Carino: calculates total attribution effects using logarithmic...

In R-Finance/PortfolioAttribution: Performance attribution tools used for identifying sources of portfolio return and risk.

Description

Calculates total attribution effects over multiple periods using logarithmic linking method. Used internally by the Attribution function. Arithmetic attribution effects do not naturally link over time. This function uses logarithmic smoothing to adjust attribution effects so that they can be summed up over multiple periods. Attribution effect are multiplied by the adjustment factor:

At' = At * kt / k

where

k_{t} = \frac{log(1 + R_{pt}) - log(1 + R_{bt})}{R_{pt} - R_{bt}}

k = \frac{log(1 + R_{p}) - log(1 + R_{b})}{R_{p} - R_{b}}

In case if portfolio and benchmark returns are equal:

kt = 1 / (1 + Rpt)

where At' - adjusted attribution effects at period t, At - unadjusted attribution effects at period t, Rpt - portfolio returns at period t, Rbt - benchmark returns at period t, Rp - total portfolio returns, Rb - total benchmark returns, n - number of periods The total arithmetic excess returns can be explained in terms of the sum of adjusted attribution effects:

R_{p} - R_{b} = ∑^{n}_{t=1}≤ft(Allocation_{t}+Selection_{t}+ Interaction_{t}\right)

Usage

  Carino(rp, rb, attributions, adjusted)

Arguments

rp	xts of portfolio returns
rb	xts of benchmark returns
attributions	xts with attribution effects
adjusted	TRUE/FALSE, whether to show original or smoothed attribution effects for each period

Value

returns a data frame with original attribution effects and total attribution effects over multiple periods

Author(s)

Andrii Babii

References

Christopherson, Jon A., Carino, David R., Ferson, Wayne E. Portfolio Performance Measurement and Benchmarking. McGraw-Hill. 2009. Chapter 19
Bacon, C. Practical Portfolio Performance Measurement and Attribution. Wiley. 2004. p. 191-193
Carino, D. (1999) Combining attribution effects over time. The Journal of Performance Measurement. Summer. p. 5-14

See Also

Attribution
Menchero
Grap
Frongello
Attribution.geometric

Examples

data(attrib)
Carino(rp = attrib.returns[, 21], rb = attrib.returns[, 22], attributions = attrib.allocation, adjusted = FALSE)

R-Finance/PortfolioAttribution documentation built on May 8, 2019, 4:48 a.m.