凯利公式的正确算法

凯利公式的正确算法

有一个扔硬币的游戏:假设你有100元,如果硬币为正面,你就赢得投入金额的2倍;如果硬币为反面,你只输掉投入金额。比如,你押注10元,如果硬币为正面,那你赚了20元,本金加赚的就变成了120元;如果硬币为反面,那你就亏了10元,本金还剩下90元,你觉得怎么押注才能让自己的收益最大化呢?

简单来讲,凯利公式是一个根据赔率来计算最佳投注比例,以此来获得最高赌博收益的公式。

在巴菲特、查理·芒格和比尔·格罗斯的推广下,这个公式早已风靡投资圈,被称为“资金管理神器”。

凯利公式有个最基本的道理:正期望值的游戏才可以下注。

算法难点:赔率b的确定最近在凯利公式交流群里,很多人还是弄不清楚具体的计算方法。实际上大部分都纠结在赔率b上。赔率的b应该是盈亏比,就是承担失去多少本金的风险,获得多少本金的收益。比如说,很多人说1赔1.985,看清来还挺诱人的。实际上,承担了失去1的风险,获得0.985的收益,那个1只是人家把下注的本金还给你而已。 在股市里,承担亏5%的风险,获得10%的收益,那么b就等于10%/5%=2,所以,实际上很简单,核心在于b的确定。在计算中,用到原始公式,详细请看下文。 (一)娱乐场模式: f*=(pb-q)/bp是成功率,q是失败率,b是盈亏比b=赢/输 赢不包含本金例: 某局,1赔1.985,实际净赔率0.985, 成功率50%,问最佳下注比例多少? f*=(0.5x0.985-0.5)/0.985=-0.76% 负的,说明不能下注 几乎所有的赌博游戏,结果都是负的所以,按照凯利的结果是不能参与的!(二)股市模式 f*=p/r2-q/r1或(pr1-qr2)/(r1*r2)

其中,r1为止盈,r2为止损

例1,止盈10%,止损5%,成功率50%那么代入就可以计算了f*=50%/5%-50%/10%=5例2,止盈20%,止损10%,成功率50%f*=50%/10%-50%/20%=2.5 进一步解析, 5倍杠杆?2.5倍杠杆? 例1中,如果止损500%*5%=25% 例2中,如果止损250%*10%=25% 由此可知 当b=2时即 10%/5%=2, 20%/10%=2最佳的亏损比例是原始本金的25%与f*=(pb-q)/b的结论一致 凯利公式的详细说明,点击查看https://www.moshike.com/a/1583.html

温馨提示:以上仅为理论计算,股市和期货的概率和赔率随时都在变化,不可简单套用,加杠杆有爆仓风险,请谨慎加杠杆。

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