Cumulative Return between two dates

I have a table that carries data with cumulative return of some instrument. Data is described with start date, end date and cumulative return for date range (start-end):

``````Start Date|End Date  |Cumulative Return
06/23/2013|03/17/2015|0.358702433
07/07/2013|03/17/2015|0.38655325
``````

But now, I need to calculate cumulative returns for other date ranges, for instance a cumulative return between 06/23/2013 and 07/07/2013 . Is is possible to do it with some generic formula?

Thanks

• No, there is no way, unless you know the exact market value of the first instrument on 7/7/2013, or the first instrument is a zero coupon bond classified as held to maturity. Aug 20, 2015 at 10:09
• If there is a return of x% from 06/23/2013 to 07/07/2013 and this would combined with the bottom return it would equal the first return is what I'd use to set up an equation to compute the desired result. Aug 20, 2015 at 14:12

2 Answers

Cumulative returns are the total return percentages between two dates. In the case of having two date-ranges with a single common one it does go down to simple math.

Example

start money 100 doesn't have to be correct

start date 1/1/2010

end date 1/1/2015 ; 1/1/2020

cumulative return 1/1/2010 — 1/1/2015 = 1

cumulative return 1/1/2010 — 1/1/2020 = 2

It is then easy to count the other third range.

end money = start money + start money * cumulative return = 200 ; 300

cumulative return 1/1/2015 — 1/1/2020 = 200 / 300 = 0.667

This method only works for the cases where the ranges have a common end point.

07/07/2013 to 03/17/2015 is 618 days

``````p = 100;
s = p (1 + 0.38655325) = 138.655325
``````

Daily rate over the 618 day period

``````r = (1 + 0.38655325)^(1/618) - 1
``````

Check

``````p (1 + r)^618 = 138.655325
``````

06/23/2013 to 03/17/2015 is 632 days; starts 14 days earlier

``````p = 100;
s2 = p (1 + 0.358702433) = 135.8702433
``````

In the first 14 days

``````p2 = p (1 + y)^14
``````

The remaining 618 days

``````Solve[p2 (1 + r)^618 == s2, y]

y = -0.001448295953242864
``````

The daily rate for the first 14 days is negative, which is not surprising since the return for the longer 632 day period (`0.358702433`) is less than that for the shorter 618 day period (`0.38655325`).

Check

``````p (1 + y)^14*(1 + r)^618 = 135.8702433
``````

Note, `y = -1.9985517040096623` also satisfies the equation but is not a realistic answer here.