Bond Equivalent Yield (BEY) Calculator
From face value, purchase price and days to maturity, compute the bond equivalent yield (annualised, 365-day basis).
輸入資料
計算結果
重點速覽：BEY = (face value - purchase price) / purchase price x (365 / days to maturity). It annualises a discount instrument's return on a 365-day, no-compounding basis so it can be compared with coupon bonds. Example: face HK$10,000, price HK$9,800, 182 days → (200/9,800) x (365/182) ≈ 4.07%. BEY is the US/Treasury convention; it differs from the coupon yield and from the 360-day money-market yield. WARNING: BEY ignores compounding; for long maturities it overstates the effective annual yield — use EAR for a true compare. Education only, not advice.
計算公式
持有期收益率 = (面值 − 買入價格) ÷ 買入價格。
BEY = 持有期收益率 × (365 ÷ 距到期天數) × 100%。
$$BEY = \dfrac{F - P}{P} \times \dfrac{365}{d} \times 100\%$$$$\text{持有期收益率} = \dfrac{F - P}{P}$$使用說明
- Enter the face value and the purchase price.
- Enter the days to maturity.
- View the bond equivalent yield.
面值 HK$1,000 時，不同買入價格與距到期天數對應的持有期收益率與 BEY
| 買入價格 | 距到期天數 | 持有期收益率 | 債券等價殖利率 (BEY) |
|---|---|---|---|
| HK$990 | 90 天 | 1.0101% | 4.0965% |
| HK$985 | 91 天 | 1.5228% | 6.1081% |
| HK$980 | 180 天 | 2.0408% | 4.1383% |
| HK$970 | 180 天 | 3.0928% | 6.2715% |
| HK$950 | 270 天 | 5.2632% | 7.1150% |
理財情境案例
案例一：把 180 天折價收益年化
一張面值 HK$1,000 的短期票據，你以 HK$970 折價買入，距到期 180 天。持有期收益率 = (1,000 − 970) ÷ 970 = 3.0928%。
年化：BEY = 3.0928% × (365 ÷ 180) ≈ 6.2715%。這代表若把這種收益率延伸到一整年，相當於 6.27% 的年化回報。
結論：單看 3.09% 會低估這張債券的吸引力 — 因為它只用半年就賺到了。年化後才知道它其實優於一張『年化 6% 的一年期債券』。
案例二：用 BEY 比較不同天期的貼現工具
工具 A：以 HK$990 買入、90 天到期，BEY ≈ 4.0965%;工具 B：以 HK$950 買入、270 天到期，BEY ≈ 7.1150%。
雖然 A 的持有期收益率 (1.01%) 遠低於 B (5.26%)，但兩者天期不同，直接比持有期收益不公平;年化成 BEY 後，B 明顯更划算。
結論：BEY 把天期差異抹平，讓不同期限的折價工具站在同一比較基礎上。挑選短期停泊資金的工具時，應比 BEY 而非表面差價。
常見問題
What is bond equivalent yield?
BEY annualises a discount instrument's gain (face - price) to a yearly figure on a 365-day basis, so it can be lined up against coupon-bond yields. It is the standard US/Treasury comparison convention.
How is BEY different from the coupon yield?
Coupon yield = annual coupon / face value. BEY is for zero-coupon/discount bonds and uses the discount (face - price) over the holding period, annualised. They measure different things; BEY is the 'equivalent' so the two can be compared.
What about the 360-day money-market yield?
Money-market instruments often quote a 360-day basis; BEY uses 365 days, so BEY is slightly higher for the same instrument. Always check which day-count and basis a quote uses before comparing.
Does BEY consider compounding?
No. BEY annualises linearly without compounding or reinvestment. For short maturities the gap is small; for long maturities it overstates the effective annual yield. For a true effective compare use the EAR.
How does this apply in Hong Kong?
Use BEY to compare HKD discount instruments, Treasury bills or Exchange Fund Notes against coupon bonds. Hong Kong rates are tied to HIBOR/US rates, so the same yield conventions apply. Consult the HKMA and IFEC for bond basics. This tool is educational, not advice.
相關工具
參考資料
內容審核：香港計算器財經團隊。計算邏輯與公式參考香港金融管理局（HKMA）及投資者及理財教育委員會（IFEC）之個人理財計算指引，結果僅供參考，實際以相關機構公佈為準。