equity performance attribution - seb group · as a practical illustration of the model, we focus on...

2012 Vol. 4

Equity Performance AttributionSEB Asset Management

Editorial

SEB Asset ManagementSEB-husetBernstorffsgade 501577 Copenhagen VPhone: +45 33 28 14 00

Authors:

Client Executive: Nicolaj Holm-Christiansen Phone: +45 33 28 14 74 E-mail: [email protected]

Portfolio Manager, TAA: Peter Lorin RasmussenPhone: +45 33 28 14 22E-mail: [email protected]

Portfolio Manager, Fixed Income: Michael Denbæk Phone: +45 33 28 14 53 E-mail: [email protected]

Portfolio Manager, European Equities: Ulrik Ellesgaard Phone: +45 33 28 14 17 E-mail: [email protected]

Portfolio Manager, Fixed Income & TAA: Tore Davidsen Phone: +45 33 28 14 25 E-mail: [email protected]

This document produced by SEB contains general marketing information about its investment products. Although the content is based on sources jud-ged to be reliable, SEB will not be liable for any omissions or inaccuracies, or for any loss whatsoever which arises from reliance on it. If investment research is referred to, you should if possible read the full report and the disclosures contained within it. Information relating to taxes may become outdated and may not fit your individual circumstances. Investment products produce a return linked to risk. Their value may fall as well as rise, and historic returns are no guarantee of future returns; in some ca-ses, losses can exceed the initial amount invested. Where either funds or you invest in securities denominated in a foreign currency, changes in exchange rates can impact the return. You alone are responsible for your investment decisions and you should al-ways obtain detailed information before taking them. For more information, please see the relevant simplified prospectus for the funds, and the relevant information brochure for funds and for structured products. If necessary you should seek advice tailored to your individual circumstances from your SEB advisor.Skandinaviska Enskilda Banken AB (publ) is incorporated in Sweden as a Li-mited Liability Company. It is regulated by Finansinspektionen, and by the local financial regulators in each of the jurisdictions in which it has branches or subsidiaries. Skandinaviska Enskilda Banken AB, Bernstorffsgade 50, 1577 København V

Disclaimer

Table of Contents

Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4Active Weights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4Returns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5Allocation Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7Selection Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9Interaction Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10Currency Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Total Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12A Combined View of All the Effects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Segregation over Countries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Additional Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15Appendix 1: Derivation of Attribution Model. . . . . . . . . . . . . . . . . . . . .16Appendix 2: Aggregation over Time . . . . . . . . . . . . . . . . . . . . . . . . . . . .18

Editorial

Introduction

Factors

In this note, we present, explain and interpret SEB Asset Management’s per-formance attribution model for global equity portfolios. We hereby seek to deliver a guide as to how to read and interpret the figures and tables in our model.

SEB Asset Management’s attribution model is more detailed and flexible than most standard models in the market, which provides it with both pros and cons. On the positive side, our model enables us to illustrate specific return features which we find important. Many of these features cannot be found in the standard models. On the negative side, it does require a so-mewhat deeper understanding of the underlying mechanics.

This leaves the note with a dual purpose. It serves both as a guide to the qualitative interpretation as well as a rigorous mathematical documenta-tion. In recognition of this, we have sought to keep the main text as concise and non-mathematical as possible, and have kept most of the derivations in the Appendices. We thereby seek to make the note accessible to anyone; also to those for whom equations are a happily forgotten thing of the past.

As a practical illustration of the model, we focus on the performance of our European small cap equity fund: SEBinvest Europa Small Cap (DK0016283211) from 1 January 2012 to 30 June 2012. The benchmark of the fund is the MSCI Europe Small Cap Net Dividend index (Bloomberg: NCUDE15 Index).

Irrespective of whether we consider equity, balanced or fixed income port-folios, the purpose of any attribution model is to illustrate and quantify the effect of allocation decisions on performance (excess return of the portfolio over the benchmark). However, different effects may be more relevant for different types of portfolios: An asset allocation portfolio manager might seek to generate performance by timing the market risk premium whereas an equity portfolio manager is usually – but not always – more focused on pure stock picking. In terms of performance attribution models, this implies that the two types of portfolio managers might want to focus on different attribution effects; the former on the allocation effect, the latter on the se-lection effect. The purpose being to highlight the primary source of their performance.

The nature of the active bets in a stock pick equity portfolio – such as the SEBinvest Europe Small Cap fund – implies that the performance attribu-tion should primarily highlight the effect of stock picking. Furthermore, when analyzing multi-currency equity portfolios, it is necessary that the performance attribution allows for isolation of the contribution from cur-rency so that other effects are not distorted by currency movements. As a consequence hereof, SEB Asset Management’s attribution model for equity portfolios sets itself apart from the traditional models in the market by pro-viding full transparency of currency effects in the performance.

Notation

Active Weights The active weights are defined as the portfolio weight minus the benchmark weight. They influence only the allocation, interaction and currency effects.

Table 2 presents the active weights of SEBinvest Europa Small Cap. The tab-le should be read as follows: Each row represents the average active weight of a specific sector in a given period. For example, we see that the portfolio on average was underweight Energy by -1.9%-points in February, while on average it was overweight Industrials by +15%-points over the full period (see the column furthest to the right).

In order to increase the readability of the note, we present an overview of the notation in Table 1. Note that everything is expressed in terms of sectors and DKK.

Tabel 1: Notation

Description Notation

Portfolio weight of sector i pfwi

Benchmark weight of sector i bmwi

Portfolio local currency return of sector i pfri, loc

Benchmark local currency return of sector i bmri, loc

Portfolio currency return of sector i curi, pf Benchmark currency return of sector i curi, bm Portfolio DKK (%) return of sector i pfri, DKK Benchmark DKK (%) return of sector i bmri, DKK Portfolio local currency return PFRloc Benchmark local currency return BMRloc

Currency return of benchmark curBM

Our model splits the performance into four separate effects: An allocation, a selection, an interaction and a currency effect. When combined, the four effects constitute the performance. Each effect will be described, explained and interpreted in the following sections.

