量化計算器與風險定價工具 · E-E-A-T 透明公式驗證
ETFYield Lab 機構級金融與風險量化計算器中心
ETFYield Lab 所有量化工具均在瀏覽器本地確定性運行，完整披露底層數學公式、市場計息慣例（ACT/360 與 ACT/365）及模型邊界假設，數據絕不離開您的終端。
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互動式金融與風險量化計算器目錄
每款計算器均提供即時敏感度階梯表、明確公式推導與邊界條件說明。
ETF expense ratio calculator
How much two expense ratios cost you over time, with regular contributions.
Each year: Value = (Value × (1 + gross return)) × (1 − expense ratio) + contribution
Bond yield & duration calculator
Yield to maturity, Macaulay and modified duration, convexity and DV01 from a bond’s price.
Price = Σ CFₜ ÷ (1 + y ÷ f)^(t × f)
Dividend reinvestment calculator
Project an income portfolio with and without reinvesting dividends.
Each year: shares += shares × dividend per share × (1 − tax) ÷ price
T-Bill vs duration ETF tax-equivalent yield comparator
Compare state-tax-exempt US Treasury bills against fully taxable bond ETFs and duration risk.
After-tax T-Bill yield = y_tbill × (1 − [t_fed + t_state × (1 − exempt%)])
量化模型公式、計息慣例與審慎假設一覽表
透明展示各工具的核心數學恆等式與模型適用限制，便於合規與風控團隊交叉複核。
| 量化工具名稱 | 核心數學公式 | 關鍵審慎假設與邊界條件 | 直達入口 |
|---|---|---|---|
| ETF expense ratio calculator | Each year: Value = (Value × (1 + gross return)) × (1 − expense ratio) + contribution | Contributions are added at the end of each year. Returns are constant and before tax. | 開啟互動式計算器 → |
| Bond yield & duration calculator | Price = Σ CFₜ ÷ (1 + y ÷ f)^(t × f) ; Macaulay duration = Σ t × PV(CFₜ) ÷ Price ; Modified duration = Macaulay ÷ (1 + y ÷ f) | Assumes the bond is priced on a coupon date (no accrued interest) and that all payments are made in full. | 開啟互動式計算器 → |
| Dividend reinvestment calculator | Each year: shares += shares × dividend per share × (1 − tax) ÷ price | Annual compounding, constant growth rates and no trading costs. | 開啟互動式計算器 → |
| T-Bill vs duration ETF tax-equivalent yield comparator | After-tax T-Bill yield = y_tbill × (1 − [t_fed + t_state × (1 − exempt%)]) ; Tax-equivalent yield = After-tax T-Bill yield ÷ (1 − (t_fed + t_state)) ; Duration break-even yield rise = After-tax ETF yield ÷ Modified duration | Models ordinary income tax on distributions; does not model capital gains tax on price changes. | 開啟互動式計算器 → |
關聯監管核驗、機構評級與開放數據導航
關於金融量化計算器的常見問題（FAQ）
ETFYield Lab 的量化計算器如何在保證隱私的前提下運行？
所有輸入參數（部位規模、波動率、利率與稅率）均在您的瀏覽器本地記憶體中即時運算，不會向伺服器發送任何交易或持倉數據。
為什麼計算器同時展示公式與模型假設限制？
根據機構級 E-E-A-T 透明度標準，任何量化輸出都依賴於計息基準（如 ACT/360 vs ACT/365）和分佈假設。公開公式便於風控團隊獨立重現結果。
這些計算結果是否構成投資建議或監管背書？
不構成。所有計算結果僅供量化研究與風險參數校準參考，實際交易前請結合持牌機構合約條款與官方監管登記冊進行核實。
免責聲明：本頁量化工具僅供金融工程研究與教育參考，不構成任何投資或交易建議。在做出資金決策前，請務必透過官方監管登記冊獨立核實簽約主體資質。