Why a Tresaury bill's bond equivalent yield is always different from the discount yield?
The bond equivalent yield and the discount yield are two different methods of expressing the yield on a Treasury bill. The reason they are not the same is because they are based on different calculations and assumptions.
The discount yield is a simple interest rate calculation that is based on the difference between the purchase price of the Treasury bill and its face value at maturity. It is calculated by dividing the discount (the difference between the purchase price and the face value) by the face value of the bill, and then annualizing the result. The discount yield does not take into account the time value of money or any interest payments that might be received during the term of the bill.
The bond equivalent yield, on the other hand, is an annualized yield that takes into account the time value of money. It is an estimate of the yield on a Treasury bill if it were held as a bond with interest payments spread evenly over the term. The bond equivalent yield is calculated using the following formula:
Bond Equivalent Yield = ((Face Value - Purchase Price) / Purchase Price) * (365 / Number of Days to Maturity)
The bond equivalent yield assumes that the Treasury bill is purchased at a discount and held to maturity, with the investor receiving the face value at maturity. The yield is expressed on an annual basis to facilitate comparison with other interest-bearing securities.
Since the discount yield and the bond equivalent yield are calculated using different formulas and assumptions, they will typically result in different values. The bond equivalent yield tends to be higher than the discount yield because it takes into account the time value of money and assumes the investor receives the face value at maturity. It provides a more accurate measure of the yield on a Treasury bill if it were held as a bond.