Bond Equivalent Yield

Money market instruments — treasury bills, commercial paper, certificates of deposit — have a single cash flow and mature inside a year. A 34-day bill and a 182-day bill cannot be compared by their raw discounts, because the holding periods differ.

Bond equivalent yield puts them on a common basis. It takes the gain over the purchase price, and scales it up to a full year using a 365-day year — the Actual/365 convention prevalent in the Indian money market.

It is a simple annualisation. Nothing is compounded, because there is nothing to reinvest before maturity.

Treasury bills are issued at a discount to the face value of Rs 100 and redeemed at par. The investor's entire return is the difference between what he paid and the Rs 100 he collects.

BEY divides that gain by the price — the money actually at risk — and then annualises by 365 over the days to maturity.

The companion measure, discount yield, answers a deliberately different question: it divides the same gain by the face value and annualises on a 360-day year with 30-day months. Because the divisor is larger (100 rather than the discounted price) and the year is shorter, discount yield always comes out below BEY on the same bill.

The distinction matters commercially, not just academically: 91-day T-bill futures are quoted as 100 minus the futures discount yield, so it is discount yield, not BEY, that drives the contract.

             Face value − Price      365
BEY   =    ──────────────────  ×  ───────────────  × 100
                   Price            Days to maturity

Against the money market's other annualisation:

Discount yield = (Face value − Price) × 360 ÷ (Face value × Days to maturity)

And against the compounded measure, which is a different thing again:

Effective annual yield = (1 + r/m)^m − 1

The workbook's bill. A T-bill maturing on 25 November 2021 trades at Rs 99.6898 with a value date of 22 October 2021 — 34 days to maturity.

BEY = (100 − 99.6898) ÷ 99.6898 × 365 ÷ 34 × 100
    = 0.0031117 × 10.7353 × 100
    = 3.34%

In rupees. Buy Rs 1 crore of face value at that price:

The same bill on a discount yield basis:

Discount yield = (100 − 99.6898) × 360 ÷ (100 × 34)
               = 0.3102 × 360 ÷ 3,400
               = 3.28%

Six basis points apart on the same piece of paper, on the same day — one dividing by Rs 99.6898 over 365 days, the other by Rs 100 over 360 days. A 91-day T-bill futures contract on this bill would be quoted at 100 − 3.28 = 96.72, not at 96.66.

The same method gives the yield on commercial paper and certificates of deposit.

Chapter 1, section 1.10.2.3 (Yield for Money Market), introduces BEY with exactly the T-bill above, and section 1.10.2.4 follows with effective yield. Discount yield sits between them, flagged as the measure that matters for trading 91-day T-bill futures — which is where Chapter 3 picks it up.

The question forms are: compute BEY from a price and a settlement date; identify which yield measure uses 360 days; and recognise that multiplying a semi-annual yield by two understates the effective annual yield.

• BEY divides by price; discount yield divides by face value. This single difference produces two different answers on every bill, and the question usually supplies both figures to see which you pick up.
• BEY uses 365 days (Actual/365); discount yield uses 360 with 30-day months. Neither uses 366, and neither compounds.
• BEY is not the effective yield. Effective yield is (1 + r/m)^m − 1 — a 4.20% annual coupon paid monthly is worth 4.28% effective. BEY has no compounding in it at all.
• Doubling a semi-annual yield underestimates the effective annual yield. The workbook flags this specifically: use (1 + semi-annual rate)² − 1.
• The 91-day T-bill futures quote runs off discount yield, not BEY — and the contract value formula 2,000 × (100 − 0.25y) uses a quarter of a year, not 91 ÷ 365.
• Days to maturity is counted from the value date, not the trade date. In the example the 34 days run from 22 October, the settlement date.