What it means
Short-term government and corporate securities are often sold below face value and repaid at face value on the due date. The investor's return is the difference between those two amounts.
Discount yield turns that difference into an annual rate so that securities with different lives can be compared. The calculation takes the gain, divides it by the face value, and scales the result up to a year using a 360-day convention in many markets.
This is the traditional convention in the money market, and it is why newspapers and dealers often quote treasury bills this way. It is simple to calculate but not an intuitive measure of what the investor actually earns.
The weakness is that the base is the face value, which is larger than the amount invested. As a result, the discount yield is always lower than the return measured on the price paid.
To compare a bill with a bond or a savings account, investors use a bond-equivalent yield, which divides the gain by the price paid and uses a 365-day year. For a company treasurer, this matters whenever cash is placed in bills or whenever short-term borrowing is priced as a discount.
Comparing a quote of 6.00% on a bill with 6.10% on a deposit can be misleading unless both are converted to the same basis. A few minutes spent standardising the quotes avoids picking the wrong option.
A nuance is that the gap between the two measures grows as the rate rises and as the maturity lengthens. For very short bills at low rates the difference is small, but for longer bills at higher rates it can be a meaningful fraction of a percentage point.
In practice
Real-world examples.
Example
A fund manager sees a 6-month bill quoted at a discount yield of 4.00%. Before comparing it with a bond, she converts the quote into a bond-equivalent yield, which comes out higher. She finds the bill is more attractive than it first appeared.
Example
A company treasurer places $3,000,000 of surplus cash in 60-day bills. The dealer quotes the price in terms of a discount yield, and the treasurer uses a spreadsheet to convert it to a rate on the amount invested. The figure is then recorded as the expected interest income.
Example
A university investment office compares a bill with a bank deposit that quotes a simple annual rate. The office converts both to the same basis before deciding. It places the cash with the bank because the deposit offered a higher true yield.
Formula
Calculation
Discount yield = (face value - price) / face value x 360 / days to maturity
A treasury bill has a face value of $10,000 and is bought for $9,800, with 120 days to maturity. The gain is $10,000 - $9,800 = $200. Discount yield = 200 / 10,000 x 360 / 120 = 0.02 x 3 = 0.06, or 6.00%. The bond-equivalent yield is 200 / 9,800 x 365 / 120 = 0.020408 x 3.0417 = 0.0621, or about 6.21%, which is the fairer measure of the investor's return.Case study
Seen in the real world.
Eastgate Components is an illustrative, fictional manufacturer that had $2,500,000 of cash to invest for 90 days. A dealer offered a bill at a discount yield of 5.20%, while the company's bank offered a deposit at a simple annual rate of 5.30%.
On first look, the deposit appeared marginally better. The finance analyst converted the bill: the discount on $2,500,000 for 90 days at 5.20% is $2,500,000 x 0.052 x 90 / 360 = $32,500, so the price is $2,467,500, and the bond-equivalent yield is 32,500 / 2,467,500 x 365 / 90 = 5.34%.
The bill therefore beat the deposit by 0.04 percentage points, which is worth about $250 over the period. The illustrative lesson is that quotes are only comparable once converted to the same basis, and a quick conversion changed the decision.
Watch out
Common mistakes.
- Comparing a discount yield directly with the interest rate on a deposit or bond, when the two use different bases and day counts.
- Believing the discount yield is the actual return on the money invested, when it is calculated on face value and so understates it.
- Using the wrong day-count convention, which can shift the result by several hundredths of a percentage point.
Questions
People also ask.
Why is the discount yield lower than the true return?
Because the gain is divided by the face value, which is larger than the price paid, so the percentage comes out smaller.
Where is discount yield used?
It is used mainly for treasury bills, commercial paper and other short-term discount securities.
How do I convert to a bond-equivalent yield?
Divide the gain by the price paid, then multiply by 365 and divide by the days to maturity.
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