As a general note, the results of our attribution model can be aggregated across sectors, countries, market capitalization, etc. In this note, we focus on the sector level.

ReturnsThe absolute returns – both in DKK and in local currency – influence all four attribution effects. Tables 3 to 6 show the absolute returns of the portfolio and the benchmark both in local currency and DKK. All the tables should be read as follows: Each row represents the return of a given sector in a given period. The bottom row represents the aggregated return of either the portfolio or the benchmark. An example: Table 3 shows that the portfolio generated an absolute return of +10.4% measured in DKK during the first half of 2012. Furthermore, we see that – as a very specific example – Energy generated a negative return of -7.3% in May measured in DKK.

Table 2: Active weights of the SEBinvest Europa Small Cap - 1 January to 30 June 2012

+0.0+0.0-0.0+0.0-0.0+0.0+0.0Total

+3.5+5.5+4.3+1.9+2.9+3.2+3.3Cash

+0.5+0.3+0.5+0.6+0.7+0.6+0.6Utilities

-1.5-1.4-1.6-1.5-1.4-1.4-1.4Telecommunication Services

-4.2-3.2-3.7-4.0-4.5-5.1-4.9Materials

-2.1-2.8-2.6-2.6-2.7-1.0-0.6Information Technology

+15.0+14.1+14.2+16.4+18.3+14.6+12.5Industrials

+2.7+4.3+3.1+1.9+1.1+2.7+3.1Health Care

-11.2-12.7-11.9-10.5-10.9-10.2-10.7Financials

-0.7+0.3+0.3-0.3-1.5-1.9-1.0Energy

+4.4+3.4+3.8+4.3+4.5+4.9+5.3Consumer Staples

-6.5-7.6-6.5-6.2-6.3-6.4-6.1Consumer Discretionary

TotalJunMayAprMarFebJanSector

+0.0+0.0-0.0+0.0-0.0+0.0+0.0Total

+3.5+5.5+4.3+1.9+2.9+3.2+3.3Cash

+0.5+0.3+0.5+0.6+0.7+0.6+0.6Utilities

-1.5-1.4-1.6-1.5-1.4-1.4-1.4Telecommunication Services

-4.2-3.2-3.7-4.0-4.5-5.1-4.9Materials

-2.1-2.8-2.6-2.6-2.7-1.0-0.6Information Technology

+15.0+14.1+14.2+16.4+18.3+14.6+12.5Industrials

+2.7+4.3+3.1+1.9+1.1+2.7+3.1Health Care

-11.2-12.7-11.9-10.5-10.9-10.2-10.7Financials

-0.7+0.3+0.3-0.3-1.5-1.9-1.0Energy

+4.4+3.4+3.8+4.3+4.5+4.9+5.3Consumer Staples

-6.5-7.6-6.5-6.2-6.3-6.4-6.1Consumer Discretionary


In the interpretation of the allocation, the interaction and the currency ef-fects, the table of active weights is useful.

