Attribution.geometric: performs sector-based geometric attribution

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

Description

Performs sector-based geometric attribution of excess return. Calculates total geometric attribution effects over multiple periods. Used internally by the Attribution function. Geometric attribution effects in the contrast with arithmetic do naturally link over time multiplicatively:

\frac{(1+R_{p})}{1+R_{b}}-1=∏^{n}_{t=1}(1+A_{t}^{G})\times ∏^{n}_{t=1}(1+S{}_{t}^{G})-1

Total allocation effect at time t:

A_{t}^{G}=\frac{1+b_{S}}{1+R_{bt}}-1

Total selection effect at time t:

S_{t}^{G}=\frac{1+R_{pt}}{1+b_{S}}-1

Semi-notional fund:

b_{S}=∑^{n}_{i=1}w_{pi}\times R_{bi}

wpt - portfolio weights at time t, wbt - benchmark weights at time t, rt - portfolio returns at time t, bt - benchmark returns at time t, r - total portfolio returns b - total benchmark returns n - number of periods

Usage

  Attribution.geometric(Rp, wp, Rb, wb, Rpl = NA, Rbl = NA,
    Rbh = NA)

Arguments

Rp	xts of portfolio returns
wp	xts of portfolio weights
Rb	xts of benchmark returns
wb	xts of benchmark weights
Rpl	xts, data frame or matrix of portfolio returns in local currency
Rbl	xts, data frame or matrix of benchmark returns in local currency
Rbh	xts, data frame or matrix of benchmark returns hedged into the base currency

Details

The multi-currency geometric attribution is handled following the Appendix A (Bacon, 2004).

The individual selection effects are computed using:

w_{pi}\times≤ft(\frac{1+R_{pLi}}{1+R_{bLi}}-1\right)\times ≤ft(\frac{1+R_{bLi}}{1+b_{SL}}\right)

The individual allocation effects are computed using:

(w_{pi}-w_{bi})\times≤ft(\frac{1+R_{bHi}}{1+b_{L}}-1\right)

Where the total semi-notional returns hedged into the base currency were used:

b_{SH} = ∑_{i}w_{pi}\times R_{bi}((w_{pi} - w_{bi})R_{bHi} + w_{bi}R_{bLi})

Total semi-notional returns in the local currency:

b_{SL} = ∑_{i}w_{pi}R_{bLi}

RpLi - portfolio returns in the local currency RbLi - benchmark returns in the local currency RbHi - benchmark returns hedged into the base currency bL - total benchmark returns in the local currency rL - total portfolio returns in the local currency The total excess returns are decomposed into:

\frac{(1+R_{p})}{1+R_{b}}-1=\frac{1+r_{L}}{1+b_{SL}}\times\frac{1+ b_{SH}}{1+b_{L}}\times\frac{1+b_{SL}}{1+b_{SH}}\times\frac{1+R_{p}}{1+r_{L}} \times\frac{1+b_{L}}{1+R_{b}}-1

where the first term corresponds to the selection, second to the allocation, third to the hedging cost transferred and the last two to the naive currency attribution

Value

This function returns the list with attribution effects (allocation or selection effect) including total multi-period attribution effects

Author(s)

Andrii Babii

References

Christopherson, Jon A., Carino, David R., Ferson, Wayne E. Portfolio Performance Measurement and Benchmarking. McGraw-Hill. 2009. Chapter 18-19
Bacon, C. Practical Portfolio Performance Measurement and Attribution. Wiley. 2004. Chapter 5, 8, Appendix A

See Also

Attribution

Examples

data(attrib)
Attribution.geometric(Rp = attrib.returns[, 1:10], wp = attrib.weights[1, ],
Rb = attrib.returns[, 11:20], wb = attrib.weights[2, ])

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