Yield measures for T-bills

Yields on Treasury bills are expressed as a discount from face value and their maturity is often less than a year.

Bank discount yield (BDY)
Annualized discount from face value. It is not a meaningful measure of the return earned by investors.

BDY = [(F-P)/F ] x (360 / t).

Where:
F- Face value
P- Purchase price
t - Days to maturity

Problem:
· Use face value as denominator but not purchase price
· Based on 360-day but not 365 day
· On simple interest basis, but not compounding

Holding period yield (HPY)
The total return received from holding an asset or portfolio of assets. Holding period yield is calculated as the sum of all income and capital growth divided by the value at the beginning of the period being measured.

HPY = (P - F) / P

Problem:
· Difficult to compare with other instruments with different time frame.

Effective annual yield (EAY)
Take account of compound interest and is on 365 day basis.

EAY= (F / P)^{(365 / t)} – 1

Problem:
· Implicit reinvestment assumption of all yield to maturity type measures.

Money market yield (MMY)
Its assumption of 360 day year makes T-bills comparable to yield bearing money market instruments that are applied on 360 day basis. It equals to the annualized HPY.

MMY= [(P - F) / P] x (360 /t)

Problem:
· On simple interest basis, but not compounding

Bond Equivalent Yield (BEY)
So-called Annual Percentage Rate (APR ), converting the yield of a money market instrument, such as a Treasury bill, into the equivalent yield of a Treasury bond in order to compare efficiency ( equivalent annual yield of a bond).

The BEY is the yield that is quoted in newspapers.

BEY = [(F-P)/P] x (360/t)

Problems:
· Use simple interest to annualize


The yields are inter-convertible:

EAY= (1+HPY) ^{(365 /t)} –1
EAY=[1+BEY(t/360)] ^{(365 /t)}
MMY= (HPY)( 360/t)
MMY= 360x(BDY)/ {(360-t)xBDY}

Yield of Zero-coupon bond:
Price zero-coupon bond with N years remaining
P= F / (1 + Y/2)^{(2 x N)}
Yield of zero-coupon bond
Y= {(F / P)^{[1 / (2 x N)]} - 1}x2