&&strong&A. 静态止损：即亏损本金的固定数额后撤出投资&/strong&&/p&&p&kelly_position = (pwin/c - ploss/b)×stopline &/p&&p&stopline应为此时剩余可承受的损失/本金base。&/p&&br&&p&举例：base=100元，输20元止损。initial_stopline = 0.2。假设损失率c = 0.04 &/p&&br&&p&第一次，赔了4块，base=96，stopline = （20-4）/96 = 0.16 &/p&&p&第n次，输输赢赢后，base = 250，stopline = （150+20）/250 = 0.68&/p&&br&&br&&p&&strong&B. 动态止损：即亏损剩余资金的一定比例后撤出投资&/strong&&/p&&p&比如动态20%止损。base =100元，赚到200元后，如亏损到160元即止损。&br&&/p&&br&&p&这个具体实验就留给各位自己研究啦~~&/p&&br&&br&&blockquote&&h3&&strong&Bonus：小结一下&/strong&&br&&/h3&&/blockquote&&p&好啦，少年。真正赚钱的是找有效的因子or信号，使得Pwin尽可能大，b尽可能大。无论是以往大家关注的一些技术指标（各种金叉、死叉）还是量价指标（放量、突破等等）又或者是财务指标，都可以作为一个信号。&/p&&br&&p&统计历史信号出现时的一个表现，得到这个信号产生的收益的分布。只要这个信号的收益分布正偏一些些，就是纯纯的Alpha啊。当然这个因子or信号的挖掘，就是作为矿工孜孜不倦追求的终极目标了。当你找到这样一个神奇的信号，配上凯利公式会让你的财富增加更快~&/p&&br&&p&好啦，说完啦。挖信号去了~&/p&&br&&figure&&img src=&https://pic1.zhimg.com/11af0e038d2d4cd5c5cfe5_b.jpg& data-rawwidth=&200& data-rawheight=&200& class=&content_image& width=&200&&&/figure&&br&&p&&strong&致谢&/strong&&/p&&p&本文研究工具为IPython Notebook 2.7。API来自聚宽（JoinQuant），在此表示感谢。&/p&&p&更多扩展可见：&a href=&https://link.zhihu.com/?target=https%3A//www.joinquant.com/post/1311& class=& wrap external& target=&_blank& rel=&nofollow noreferrer&&好多凯利公式的文章，但好像没有说透彻的……&/a&&/p&&p&关于凯利和他的财富公式，有一本书专门介绍这个。&a href=&https://link.zhihu.com/?target=http%3A//pan.baidu.com/s/1csjyDg& class=& wrap external& target=&_blank& rel=&nofollow noreferrer&&财富公式：玩转拉斯维加斯和华尔街的故事.PDF&/a&，密码：i8fi。&/p&&br&最后：附上凯利的论文，&a href=&https://link.zhihu.com/?target=http%3A//www.princeton.edu/%7Ewbialek/rome/refs/kelly_56.pdf& class=& wrap external& target=&_blank& rel=&nofollow noreferrer&&A New Interpretation of Information Rate&/a&&br&&br&&p&资源共享，是人类进步的推动力&br&&/p&&p&&b&『分享文章+关注公众号』&/b&&/p&&p&回复&b&『大数据书籍』&/b&or&b&『量化书籍』&/b&领取&/p&&figure&&img src=&https://pic1.zhimg.com/be1f473b7ced75530ed01_b.jpg& data-rawwidth=&720& data-rawheight=&405& class=&origin_image zh-lightbox-thumb& width=&720& data-original=&https://pic1.zhimg.com/be1f473b7ced75530ed01_r.jpg&&&/figure&&blockquote&更多内容：&a href=&https://zhuanlan.zhihu.com/quantstory& class=&internal&&神秘的宽客们 - 知乎专栏&/a&&/blockquote&
今天我们介绍一个神奇的人，和他神奇的公式。目前网络上传播较广的一篇讲凯利公式前世今生的文章，个人认为深度不够，而且思路是有问题的。大家不要看多了走偏路。最近也花了一些力气做梳理，把这篇分享出来，尽量做到讲对，讲透，也是提醒各位，低头挖矿，…
