Identifier: C2T1L3 | Revision: 2026-10-26

Decision and objectives

Two dealers quote the same bill at a 20% discount rate and a 22.22% investment yield. They may describe the same cash flows using different denominators. Before choosing the larger number, reconcile the quote to price. A quotation convention is a translation rule, not an extra payment from the issuer.

Objectives: Convert price into money-market yield; Compare discount and investment yield bases; Translate annualized quotes into dated cash.

Prerequisites: C2T1L2.

Mechanics

A pure discount instrument has no periodic coupon and pays its specified redemption amount at maturity. Its price can be quoted directly per 100 nominal or indirectly as a rate. Define redemption F, purchase price P, remaining days d and annual day basis B. Investment-basis simple yield divides gain by purchase price; bank-discount style yield divides gain by redemption. These are teaching conventions and must not be assumed to be the actual Borsa convention for every security.

Price and return drivers

Simple investment yield y = (F / P − 1) × B / d, so P = F / (1 + y × d / B). Discount rate q = (F − P) / F × B / d, so P = F × (1 − q × d / B). Effective annual yield = (F / P)^(B/d) − 1. The power means repeatedly applying the same period growth; it does not forecast that reinvestment will remain possible at that rate.

Use matching day bases and settlement dates. A quoted annual percentage cannot simply be added to a six-month purchase amount. For a comparison, first reconstruct the redemption cash, then net costs, then the common holding-period return.

Worked case

Hypothetical bill: F = TRY 100,000; P = TRY 90,000; d = 180 actual days; B = 360; no coupon, fees, financing or tax. Gain is TRY 10,000. Holding return = 10,000 / 90,000 = 11.1111%. Simple investment yield = 11.1111% × 360 / 180 = 22.2222%. Discount rate = 10,000 / 100,000 × 360 / 180 = 20%. Both translate to the same price.

Effective annual yield = (100,000 / 90,000)^2 − 1 = 23.4568%, because a second identical period compounds on the first period's gain. With TRY 200 total investor fees paid at purchase, net initial outlay is TRY 90,200 and net holding return is 9,800 / 90,200 = 10.8647%. Do not deduct that fee again at redemption.

Adverse case

If a TRY 10,000 purchase is described as earning 22.2222% for 180 days, the statement overstates money income: this rate is annualized. At the stated simple basis, 10,000 × 22.2222% × 180 / 360 is approximately TRY 1,111.11, not TRY 2,222.22. Separately, an early sale below purchase price can create a loss despite a positive yield-to-redemption quote.

Practical use

Request the dealer's yield formula, day basis, settlement date and whether the quote is gross or net. Borsa records include price and yield fields; a screen rate alone cannot establish the cash debit. Reconcile the confirmation to the nominal amount and quoted price. Spreads can be embedded in the executable quote, while commissions and custody may be additional. A hypothetical zero tax does not establish an exemption.

Decision boundaries

Compare yields only after matching conventions, currency, remaining days, credit exposure and cost boundary. Reject a sales comparison that cannot identify its denominator or uses maturity rather than settlement to count days. Discount rates can also produce nonsensical negative prices under extreme inputs; that signals an invalid application of the simple formula, not a free borrowing opportunity.

Practice and references

Exercise: a hypothetical 90-day TRY 50,000 redemption is offered at simple investment yield 24% on ACT/360; no costs or tax. Answer: P = 50,000 / (1 + 0.24 × 90 / 360) = TRY 47,169.81. Gain = TRY 2,830.19; holding return = 6%. Its discount-basis annual rate is (50,000 − 47,169.8113) / 50,000 × 4 = 22.6415%.

Takeaway: the same bill has different valid yield numbers; the cash flows resolve the comparison.

Reference guide: treasury-bill, bill-simple-yield, bill-discount-rate, Discount yield, Investment yield.

Next: C2T1L4. Topic test: C2T1.

Primary sources (checked 2026-10-26; changing terms require a publication recheck): Borsa Istanbul Debt Securities Market products — Public Debt Instruments; Private Sector Debt Instruments; Lease Certificates; Eurobonds; Debt Securities Market data reporting and acceptance formats — Fields 29–36.

Shared reference guide