[R-SIG-Finance] Question about the Ulcer Index calculation in PerformanceAnalytics

[Ilya Kipnis]

Eric,

Thanks for the clarification on that part. The one *other* part that has me
scratching my head, though, is the use of the DrawdownPeak function, which
doesn't have quite the exact same calculations as the usual drawdown curve
I'm accustomed to. Is there a reason for using this less common drawdown
trajectory calculation, as opposed to the original drawdown curve?

-Ilya

On Sun, Mar 7, 2021 at 8:27 PM Eric Berger <ericjberger using gmail.com> wrote:

> Hi Ilya,
> You  write that UI is a std dev of something, but that is not how it is
> defined.
> To be a standard deviation, there would have to be a subtraction of a mean
> somewhere, and that is not present. (Technically, UI is the square root of
> a semivariance.)
>
> I hope that helps,
> Eric
>
>
> On Sun, Mar 7, 2021 at 3:22 PM Ilya Kipnis <ilya.kipnis using gmail.com> wrote:
>
>> 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.
>> _______________________________________________
>> R-SIG-Finance using r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-sig-finance
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>> -- Also note that this is not the r-help list where general R questions
>> should go.
>>
>

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