Discount Yield

Fixed income markets have standard formulas for quoting the yield on various instruments. Because instruments are often quoted with yields instead of prices, the formulas must be applied precisely to obtain the price that corresponds with a quoted yield. Most of the formulas evolved before the age of computers, so they represent a tradeoff between

  • ease of computation using pencil and paper, and
  • a reasonable representation of economic return.

Yields for discount instruments traded in the money market are generally quoted on a bank discount basis, which amply illustrates this tradeoff. The bank discount yield (or simply discount yield) of a discount instrument having face value 100 is calculated as

[1]

Day counts are almost always on an actual/360 basis, but check the convention for your particular market.

Generally, market conventions for calculating yields are specified so those yields can be interpreted as interest rates. This would be the case with the formula for discount yield if the denominator in [1] were the instrument’s price as opposed to its face value 100. Obviously, dividing by a round number like 100 is easier than dividing by a price, which explains the logic behind the formula. It means that discount yields cannot be directly compared with yields or interest rates quoted for other instruments. To facilitate such comparisons, discount yields for discount instruments may be converted to bond-equivalent yields.

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