Menchero: calculates total attribution effects using Menchero smoothing

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

At' = At * (M + at)

where

M=\frac{\frac{1}{n}(R_{p}-R_{b})}{(1+R_{p})^{\frac{1}{n}}- (1+R_{b})^{\frac{1}{n}}}

a_{t} = ≤ft(\frac{R_{p}-R_{b}-M\times∑^{n}_{t=1}(R_{pt}- R_{bt})}{∑^{n}_{t=1}(R_{pt}-R_{bt})^{2}}\right)\times(R_{pt}-R_{bt})

In case if portfolio and benchmark returns are equal the limit of the above value is used:

M = (1 + rp)^((n - 1) / n)

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

Usage

  Menchero(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

Details

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)

Value

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

Author(s)

Andrii Babii

References

Bacon, C. Practical Portfolio Performance Measurement and Attribution. Wiley. 2004. p. 194-196
Menchero, J. (2000) An optimized approach to linking attribution effects over time. Journal of Performance Measurement. Fall. p. 36-42

See Also

Attribution
Carino
Grap
Frongello
Attribution.geometric

Examples

data(attrib)
Menchero(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.