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Consider this T-Bill (912796TE9) that was purchased on 2019-10-30 and matures on 2020-02-06:

enter image description here

I'm trying to work through some of the basics of the yield calculation.

The days until maturity is 99. (2020-02-06 minus 2019-10-30). That's easy enough.

The price is 99.563575. That's equal to 100 - ((discount) * (99/360)). Again, pretty straightforward.

Where I'm running into trouble is the yield. According to this page we should compute:

yield = ((100-price)/price) * (365/daysLeft)

By my calculations, that generates a yield of around 1.616095%. But as you can see from the screenshot, the actual yield is 1.620522%. So I'm off.

Now it turns out, if I plug 366 into the equation instead of 365, I get the correct result. Why is that? Presumably it has something to do with 2020 being a leap year. But a good fraction of the holding period takes place in 2019 which is not a leap year. What's the rule on this? If any fraction of the holding period until maturity touches a leap year then 366 shall be used?

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Due to the leap year 366 days need to be used here to match UST conventions (which is ACT/ACT). In this case it doesn't matter whether your interest period extends to only 1 day after the 29th of February or, e.g., 200. In fact if you look at the daycount description of the bill it says:

"the day count basis for price and yield calculations is 365 depending on the number of actual days in year counting forward from the Original Issue Date. The basis will usually be 365 but if the year following the issue date includes February 29th then it's 366".

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    $\begingroup$ But the day count stat for this bill is actually ACT/360, according to Bloomberg, not ACT/ACT. The use of ACT/360 allowed me to correctly derive the price from the 'discount price' in my calcs above. So you're saying there are in fact two day counts, one for price calculation and one for yield calcs? $\endgroup$
    – Yippie McSmashmouth
    Commented Nov 1, 2019 at 16:22
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    $\begingroup$ You can find above quote on the description page of the bond in BBG if you click on the calculation type. ACT/ACT is only used for yield calcs (which is the UST convention); discount calcs follows the usual money market conventions as you have correctly stated. $\endgroup$
    – oronimbus
    Commented Nov 1, 2019 at 19:10

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