Table 3: Absolute portfolio returns measured in DKK

+10.4+2.3-7.4+1.7+0.3+6.5+7.4Portfolio

-0.2-0.2-0.2+0.1-0.0+0.2-0.0Cash

+3.4+7.5-5.5-6.3+3.6+2.6+2.2Utilities

+0.0+0.0+0.0+0.0+0.0+0.0+0.0Telecommunication Services

+33.8+2.5-2.3+7.5+3.3+12.2+7.2Materials

+7.6+1.7-11.0+1.7+2.6+10.4+3.1Information Technology

+4.6+1.4-10.1+0.5-3.2+6.1+11.1Industrials

+28.0+5.8-1.1+5.0+8.6+2.7+4.4Health Care

+13.2+4.9-6.0+0.0+2.3+6.8+4.9Financials

+23.0-1.0-7.3+10.9+2.5+10.6+6.6Energy

+11.0+3.9-1.6-2.3+1.4+4.6+4.9Consumer Staples

+11.2+0.6-11.7+2.8+2.1+7.9+10.5Consumer Discretionary


+10.4+2.3-7.4+1.7+0.3+6.5+7.4Portfolio

-0.2-0.2-0.2+0.1-0.0+0.2-0.0Cash

+3.4+7.5-5.5-6.3+3.6+2.6+2.2Utilities


+33.8+2.5-2.3+7.5+3.3+12.2+7.2Materials


+4.6+1.4-10.1+0.5-3.2+6.1+11.1Industrials

+28.0+5.8-1.1+5.0+8.6+2.7+4.4Health Care

+13.2+4.9-6.0+0.0+2.3+6.8+4.9Financials

+23.0-1.0-7.3+10.9+2.5+10.6+6.6Energy




Table 4: Absolute benchmark returns measured in DKK

+10.1+2.2-7.2+0.2+0.1+6.0+9.1Benchmark

+0.0+0.0+0.0+0.0+0.0+0.0+0.0Cash

+1.2+3.8-3.0+0.1+0.8+0.9-1.2Utilities

+29.9+10.0-0.7+3.9+7.4+0.7+5.8Telecommunication Services

+4.6+1.2-10.4-0.3-1.9+5.0+12.4Materials


+6.6+0.6-8.9+0.2-0.6+6.6+9.6Industrials

+14.4+0.8-1.5+4.1+2.4+1.9+6.0Health Care

+7.6+5.4-6.7-1.0-0.2+3.5+6.9Financials

+5.8-1.3-11.2+2.4-6.2+12.8+11.3Energy


+15.4+3.1-7.3-1.0+2.4+6.6+11.7Consumer Discretionary


+10.1+2.2-7.2+0.2+0.1+6.0+9.1Benchmark

+0.0+0.0+0.0+0.0+0.0+0.0+0.0Cash

+1.2+3.8-3.0+0.1+0.8+0.9-1.2Utilities


+4.6+1.2-10.4-0.3-1.9+5.0+12.4Materials


+6.6+0.6-8.9+0.2-0.6+6.6+9.6Industrials

+14.4+0.8-1.5+4.1+2.4+1.9+6.0Health Care

+7.6+5.4-6.7-1.0-0.2+3.5+6.9Financials

+5.8-1.3-11.2+2.4-6.2+12.8+11.3Energy




Table 5: Absolute local currency for the portfolio

+9.3+2.2-7.6+1.2+0.1+6.5+7.2Portfolio

+0.0+0.0+0.0+0.0+0.0+0.0+0.0Cash

+3.4+7.5-5.4-6.3+3.6+2.6+2.1Utilities


+31.6+2.8-2.9+6.3+3.0+12.7+6.7Materials


+3.5+1.3-10.3+0.0-3.4+6.2+10.9Industrials

+28.0+5.7-1.0+5.0+8.5+2.7+4.4Health Care

+11.9+5.1-6.3-0.6+2.1+7.1+4.5Financials

+19.5-0.9-8.0+9.7+3.2+9.6+5.7Energy




+9.3+2.2-7.6+1.2+0.1+6.5+7.2Portfolio

+0.0+0.0+0.0+0.0+0.0+0.0+0.0Cash

+3.4+7.5-5.4-6.3+3.6+2.6+2.1Utilities


+31.6+2.8-2.9+6.3+3.0+12.7+6.7Materials


+3.5+1.3-10.3+0.0-3.4+6.2+10.9Industrials

+28.0+5.7-1.0+5.0+8.5+2.7+4.4Health Care

+11.9+5.1-6.3-0.6+2.1+7.1+4.5Financials

+19.5-0.9-8.0+9.7+3.2+9.6+5.7Energy




Table 6: Absolute local currency for the benchmark

+8.4+2.3-7.6-0.6-0.0+6.1+8.7Benchmark

+0.0+0.0+0.0+0.0+0.0+0.0+0.0Cash

-0.6+4.2-3.7-1.1+0.5+1.4-1.6Utilities


+3.0+1.3-10.8-1.2-2.1+5.3+12.0Materials


+5.1+0.6-9.2-0.5-0.8+6.8+9.2Industrials

+13.6+0.6-1.4+3.9+2.3+1.8+5.7Health Care

+6.0+5.4-7.0-1.8-0.3+3.7+6.5Financials

+3.1-1.0-11.9+1.1-6.0+12.4+10.6Energy




+8.4+2.3-7.6-0.6-0.0+6.1+8.7Benchmark

+0.0+0.0+0.0+0.0+0.0+0.0+0.0Cash

-0.6+4.2-3.7-1.1+0.5+1.4-1.6Utilities


+3.0+1.3-10.8-1.2-2.1+5.3+12.0Materials


+5.1+0.6-9.2-0.5-0.8+6.8+9.2Industrials

+13.6+0.6-1.4+3.9+2.3+1.8+5.7Health Care

+6.0+5.4-7.0-1.8-0.3+3.7+6.5Financials

+3.1-1.0-11.9+1.1-6.0+12.4+10.6Energy




The allocation effect quantifies the portion of the performance which can be attributed to the active sector allocation. That is, it quantifies what the performance would have been if the return of each sector in the portfolio was exactly identical to the return of each sector in the benchmark. If a port-folio manager generates his performance by sector rotation – for example timing the cycle between cyclical and defensive sectors – then this would be quantified by the allocation effect.

Allocation Effect

We calculate the allocation effect of sector i as:

alloci = ( pfwi - bmwi )( bmri, loc - BMRloc )

In words, the allocation effect is calculated as the active weight multiplied by the relative return between the individual sector of the benchmark and the total benchmark. This implies that the allocation effect can become positive only if the portfolio has been over-/underweight in those sectors which have delivered a positive/negative return relative to the total bench-mark – all in local currency.

To illustrate, Table 7 presents the allocation effects over time for SEBinvest Europa Small Cap. The table should be read as follows: The bottom row re-presents the total allocation effect for each month; the last column covers the entire period. Each row represents the contribution to the total alloca-tion effect from individual sectors. All numbers are measured in percentage points. For example, we see that the sector allocation contributed negatively to the performance by -0.56%-points in January. This was primarily caused by a large overweight to cash in a period where the total benchmark return was positive. As this example hints, it is usually very informative to keep the active weights and returns in mind when interpreting the allocation effect.

Table 7: Allocation effect of SEBinvest Europa Small Cap – 1 January to 30 June 2012

