Explain money market yield measures and the conventions they follow
The idea
Short-term instruments are quoted on conventions that are not comparable without conversion. A discount-basis quote, used for Treasury bills in some markets, expresses the discount as a percentage of face value rather than of the price paid, which understates the true return. An add-on rate expresses interest as a percentage of the amount invested, which is the economically meaningful measure. Day count conventions differ too — actual over 360, actual over 365, thirty over 360 — and a rate quoted on a 360-day year is not comparable to one quoted on 365 until it is restated.
Formulas
Bond equivalent yield of a money market instrument
BEY = HPY × (365 ÷ t)
- HPY
- the holding period yield, the gain ÷ the price actually paid
- t
- days held
Money market instruments are quoted on a discount or add-on basis and on 360 or 365 days, and none of those are comparable until they are on one basis. A discount rate is struck on face value rather than the price paid, so it always understates the return.
A practice question
Why does a discount-basis quote understate the true return on a Treasury bill?
- Because it excludes the couponWhy not: A bill has no coupon — the entire return is the discount, and that discount is what the quote is built from.
- Because it divides by face value — correct
- Because it uses a 365-day yearWhy not: It uses 360, which by itself makes an annualised figure *larger*. The understatement comes from dividing by face value.
The discount is expressed as a percentage of face rather than of the smaller amount actually invested. Dividing by the larger figure produces a smaller percentage, while the add-on rate divides by what was paid, which is the return an investor actually earns.
A harder one
Two money market rates are quoted, one on actual over 360 and one on actual over 365. What must be done before comparing them?
- Nothing, the conventions are equivalentWhy not: They produce different numbers for identical cash flows — about 1.4% apart in relative terms, which is enough to reverse a ranking.
- Adjust both for credit riskWhy not: A sensible step if the issuers differ, but it does not address the problem stated, which is that the two figures are in different units.
- Restate one onto the other's day count basis — correct
A 360-day year makes a rate appear lower than the same economics stated on 365. Comparing them directly is comparing different units.
The hardest tier
Why do money market conventions persist despite being a known source of confusion?
- Because they are embedded in enormous existing markets — correct
- Because regulators require themWhy not: They predate the regulators and are market practice. What regulation requires is disclosure sufficient for comparison.
- Because the differences are immaterial in practiceWhy not: On a large short-term position the difference is real money, and it is systematic rather than random.
The conventions are arbitrary and the conversions are simple. Changing them would require repapering trillions in outstanding contracts to fix a problem a spreadsheet already solves.
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