What it means
Instruments quoted on this basis pay no interest along the way. Instead you buy at a discount and receive the full face value at maturity, so your entire return is the gap between the two prices.
The convention dates from an era of manual calculation, when dividing by a round 360 and by the face value made the sums quick to do by hand. It survives because whole markets, most obviously the Treasury bill market, still quote and trade on it, and changing the convention would break decades of price history.
The consequence is a small but systematic understatement. Dividing the discount by face value rather than by the smaller amount you actually invested shrinks the percentage, and using 360 days instead of 365 shrinks the annualisation factor, so the quoted rate is always below the true yield.
To compare a bill fairly against a term deposit or a money market fund, you convert the quote into a bond equivalent yield, which divides by the purchase price and annualises over 365 days. The gap is modest on very short paper and widens as maturity lengthens and rates rise.
The practical rule for a non-specialist is simple: never compare a discount basis quote directly with an interest rate quoted any other way. Convert first, then decide, because the difference is usually enough to change which option looks better.
In practice
Real-world examples.
Example
A corporate treasurer buys a 90-day bill with a face value of $2,000,000 quoted at 4.8% on a bank discount basis. The discount is $2,000,000 x 0.048 x 90 / 360 = $24,000, so the purchase price is $1,976,000 and $2,000,000 is repaid at maturity.
Example
A finance director compares a 180-day bill quoted at 3.00% on a discount basis with a term deposit paying 3.05% on a simple 365-day basis. Converting the bill to its bond equivalent yield of about 3.09% shows the bill is actually the better deal, despite the lower headline number.
Example
An analyst reviewing a cash portfolio sees a 91-day bill quoted at 3.20% on a bank discount basis alongside a money market fund yielding 3.25%. Converted, the bill returns about 3.27%, so the apparently lower quote wins once the convention is stripped out.
Formula
Calculation
Bank discount rate = ((Face value - Purchase price) / Face value) x (360 / days to maturity).
A treasury team buys a bill with a face value of $1,000,000 for $985,000, maturing in 180 days. The discount is $1,000,000 - $985,000 = $15,000. As a fraction of face value that is $15,000 / $1,000,000 = 0.015, or 1.5%. Annualising gives 360 / 180 = 2, so the quoted bank discount rate is 1.5% x 2 = 3.00%.
The bond equivalent yield tells the truer story: ($15,000 / $985,000) x (365 / 180) = 0.015228 x 2.0278 = 0.030880, or about 3.09%. The real return is roughly 0.09 percentage points higher than the quote suggests.Case study
Seen in the real world.
Northfield Components is an illustrative, wholly fictional manufacturer created to show the mechanics. After a large customer prepayment it held $5,000,000 that it would not need for roughly four months, and the board asked whether the money should sit in the current account or be put to work.
The treasury team bought a 120-day bill quoted at 4.5% on a bank discount basis. The discount came to $5,000,000 x 0.045 x 120 / 360 = $75,000, so the bill cost $4,925,000 and repaid $5,000,000 at maturity. Measured properly, the return on money actually invested was $75,000 / $4,925,000 = 1.52% over 120 days, which annualises to about 4.63%.
The point of this fictional example is the gap between 4.50% and 4.63%. The board had been comparing the quoted rate with a 4.55% deposit offer and had nearly turned the bill down, when on a like-for-like basis the bill was clearly ahead.
Watch out
Common mistakes.
- Comparing a bank discount basis quote directly with a deposit rate, which understates the bill and can push a treasurer into the worse option.
- Dividing the discount by the purchase price when calculating the quoted rate, which gives a different number from the one the market is actually using.
- Using 365 days in the annualisation of a discount basis quote, when the convention specifically uses 360.
Questions
People also ask.
Why does the calculation use face value instead of what I paid?
It is purely a historical quoting convention that made manual calculation easier, not a statement about the economics of the trade.
Is the bank discount rate the same as the yield I earn?
No, it is always slightly lower than the true yield, because it divides by the larger face value and annualises over a shorter 360-day year.
Which instruments are quoted this way?
Treasury bills are the main example, along with much commercial paper and many banker's acceptances in the short-term money markets.
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