-1.02-0.77+0.35+0.25-0.13-0.15-0.56Total

-0.29-0.07+0.26-0.01-0.03-0.17-0.30Cash

-0.06+0.01+0.02-0.00+0.00-0.03-0.06Utilities

-0.27-0.11-0.10-0.05-0.10+0.07+0.05Telecommunication Services

+0.20+0.03+0.12+0.02+0.10+0.04-0.15Materials

-0.14+0.06-0.04-0.02-0.07-0.04-0.00Information Technology

-0.54-0.23-0.23+0.01-0.15+0.10+0.03Industrials

+0.02-0.09+0.18+0.08+0.03-0.15-0.07Health Care

+0.17-0.40-0.06+0.13+0.04+0.24+0.24Financials

+0.02+0.03-0.01-0.01+0.12-0.12-0.00Energy

+0.18+0.08+0.18-0.00+0.06-0.03-0.15Consumer Staples

-0.31-0.07+0.02+0.09-0.14-0.05-0.15Consumer Discretionary

TotalJunMayAprMarFebJanDate

-1.02-0.77+0.35+0.25-0.13-0.15-0.56Total

-0.29-0.07+0.26-0.01-0.03-0.17-0.30Cash

-0.06+0.01+0.02-0.00+0.00-0.03-0.06Utilities

-0.27-0.11-0.10-0.05-0.10+0.07+0.05Telecommunication Services

+0.20+0.03+0.12+0.02+0.10+0.04-0.15Materials

-0.14+0.06-0.04-0.02-0.07-0.04-0.00Information Technology

-0.54-0.23-0.23+0.01-0.15+0.10+0.03Industrials

+0.02-0.09+0.18+0.08+0.03-0.15-0.07Health Care

+0.17-0.40-0.06+0.13+0.04+0.24+0.24Financials

+0.02+0.03-0.01-0.01+0.12-0.12-0.00Energy

+0.18+0.08+0.18-0.00+0.06-0.03-0.15Consumer Staples

-0.31-0.07+0.02+0.09-0.14-0.05-0.15Consumer Discretionary

TotalJunMayAprMarFebJanDate

Note that it is not possible to simply add allocation effects over time (i.e., horizontally in the table) due to compounding. It is, however, always pos-sible to aggregate the allocation effects across sectors (i.e., vertically in the table). In Appendix 2 it is described how the numbers, by transformation, can become additive over time as well.

The selection effect quantifies the portion of the performance which can be attributed to stock picking. That is, what the return of the portfolio would have been if the weights of each individual sector in the portfolio were iden-tical to the weights of each individual sector in the benchmark.

The selection effect of sector i is calculated as:

seleci = ( pfri, loc - bmri, loc )bmwi

In words, the selection effect is calculated as the relative local currency re-turn of a given sector multiplied by the weight of the sector in the bench-mark. This implies that the selection effect is positive only when there has been over-/underweights in stocks which have out-/underperformed their sector peers.

To illustrate, Table 8 presents the selection effects over time for SEBinvest Europa Small Cap. The table should be read as Table 7. For example, the total selection effect is +3.48%-points, implying that had there been no sec-tor bets in the portfolio, the performance of the portfolio would have been +3.48%-points – measured in local currency.

Table 8: Selection effect of SEBinvest Europa Small Cap – 1 January to 30 June 2012

+3.48+0.12-0.22+2.30+1.27+1.38-1.70Total

+0.00+0.00+0.00+0.00+0.00+0.00+0.00Cash

+0.10+0.07-0.03-0.10+0.06+0.02+0.08Utilities

-0.38-0.14+0.02-0.04-0.10-0.02-0.08Telecommunication Services

+2.50+0.14+0.72+0.69+0.48+0.68-0.48Materials

-0.85+0.16-0.52+0.09-0.01+0.15-0.63Information Technology

-0.41+0.16-0.27+0.15-0.65-0.14+0.43Industrials

+0.83+0.33+0.03+0.07+0.36+0.06-0.09Health Care

+1.19-0.07+0.15+0.23+0.48+0.68-0.40Financials

+1.24+0.01+0.29+0.61+0.67-0.17-0.33Energy

-0.17-0.02+0.04-0.09-0.01-0.03-0.05Consumer Staples

-0.58-0.51-0.67+0.70-0.02+0.15-0.14Consumer Discretionary


+3.48+0.12-0.22+2.30+1.27+1.38-1.70Total

+0.00+0.00+0.00+0.00+0.00+0.00+0.00Cash

+0.10+0.07-0.03-0.10+0.06+0.02+0.08Utilities

-0.38-0.14+0.02-0.04-0.10-0.02-0.08Telecommunication Services

+2.50+0.14+0.72+0.69+0.48+0.68-0.48Materials


-0.41+0.16-0.27+0.15-0.65-0.14+0.43Industrials

+0.83+0.33+0.03+0.07+0.36+0.06-0.09Health Care

+1.19-0.07+0.15+0.23+0.48+0.68-0.40Financials

+1.24+0.01+0.29+0.61+0.67-0.17-0.33Energy


-0.58-0.51-0.67+0.70-0.02+0.15-0.14Consumer Discretionary


For the SEBinvest Europa Small Cap fund we would like to stress that the selection effect dominates the allocation effect in numerical terms. This il-lustrates the purpose and investment strategy of SEBinvest Europa Small Cap. It is a portfolio where the performance is not intended to be generated by large sector bets, but rather by stock picking.

Selection Effect

Interaction Effect The interaction effect is usually the hardest effect to comprehend, as it is in some respect a residual of the allocation and the selection effect. One way to interpret the interaction effect is to consider it the portion of the performance which can be attributed to additional selection effects in the portfolio’s over- and underweights. However, the interaction effect is best explained by an example: Consider a portfolio with an overweight of Indu-strials and a positive selection effect on that sector. Then the interaction is positive because the portfolio obtains a “selection” effect in the overweight.

The interaction effect of sector i is calculated as:

interi = ( pfri, loc - bmri, loc )( pfwi - bmwi )

In words, the interaction effect is calculated as the active weight multiplied by the relative sector return.

To illustrate, Table 9 presents the interaction effects over time for SEBinvest Europa Small Cap. The table should be read as Table 7 and 8. For example, the interaction effect contributes -1.63%-points to the performance. This is not caused by a negative stock picking effect but rather by a suboptimal sector allocation. This leads to another interpretation of the interaction ef-fect: It measures the degree to which the selection effect is multiplied/ero-ded by the sector allocation of the portfolio (the interaction effect is even more difficult to explain than the offside rule in football!).

