CODEWITHSUNDEEP
rperformanceanalytics
DanielMc
DanielMc

Reputation: 139

"geometric" argument of chart.CumReturns function

I need an explanation of what the geometric argument of the function chart.CumReturns does. The help on that argument says:

utilize geometric chaining (TRUE) or simple/arithmetic chaining (FALSE) to aggregate returns, default TRUE

My data is comprised of simple returns and not log-returns. I guess this has an impact as well.

Any help on what the difference is between geometric and arithmetic chaining is, I would be thankful.

P.S. I should probably go back to finance 101...

Upvotes: 0

Views: 279

Answers (1)

FXQuantTrader
FXQuantTrader

Reputation: 6891

The geometric argument specifies how the individual returns are accumulated.

Let's look at how monthly returns for one year are accumulated using both methods:

library(PerformanceAnalytics)

data(edhec)
x <- edhec["2008", "Funds of Funds"]
x

# Funds of Funds
# 2008-01-31        -0.0272
# 2008-02-29         0.0142
# 2008-03-31        -0.0262
# 2008-04-30         0.0097
# 2008-05-31         0.0172
# 2008-06-30        -0.0068
# 2008-07-31        -0.0264
# 2008-08-31        -0.0156
# 2008-09-30        -0.0618
# 2008-10-31        -0.0600
# 2008-11-30        -0.0192
# 2008-12-31        -0.0119

# When geometric = TRUE, this is how cumulative returns are computed:
cumprod(1 + x) - 1
# Funds of Funds
# 2008-01-31    -0.02720000
# 2008-02-29    -0.01338624
# 2008-03-31    -0.03923552
# 2008-04-30    -0.02991611
# 2008-05-31    -0.01323066
# 2008-06-30    -0.01994069
# 2008-07-31    -0.04581426
# 2008-08-31    -0.06069956
# 2008-09-30    -0.11874832
# 2008-10-31    -0.17162342
# 2008-11-30    -0.18752825
# 2008-12-31    -0.19719667

# When geometric = FALSE, this is how cumulative returns are computed:
cumsum(x)

#           Funds of Funds
# 2008-01-31        -0.0272
# 2008-02-29        -0.0130
# 2008-03-31        -0.0392
# 2008-04-30        -0.0295
# 2008-05-31        -0.0123
# 2008-06-30        -0.0191
# 2008-07-31        -0.0455
# 2008-08-31        -0.0611
# 2008-09-30        -0.1229
# 2008-10-31        -0.1829
# 2008-11-30        -0.2021
# 2008-12-31        -0.2140

When geometric is true, the cumulative return of n returns is computed as cr = 1 * (1 + i1)(1 + i2)...(1+in) - 1. You would use this option if you assume the original investment (say $1 here) is reinvested along with any investment earnings. This is the same kind of interest compounding you earn on your savings account.

When geometric is false, the cumulative return of n returns is computed as cr = i1 + i2 + ... + in. You might use this option if you assume that you invest (say) $1 at the start of each interval, and investment returns you earn over each interval are not invested in the next interval, you just again invest the original $1 for the next interval.

Slightly aside, be aware of the different between 'simple' and 'compound' interest -- you refer to 'simple returns' and that can be interpreted as how simple interest is accumulated over time. This link might help form part of that finance 101 review: https://www.investopedia.com/ask/answers/042315/what-difference-between-compounding-interest-and-simple-interest.asp.

Upvotes: 1

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