Accrued Interest Bond – Definition

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Accrued Interest (Bond) Definition

The accrued interest of a bond is the amount of interest earned on the bond but awaiting payment. This interest is accumulated from when a bond coupon is issued.

In bond trading, the buyer pays the seller the market price of the bond plus the accrued interest since this is the bond sale’s settlement price.

The settlement price, however, only occurs in the transaction belonging to the interest-bearing, coupon-paying bond.

Income bonds are exempted since they pay interest only when they are profitable.

The formula for calculating accrued interest is given below

Accrued interest = coupon rate expressed in decimal * interest period annual score * face value.

A Little More on What is Accrued Interest

If the bond is sold before the date of interest payment, then the seller does not own the interest. However, before this, the purchaser must first reimburse the seller accordingly for the holding time of the bond from the previous payment date to the settlement date.

Example of accrued interest

Assume an interest payment date is January 1and July 1 for a bond with a value of $100,000 and a 10% interest rate. If the bond were to be sold on March 1, the accrued interest would be $1,667. This amount is calculated using the formula as follows.

0.01 x 2/12 x $100,000 = $1,667

References for Accrued Interest

Academic Research on Accrued Interest

  • Liquidity, maturity, and the yields on US Treasury securities, Amid, Y., & Mendelson, H. (1991). The Journal of Finance, 46(4), 1411-1425. This paper investigates the effects that asset liquidity has on expected returns for assets with infinite maturities like stocks. These effects are examined for assets with a matched maturity of fewer than six months like bonds and treasury bills.
  • Valuing credit default swaps I: No counterparty default risk, Hull, J. C., & White, A. (2000). NYU Working Paper No. FIN-00-021. This paper gives a methodology for valuing credit default swaps when the payoff becomes contingent on default by a single reference entity, and counterparty default risk is not available. It also examines the sensitivity of credit default swap valuations to the expected recovery rate assumptions.
  • Valuing credit default swaps II: Modeling default correlations, Hull, J. C., & White, A. (2000). NYU Working Paper No. FIN-00-022.This paper extends the analysis that is in Valuing Credit Default Swaps I. It then creates a model default correlation that exist between different corporate and sovereign entities, to be applied when valuing vanilla credit default swaps and to basket credit default swaps.
  • The relationship between credit default swap spreads, bond yields, and credit rating announcements, Hull, J., Predescu, M., & White, A. (2004). Journal of Banking & Finance, 28(11), 2789-2811. This article analyses the data on credit default swap spreads which are collected by credit derivatives brokers.
  • Fundamental economic variables, expected returns, and bond fund performance, Elton, E. J., Gruber, M. J., & Blake, C. R. (1995). The Journal of Finance, 50(4), 1229-1256.  This article develops relative pricing models which successfully explain the expected returns in the bond market. It does this by using indexes and unanticipated changes in the economic variables as the factors that drive security returns.
  • The intersection of market and credit risk, Jarrow, R. A., & Turnbull, S. M. (2000). Journal of Banking & Finance, 24(1-2), 271-299. This paper explains two ways used to price credit risky instruments, the structural approach and the reduced form approach. It also argues that default risk and recovery rate uncertainty are not the only factors determining credit spread. It attempts to incorporate convenience yield as another factor determining the credit spread.
  • Seasonality in daily bond returns, Jordan, S. D., & Jordan, B. D. (1991). Journal of Financial and Quantitative Analysis, 26(2), 269-285. The paper tests corporate bond returns for seasonal patterns utilizing the Dow Jones Composite Bond Average. It investigates every seasonal pattern documented for equities.
  • Stocks, bonds, bills, and inflation: year-by-year historical returns (1926-1974), Ibbotson, R. G., & Sinquefield, R. A. (1976). The Journal of Business, 49(1), 11-47. This paper presents several derived series that represent the parts that constitute of asset returns.
  • An empirical analysis of the dynamic relation between investment‐grade bonds and credit default swaps, Blanco, R., Brennan, S., & Marsh, I. W. (2005). The journal of Finance, 60(5), 2255-2281. This study tests the credit default swap theoretical equivalence in terms of prices and credit spreads. It also attempts to find support for the parity relation as an equilibrium condition.
  • Immunizing default-free bond portfolios with a duration vector, Chambers, D. R., Carleton, W. T., & McEnally, R. W. (1988). Journal of financial and quantitative analysis, 23(1), 89-104. This paper demonstrates that a default-free bond’s finite and non-instant return can be expressed as a vector product arising from a duration vector and a shift vector. However, all this is under the assumption that term structures of interest rates continuously compounded can be given as polynomial.
  • Managerial control of voting rights: Financing policies and the market for corporate control, Stulz, R. (1988). Journal of financial Economics, 20, 25-54. This study examines how the managerial control of voting rights can affect a firm’s value and financing policies. It shows how an increase in the voting rights controlled by management can decrease a successful tender offers probability and increase the premium offered should a tender offer be made.

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