Explain why bank discount yield is lower than bond equivalent yield.

The bank discount yield (BDY) is lower than the bond equivalent yield (BEY) due to differences in their calculation methods and the time value of money.

1. Bank Discount Yield (BDY) is calculated as: $$\text{BDY}=\frac{\text{Discount}}{\text{Face Value}}\times \frac{360}{\text{Days to Maturity}}$$ It uses a 360-day year (banker’s convention) and the discount amount (face value minus price), which understates the true yield.

2. Bond Equivalent Yield (BEY) adjusts for the actual investment amount (purchase price) and uses a 365-day year: $$\text{BEY}=\frac{\text{Discount}}{\text{Purchase Price}}\times \frac{365}{\text{Days to Maturity}}$$ Since the purchase price is lower than the face value, BEY is higher than BDY.

Thus, BEY > BDY because it accounts for the true cost of investment and a more accurate annualization period.