Attribution: performs sector-based single-level attribution

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

Description

Performs sector-based single-level attribution analysis. Portfolio performance measured relative to a benchmark gives an indication of the value-added by the portfolio. Equipped with weights and returns of portfolio segments, we can dissect the value-added into useful components. This function is based on the sector-based approach to the attribution. The workhorse is the Brinson model that explains the arithmetic difference between portfolio and benchmark returns. That is it breaks down the arithmetic excess returns at one level. If returns and weights are available at the lowest level (e.g. for individual instruments), the aggregation up to the chosen level from the hierarchy can be done using Return.level function. The attribution effects can be computed for several periods. The multi-period summary is obtained using one of linking methods: Carino, Menchero, GRAP, Frongello or Davies Laker. It also allows to break down the geometric excess returns, which link naturally over time. Finally, it annualizes arithmetic and geometric excess returns similarly to the portfolio and/or benchmark returns annualization.

Usage

  Attribution(Rp, wp, Rb, wb, wpf = NA, wbf = NA, S = NA,
    F = NA, Rpl = NA, Rbl = NA, Rbh = NA, bf = FALSE,
    method = c("none", "top.down", "bottom.up"),
    linking = c("carino", "menchero", "grap", "frongello", "davies.laker"),
    geometric = FALSE, adjusted = FALSE)

Arguments

Rp	T x n xts, data frame or matrix of portfolio returns
wp	vector, xts, data frame or matrix of portfolio weights
Rb	T x n xts, data frame or matrix of benchmark returns
wb	vector, xts, data frame or matrix of benchmark weights
method	Used to select the priority between allocation and selection effects in arithmetic attribution. May be any of: none - present allocation, selection and interaction effects independently, top.down - the priority is given to the sector allocation. Interaction term is combined with the security selection effect, bottom.up - the priority is given to the security selection. Interaction term is combined with the sector allocation effect By default "none" is selected
wpf	vector, xts, data frame or matrix with portfolio weights of currency forward contracts
wbf	vector, xts, data frame or matrix with benchmark weights of currency forward contracts
S	(T+1) x n xts, data frame or matrix with spot rates. The first date should coincide with the first date of portfolio returns
F	(T+1) x n xts, data frame or matrix with forward rates. The first date should coincide with the first date of portfolio returns
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
bf	TRUE for Brinson and Fachler and FALSE for Brinson, Hood and Beebower arithmetic attribution. By default Brinson, Hood and Beebower attribution is selected
linking	Used to select the linking method to present the multi-period summary of arithmetic attribution effects. May be any of: carino - logarithmic linking coefficient method menchero - Menchero's smoothing algorithm grap - linking approach developed by GRAP frongello - Frongello's linking method davies.laker - Davies and Laker's linking method By default Carino linking is selected
geometric	TRUE/FALSE, whether to use geometric or arithmetic excess returns for the attribution analysis. By default arithmetic is selected
adjusted	TRUE/FALSE, whether to show original or smoothed attribution effects for each period. By default unadjusted attribution effects are returned

Details

The arithmetic excess returns are decomposed into the sum of allocation, selection and interaction effects across n sectors:

R_{p}-R_{b}=∑^{n}_{i=1}≤ft(A_{i}+S_{i}+I_{i}\right)

The arithmetic attribution effects for the category i are computed as suggested in the Brinson, Hood and Beebower (1986): Allocation effect

Ai = (wpi - wbi) * Rbi

Selection effect

Si = wpi * (Rpi - Rbi)

Interaction effect

Ii = (wpi - wbi) * Rpi - Rbi

Rp - total portfolio returns, Rb - total benchmark returns, wpi - weights of the category i in the portfolio, wbi - weights of the category i in the benchmark, Rpi - returns of the portfolio category i, Rbi - returns of the benchmark category i. If Brinson and Fachler (1985) is selected the allocation effect differs:

Ai = (wpi - wbi) * (Rbi - Rb)

