Bond Calculator — Yield, Price, Duration

With the BNA policy rate (taxa basica) at 17.5% and 10-year OTNR yields near 19.75%, the spread between different Angolan fixed-income instruments can translate to differences of hundreds of thousands of kwanza in total return on a typical institutional allocation. This calculator provides real-time computation of yields, prices, duration, and convexity across all Angolan government bond types – enabling precise scenario analysis for portfolio construction and risk management.

How to Use the Calculator

Select your instrument type and enter the required parameters. The calculator computes results in real time as you adjust inputs. Below is a step-by-step guide for each instrument class.

Bilhetes do Tesouro (Treasury Bills) – Zero-Coupon

For BTs, enter the following:

• Face Value (Valor Nominal): The par amount at maturity. Minimum investment is Kz 100,000.
• Purchase Price (Preco de Compra): The discounted price paid at auction or in the secondary market. For example, a 364-day BT with a yield of 16.50% would be purchased at approximately Kz 85,837 per Kz 100,000 face value.
• Days to Maturity (Dias ate Vencimento): Select 91, 182, or 364 days for standard tenors, or enter a custom value for secondary-market purchases between auction dates.

The calculator will output:

• Discount Yield (Taxa de Desconto): The annualized return based on the discount from face value.
• Bond-Equivalent Yield (Taxa Equivalente): The yield adjusted for semi-annual compounding, enabling direct comparison with coupon-bearing OTNRs.
• Total Return (Retorno Total): The absolute kwanza gain at maturity.

Example: A 364-day BT purchased at Kz 85,837 per Kz 100,000 face value produces a discount yield of 16.50% and a total return of Kz 14,163 per unit. On an investment of Kz 10 million (100 units), the total return at maturity would be approximately Kz 1,416,300. For current BT yields, see the 91-day, 182-day, and 364-day pages.

OTNRs (Fixed-Rate Treasury Bonds) – Coupon-Bearing

For OTNRs, enter:

• Face Value (Valor Nominal): Par amount. Minimum investment is Kz 1,000,000.
• Coupon Rate (Taxa de Cupao): The annual coupon percentage set at auction (e.g., 18.40% for a recent 5-year OTNR).
• Settlement Date (Data de Liquidacao): The date of purchase.
• Maturity Date (Data de Vencimento): The bond’s final payment date.
• Market Yield (Taxa de Mercado): The yield at which you are purchasing (for secondary-market transactions) or the auction yield (for primary purchases).

The calculator will output:

• Clean Price (Preco Limpo): The quoted price excluding accrued interest.
• Dirty Price (Preco Sujo): The actual settlement price including accrued interest.
• Accrued Interest (Juros Acumulados): Interest earned since the last coupon payment.
• Modified Duration (Duracao Modificada): The bond’s price sensitivity to a 1% change in yield. A modified duration of 4.2 means the bond’s price would move approximately 4.2% for each 100 bps yield change.
• Macaulay Duration (Duracao de Macaulay): The weighted-average time to receive the bond’s cash flows.
• Convexity (Convexidade): The second-order price sensitivity, which causes the actual price change to exceed the duration estimate for large yield moves.
• Yield to Maturity (Rentabilidade ate Vencimento): The internal rate of return assuming the bond is held to maturity and all coupons are reinvested at the same yield.

Example: A 5-year OTNR with an 18.40% coupon, 4.5 years remaining, purchased at a market yield of 18.00%, would have:

If the BNA cuts rates by an additional 100 bps and market yields decline to 17.00%, the price would increase by approximately 3.42% (duration effect) plus 0.07% (convexity effect), generating a capital gain of roughly Kz 35,300 per Kz 1,000,000 face value – in addition to the semi-annual coupon income of Kz 92,000.

OTX (Foreign-Currency-Indexed Bonds)

For OTX instruments, the calculator requires two additional inputs:

• Reference Exchange Rate at Issue (Taxa de Cambio na Emissao): The BNA reference rate on the bond’s issue date (e.g., Kz 830.50/USD).
• Current Exchange Rate (Taxa de Cambio Atual): The prevailing BNA reference rate (currently approximately Kz 914.60/USD).

The calculator adjusts all kwanza cash flows by the ratio of current-to-issuance exchange rates. This means:

• Principal adjustment: If the kwanza has depreciated from Kz 830.50 to Kz 914.60 since issuance, the redemption value per Kz 1,000,000 face value is adjusted to approximately Kz 1,101,265 (a 10.1% uplift).
• Coupon adjustment: Semi-annual coupons are similarly scaled, so a 7.25% coupon on the adjusted principal generates higher kwanza cash flows.
• Effective yield in AOA terms: The calculator computes the total kwanza-equivalent yield, which combines the stated USD coupon yield with the FX depreciation effect.

Example: An OTX USD 3-year bond issued at Kz 830.50/USD with a 7.25% coupon, purchased 1 year after issuance when USD/AOA is Kz 914.60:

This effective AOA yield of approximately 17.8% is directly comparable to the OTNR curve, enabling investors to assess whether the OTX’s implicit FX hedge is priced efficiently. For more on the OTX vs OTNR trade-off, see the bond comparison page and the FX play strategy.

Methodology and Conventions

Day-Count Conventions

• BTs: Actual/365 day count, consistent with BNA and BODIVA conventions.
• OTNRs: 30/360 day count for accrued interest calculations, Actual/Actual for yield calculations.
• OTX: Actual/360, following international conventions for FX-linked instruments.
• Eurobonds: 30/360 (ISMA), consistent with international Eurobond market standards.

Compounding

• BTs: Simple interest (discount yield) and bond-equivalent yield (semi-annual compounding) are both provided.
• OTNRs and OTX: Semi-annual compounding, consistent with the coupon payment frequency.
• Eurobonds: Semi-annual compounding.

Price Quotes

Clean prices are quoted as a percentage of face value (e.g., 101.325 means Kz 1,013,250 per Kz 1,000,000 face). Settlement occurs at the dirty price, which adds accrued interest. BODIVA’s secondary market uses T+2 settlement for all domestic instruments.

Practical Applications

The calculator supports several key analytical workflows:

1. Pre-auction preparation: Model different yield scenarios before submitting bids in primary market auctions. Use the auction calendar to identify upcoming opportunities.
2. Secondary-market trading: Compute fair value when evaluating offers in the secondary market. Compare the calculated yield against the yield curve to identify rich/cheap instruments.
3. Portfolio duration management: Use the duration and convexity outputs to measure portfolio-level interest-rate sensitivity and construct hedges.
4. FX scenario analysis: For OTX instruments, model different exchange-rate paths to compare kwanza-equivalent returns against OTNRs.
5. Real-yield computation: Subtract the latest inflation reading (15.7% YoY, INE December 2025) from nominal yields to assess real yield across the curve.

For assistance interpreting the results or understanding the investment process, consult the bond FAQ, the glossary of terms, or the how to invest guide.

Disclaimer

Results are for informational purposes only and do not constitute investment advice. Actual returns may vary based on market conditions, transaction costs, custodian fees, and tax treatment. The calculator uses standard bond-pricing formulas and does not account for credit risk, liquidity risk, or potential changes in tax legislation. For tax implications on bond income, see the tax guide. All data sourced from BNA, BODIVA, and INE publications.