Estimating HPY using BDY

[gdiddy]

Part (c) of problem number 9 on page 237 of volume 1 says to “[e]xplain how the bank discount yield can be converted to an estimate of the holding period return Cavell can expect if she holds the T-bill to maturity.”
According the explanation in the appendix, however, we’re given the answer that we should convert the RBD to a money market yield (RMM) and divide by 4 to arrive at an estimate.
I don’t like this explanation. Here’s why:
RBD = (D/F) x (360/t)
RMM = RBD x (F/P)
RMM also = HPY x (360/t)
By using property of identities…
RBD x (F/P) = HPY x (360/t)
Solving for HPY…
(RBD x F x t) / (P x 360) = HPY
Won’t this give the precise answer–rather than an estimate–for calculating HPY starting from the BDY?
I think the vantage point of the book is in the re-arrangement of the equation above:
(RBD x F/P) x (t/360) = HPY
RMM x (t/360) = HPY
Am I right with this assumption?

 

[Dreary]

Yes, it is correct. Your formula is actually what they are asking for! That is:
Your formula: (RBD x F x t) / (P x 360) = HPY
What was asked for: Convert RBD to RMM ==> RMM = RBD x (F/P) then divide by 4
=====> RMM /4 = RBD x (F/P) (90/360) which is exactly the same as your formula. There is no estimate other than that.
Dreary