# Multi Period Return Table

For performance presentation a multi period (or multi horizon) table is needed. What I mean is a table showing the trailing month, quarter, YTD, and other sub periods up to since inception.

So I want to have an easy way to calculate this with returns input of arbitrary length and frequency. In other words, input can be a daily series of 2 years of data, a monthly series of 10 years of data, etc.

This is a straightforward task to do in Excel, although it can be prone to formula typos and other known drawbacks.

I am looking for an R implementation. Have looked at PerformanceAnalytics, which is able to calculate annualized since inception or a calendar year table with months. However, these functions are limited as the calendar table requires monthly data and there is no flexibility for calculating sub-periods other than since inception.

I recognize I can write a custom function for this; however, this seems to be a very common way to show data in the industry that I would imagine there is some implementation already.

Computing total returns for a fixed period is fairly simple (last price divided by first price minus 1), so the frequency of observations (hourly, daily, weekly, ...) does not matter. But you will need a tool to limit your time-series to the window of interest, such as the previous two years.

For this, I'd suggest to learn about a time-series class. An example, for which I use zoo. It turns out that zoo comes with a method window that allows you to extract a specified time window.

Download data for the DAX (a German stock market index) from Yahoo:

library("tseries")
P <- drop(get.hist.quote("^GDAXI", quote = "Close", retclass = "zoo"))
plot(P)


For computing returns, I will use the package PMwR (which I maintain).

library("PMwR")
returns(P, period = "mtd")
## -1.8%  [31 Oct 2018 -- 21 Nov 2018]
returns(P, period = "ytd")
## -13.0%  [29 Dec 2017 -- 21 Nov 2018]

## returns over the previous 2 years
returns(window(P, start = Sys.Date()-365*2), period = "itd")
## 4.9%  [22 Nov 2016 -- 21 Nov 2018]

## returns over the previous 3 years
returns(window(P, start = Sys.Date()-365*3), period = "itd")
## 1.4%  [23 Nov 2015 -- 21 Nov 2018]


To select other periods, simply set the start and end arguments to window.

If you want a quick overview, you may also say

summary(as.NAVseries(P), na.rm = TRUE)
## ---------------------------------------------------------
## 02 Jan 1991 ==> 21 Nov 2018   (7189 data points, 133 NAs)
##     1359.43         11244.2
## ---------------------------------------------------------
## High               13559.60  (23 Jan 2018)
## Low                 1317.17  (15 Jan 1991)
## ---------------------------------------------------------
## Return (%)              7.9  (annualised)
## ---------------------------------------------------------
## Max. drawdown (%)      72.7
## _ peak              8064.97  (07 Mar 2000)
## _ trough            2202.96  (12 Mar 2003)
## _ recovery                   (20 Jun 2007)
## _ underwater now (%)   17.1
## ---------------------------------------------------------
## Volatility (%)         20.2  (annualised)
## _ upside               15.0
## _ downside             13.7
## ---------------------------------------------------------
##
## Monthly returns  ▁▁▂▇█▁▁
##
##        Jan   Feb  Mar  Apr  May  Jun   Jul   Aug   Sep   Oct   Nov   Dec   YTD
## 1991   4.5  10.1 -3.1  6.0  6.3 -4.9  -0.3   1.9  -2.7  -1.6  -0.6   0.4  16.0
## 1992   6.9   3.6 -1.6  0.6  4.5 -2.8  -8.3  -4.9  -3.9   1.3   3.7  -0.4  -2.5
## [ ...... ]
## 2015   9.1   6.6  5.0 -4.3 -0.4 -4.1   3.3  -9.3  -5.8  12.3   4.9  -5.6   9.6
## 2016  -8.8  -3.1  5.0  0.7  2.2 -5.7   6.8   2.5  -0.8   1.5  -0.2   7.9   6.9
## 2017   0.5   2.6  4.0  1.0  1.4 -2.3  -1.7  -0.5   6.4   3.1  -1.6  -0.8  12.5
## 2018   2.1  -5.7 -2.7  4.3 -0.1 -2.4   4.1  -3.4  -0.9  -6.5  -1.8       -13.0

• Thanks. This addresses my original question. However, the return calculations assumes one is working with prices, is there a way to use this if instead we have a returns series? Of course, I can convert the returns to some index/price series, but my data output is in returns for so would be great to skip one step. – Juan Mier Nov 26 '18 at 15:43
• The function only works with prices. But you may easily convert returns to prices with cumprod(1+c(0, r)) for a numeric vector r. This also works for zoo series, but you may want to add an appropriate initial timestamp. – Enrico Schumann Nov 28 '18 at 19:24

When it is required to treat a lot of data, I expect that using numpy and pandas in a python prototyping environement will be the best solution.

• Pre-process you data with numpy and pandas according to your needs

after that