问题 1 :假设你每次拿出一半资金来赌,用抛硬币决定胜负,抛 100 次的情况下,你获胜的概率是多少?
问题 2 :如果你单个交易胜率为 55% ,每次交易的亏赢风险为 2.5% ,交易 100 次后你获胜的概率是多少? 预期回报是多少?
问题 3 :多次交易后的风险和报酬成正比吗?
问题 4 :已知交易的胜率,怎样选择风险?
问题 5 :某期权交易员的交易胜率只有 20% ,每次交易如果输,将损失 1% 的资金,如果赢,将赚 5% 的资金。多次交易后他能赢吗?
TCT 交易风险和回报 概率计算公式 :
基本的假设:
1 .进行 N 次交易
2 .每次交易的获胜的概率为 W
3.每次交易的或亏 L 或赢 G(风险)
那么在进行 N 次交易后获胜的概率 P 是:
P = P(W,L,G,N)
预期回报E 是:
E = E(L,G,N) (和风险,交易次数 N 有关,和胜率 W 无关!)
现在用计算结果来回答上面所提出的几个问题:
问题1:
P(50% ,50% ,50% ,100) = 0.33% ,获胜的概率连 1% 都不到。
问题2:
P (55% ,2.5% ,2.5% ,100) = 81.73% , E (2.5% ,2.5% ,100) = 21.67%
问题 3:
见以下计算结果(以 55% 的胜率, 100 次交易, 风险 逐步增加为例):
P (55% , 1.25% ,125% ,100) = 81.73% , E (1.25% ,1.25% ,100) = 10.85%
P (55% , 2.5% ,2.5% ,100) = 81.73% , E (2.5% ,2.5% ,100) = 21.67%
P (55% ,5.0% ,5.0% ,100) = 75.06% , E (5.0% ,5.0% ,100) = 51.74%
P (55% ,10% ,10% ,100) = 69.31% , E (10% ,10% ,100) = 124.57%
P (55% ,15% ,15% ,100) = 61.96% , E (15% ,15% ,100) = 226.87%
P (55% ,20% ,20% ,100) = 46.13% , E (20% ,20% ,100) = 505.41%
P (55% ,25% ,25% ,100) = 38.28% , E (25% ,25% ,100) = 822.36%
P (55% ,30% ,30% ,100) = 30.87% , E (30% ,30% ,100) = 1312.15%
从以上计算结果可见,随着风险的增加,预期报酬也在增加,但获胜的概率同时降低。当风险高过 20% 时,获胜的概率已不到 50% 。在低风险区( 1.25% , 2.5% ),预期报酬基本上和风险成正比( 10.85% , 21.67% )。但随着风险的增加,预期报酬将呈几何增长。例如当风险从 15% 提高到 20% 时,预期报酬从 226.87% 提高到 505.41% !其原因是当风险增加时,复利的影响也迅速增加。所以当所用风险低时,多次交易的报酬和风险基本上是成正比的,但在高风险时报酬成几何增长。
问题 4:
这个问题取决于你想要的取胜概率,用公式可算出在一定的获胜概率下所对应的风险。
问题 5:
能赢!在 50 , 100 , 200 次交易后,他的获胜概率和预期回报分别是:
P (20% ,1% ,5% ,50) = 69.27% , E (1% ,5% ,50 ) = 169.16%
P (20% ,1% ,5% ,100) = 72.88% , E (1%, 5% ,100 ) = 624.46%
P (20% ,1% ,5% ,200) = 83.44% , E (1% ,5% ,200 ) = 5148.49%
用此公式还可以得到许多有趣的结论。将 ’ 交易 ’ 换成 ’ 赌博 ’ ,此公式也一样适用。
祝大家感恩节快乐!来年发大财!
附Excel VBA计算程序:
Function WinningProbability(TotalTrade As Double, WinPctPerTrade As Double, Gain As Double, Loss As Double) As Double
Dim MinWins As Double
Dim Probability As Double
Dim Wins As Double
MinWins = Application.WorksheetFunction.RoundUp(TotalTrade * Log(1 - Loss) / (Log((1 - Loss) / (1 + Gain))), 0)
Probability = 0
For Wins = TotalTrade To MinWins Step -1
Probability = Probability + WinPctPerTrade ^ Wins * (1 - WinPctPerTrade) ^ (TotalTrade - Wins) * Application.WorksheetFunction.ComBin(TotalTrade, Wins)
Next
WinningProbability = Probability
End Function
Function WinningRtn(TotalTrade As Double, Gain As Double, Loss As Double) As Double
Dim MinWins As Double
Dim TotalRtn As Double
Dim Wins As Double
Dim TotalTest As Double
MinWins = Application.WorksheetFunction.RoundUp(TotalTrade * Log(1 - Loss) / (Log((1 - Loss) / (1 + Gain))), 0)
TotalRtn = 0
For Wins = TotalTrade To MinWins Step -1
TotalRtn = TotalRtn + (1 + Gain) ^ Wins * (1 - Loss) ^ (TotalTrade - Wins) * Application.WorksheetFunction.ComBin(TotalTrade, Wins)
Next
TotalTest = 0
For Wins = TotalTrade To MinWins Step -1
TotalTest = TotalTest + Application.WorksheetFunction.ComBin(TotalTrade, Wins)
Next
WinningRtn = TotalRtn / TotalTest - 1
End Function