Guide · Fixed income · Updated 2026-09-23

The yield the RBI prints for a treasury bill is simple interest on the price, and every comparison has to restate it first

A treasury bill yield is quoted as though it were a property of the bill. It is a property of a formula: the auction produces a price, and turning the price into an annual rate means choosing what to divide the discount by and whether to compound. This page derives each choice, proves on the RBI’s own figures which one it uses, measures what that choice leaves out on a year of real auctions, and restates a bill, a bank deposit and a liquid fund on one basis before comparing them.

A bill is a price, and the yield is arithmetic done on it

The RBI’s primer on the government securities market describes treasury bills as zero coupon securities: they pay no interest, and are issued at a discount and redeemed at face value (question 1.3). They come in three tenors, 91, 182 and 364 days, are auctioned usually every Wednesday and settle on the next working day (question 3.3). The holder’s whole return is the gap between the price paid and the 100 received.

The auction sets that price bidder by bidder. The RBI’s notice for the auction of 23 September 2026 (press release 2026-2027/1148) states that it is price based and uses the multiple price method, so each successful competitive bidder pays the price it bid (primer, question 4.2). The cut-off price is the lowest price accepted. The weighted average price is what successful bidders paid on average, and by construction it is at or above the cut-off.

The fifth column is the only return either side contracts for: 1.3438 per cent on the money paid for the 91-day bill, over 91 days, and 6.0728 per cent for the 364-day bill, over 364. A yield is that holding-period return restated per year, and the restatement is where the conventions part.

Three divisions of one discount

Write P for the price per 100 of face value and D for the days to maturity. The discount is 100 minus P, and three conventions turn it into an annual rate.

The discount yield divides the discount by the face value: (100 - P) ÷ 100 × 365 ÷ D. It measures the discount as a share of what will be repaid, not of what was invested. Bank discount formulas in textbooks often use a 360-day year as well, which lowers it further; every figure on this page uses 365, so the differences below are conventions rather than calendars.

The money market yield divides the same discount by the price actually paid: (100 - P) ÷ P × 365 ÷ D. It is simple interest on the money invested, stated per year, and because P is below 100 it always exceeds the discount yield: it equals the discount yield divided by P ÷ 100.

The effective annual yield compounds the holding-period return as many times as the tenor fits into a year: (100 ÷ P) raised to the power 365 ÷ D, less 1. For a 91-day bill that is 4.011 compoundings a year; for a 364-day bill, 1.003.

The day count is fixed. The primer specifies the money market convention of actual/365 for bills, actual days over a 365-day year, against 30/360 for dated government bonds (question 25). A bill yield and a bond yield therefore sit on different bases before compounding is even considered, a difference the guide to bond price and yield flags from the bond side.

The RBI’s number is a money market yield, proved on its own prices

The primer states the formula for a bill’s yield at question 26: the discount over the purchase price, times 365 over the days to maturity. Its illustration, a 91-day bill issued at 98.20, gives 7.3521 per cent, and the same bill at 99 with 50 days left gives 7.3737; the function behind every figure on this page returns both. A primer describes; the auction results are the practice, so the test was run on them. Each full result prints a cut-off price and a weighted average price for each tenor with a yield beside each, and nine results between 10 September 2025 and 23 September 2026 give 54 pairs. Each convention was applied to each printed price and compared with the printed yield.

The money market yield reproduces all 54; its largest miss, 0.005 of a basis point (a hundredth of one per cent), is the rounding of the printed fourth decimal. The discount yield misses all 54 by up to 34.9 basis points, 42.7 on a 360-day year. The effective annual yield misses all 54 by up to 11.5, and even on 364-day bills, where its miss shrinks to hundredths of a basis point, the fourth decimal shows it. A test that tells the conventions apart makes its agreement with one of them mean something, and a calculator built for another market, dividing by 360 or by face value, reproduces none of the RBI’s figures.

Two corrections follow. The published figure is not a discount rate: it is computed on the price, not on the face value. And it is not a compounded return, although each result prints it as “YTM”, the label a bond’s compounded yield to maturity carries. It is simple interest at an annual rate, exactly comparable only with another simple actual/365 rate over the same number of days.

