Financial Markets and Institutions (2-downloads)

Discounting the Price of Treasury

Securities to Pay the Interest

Most money market securities do not pay interest. Instead, the investor pays less

for the security than it will be worth when it matures, and the increase in price pro-

vides a return. This is called discounting and is common to short-term securities

because they often mature before the issuer can mail out interest checks. (We dis-

cussed discounting in Chapter 3.)

Table 11.3 shows the results of a typical Treasury bill auction as reported on

the Treasury direct Web site. If we look at the first listing we see that the 28-day

Treasury bill sold for $99.988722 per $100. This means that a $1,000 bill was dis-

counted to $999.89. The table also reports the discount rate % and the investment

rate %. The discount rate % is computed as:

(1)

where

i

discount

= annualized discount rate %

P

= purchase price

F

= face or maturity value

n

= number of days until maturity

Notice a few features about this equation. First, the return is computed using the face

amount in the denominator. You will actually pay less than the face amount, since this

is sold as a discount instrument, so the return is underestimated. Second, a 

360-day year (30 

⫻ 12) is used when annualizing the return. This also underestimates

the return when compared to using a 365-day year.

The investment rate % is computed as:

(2)

i

investment

⫽

F

⫺ P

P

⫻

365

n

i

discount

⫽

F

⫺ P

F

⫻

360

n

---

262

Part 5 Financial Markets

The investment rate % is a more accurate representation of what an investor will

earn since it uses the actual number of days per year and the true initial investment

in its calculation. Note that when computing the investment rate % the Treasury uses

the actual number of days in the following year. This means that there are 366 days

in leap years.

TA B L E   1 1 . 3

Recent Bill Auction Results