# 期望值

> 期望值係將一筆交易嘅平均結果換算成「每單位風險」嘅形式：勝率乘以盈虧比，再減去敗率。勝率 45%、盈虧比 2:1 嘅策略，期望值為 +0.35，即係喺足夠長嘅一串交易入面，每冒 1 單位風險平均賺 0.35 單位。當期望值為零或為負時，無論點調倉位、加槓桿或者提高紀律性，呢個策略都唔可能賺錢。

Canonical HTML page: https://qanterion.com/zh-HK/glossary/expectancy
更新於: 2026-08-18
又稱: 單筆期望回報, 優勢

## 計算方式

```
Expectancy per unit risked = (Win rate × Payoff ratio) − Loss rate

Break-even win rate = 1 ÷ (Payoff ratio + 1)
Expectancy ≤ 0 means no position size makes the strategy profitable.
```

## 實算例子

勝率 45%、盈虧比 2:1 → (0.45 × 2) − 0.55 = 每單位風險 +0.35。

## 淨係睇勝率毫無意義

如果嗰一次虧損比九次盈利加埋仲大，90% 嘅勝率都係蝕錢策略；而喺 3:1 嘅盈虧比下，35% 嘅勝率反而好賺。期望值係同時將兩者結合起嚟嘅最簡數字，呢個就係點解評估一個策略時，佢係第一個應該計嘅統計量，亦係最後一個應該被丟掉嘅。

## 成本係喺期望值度扣，唔係喺利潤度扣

手續費、滑點同資金費係按筆扣除嘅，所以佢哋直接壓低盈虧比。一個毛期望值 +0.1 單位、來回成本 0.12 單位嘅策略，本質上係蝕錢嘅——但喺任何忽略摩擦成本嘅回測入面，佢睇落都好似賺錢咁。

## 常見誤讀

喺細樣本上計出嘅期望值經常被當成策略嘅固有屬性。佢只係一個估計值，而且好唔穩定：幾十筆交易根本唔足以區分真實優勢同一段運氣好嘅行情——過度擬合嘅系統就係咁樣帶住一份睇落好有信心嘅統計數據入實盤。

## 親手計一計

- 凱利公式計算機: https://qanterion.com/zh-HK/tools/kelly-criterion-calculator
- 破產機率計算機: https://qanterion.com/zh-HK/tools/risk-of-ruin-calculator

## 相關詞條

- 破產機率: https://qanterion.com/zh-HK/glossary/risk-of-ruin
- 倉位管理: https://qanterion.com/zh-HK/glossary/position-sizing
- 滑點: https://qanterion.com/zh-HK/glossary/slippage

## 參考資料

- [A New Interpretation of Information Rate](https://www.princeton.edu/~wbialek/rome/refs/kelly_56.pdf) — J. L. Kelly, Jr., Bell System Technical Journal (hosted by Princeton University)
- [Optimal Gambling Systems for Favorable Games](https://digicoll.lib.berkeley.edu/record/112884) — L. Breiman, Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability (UC Berkeley Library Digital Collections)
- [Good and bad properties of the Kelly criterion](https://www.stat.berkeley.edu/~aldous/157/Papers/Good_Bad_Kelly.pdf) — L. C. MacLean, E. O. Thorp, W. T. Ziemba (hosted by UC Berkeley Department of Statistics)

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## Risk notice

本術語表用於教學。此處內容不構成投資建議，頁面所述任何指標都無法預測未來結果。