Key Concepts

You have learned how to get the price, or the yield, of a bond through using a formula. However, you did this with bonds having complete periods of time to be redeemed. For example, we supposed that the Shell bond was going to mature in exactly four years. What happens, then, when a bond is purchased that has an uncompleted period of time until maturity? What is its price and/or yield? Let's take an example.

The situation here is a little different to the examples we have used in previous cases. We need to use the formula you used in the Trading Department, but it needs to be altered slightly, as we are not dealing with precisely two years - there are 2.5 years to maturity.

We can work such formulas out by using the calculation facility in a spreadsheet such as Excel.

This is the formula that we will use:

Using the formula, the yield will work out at 3.8%

How have we done this? Well, as we didn't have exact periods of time, we had to work out a different way to approach it. So, we approached the next exact period of time (21/06/2004), which is 0.5 years away, and then added a year each time after that.

What happens if we buy the bond in a time that is not 0.5 times exactly until the next coupon? This is going to be relatively unusual but not unheard of, so we need to be able to deal with it. Again, an example will serve to illustrate this.

What would happen if we bought the Vodafone bond on 10th May 2008? We need to count the days from 10th May 2008 to 21st June 2008; there are 42 days between these two dates. If we express these days as a percentage of the year, we will get: 42/365 = 11.5% of a year. Then we can substitute this into the formula:

Simplifying this, we get:

The key, therefore, is to remember to calculate the time period differential and then work from there in whole time periods, such as years.