Pure discount instruments such as T-bills are quoted differently than U.S. government bonds. They are quoted on a bank discount basis rather than on a price basis:
Bank discount yield is not a meaningful measure of the return on investment because:
Holding period yield (HPY) is the return earned by an investor if the money market instrument is held until maturity:
Since a pure discount instrument (e.g., a T-bill) makes no interest payment, its HPY is (P1 - P0)/P0.
Note that HPY is computed on the basis of purchase price, not face value. It is not an annualized yield.
The effective annual yield is the annualized HPY on the basis of a 365-day year. It incorporates the effect of compounding interest.
Money market yield (also known as CD equivalent yield) is the annualized HPY on the basis of a 360-day year using simple interest.
An investor buys a $1,000 face-value T-bill due in 60 days at a price of $990.
If we know HPY, then:
If we know EAY, then:
If we know rMM, then:
F = $2,000,000
MMY -> HPY
HPR = (Price1 + Interest - Price0) /Price0
One interest payment of 6.1875 will be received in November. This is 12.375/2.
Buying at the market, Smedley will pay the asked price of 134 9/32 or 134.28125.
HPR = (132 + 6.1875 - 134.28125)/134.28125 = 0.0291
Holding period yield calculated:
F = $1,000
D = 0.035*(50/360)*$1,000 = $4.8611
P = $1,000 - $4.8611 = $995.1389
HPY = $4.8611/$995.1389 = 0.4885%
Based on money market yield:
0.0295 = [(100,000 - P)/P] x (360/30) => P = 100,000/[1+0.0295/12] = 99,754.8
First, use the HPY to find the money market yield: rMM = (HPY) x (360/t) = .02375 x (360 / 180) = 0.0475. Then use the money market yield to find the bond discount yield: rMM = (360 rBD) / [(360 - (t) (rBD)]. In this case: 0.0475 = (360 rBD) / [(360 - (180)( rBD)]. Now solve for rBD.
0.0475 x ((360 - (180)( rBD) = (360 rBD)