## complementarynote-securitiesstatistics

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### Overview
- Recommendation 7 on Securities Statistics of the G-20 Data Gaps Initiative Phase 2 (DGI-2) is based on the methodology in the Handbook on Securities Statistics (HSS).
- Complementary Note No 1 (CN 1) provides further explanations on the calculation of accrued interest for the debtor principle for fixed interest rate debt securities.
- The HSS aligns with SNA2008 and BPM6 and is consistent with the External Debt Statistics - Guide for Compilers and Users, 2013 (EDS Guide) and the Monetary and Financial Statistics Manual and Compilation Guide 2016 (pre-publication draft).

### General considerations on accrued interest
- Definition:
  - Accrued interest on debt securities is the remuneration, accruing continuously over time, for an intertemporal exchange of funds between the holder(s) and the issuer of a debt security.
- Debtor principle versus creditor principle:
  - Accrued interest can be compiled for the debtor principle or the creditor principle.
  - For the debtor principle, accrued interest depends on market conditions at issuance.
  - For the creditor principle, accrued interest depends on market conditions at the time of purchase.
  - By convention, the HSS and international statistical standards apply the debtor principle; CN 1 explanations are based on the debtor principle.
- Composition and inclusion:
  - In the typical case where principal is channelled at issuance and redeemed at maturity, accrued interest for the debtor principle is composed of coupon payments and the difference between the redemption and the issue price.
  - Accrued interest is part of positions and transactions in debt securities and is included in positions both at market value and at nominal value.
  - The counterpart transactions to accrued interest are financial transactions in the respective debt securities.

### Calculation of accrued interest — Fixed interest rate debt securities issued at par (HSS Table A.1.1)
- Key rule:
  - For issuance at par, accrued interest for the debtor principle is generated only by coupon payments; accrued interest due to discount is zero.
  - The nominal yield to maturity at issuance equals the fixed interest rate.
  - Accrued interest (debtor principle) = nominal yield to maturity at issuance × nominal value at the beginning of the reference period.
- Numerical example (HSS Table A.1.1):
  - Issue price: 1,000 CU; annual coupon payments: 100 CU; original maturity: 5 years; redemption price: 1,000 CU; calculated nominal yield to maturity at issuance: 10%
  - Nominal value before coupon payment: 1,000.0, 1,100.0, 1,100.0, 1,100.0, 1,100.0
  - Nominal value after coupon payment: 1,000.0, 1,000.0, 1,000.0, 1,000.0, 1,000.0
  - Accrued interest: 100.0, 100.0, 100.0, 100.0, 100.0
  - Accrued interest due to coupon: 100.0, 100.0, 100.0, 100.0, 100.0
  - Accrued interest due to discount: 0.0, 0.0, 0.0, 0.0, 0.0
  - Coupon payment: -100.0, -100.0, -100.0, -100.0, -100.0
- Note:
  - Calculations do not depend on changes in the market value of the debt security.

### Calculation of accrued interest — Fixed interest rate debt securities issued at a discount (HSS Table A.1.2)
- Key steps:
  1. Calculate nominal yield to maturity at issuance based on the issue price; it is the discount rate equating the net present value of future cash flows to the issue price.
  2. Accrued interest for the debtor principle in any reference period = nominal yield to maturity at issuance × nominal value at the beginning of the reference period. The nominal value at the beginning of the period can be calculated as the net present value of future cash flows using the nominal yield at issuance.
  3. Accrued interest due to discount = accrued interest − coupon payments; it increases the nominal value from one reference period to the next. The accumulated accrued interest due to discount from issuance to maturity equals the discount.
- Numerical example (HSS Table A.1.2):
  - Issue price: 900 CU; annual coupon payments: 73.6 CU; original maturity: 5 years; redemption price: 1,000 CU; calculated nominal yield to maturity at issuance: 10%
  - Nominal value before coupon payment: 900.0, 990.0, 1,008.0, 1,027.8, 1,049.6, 1,073.6
  - Nominal value after coupon payment: 916.4, 934.4, 954.2, 976.0, 1,000.0
  - Accrued interest due to accrued interest (increment): 16.4, 34.4, 54.2, 76.0, 100.0
  - Accrued interest total: 90.0, 91.6, 93.4, 95.4, 97.6
  - Accrued interest due to coupon: 73.6, 73.6, 73.6, 73.6, 73.6
  - Accrued interest due to discount: 16.4, 18.0, 19.8, 21.8, 24.0
  - Coupon payment: -73.6, -73.6, -73.6, -73.6, -73.6
- Example calculation steps highlighted:
  - Issue price 900 CU → nominal yield to maturity at issuance 10%.
  - Accrued interest for first reference period = 900 CU * 10% = 90 CU.
  - Coupon payment at end of year 1 = 73.6 CU.
  - Accrued interest due to discount in year 1 = 90 CU − 73.6 CU = 16.4 CU.
  - Nominal value at beginning of year 2 = 916.4 CU.
  - Accrued interest for year 2 = 916.4 CU * 10% = 91.64 CU (rounded/displayed as 91.6 CU in the example table).

### Calculation of accrued interest — Zero-coupon debt securities (HSS Table A.1.3)
- Key rule:
  - Zero-coupon debt securities are fixed interest rate securities issued at a discount with coupon payment equal to zero.
  - Accrued interest for the debtor principle equals accrued interest due to discount.
- Numerical example (HSS Table A.1.3):
  - Issue price: 620.9 CU; annual coupon payments: 0.0 CU; original maturity: 5 years; redemption price: 1,000 CU; calculated nominal yield to maturity at issuance: 10%
  - Nominal value: 620.9, 683.0, 751.3, 826.4, 909.1, 1,000.0
  - Accrued interest due to accrued interest (increment): 62.1, 130.4, 205.5, 288.2, 379.1
  - Accrued interest: 62.1, 68.3, 75.1, 82.6, 90.9
  - Accrued interest due to coupon: 0.0, 0.0, 0.0, 0.0, 0.0
  - Accrued interest due to discount: 62.1, 68.3, 75.1, 82.6, 90.9
  - Coupon payment: 0.0, 0.0, 0.0, 0.0, 0.0
- Note:
  - These calculations are applicable until maturity and do not depend on changes in the market value of the debt security.

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_Source: https://www.imf.org/-/media/files/news/seminars/dgi/documents/complementarynote-securitiesstatistics.pdf_