The same auction under three conventions

The two gaps run in opposite directions along the curve. The price base, money market minus discount yield, grows with tenor, because a longer bill is bought further below 100 and dividing by 100 instead of by P matters more: 7.15 basis points at 91 days, 34.86 at 364. Compounding runs the other way: a 91-day return compounded four times a year adds 11.00 basis points, a 364-day return compounded almost exactly once adds 0.05. Whether the conventions matter more for short bills or long ones depends on the gap: the printed yield leaves out the most compounding on a short bill, and misreading it as a discount rate costs the most on a long one.

The conventions also change the shape of the curve. On printed yields the 364-day bill pays 69.94 basis points more than the 91-day bill. On effective annual yields the gap is 58.99, so about a sixth of the printed slope is compounding the 91-day figure leaves out; on discount yields it would read 42.23. A statement about the premium for lending longer inherits whichever convention its yields were quoted in.

The gaps grow with the square of the rate

Both gaps are second order in the rate, which is why they are easy to dismiss when rates are low. Write m for the money market yield and t for D ÷ 365. The price base is m × m × t ÷ (1 + m × t), close to m squared times t. The compounding gap is close to m squared times (1 - t) ÷ 2. Double the rate and each gap roughly quadruples; the first grows with tenor, and the second vanishes at a year.

At 3 per cent no gap exceeds 8.7 basis points. At 12 per cent a 364-day bill’s discount and money market yields sit 128.3 basis points apart and a 91-day bill’s compounding is worth 55.1. A convention that is rounding at one level of rates is a material difference at another, and a rule of thumb calibrated on today’s levels is wrong by a factor of four at twice them.

An annualised 91-day yield is a forecast of three more auctions

A 91-day bill contracts to pay one thing: 100 after 91 days. Stating its return per year adds an assumption about the rest of the year. The money market yield assumes that at each maturity the discount is taken out and the principal alone is reinvested, at the same price. The effective annual yield assumes that everything is reinvested, again at the same price. Neither is contracted, because the price of the next bill is set by the next auction.

The assumption can be measured. Four 91-day auctions in the past year fell exactly 91 days apart, and each bill matured on the day the next one settled, from 11 September 2025 to 10 September 2026, which is also when the 364-day bill auctioned on 10 September 2025 and the second of two 182-day bills matured. The settlement dates come from the RBI’s auction notices and the government’s quarterly calendars. A week later the chain would have broken: in the calendar for the quarter to March 2026 the auction of 18 March settled on 20 March, two days after it.

The first 91-day bill was printed at 5.51 per cent, 5.62 effective. Had the next three auctions priced like it, 100 would have grown to 105.60; with only the principal reinvested at that price, to 105.49. The next three printed 5.27, 5.32 and 5.30 per cent, and the roll ended at 105.44. The 364-day bill bought the same day ended at 105.65, exactly what its printed yield implied, because nothing in it waited to be reinvested. Short yields eased after September 2025; in a year of rising yields the roll would have finished ahead. Either way the annualised short yield carried a forecast of three auctions, and on the effective basis this one missed by 16.3 basis points.

The roll also meets a constraint the formulas ignore. Bills are bought in lots of Rs 10,000 of face value (primer, question 4.3), so a maturing holding buys back only whole lots and its discount waits as cash until it fills another. Rolled at the weighted average prices a retail bidder is allotted at, with the leftover cash earning nothing:

A holding of one or ten lots never accumulates enough discount to buy another lot, so it earns exactly simple interest, 5.33 per cent over the 364 days; only large holdings approach full compounding, 5.43. For most retail bidders the money market yield, not the effective one, describes what a roll can earn even when rates hold still. The auto-bidding facility the RBI announced for Retail Direct on 6 August 2025 reinvests maturity proceeds in auction lot sizes, with the investor choosing the share reinvested and the tenor: it automates the roll, and leaves the next auction’s price and the lot size where they were.

What a retail bid is allotted at, and what a fixed charge costs a short bill

An individual can bid in bill auctions through the RBI’s Retail Direct scheme without an intermediary. A Retail Direct Gilt account is opened and kept with the RBI free of cost (Retail Direct FAQ 12), the minimum is Rs 10,000 of face value (FAQ 29), and bids are non-competitive. Non-competitive bids are allotted at the weighted average price of the successful competitive bids (FAQ 36; primer, question 4.3). That price is unknown when the bid is placed, so a markup is applied to the amount bid (FAQ 38). The RBI charges no fee on a bid, but payment gateway charges on funding fall on the investor (FAQ 42), and the auction notice caps retail allocation at 5 per cent of the notified amount.

