# Geometric linking of returns

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• Dec 23rd 2009, 10:15 AM
merrellter
Geometric linking of returns
Equation below assumes equal time periods

(1 + S1) x (1 + S2) x ... (1 + Sn) - 1

((1+.004) * (1+.0019) * (1+.0018)) - 1 = .007718 = .77%

What would be the equation/formula for unequal time period returns using the equation above to get a time weighted return?

for example:

.004 for 10 days
.0019 for 30 days
.0018 for 50 days.

Analysis period 90 days.

Trying to time weight the individual returns within this formula or any suggestion.

A test of any suggestion would be to enter an equal weighting for each variable with the result being .007718 = .77%; the same as the first equation where variables are defined as being weighted equally.

Am completely new to forums and am not familiar with etiquette; however, I would expect to pay for work done correctly; just don't know procedure.
• Dec 23rd 2009, 06:56 PM
TKHunny
Maybe...
$((1+.004)^{10} * (1+.0019)^{30} * (1+.0018)^{50})^{\frac{1}{10+30+50}}-1 = 0.00207754654$
• Dec 23rd 2009, 08:28 PM
merrellter
Thank you, will test; test being to weight each variable equally resulting in the same answer as the initial equation; .00718.

Appreciate your try; but does not work.