Bond Accrual


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Bond Accrued Interest


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A bond is a security that allows an investor loans money to the issuer for a certain period of time and receives coupons paid by the issuer. From bond analytic perspective, there are more than 1,500 different types of bonds in global markets. They are usually distinguished by calculation types.

Each calculation type defines a specific approach used to determine coupon dates, coupon rates, accrued interests, yields, prices, and risks (durations, convexities, etc.) based on specified market conventions and security definitions.

Accrual is the amount of interest accumulated from the most recent period begin date to a settle date. Since bond accrued interests impact daily profit and loss (P&L) significantly for bond holders, it is essential to compute them precisely. The main challenge for computing accrued interest is to handle each convention correctly.

For example, accrued interests for a bond are calculated below.

bond accrued interest

Bond can be classified into different categories according to different perspectives. From coupon type and feature perspective, bonds can be grouped into:

  • Zero coupon bond
  • Fixed rate bond
  • Floating rate note
  • Fixed to float bond
  • Stripped bond
  • Amortization bond
  • Perpetual bond
  • Inflation-linked bond
  • Sinking fund bond
  • Step-up coupon bond
  • Extendable bond
  • Callable bond
  • Convertible bond
  • Bond structure note, etc.

From issuer perspective, we have:

  • Government bonds issued by:
    • Supranational agents
    • National governments
    • Provincial or state governments
    • Municipal or regional governments
  • Corporate bonds:
    • Grouped into industry
    • Grouped by credit worthiness
  • Eurobond:
    • Issued in a country other than the local one
    • Denominated in a currency other than the local one

Governments and corporates can use Eurobonds to borrow money internationally. A Eurobond is issued by an international borrower in a currency other than that of the country in which it is sold. For example, a US company could sell a Eurobond denominated in Japanese yen in Canada.

Bonds are issued through a competitive bidding process at auctions. Investors submit either a competitive or non-competitive bid for a number of issues of bonds. In a non-competitive bid, investors receive number of bonds at the price determined in the auction, while in a competitive bid, investors specify a requested return. If the requested return is too high, the investor may not receive any bonds or he may receive fewer than requested.

Once issued, bonds are heavily traded in the secondary market. The bond returns may change as investors’ view of the issuing organization or macro-economic conditions evolve.

Some bonds pay equal payments at equal intervals of time with the face value of the bond paid back a maturity, but other may not. For instance, a bond may pay irregular coupons or no accrued interest for the first period or last period. Furthermore, the day count basis for the partial period may also be different from the regular period.

Ex-dividend convention affects accrued interest as well. For settlements that occur on or after an ex-dividend date, accrued interest is calculated differently.

For example, a Canadian Government Bond is traded and quoted based on yield to maturity (YTM). The actual settlement clean price depends on the number of coupons available. For bonds with a single remaining coupon, the bond trades at a pure discount. For bonds with multiple remaining coupons, these are priced with a special formula.

Canadian government securities accrue interest on an ACT/365 basis with an accrual period limited to at most 182.5 days. If we assume a notional of 100, the accrued interest is calculated

Canadian bond accrued interest

where

  • C denotes the coupon rate for the CAD government bond,
  • Ā denotes the calendar days from last coupon to trade settlement, and
  • A denote the adjusted days from last coupon to trade settlement, where
Canadian bond accrued interest date

References