Mismatching drawdown calculations - r

Question

I would like to ask you to clarify the next question, which is of extreme importance to me, since a major part of my master's thesis relies on properly implementing the data calculated in the following example.
I hava a list of financial time series, which look like this (AUDUSD example):
Open High Low Last
1992-05-18 0.7571 0.7600 0.7565 0.7598
1992-05-19 0.7594 0.7595 0.7570 0.7573
1992-05-20 0.7569 0.7570 0.7548 0.7562
1992-05-21 0.7558 0.7590 0.7540 0.7570
1992-05-22 0.7574 0.7585 0.7555 0.7576
1992-05-25 0.7575 0.7598 0.7568 0.7582
From this data I calculate log returns for the column Last to obtain something like this
Last
1992-05-19 -0.0032957646
1992-05-20 -0.0014535847
1992-05-21 0.0010573620
1992-05-22 0.0007922884
Now I want to calculate the drawdowns in the above presented time series, which I achieve by using (from package PerformanceAnalytics)
ddStats <- drawdownsStats(timeSeries(AUDUSDLgRetLast[,1], rownames(AUDUSDLgRetLast)))
which results in the following output (here are just the first 5 lines, but it returns every single drawdown, including also one day long ones)
From Trough To Depth Length ToTrough Recovery
1 1996-12-03 2001-04-02 2007-07-13 -0.4298531511 2766 1127 1639
2 2008-07-16 2008-10-27 2011-04-08 -0.4003839141 713 74 639
3 2011-07-28 2014-01-24 2014-05-13 -0.2254426369 730 652 NA
4 1992-06-09 1993-10-04 1994-12-06 -0.1609854215 650 344 306
5 2007-07-26 2007-08-16 2007-09-28 -0.1037999707 47 16 31
Now, the problem is the following: The depth of the worst drawdown (according to the upper output) is -0.4298, whereas if I do the following calculations "by hand" I obtain
(AUDUSD[as.character(ddStats[1,1]),4]-AUDUSD[as.character(ddStats[1,2]),4])/(AUDUSD[as.character(ddStats[1,1]),4])
[1] 0.399373
To make things clearer, this are the two lines from the AUDUSD dataframe for from and through dates:
AUDUSD[as.character(ddStats[1,1]),]
Open High Low Last
1996-12-03 0.8161 0.8167 0.7845 0.7975
AUDUSD[as.character(ddStats[1,2]),]
Open High Low Last
2001-04-02 0.4858 0.4887 0.4773 0.479
Also, the other drawdown depts do not agree with the calculations "by hand". What I am missing? How come that this two numbers, which should be the same, differ for a substantial amount?

Answer 1

I have tried replicating the drawdown via:
cumsum(rets) -cummax(cumsum(rets))
where rets is the vector of your log returns.
For some reason when I calculate Drawdowns that are say less than 20% I get the same results as table.Drawdowns() & drawdownsStats() but when there is a large difference say drawdowns over 35%, then the Max Drawdown begin to diverge between calculations. More specifically the table.Drawdowns() & drawdownsStats() are overstated (at least what i noticed). I do not know why this is so, but perhaps what might help is if you use an confidence interval for large drawdowns (those over 35%) by using the Standard error of the drawdown. I would use: 0.4298531511/sqrt(1127) which is the max drawdown/sqrt(depth to trough). This would yield a +/- of 0.01280437 or a drawdown of 0.4169956 to 0.4426044 respectively, which the lower interval of 0.4169956 is much closer to you "by-hand" calculation of 0.399373. Hope it helps.