Depending on goals we can give priority to the allocation or to the selection effects. If the priority is given to the sector allocation the interaction term will be combined with the security selection effect (top-down approach). If the priority is given to the security selection, the interaction term will be combined with the asset-allocation effect (bottom-up approach). Usually we have more than one period. In that case individual arithmetic attribution effects should be adjusted using linking methods. Adjusted arithmetic attribution effects can be summed up over time to provide the multi-period summary:

R_{p}-R_{b}=∑^{T}_{t=1}≤ft(A_{t}'+S_{t}'+I_{t}'\right)

where T is the number of periods and prime stands for the adjustment. The geometric attribution effects do not suffer from the linking problem. Moreover we don't have the interaction term. For more details about the geometric attribution see the documentation to Attribution.geometric. Finally, arithmetic annualized excess returns are computed as the arithmetic difference between annualised portfolio and benchmark returns:

AAER = ra - ba

the geometric annualized excess returns are computed as the geometric difference between annualized portfolio and benchmark returns:

GAER = (1 + ra) / (1 + ba) - 1

In the case of multi-currency portfolio, the currency return, currency surprise and forward premium should be specified. The multi-currency arithmetic attribution is handled following Ankrim and Hensel (1992). Currency returns are decomposed into the sum of the currency surprise and the forward premium:

Rci = Rcei + Rfpi

where

R_{cei} = \frac{S_{i}^{t+1} - F_{i}^{t+1}}{S_{i}^{t}}

R_{fpi} = \frac{F_{i}^{t+1}}{S_{i}^{t}} - 1

Sit - spot rate for asset i at time t Fit - forward rate for asset i at time t. Excess returns are decomposed into the sum of allocation, selection and interaction effects as in the standard Brinson model:

R_{p}-R_{b}=∑^{n}_{i=1}≤ft(A_{i}+S_{i}+I_{i}\right)

However the allocation effect is computed taking into account currency effects:

Ai = (wpi - wbi) * (Rbi - Rci - Rl)

Benchmark returns adjusted to the currency:

R_{l} = ∑^{n}_{i=1}w_{bi}\times(R_{bi}-R_{ci})

The contribution from the currency is analogous to asset allocation:

C_{i} = (w_{pi} - w_{bi}) \times (R_{cei} - e) + (w_{pfi} - w_{bfi}) \times (R_{fi} - e)

where

e = ∑^{n}_{i=1}w_{bi}\times R_{cei}

The final term, forward premium, is also analogous to the asset allocation:

Rfi = (wpi - wbi) * (Rfpi - d)

where

d = ∑^{n}_{i=1}w_{bi}\times R_{fpi}

and R_{fpi} - forward premium In general if the intent is to estimate statistical parameters, the arithmetic excess return is preferred. However, due to the linking challenges, it may be preferable to use geometric excess return if the intent is to link and annualize excess returns.

Value

returns a list with the following components: excess returns with annualized excess returns over all periods, attribution effects (allocation, selection and interaction)

Author(s)

Andrii Babii

References

Ankrim, E. and Hensel, C. Multi-currency performance attribution. Russell Research Commentary. November 2002
Bacon, C. Practical Portfolio Performance Measurement and Attribution. Wiley. 2004. Chapter 5, 6, 8
Christopherson, Jon A., Carino, David R., Ferson, Wayne E. Portfolio Performance Measurement and Benchmarking. McGraw-Hill. 2009. Chapter 18-19
Brinson, G. and Fachler, N. (1985) Measuring non-US equity portfolio performance. Journal of Portfolio Management. Spring. p. 73 -76.
Gary P. Brinson, L. Randolph Hood, and Gilbert L. Beebower, Determinants of Portfolio Performance. Financial Analysts Journal. vol. 42, no. 4, July/August 1986, p. 39-44
Karnosky, D. and Singer, B. Global asset management and performance attribution. The Research Foundation of the Institute of Chartered Financial Analysts. February 1994.

See Also

Attribution.levels, Attribution.geometric

Examples

data(attrib)
Attribution(Rp = attrib.returns[, 1:10], wp = attrib.weights[1, ], Rb = attrib.returns[, 11:20],
wb = attrib.weights[2, ], method = "top.down", linking = "carino")

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