[R-SIG-Finance] Question about the Ulcer Index calculation in PerformanceAnalytics
Ilya Kipnis
||y@@k|pn|@ @end|ng |rom gm@||@com
Sun Mar 7 21:22:16 CET 2021
I'm working on porting over an interesting risk metric that I found out
about through a twitter exchange with the usual suspects (Adam Butler of
ReSolve, Wayne Himelsein) called the Serenity Ratio, found here:
https://www.keyquant.com/Download/GetFile?Filename=%5CPublications%5CKeyQuant_WhitePaper_APT_Part1.pdf
Now, I've run into an issue, namely with the calculation of the Ulcer Index:
Now, as I understand it, the Ulcer Index is the root-mean-square (read:
volatility, I.E. standard deviation) of drawdowns. However, when I check
the UlcerIndex function in R, it uses the DrawdownPeak function, which has
a different calculation than PerformanceAnalytics:::Drawdowns .
Furthermore, taking the standard deviation of *either*
PerformanceAnalytics:::Drawdowns *or* DrawdownPeak of returns yields a
different calculation than using the formal UlcerIndex function.
Here is my script. Can someone explain the choices made with the UlcerIndex
implementation in the package?
Sample script:
getSymbols('SPY', from = '1990-01-01')
spyRets <- na.omit(Return.calculate(Ad(SPY)))
compare <- cbind(PerformanceAnalytics:::Drawdowns(spyRets),
xts(DrawdownPeak(spyRets), order.by = index(spyRets)))
colnames(compare) <- c("PerfA:::Drawdowns", "DrawdownPeak")
plot(compare, legend.loc = 'bottomleft')
differentUIs <- c(StdDev(PerformanceAnalytics:::Drawdowns(spyRets)),
StdDev(DrawdownPeak(spyRets)),
UlcerIndex(spyRets))
names(differentUIs) <- c("StdDevDrawdowns", "StdDevDDPeak", "UlcerInex")
Outputs:
[image: image.png]
[image: image.png]
In the interest of replication (I.E. Python has none of these functions in
any library I know of), and for the correct calculation of other functions
dependent on the Ulcer Index (UPI, Serenity Ratio), can someone help me
resolve/understand the discrepancies here?
Thanks so much.
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