motivated by email from Gordon K.
Suppose you get reports from your money manager which gives you quarterly returns and YearToDate returns etc., and
you want to check those numbers yourself ... using the
XIRR function in Excel.
>Why?
Because it'll give you a warm feeling ... if your calculations agree
So, first we note the following (where, for a return of 12.3% we use R = 0.123)
 If R is an annual return, then each dollar grows to $(1+R) in a year ... we'll call 1+R the Gain Factor over 365 days
Example: If R = 0.123 then 1.123 is the annual Gain Factor
 Then each dollar will grow to (1+R)^{1/365} in one day ... this is the oneday Gain Factor
If R = 0.123 (meaning 12.3%) then 1.123^{1/365} = 1.000317869 is the daily Gain Factor
 Then each dollar will grow to (1+R)^{D/365} in D days ... the Dday Gain Factor
If D = 90 days then 1.123^{90/365} = 1.029 is the Gain Factor over 90 days, meaning $1.00 will grow to $1.029 in 90 days
 That means that the return, over D days, is (1+R)^{D/365}  1 ... and you'd multiply by 100 to get the percentage return, over D days
That'd be 1.029  1 = 0.029 is the return over 90 days, and multiplying by 100 gives a 90day return of 2.9%
 That means that, if D days has passed since the start of the year, then the YTD return would be:
YTD Return = (1+R)^{D/365}  1
where R is the Annualized Return (since the start of the year) and D days have passed since the start of the year. 
>And how am I supposed to calculate that Annualized Return?
Aah, that's where XIRR comes in! The Excel function always gives an Annuallized Return !
For example, suppose we start the year with $56,789 and make a bunch of deposits into our account and by the end of the
first quarter we have $67,890 (which, according to XIRR rules, we enter as a negative amount).
Further, we continue to make deposits for another quarter (to June 30) and calculate the annualized return over just this second quarter.
Then (in column D) we calculate the YTD Return ... as described above.
>I thought you needed some kind of guess, for that XIRR?
I'd normally use XIRR(A3:A11,B3:B11,0.1) where that 0.1 (or 10%) is my guess ... but if I leave it out Excel puts in 0.1 anyway
If you'd like to play with the spreadsheet, just click on the picture above
(or, if'n you like, you can RIGHTclick and
Save Target to download the spreadsheet.