Table 9: Interaction effect of SEBinvest Europa Small Cap – 1 January to 30 June 2012

-1.63+0.59-0.19-0.74-0.99-0.84+0.71Total

+0.00+0.00+0.00+0.00+0.00+0.00+0.00Cash

+0.01+0.01-0.01-0.03+0.02+0.01+0.02Utilities


-1.13-0.05-0.29-0.30-0.24-0.37+0.24Materials

+0.10-0.05+0.14-0.03-0.00-0.01+0.03Information Technology

-0.41+0.12-0.18+0.09-0.49-0.10+0.20Industrials

+0.23+0.21-0.01+0.01+0.07+0.04-0.11Health Care

-0.69+0.04-0.10-0.13-0.30-0.36+0.22Financials

-0.16-0.02-0.01-0.04-0.14+0.04+0.04Energy


+0.23+0.22+0.26-0.27-0.00-0.06+0.05Consumer Discretionary


-1.63+0.59-0.19-0.74-0.99-0.84+0.71Total

+0.00+0.00+0.00+0.00+0.00+0.00+0.00Cash

+0.01+0.01-0.01-0.03+0.02+0.01+0.02Utilities


-1.13-0.05-0.29-0.30-0.24-0.37+0.24Materials

+0.10-0.05+0.14-0.03-0.00-0.01+0.03Information Technology

-0.41+0.12-0.18+0.09-0.49-0.10+0.20Industrials

+0.23+0.21-0.01+0.01+0.07+0.04-0.11Health Care

-0.69+0.04-0.10-0.13-0.30-0.36+0.22Financials

-0.16-0.02-0.01-0.04-0.14+0.04+0.04Energy


+0.23+0.22+0.26-0.27-0.00-0.06+0.05Consumer Discretionary


The final effect in our attribution model is the currency effect. This mea-sures the effect of currency movements on the performance. For example, this could be the effect of the long GBP, EUR or CHF portfolio versus the benchmark.

The currency effect of sector i is calculated as:

curi = pfwi( pfi, cur + pfri, loc pfi, cur )

- bmwi( curi, bm - bmri, loccuri, bm )

- ( pfwi - bmwi )( curBM + BMRloccurBM )

This expression is complicated as it contains several interaction effects. However, it can be approximated by noting that some of the cross products are numerically small. That is, all the parts where the sector returns are mul-tiplied by the currency returns; for example pfri, loccuri, pf .

If we disregard the numerically small cross products the currency effect sim-plifies to:

curi = ( pfwi - bmwi )( curi, bm - curBM ) + pfw( curi, pf - curi, bm )

The first part of the equation is the allocation effect – expressed in curren-cy returns. As for the allocation effect, the currency effect is positive if the portfolio has been overweight currencies which have appreciated relatively to the total benchmark currency return. The second part is the sum of the selection and the interaction effect – expressed in currency returns. This is the portion of the currency effect which can be attributed to the intra sector currency allocation.

To illustrate, Table 10 presents the currency effects over time for SEBinvest Europa Small Cap. The table should be read as Table 7 to 9. For example, the currency effect contributes -0.50%-points to the performance. This is primarily due to a significant underweight to GBP, which will become clear in the section Segregation over countries and Table 13.

Currency Effect

Table 10: Currency effect of SEBinvest Europa Small Cap – 1 January to 30 June 2012

-0.50+0.11-0.17-0.30-0.03+0.10-0.16Total

-0.05-0.01-0.01-0.01-0.00+0.00-0.02Cash

-0.05+0.01-0.02-0.03-0.01+0.01-0.01Utilities

+0.00+0.00-0.00-0.00-0.00+0.00+0.00Telecommunication Services

+0.01-0.01+0.01+0.01-0.00+0.00+0.01Materials

-0.01+0.00-0.00-0.01+0.00+0.00+0.00Information Technology

-0.17+0.06-0.06-0.12-0.01+0.04-0.05Industrials

-0.08+0.01-0.02-0.03-0.00+0.00-0.04Health Care

-0.02-0.02-0.00-0.00+0.00-0.00-0.00Financials

+0.02+0.02-0.00-0.01-0.01+0.02+0.01Energy

-0.08-0.01-0.01-0.02+0.01-0.02-0.03Consumer Staples

-0.06+0.06-0.04-0.06-0.02+0.04-0.03Consumer Discretionary


-0.50+0.11-0.17-0.30-0.03+0.10-0.16Total

-0.05-0.01-0.01-0.01-0.00+0.00-0.02Cash

-0.05+0.01-0.02-0.03-0.01+0.01-0.01Utilities

+0.00+0.00-0.00-0.00-0.00+0.00+0.00Telecommunication Services

+0.01-0.01+0.01+0.01-0.00+0.00+0.01Materials

-0.01+0.00-0.00-0.01+0.00+0.00+0.00Information Technology

-0.17+0.06-0.06-0.12-0.01+0.04-0.05Industrials

-0.08+0.01-0.02-0.03-0.00+0.00-0.04Health Care

-0.02-0.02-0.00-0.00+0.00-0.00-0.00Financials

+0.02+0.02-0.00-0.01-0.01+0.02+0.01Energy

-0.08-0.01-0.01-0.02+0.01-0.02-0.03Consumer Staples

-0.06+0.06-0.04-0.06-0.02+0.04-0.03Consumer Discretionary


Aggregating the allocation, selection, interaction and currency effects gene-rate a total effect. This is the combined effect in DKK by each sector to the performance. Table 11 presents the total effect. The table should be read as Tables 7 to 10. For example, the performance is +0.33%-points over the period.

Table 11: Total effect of SEBinvest Europa Small Cap – 1 January to 30 June 2012

+0.33+0.04-0.23+1.51+0.11+0.50-1.70Calc diff

+10.11+2.22-7.18+0.23+0.14+5.97+9.12BM return (calc)

+10.44+2.26-7.41+1.73+0.25+6.47+7.42PF return (calc)

+0.33+0.04-0.23+1.51+0.11+0.50-1.71Total

-0.34-0.08+0.25-0.02-0.04-0.17-0.31Cash

+0.00+0.09-0.04-0.16+0.07+0.01+0.03Utilities

-0.27-0.11-0.10-0.06-0.10+0.07+0.05TelecommunicationServices

+1.58+0.11+0.56+0.42+0.34+0.35-0.39Materials


-1.53+0.10-0.74+0.13-1.29-0.10+0.61Industrials

+1.00+0.45+0.18+0.14+0.46-0.05-0.30Health Care

+0.65-0.44-0.01+0.23+0.23+0.56+0.05Financials

+1.12+0.04+0.27+0.54+0.64-0.24-0.29Energy

-0.27+0.01+0.25-0.21+0.05-0.12-0.29Consumer Staples

-0.72-0.30-0.43+0.46-0.17+0.08-0.27ConsumerDiscretionary


+0.33+0.04-0.23+1.51+0.11+0.50-1.70Calc diff

+10.11+2.22-7.18+0.23+0.14+5.97+9.12BM return (calc)

