T-Bill Yield and Money Market Maths for the CTP Exam
Price to yield, yield to price, and the discount-rate trap. All on actual/365.
A Treasury Bill (T-Bill) pays no coupon. RBI's G-Sec primer describes it as a zero coupon security issued at a discount and redeemed at face value, in three tenors: 91, 182 and 364 days. Your whole return is the gap between the price you pay and the ₹100 you get back. Every T-Bill question in the Certified Treasury Professional (CTP) exam turns on converting that gap into an annual yield, or back.
Indian money market instruments use the actual/365 day count. Keep that in mind for every formula below; the bond market's 30/360 does not apply here.
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The Formulas
Yield from price
Formula
Y = (100 minus P) / P x 365 / D x 100
Notes
RBI's form. P = price per ₹100, D = days to maturity
Price from yield
Formula
P = 100 / (1 + Y x D / 365)
Notes
Y as a decimal
Discount rate
Formula
d = (100 minus P) / 100 x 365 / D x 100
Notes
Divides by face value, so always below the yield
Holding-period return
Formula
(Sale price minus purchase price) / purchase price x 365 / days held x 100
Notes
For a bill sold before maturity
Basis conversion
Formula
Rate on 365 = rate on 360 x 365 / 360
Notes
For comparing with markets quoted on 360 days
| To find | Formula | Notes |
|---|---|---|
| Yield from price | Y = (100 minus P) / P x 365 / D x 100 | RBI's form. P = price per ₹100, D = days to maturity |
| Price from yield | P = 100 / (1 + Y x D / 365) | Y as a decimal |
| Discount rate | d = (100 minus P) / 100 x 365 / D x 100 | Divides by face value, so always below the yield |
| Holding-period return | (Sale price minus purchase price) / purchase price x 365 / days held x 100 | For a bill sold before maturity |
| Basis conversion | Rate on 365 = rate on 360 x 365 / 360 | For comparing with markets quoted on 360 days |
Worked Example 1: RBI's 91-Day Bill
RBI's primer uses a 91-day T-Bill issued at ₹98.20 per ₹100 face value.
- 1
Discount
100 minus 98.20 = ₹1.80.
- 2
Return for 91 days
1.80 / 98.20 = 0.018330, or 1.8330%.
- 3
Annualise on 365 days
1.8330% x 365 / 91 = 7.35% a year.
Worked Example 2: Price From Yield
Illustrative cut-off yields. The longer the tenor, the deeper the discount at a similar yield.
182-day at 6.80%
Working
100 / (1 + 0.068 x 182 / 365)
Price per ₹100
₹96.7205
364-day at 6.95%
Working
100 / (1 + 0.0695 x 364 / 365)
Price per ₹100
₹93.5183
| Bill | Working | Price per ₹100 |
|---|---|---|
| 182-day at 6.80% | 100 / (1 + 0.068 x 182 / 365) | ₹96.7205 |
| 364-day at 6.95% | 100 / (1 + 0.0695 x 364 / 365) | ₹93.5183 |
Discount Rate Is Not Yield
For a 91-day bill at ₹98.25, the discount rate is 1.75 / 100 x 365 / 91 = 7.02%, but the yield is 1.75 / 98.25 x 365 / 91 = 7.14%. The yield divides by the price you actually invest. Exam options often include both; RBI's T-Bill formula gives the yield.
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Worked Example 3: Selling Before Maturity
Illustrative. A treasury buys a 91-day bill at ₹98.30 and sells it 30 days later at ₹98.85.
- 1
Gain
98.85 minus 98.30 = ₹0.55 per ₹100.
- 2
Period return
0.55 / 98.30 = 0.5595%.
- 3
Annualise
0.5595% x 365 / 30 = 6.81% a year. If yields fell after purchase, the sale price rises and so does this return.
Worked Example 4: Certificate of Deposit
A CD is a negotiable money market instrument also issued at a discount. Illustrative: a 91-day CD at a 7.40% yield, ₹5 crore face value.
- 1
Price per ₹100
100 / (1 + 0.074 x 91 / 365) = ₹98.1885.
- 2
Amount paid
5,00,00,000 x 98.1885 / 100 = ₹4,90,94,245.
- 3
Investor's gain at maturity
₹5,00,00,000 minus ₹4,90,94,245 = ₹9,05,755.
Money Market Instruments at a Glance
Treasury Bill (91, 182, 364 days)
How it pays
Issued at a discount, redeemed at par
Day count
Actual/365
Where on this site
This page
Cash Management Bill (under 91 days)
How it pays
Issued at a discount, redeemed at par
Day count
Actual/365
Where on this site
This page
Certificate of Deposit
How it pays
Issued at a discount
Day count
Actual/365
Where on this site
This page
Call, notice and term money
How it pays
Simple interest on principal
Day count
Actual/365
Where on this site
Repo, TREPS and call money page
Repo and TREPS
How it pays
Repurchase price includes interest
Day count
Actual/365
Where on this site
Repo, TREPS and call money page
| Instrument | How it pays | Day count | Where on this site |
|---|---|---|---|
| Treasury Bill (91, 182, 364 days) | Issued at a discount, redeemed at par | Actual/365 | This page |
| Cash Management Bill (under 91 days) | Issued at a discount, redeemed at par | Actual/365 | This page |
| Certificate of Deposit | Issued at a discount | Actual/365 | This page |
| Call, notice and term money | Simple interest on principal | Actual/365 | Repo, TREPS and call money page |
| Repo and TREPS | Repurchase price includes interest | Actual/365 | Repo, TREPS and call money page |
T-Bill Facts the Exam Asks
- check_circleRBI usually auctions T-Bills every Wednesday, and settlement is T+1, the next working day.
- check_circleRBI issues a quarterly calendar of T-Bill auctions in the last week of the preceding quarter.
- check_circleCash Management Bills meet the Government's temporary cash mismatches. They have the generic character of T-Bills, tenors under 91 days, and count for SLR.
- check_circleConversion: 7.20% on a 360-day basis is 7.20 x 365 / 360 = 7.30% on 365 days.
FAQs
How is the yield on a T-Bill calculated?expand_more
Yield = (100 minus price) / price x 365 / days to maturity x 100. A 91-day bill at ₹98.20 yields 1.80 / 98.20 x 365 / 91 = 7.35%.
Why is the T-Bill yield higher than its discount rate?expand_more
The discount rate divides the discount by face value (₹100). The yield divides it by the price, which is smaller, so the yield is always higher.
Do T-Bills pay interest?expand_more
No. They are zero coupon securities. The return is the difference between the issue price and the face value paid at maturity.
Which day count is used for T-Bills in India?expand_more
Actual/365. G-Sec accrued interest uses 30/360 instead.
Access exam-specific mock tests directly from your Android device.Next steps
- G-Sec Auctions & STRIPSarrow_forward
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