Analyzing draw-downs

Chart: Cumulative 500 random returns

Let's take a series of randomly generated 500 returns in the range of 0.92 to 1.10 (or -8% to +10%).

Now, let's try to calculate some basic potential loss statistics for this series based on the observed draw-downs:

Number of the draw-down losing sequences:

> downsN
[1] 228

First draw-downs losing sequences:

d(dd_stats)
     start stop length         loss
[1,]     1    1      1 -0.005949528
[2,]     2    3      2 -0.122208798
[3,]     4    4      1 -0.024784714
[4,]     5    6      2 -0.098330307
[5,]     7    8      2 -0.060649554
[6,]     9   11      3 -0.137897672

The worst draw-down losing sequence in terms of value:

> min(sapply(drawdowns, function(x) x$result-1))
[1] -0.2625977

The longest draw-down losing sequence:

> max(sapply(drawdowns, function(x) x$length))
[1] 6

Average loss of draw-down losing sequences:

> mean(sapply(drawdowns, function(x) x$result-1))
[1] -0.07221781

The bottom, peak and the last value of the process:

> min(cumreturns)-1; max(cumreturns)-1; cumreturns[length(cumreturns)]-1
[1] -0.0683741
[1] 46.30488
[1] 38.46427

UPDATE 2012-02-10

Chart: Cumulative random sequence of 500 returns [-8%, +10%] and draw-down line

Above I did calculate the statistics for losing sequences not draw down.

The correct results (for a different random process) should be:

> downsN # number of losing sequences
[1] 214
> 
> head(dd_stats)
     start stop length         loss
[1,]     1    1      1 -0.039665746
[2,]     2    3      2 -0.097175026
[3,]     4    4      1 -0.001900723
[4,]     5    6      2 -0.076761609
[5,]     7    8      2 -0.083846687
[6,]     9   10      2 -0.062338201
> 
> min(sapply(drawdowns, function(x) x$result-1)) # worst sequence
[1] -0.2556858
> 
> mean(sapply(drawdowns, function(x) x$result-1)) # average sequence
[1] -0.06519456
> 
> max(sapply(drawdowns, function(x) x$length)) # longest sequence
[1] 6
> 
> mean(sapply(drawdowns, function(x) x$length)) # average length of sequence
[1] 1.658915
> 
> # bottom, top, last result
> min(cumreturns)-1; max(cumreturns)-1; cumreturns[length(cumreturns)]-1
[1] -0.06119829
[1] 161.2614
[1] 85.06354
> 
> 
> min(dd) # worst draw down
[1] -0.5623983

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