+10.44+2.26-7.41+1.73+0.25+6.47+7.42PF return (calc)

+0.33+0.04-0.23+1.51+0.11+0.50-1.71Total

-0.34-0.08+0.25-0.02-0.04-0.17-0.31Cash

+0.00+0.09-0.04-0.16+0.07+0.01+0.03Utilities

-0.27-0.11-0.10-0.06-0.10+0.07+0.05TelecommunicationServices

+1.58+0.11+0.56+0.42+0.34+0.35-0.39Materials


-1.53+0.10-0.74+0.13-1.29-0.10+0.61Industrials

+1.00+0.45+0.18+0.14+0.46-0.05-0.30Health Care

+0.65-0.44-0.01+0.23+0.23+0.56+0.05Financials

+1.12+0.04+0.27+0.54+0.64-0.24-0.29Energy

-0.27+0.01+0.25-0.21+0.05-0.12-0.29Consumer Staples

-0.72-0.30-0.43+0.46-0.17+0.08-0.27ConsumerDiscretionary


Total Effect

Tables 7 to 11 presented the allocation, selection, interaction, currency and total effects over time. Alternatively, the effects can be presented in a table where the time dimension is removed. This is illustrated in Table 12. The numbers are the same as those in the rightmost column of Tables 7 to 11.

Table 12: Combined effects of SEBinvest Europa Small Cap – 1 January to 30 June 2012

+0.33-0.50-1.63+3.48-1.02Total

-0.34-0.05+0.00+0.00-0.29Cash

+0.00-0.05+0.01+0.10-0.06Utilities

-0.27+0.00+0.38-0.38-0.27TelecommunicationServices

+1.58+0.01-1.13+2.50+0.20Materials

-0.91-0.01+0.10-0.85-0.14Information Technology

-1.53-0.17-0.41-0.41-0.54Industrials

+1.00-0.08+0.23+0.83+0.02Health Care

+0.65-0.02-0.69+1.19+0.17Financials

+1.12+0.02-0.16+1.24+0.02Energy

-0.27-0.08-0.19-0.17+0.18Consumer Staples

-0.72-0.06+0.23-0.58-0.31ConsumerDiscretionary

TotalCurrencyInteractionSelectionAllocationSector

+0.33-0.50-1.63+3.48-1.02Total

-0.34-0.05+0.00+0.00-0.29Cash

+0.00-0.05+0.01+0.10-0.06Utilities

-0.27+0.00+0.38-0.38-0.27TelecommunicationServices

+1.58+0.01-1.13+2.50+0.20Materials

-0.91-0.01+0.10-0.85-0.14Information Technology

-1.53-0.17-0.41-0.41-0.54Industrials

+1.00-0.08+0.23+0.83+0.02Health Care

+0.65-0.02-0.69+1.19+0.17Financials

+1.12+0.02-0.16+1.24+0.02Energy

-0.27-0.08-0.19-0.17+0.18Consumer Staples

-0.72-0.06+0.23-0.58-0.31ConsumerDiscretionary

TotalCurrencyInteractionSelectionAllocationSector

A Combined View of All the Effects

Segregation over Countries

The previous analysis has been based on sectors. To illustrate that the mo-del can be based on other classifications, Table 13 shows the analysis based on countries.

Table 13: Combined effects over countries of SEBinvest Europa Small Cap – 1 January to 30 June 2012

