I am currently reading the following paper https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2750064 . On page 57 the researchers state that they calculate the logarithmized average monthly returns as calculated over four non overlapping periods.
The price series looks as follows:
price_mth0 price_mth1 price_mth2 price_mth3 price_mth4 price_mth5 price_mth6 price_mth7 price_mth8 price_mth9 price_mth10 price_mth11 price_mth12
100 99.89974213 90.88634491 105.1879883 100.2683334 92.54978943 93.88592529 79.42245483 75.91511536 74.78253937 86.61391449 82.77873993 83.12158203
And the calculated returns are
lnreturn_lag1m3m lnreturn_lag4m6m lnreturn_lag7m9m lnreturn_lag10m12m
0.03523995 -0.075832009 -0.037889559 0.016859641
Unfortunately they do not state a formula. I tried several different ways to come to their results but I cannot come up with the right formula. Can anyone helpe me?
For me the correct calculation should be
(ln( 82.77873993) - ln(75.91511536)) / 3
However, this has 0.02885182 as a result and not 0.03523995
