There are two…
(HPR * 365/Days to Maturity)
[(1+HPR)^182.5/DTM]*2
they give different answers…
Jane Acompora i s calculating equivalent annualized yields based on the 1 . 3 % holding period yield of a 90-day loan . The correct ordering of the annual money market yield (MMY), effective yield (EAY), and bond equivalent yield (BEY) i s : A . MMY < EAY < BEY. B . MMY < BEY < EAY. C . BEY < EAY < MMY No calculations are really necessary here since the MMY involves no compounding and a 360-day year, the BEY requires compounding the quarterly HPR to a semiannual rate and doubling that rate, and the EAY requires compounding for the entire year based on a 365 -day year. A numerical example of these calculations based on a 90-day holding period yield of 1 . 3% is: the money market yield is 1 .3% x 360 I 90 = 5.20%, the bond equivalent yield is 2 x [(1 .0 1 3) ^182.5/90 - 1] = 0.05 3 1 = 5 . 3 1 %, which is two times the effective semiannual rate of return, and the effective annual yield is 1 .0 1 3 365 1 90 - 1 = 0.0538 = 5 .38%. Calculating the semiannual effective yield using 1 80 days instead of 1 82.5 does not change the order.
0.013*365/90=.05272