+0.33-0.50+2.18+0.32-1.66Total

+0.19-0.05+0.06+0.10+0.08Østrig

-0.24+0.07-0.35-0.06+0.11USA

+0.19-0.15+0.04+0.10+0.20Tyskland

-0.10+0.01+0.01-0.16+0.03Sverige

-2.09-0.24+1.06-2.21-0.70Storbritannien

+0.02-0.06+0.56+0.44-0.91Spanien

+0.04+0.05-0.09+0.09-0.02Schweiz

+0.09+0.01-0.03+0.03+0.08Portugal

+0.87-0.02-0.08+1.02-0.05Norge

+0.01+0.00-0.00+0.00+0.01Liechtenstein

-0.06-0.01+0.07-0.07-0.05Jersey

+0.18-0.01+0.04+0.24-0.09Italien

+0.49+0.04+0.13+0.30+0.02Irland

-0.67-0.08-0.40-0.26+0.07Holland

-0.02-0.00+0.02-0.02-0.01Guernsey

-0.04+0.01+0.14-0.14-0.05Grækenland

+1.00-0.04+0.31+0.82-0.09Frankrig

+0.63-0.04+0.44+0.48-0.24Finland

+0.01-0.00-0.01+0.01+0.01Europa

-0.20+0.03+0.29-0.45-0.07Danmark

+0.17+0.01-0.08+0.10+0.15Cypern

-0.34-0.05+0.00+0.00-0.29Cash

+0.03-0.00-0.02+0.02+0.03Canada

+0.06-0.00-0.05+0.05+0.06Bermuda

+0.09+0.03+0.10-0.10+0.07Belgien

-0.00+0.00+0.01-0.01-0.00Bahamas

TotalCurrencyInteractionSelectionAllocationCountry

+0.33-0.50+2.18+0.32-1.66Total

+0.19-0.05+0.06+0.10+0.08Østrig

-0.24+0.07-0.35-0.06+0.11USA

+0.19-0.15+0.04+0.10+0.20Tyskland

-0.10+0.01+0.01-0.16+0.03Sverige

-2.09-0.24+1.06-2.21-0.70Storbritannien

+0.02-0.06+0.56+0.44-0.91Spanien

+0.04+0.05-0.09+0.09-0.02Schweiz

+0.09+0.01-0.03+0.03+0.08Portugal

+0.87-0.02-0.08+1.02-0.05Norge

+0.01+0.00-0.00+0.00+0.01Liechtenstein

-0.06-0.01+0.07-0.07-0.05Jersey

+0.18-0.01+0.04+0.24-0.09Italien

+0.49+0.04+0.13+0.30+0.02Irland

-0.67-0.08-0.40-0.26+0.07Holland

-0.02-0.00+0.02-0.02-0.01Guernsey

-0.04+0.01+0.14-0.14-0.05Grækenland

+1.00-0.04+0.31+0.82-0.09Frankrig

+0.63-0.04+0.44+0.48-0.24Finland

+0.01-0.00-0.01+0.01+0.01Europa

-0.20+0.03+0.29-0.45-0.07Danmark

+0.17+0.01-0.08+0.10+0.15Cypern

-0.34-0.05+0.00+0.00-0.29Cash

+0.03-0.00-0.02+0.02+0.03Canada

+0.06-0.00-0.05+0.05+0.06Bermuda

+0.09+0.03+0.10-0.10+0.07Belgien

-0.00+0.00+0.01-0.01-0.00Bahamas

TotalCurrencyInteractionSelectionAllocationCountry

This note presents only a small part of the output which we are able to pro-duce. We emphasize that the analysis could go deeper into the numbers, splitting for example the currency effect into parts originating from the al-location, the selection and the interaction effects. Furthermore, we can pro-duce numbers based on a range of different classifications such as market capitalization, industry groups or currencies. In addition, the base currency can be changed to ones liking.

In essence, the model is very flexible in terms of output. This means that we can produce just about any output you wish to see.

Additional Features

This note has presented SEB Asset Management’s performance attribution model for global equity portfolios. It has described how all the numbers are calculated and how they should be interpreted.

Focus of the main text is on the interpretation. In the appendix, all the deri-vations are described.

Summary

In the following, we prove that the sum of the four effects: allocation, selec-tion, interaction and currency is equal to the total performance.

Formally we show that:

Where we note that:

To prove the above, start by looking at the model expressed in local cur-rency. That is, show that the total effect in local currency is the sum of the allocation, selection and interaction effect:

To do so, we focus on the left-hand side of the equation:

Here we note that both the portfolio and benchmark weights sum to one:

And that BMRloc is a scalar, which implies that:

We have thereby shown that:

In words: The local currency excess return is equal to the sum of the alloca-tion, the selection and the interaction effect.

Now we need to show that the excess return in DKK is equal to the sum of the allocation, the interaction, the selection and the currency effect. To do so, start by looking at the direct excess return in DKK:

Equity Performance Attribution.doc

13(15)

Appendix 1: Derivation of attribution model

In the following, we prove that the sum of the four effects: allocation, selection, interaction and currency is equal to the total performance. Formally we show that:

i

ii

ii

ii

ii

i totalcurrerintselecalloc

Where we note that:

i

DKKiii

DKKiiDKKDKKi

i bmrbmwpfrpfwBMRPFRtotal ,,

To prove the above, start by looking at the model expressed in local currency. That is, show that the total effect in local currency is the sum of the allocation, selection and interaction effect:

i

loc,ii

ii

ii

i totalerintselecalloc


i i iloci

ilociloc,iiloc,ii

iiiloc,iloc,i

i iiloc,iloc,ilocloc,iii

ii

ii

ii

BMRbmwBMRpfwbmrbmwpfrpfw

)bmwpfw)(bmrpfr(

bmw)bmrpfr()BMRbmr)(bmwpfw(

erintselecalloc


1

1

ii

ii

pfw

bmw

And that is a scalar, which implies that: locBMR

i

locii

loci BMRbmwBMRpfw


i iloclocloc,iiloc,ii

ii

ii

ii

BMRPFRbmrbmwpfrpfw

erintselecalloc

In words: The local currency excess return is equal to the sum of the allocation, the selection and the interaction effect.


13(15)



i

ii

ii

ii

ii

i totalcurrerselecalloc int

Where we note that:

i

DKKiii

DKKiiDKKDKKi



i

locii

ii

ii

i totalerselecalloc ,int


i i iloci

ilocilociilocii

i iiilociloci

iilocilociloclociii

ii

ii

ii


bmwpfwbmrpfrbmwbmrpfrBMRbmrbmwpfw

erselecalloc

,,

,,,,, ))(()())((

int


1

1

ii

ii

pfw

bmw


i

locii

loci BMRbmwBMRpfw


i i

locloclociilociii

ii

ii

i BMRPFRbmrbmwpfrpfwerselecalloc ,,int

In words: The local currency excess return is equal to the sum of the allocation, the selection and the interaction effect. Now we need to show that the excess return in DKK is equal to the sum of the allocation, the interaction, the selection and the currency effect. To do so, start by looking at the direct excess return in DKK:


