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there must be something very basic that I did not get....

I am reading a book. And it says the implied repo rate is defined as IRR = ( invoice price / cash bond price - 1) * 360/ n, where is the number of days to the delivery date.. and this book also says the last delivery date (when n is bigger) implies a higher IRR...

The statement is only true when IRR is negative, but is this always the case?

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    $\begingroup$ In which book did you read this? $\endgroup$ – Bob Jansen Jul 8 '18 at 8:51
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It's because $Invoice Price$ in your equation is the Dirty Invoice Price, meaning $$Invoice Price= Futures Price*Conversion Factor + Accrued Interest$$. The Accrued Interest grows as the delivery date lengthens, making the IRR typically more positive at month end in most situations.

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  • $\begingroup$ but, the cash bond price also includes accrued Interest, also IRR decrease while n increases assuming IRR is a positive number $\endgroup$ – PeacePanda Jul 10 '18 at 23:06
  • $\begingroup$ The cash bond price includes accrued up to today , but the invoice price includes accrued up to the delivery date. $\endgroup$ – dm63 Jul 10 '18 at 23:54
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Implied repo is the rate of return you earn by shorting the futures and buying the CTD of the security. The short exercises the right to deliver the security to the long. Essentially, the short is long this optionality. If they wait until the last delivery date, the invoice price will includes accrued interest will be higher. Secondly, if there's a coupon payment, this will also be added. These factors increases your implied repo rate.

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