This has been bothering me for a little while:
I have a 90 day holding period yield of 1.3%. The annual rate would be:
(1 + 0.013)^(365/90) -1 = 0.0537787
The BDY would be:
2 * [(1 + 0.013)^(365/180) -1] = 0.0530745
along the same lines, if I take the annual rate and try to get back to the BDY:
2 * [(1 + 0.0537787)^(.5) -1] = 0.0530745
HOWEVER, my question is why do I have to use 0.5 as the exponent to get back to the semi-annual rate instead of 180/365? If I use 180/365 I get a different number:
2 * [(1 + 0.0537787)^(180/365) -1] = 0.0523380
you could use either i guess but 180/365 does not = .5
Just confused as why going from 1.3% 90 day HPY using 365/90 for an annual or 365/180 to a semi-annual gets me to certain numbers, but going back from the annual rate to the semi-annual, I can’t use 180/365, and instead need to use 0.5 to get to that number?
I feel like it should be consistant and since it isn’t, I must be thinking of something the wrong way?
After thinking about this, I guess it is just a matter of convention. The BDY is 2 * the semi-annual yield so when you have the annual rate of 0.0537787 and you want to go back to semi-annual, you have to think in terms of 1/2 a year so the exponent is 0.5, not 180 days.
Let me know if my reasoning is incorrect, thanks.