Time return

Unlike equities, coupon-bearing securities guarantee a certain return to the holder due to the passage of time. If the markets did not move in any way, the holder of a coupon-bearing bond would still receive one or more coupon payments per year. If the holder only owned the bond for part of the year, he would receive part of the regular coupon payment, with the amount proportional to the time he had owned the security. The majority of fixed-income securities pay some sort of coupon, so this is an important source of return in the fixed income markets.

The terms coupon return and time return are often used interchangably, since all can be seen as names for return that does not arise from changes in the market's term structure. However, the two terms are not strictly equivalent. Securities that pay no coupon, such as zero-coupon bonds or bank bills, show return that is purely due to the passage of time, which causes the security's price to approach par. A better alternative is 'yield return' or 'carry'.

There are several ways in which one can measure a security's return due to the passage of time while ignoring changes in the term structure. One of the simplest is to use the security's yield to maturity (or YTM). YTM is the single rate $y$ that, when used to discount a security’s cash flows, gives the current security price $P$ :

P=\sum_{i=1}^N \frac{C_i}{\left(1+y\right)^{t_i}}

where $C_i$ is cash flow $i$ , and $t_i$ is the interval in years between the present and that cash flow.

YTM has the property that, if unchanged over a short period, it equals the security’s total rate of return. A bond’s return due to yield $r_{yield}$ is therefore closely approximated by

r_{yield} = y \cdot \delta \tau

where $y$ is the security’s yield to maturity, and $\delta \tau$ is the elapsed time in years.