Can the bank discount yield be converted to holding period yield and vice versa when the face value and purchase price of the t-bill is not given?
You can solve for the face value with the discount, bank discount yield, and time to maturity given. As a result, you can also get the purchase price by then subtractiving the discount from the face value. But without being able to determine those values and not having them given you can’t convert the bank discount yield to a HPY and vice versa. You need some details as the HPY isn’t a plugable function in the bank discount yield.
If you know r(bd), you can can calculate r(mm) r(mm) = 360 * r(bd)/ 360 - (t * r(bd) ) But r(mm) is also HPY * 360/t So HPY * 360/t = 360 * r(bd)/ 360 - t * r(bd) Thats the equation
Example. An investor buys a $1,000 face-value T-bill due in 60 days at a price of $990. Bank discount yield: (1000 - 990)/1000 x 360/60 = 6% Holding period yield: (1000 - 990)/990 = 1.0101% Money market yield: (360 x 6%)/(360 - 60 x 6%) = 6.0606%. See this: Holding period yield = Money market yield * t/360 = 6.0606%/6 = 1.0101% Here HPY means the yield he will get if he holds this puppy until maturity.