Because the weighted average price sits above the cut-off, a retail bidder’s yield sits below the headline yield. Stock exchanges may also aggregate non-competitive bids (primer, question 4.3), the route by which many Indian brokers take a client’s bid to the auction, and the primer’s April 2020 edition, citing the RBI’s scheme of 23 November 2017, lets an aggregator recover up to six paise per 100 of face value. A charge fixed per 100 of face value costs more yield the shorter the bill, because the same rupees are annualised over fewer days.

Six paise costs a 364-day bill 6.8 basis points and a 91-day bill 24.7, nearly a quarter of a percentage point. A route that looks cheap per rupee can be expensive per year, so the yield worth comparing is the one computed on the price actually paid, charges included.

A deposit, a liquid fund and a bill on one basis

A bank deposit is quoted as an annual rate before compounding. The published method of a large public sector bank calculates term deposit interest at quarterly intervals, and simple interest for the actual days over 365 on deposits of under three months. A one-year reinvestment deposit, where interest is added to principal at the contracted rate (RBI FAQ on the interest rate on deposits directions, question 2), therefore earns more than its quoted rate, while a deposit of under three months earns on exactly the RBI’s basis for bills. Banks may levy a penalty for premature withdrawal under a board-approved policy (the same FAQ, question 12), and deposit insurance covers up to Rs 5 lakh per depositor per bank, principal and interest together (DICGC).

A liquid fund holds securities with not more than 91 days to maturity (AMFI’s summary of the SEBI scheme categories), and its net asset value carries each day’s income into the next, so the fund compounds inside itself, after its expenses. SEBI’s Master Circular for Mutual Funds lets overnight, liquid and money market funds advertise a simple annualisation over at least 7, 15 and 30 days (paragraph 13.3.3), shows periods of a year and more as compound annual growth (paragraph 13.3.1.1), and names the one-year treasury bill as the additional benchmark for debt schemes of up to a year (paragraph 13.3.4). A fund’s yield records what its portfolio earned; a bill’s is fixed by its price for its term.

A bill held to maturity returns exactly its holding-period return, before any charge; sold early, it returns the market price on the day of sale.

The first row holds a coincidence worth knowing. A 91-day bill compounds 4.011 times a year and a deposit four, so the printed 91-day yield and a quarterly deposit quote are almost like for like, 5.39 against 5.39. The longer bills are not. A one-year deposit quoted at 5.96 per cent, compounded quarterly, pays the same effective yield as the 364-day bill, 6.09, so a bill printed at 6.09 and a deposit quoted at 6.00 are not 9 basis points apart in the bill’s favour: the deposit’s 6.00 compounds to 6.14 and leads by 4.6, before tax, risk and liquidity. Against a liquid fund the error runs the other way. A fund whose 7-day simple annualised yield is 5.36 per cent is compounding at the 91-day bill’s effective 5.50, though the bill’s printed figure reads 5.39; and a fund’s one-year return, compounded and net of costs, set beside a 91-day bill’s printed yield is flattered by 11.00 basis points of compounding the bill’s figure leaves out. For purchase timing on the fund side, the guide to which NAV a purchase gets sets out when money starts earning.

Tax applies one rate to all three and changes the timing

For a resident individual the three returns reach the same slab rate by different routes.

At a single marginal rate s, each after-tax holding-period return is (1 - s) times the pre-tax one, so tax at one rate cannot reverse a comparison of returns over the same period made on a common basis. What it changes is timing and set-off. A fund’s gain is taxed only on redemption, so tax on a year’s internal compounding waits until the units are sold. A deposit’s interest is taxed year by year, and the tax a bank deducts at source is a prepayment of the same liability, not an extra cost. For a bill, the classification decides the year in which the discount is taxed when a bill straddles 31 March and which losses can absorb it; if it is a capital gain it can only be short term, because no bill runs longer than 364 days.

What the yield is for

A bill’s price is the fact the auction produces, and the yield is a unit for setting that price against other prices. Each convention is exact for the comparison it was built for: the money market yield against other simple actual/365 rates of the same term, the effective annual yield against anything that compounds, the holding-period return against money in hand. Error enters when a number built for one comparison is carried into another.

The discipline is short: take the price, the days and the charges, compute the holding-period return, restate every alternative on the same basis, and only then compare. Treating a quoted yield as an output to rebuild from a published price, rather than a fact to accept, is how fixed income is taught here: as arithmetic checked against the market’s own numbers, not vocabulary to memorise.