How is yield in different markets measured?

The yield on a money market instrument depends on whether it is a discount instrument or add-on instrument.  Discount instruments, such as Euronotes and often Euro-CP, are issued at a discount to their face value so as to include interest at maturity and quoted at a discount rate (DR) on a discount basis.

Add-on instruments, such as Euro-CDs, are issued at their face value and receive the payment of interest when principal is repaid at maturity and quoted at an add-on rate (AOR) as an annual percentage rate (bond equivalent yield) on an add-on basis.  Yield on money market instruments is annualized and stated on a simple interest basis – not compounded.

The present value (PV) of an add-on instrument is calculated as follows, where F is its face value, t is the number of days to maturity, and T is the number of days in the year:

PV_AOR = F/[(1 + t/T) x AOR]

Typically, money market yields are converted to the bond equivalent yield (BEY), which restates the money market rate on a 365-day add-on rate basis.  Where the yield (and interest) on a discount instrument is the increase in its price relative to its face value at maturity, the yield on an add-on instrument is the interest paid on the instrument at its maturity.  Unlike discount yield, which is based on face value, AOR is based on price (P).

The formulas used to calculate the discount rate (DR) of a discount instrument in order to compare it to the add-on rate (AOR) of an add-on instrument, and vice versa, stated as an annual percentage, are, where P is the price, F is face value, t is the number of days between trade settlement and maturity, and T is the number of days in the year:

DR = (t/T) x (F − P)/F
AOR = (t/T) x (F − P)/P

US Treasury notes and bonds as well as US municipal and corporate bonds, Canadian government bonds and UK gilts are semiannual bonds that pay a fixed-rate of interest (coupon) twice a year (semiannually).  The debt capital market instruments of most continental European countries and in the Euromarket (offshore market) are annual-pay bonds that make coupon payment once a year (annually) and quoted in terms of their effective annual yield to maturity.

In those debt capital markets where annual-pay bonds trade, it is the market convention to quote annual yield to maturity on an annual-pay basis as an effective annualized yield (EAY).  The effective annual yield to maturity is an effective annualized yield (EAY) and the actual yield received by bond investors that takes the compounding of interest into account.  However, the semiannual yield to maturity is commonly quoted also for these annual-pay bonds.