&figure&&img src=&https://pic1.zhimg.com/v2-89c2a15ffeb76da666ac39_b.jpg& data-rawwidth=&735& data-rawheight=&452& class=&origin_image zh-lightbox-thumb& width=&735& data-original=&https://pic1.zhimg.com/v2-89c2a15ffeb76da666ac39_r.jpg&&&/figure&&h1&&strong&文 | 君临&/strong&&br&&/h1&&br&&h1&1、罗斯福和杜鲁门&/h1&&figure&&img src=&https://pic1.zhimg.com/v2-6b5edf6fbdacb5da1e587_b.jpg& data-rawwidth=&355& data-rawheight=&247& class=&content_image& width=&355&&&/figure&&br&&p&年，连续20年，民主党总统牢牢掌握着政权。这个时期的股市，由于战争的动荡，处于漫长的熊市修复阶段，投机者们完全被股市吓破了胆，躲得远远的。&/p&&p&作为民主党总统，他们的执政思路很简单：加税、投资、严厉金融监控、建设福利社会。比如1933年，证券法出台，此后施行了分业管理、利率管制、存款保险等一系列举措，将金融风险纳入到管控的轨道上来。&/p&&p&这些措施成了以后美国两党的鲜明区别：民主党崇尚大政府，加税+引导投资。共和党则相反，崇尚小政府，减税+放松管制。不同的治理思路，带来了迥异的资本市场表现，在后面的世纪大牛市中，我们将看的一清二楚。&/p&&br&&br&&h1&2、艾森豪威尔&/h1&&figure&&img src=&https://pic3.zhimg.com/v2-40b7a7da1ac_b.jpg& data-rawwidth=&374& data-rawheight=&277& class=&content_image& width=&374&&&/figure&&br&&p&年，二战盟军总司令艾森豪威尔上台，代表共和党执政了8年。&/p&&p&艾森豪威尔醉心于军政，和苏联在国际舞台上争锋，经济上基本交给了他的内阁来打理。这批人几乎全部来自洛克菲勒、摩根、杜邦、通用汽车的高管。&/p&&p&尤其是通用汽车的高管，在这届政府中具有强大的施政影响力，在某次参议院听证会上，面对参议员的质询，如果一项决策有利于美国但不利于通用汽车，他该当如何？曾经当过通用汽车总经理的该名部长说出了一段名言，“多年来我一向认为，凡是对美国有利的对通用也有利，反之，凡是对通用汽车有利的，对美国也有利。”&/p&&p&那么什么是对通用汽车最有利的呢？当然是交通基础设施的便利了，所以在1950年代，一张覆盖全国的高速公路网建设被打造了出来。以此为起点，美国战后的黄金年代正式拉开帷幕，加上减税、放松金融管制的刺激，道琼斯工业平均指数涨了239.5%，是除1990年代外道指表现最好的十年。&/p&&p&内需市场繁荣下，最好的股票是什么呢？答案是：房地产、建筑业、钢铁、有色金属、造纸、保龄球……这些行业的股票占据了1950年代资本市场的主流，投资者只要买了就能挣到钱，可以悠闲的享受惬意的午餐，俗称“三杯马提尼酒的时代”。&/p&&br&&br&&h1&3、肯尼迪、约翰逊&/h1&&figure&&img src=&https://pic1.zhimg.com/v2-a7bdb8acf60c6abf1d8aa2be3397ad36_b.jpg& data-rawwidth=&344& data-rawheight=&254& class=&content_image& width=&344&&&/figure&&br&&p&年，民主党再次上台执政，面对赫鲁晓夫治下的苏联咄咄逼人的扩张，年轻的肯尼迪发动了一项250亿美元的阿波罗登月计划，这项计划对整个60年代的投资市场产生了深远的影响。&/p&&p&太空主题和高科技主题的电子股成为了这个时代的主旋律，摩托罗拉、德州仪器、惠普、拍立得、施乐等电子公司成为每天媒体报道的焦点，就像90年代的互联网公司，只要带个“.com”就会被捧上天一样，这个时代只要是个电子公司，后缀带个“trons”都会被投资者们疯狂买入。&/p&&p&这是战后第一次的成长股泡沫，著名的成长股投资者费雪在风口下封神。他的两只代表股票，德州仪器涨幅超过30倍，摩托罗拉涨幅超过19倍，1959年出版的《怎样选择成长股》，更是成为《纽约时报》有史以来登上畅销书排行榜的第一部投资方面的著作。&/p&&br&&br&&h1&4、尼克松、福特&/h1&&figure&&img src=&https://pic4.zhimg.com/v2-87d8cbb7dabfd017fdb89a_b.jpg& data-rawwidth=&373& data-rawheight=&244& class=&content_image& width=&373&&&/figure&&br&&p&年，共和党回归，尼克松放弃了和共产世界的对抗。作为美国总统，他第一次访问了苏联，和中国建立了外交关系，成为了中国人民的老朋友，撤出了越南战争。所有这些对抗的结束，预示着财政大幅支出的告一段落，“休养生息”成为时代的主题。&/p&&p&在投资市场，高科技成长股的概念也丧失了魅力，内需价值大盘股重归主流。通用电气、宝丽来、可口可乐、麦当劳、迪斯尼、雅芳等消费行业龙头被认为是“信得