A discount rate is not directly comparable with a rate of return (yield). This is because the discount rate is applied to par value to obtain the price, whereas an interest rate shows the return on funds employed (the price paid).

To make a strict comparison between the two it is necessary to convert the discount rate into a yield (the true yield). This can be done using the following formula:

Looking at our 90 day T-bill with a price of $97,750.00, and a discount rate of 9%, what is the true yield on the instrument?

The calculation is as follows:

So a 90 day security with a discount rate of 9% will actually have a yield of 9.21%.

As the price paid for a discount security is always less than par value, it is easy to see that a discount rate will always understate the return on funds employed, the true yield.

Day count conventions

So far in our calculations we have assumed a 30 day month and a 360 year. The astute among you will have noted that a year actually has 365 days and the number of days in a month vary. Why then have we made this assumption?

Calculations in financial markets use different day count conventions depending on the instrument and the currency. The main conventions are:

• Actual/365 (A/365)      
• Actual/360 (A/360)

The actual/365 convention means that the day count is the actual number of days between the value date and maturity, while the annual basis is 365 days (even in a leap year). This convention is used in Sterling (£) money markets.

The more commonly used convention - sometimes referred to as the money market basis - is actual/360 (A/360). Indeed, this is the convention adopted by eurozone money markets.

The actual/360 convention means that the day count is the actual number of days between the value date and maturity, while the annual basis is 360 days.