13(15)



i

ii

ii

ii

ii


Where we note that:

i

DKKiii

DKKiiDKKDKKi



i

loc,ii

ii

ii



i i iloci

ilociloc,iiloc,ii

iiiloc,iloc,i


ii

ii

ii


)bmwpfw)(bmrpfr(


erintselecalloc


1

1

ii

ii

pfw

bmw


i

locii

loci BMRbmwBMRpfw



ii

ii

ii

BMRPFRbmrbmwpfrpfw

erintselecalloc



13(15)



i

ii

ii

ii

ii


Where we note that:

i

DKKiii

DKKiiDKKDKKi



i

loc,ii

ii

ii



i i iloci

ilociloc,iiloc,ii

iiiloc,iloc,i


ii

ii

ii


)bmwpfw)(bmrpfr(


erintselecalloc


1

1

ii

ii

pfw

bmw


i

locii

loci BMRbmwBMRpfw



ii

ii

ii

BMRPFRbmrbmwpfrpfw

erintselecalloc



13(15)



i

ii

ii

ii

ii


Where we note that:

i

DKKiii

DKKiiDKKDKKi



i

locii

ii

ii



i i iloci

ilocilociilocii

i iiilociloci

iilocilociloclociii

ii

ii

ii



erselecalloc

,,

,,,,, ))(()())((

int


1

1

ii

ii

pfw

bmw


i

locii

loci BMRbmwBMRpfw


i i

locloclociilociii

ii

ii




13(15)



i

ii

ii

ii

ii


Where we note that:

i

DKKiii

DKKiiDKKDKKi



i

locii

ii

ii



i i iloci

ilocilociilocii

i iiilociloci

iilocilociloclociii

ii

ii

ii



erselecalloc

,,

,,,,, ))(()())((

int


1

1

ii

ii

pfw

bmw


i

locii

loci BMRbmwBMRpfw


i i

locloclociilociii

ii

ii




13(15)



i

ii

ii

ii

ii


Where we note that:

i

DKKiii

DKKiiDKKDKKi



i

loc,ii

ii

ii



i i iloci

ilociloc,iiloc,ii

iiiloc,iloc,i


ii

ii

ii


)bmwpfw)(bmrpfr(


erintselecalloc


1

1

ii

ii

pfw

bmw


i

locii

loci BMRbmwBMRpfw



ii

ii

ii

BMRPFRbmrbmwpfrpfw

erintselecalloc



14(15)

BMlocPFlocBMPFlocloc

locBMlocPF

DKKDKK

curBMRcurPFRcurcurBMRPFRBMRcurPFRcur

BMRPFR

1)1)(1(1)1)(1(

Now we show that:

i i

ilocii

DKKi curtotaltotal ,,

First note that we want to show that:

BMlocPFlocBMPFi

i curBMRcurPFRcurcurcur

Remember that:

))(()(

)(

,,,

,,,

BMlocBMii

bmilocibmii

pfilocipfiii

curBMRcurbmwpfwcurbmrcurbmw

curpfrcurpfwcur

Now sum the currency effects:

iBMlocBMii

ibmilocibmii

ipfilocipfii

ii

curBMRcurbmwpfw

curbmrcurbmw

curpfrcurpfwcur

))((

)(

)(

,,,

,,,

Note that is a scalar. )( BMlocBM curBMRcur

Then note that because both the portfolio and benchmark weights sum to 1. 0)( i

ii bmwpfw

Then rewrite it all:

BMlocPFlocBMPFi

i

ibmilocibmii

ipfilocipfii

ii

curBMRcurPFRcurcurcur

curbmrcurbmwcurpfrcurpfwcur

)()( ,,,,,,

Hereby, we have shown that the excess return in DKK is equal to the sum of the allocation, the selection, the interaction and the currency effects.

Appendix 1: Derivation of the Attribution Model

Now we show that:


Remember that:


Note that (curBM + BMRloccurBM) is a scalar.

Then note that because both the portfolio and

benchmark weights sum to 1.




14(15)


locBMlocPF

DKKDKK


BMRPFR

1)1)(1(1)1)(1(

Now we show that:

i i

ilocii



BMlocPFlocBMPFi


Remember that:

))(()(

)(

,,,

,,,

BMlocBMii

bmilocibmii

pfilocipfiii


curpfrcurpfwcur


iBMlocBMii

ibmilocibmii

ipfilocipfii

ii

curBMRcurbmwpfw

curbmrcurbmw

curpfrcurpfwcur

))((

)(

)(

,,,

,,,



ii bmwpfw


BMlocPFlocBMPFi

i

ibmilocibmii

ipfilocipfii

ii



)()( ,,,,,,



14(15)


locBMlocPF

DKKDKK


BMRPFR

1)1)(1(1)1)(1(

Now we show that:

i i

ilocii



BMlocPFlocBMPFi


Remember that:

))(()(

)(

,,,

,,,

BMlocBMii

bmilocibmii

pfilocipfiii


curpfrcurpfwcur


iBMlocBMii

ibmilocibmii

ipfilocipfii

ii

curBMRcurbmwpfw

curbmrcurbmw

curpfrcurpfwcur

))((

)(

)(

,,,

,,,



ii bmwpfw


BMlocPFlocBMPFi

i

ibmilocibmii

ipfilocipfii

ii



)()( ,,,,,,



14(15)


locBMlocPF

DKKDKK


BMRPFR

1)1)(1(1)1)(1(

Now we show that:

i i

ilocii



BMlocPFlocBMPFi


Remember that:

))(()(

)(

,,,

,,,

BMlocBMii

bmilocibmii

pfilocipfiii


curpfrcurpfwcur


iBMlocBMii

ibmilocibmii

ipfilocipfii

ii

curBMRcurbmwpfw

curbmrcurbmw

curpfrcurpfwcur

))((

)(

)(

,,,

,,,



ii bmwpfw


BMlocPFlocBMPFi

i

ibmilocibmii

ipfilocipfii

ii



)()( ,,,,,,



14(15)


locBMlocPF

DKKDKK


BMRPFR

1)1)(1(1)1)(1(

Now we show that:

i i

ilocii



BMlocPFlocBMPFi


Remember that:

))(()(

)(

,,,

,,,

BMlocBMii

bmilocibmii

pfilocipfiii


curpfrcurpfwcur


iBMlocBMii

ibmilocibmii

ipfilocipfii

ii

curBMRcurbmwpfw

curbmrcurbmw

curpfrcurpfwcur

))((

)(

)(

,,,

,,,



ii bmwpfw


BMlocPFlocBMPFi

i

ibmilocibmii

ipfilocipfii

ii



)()( ,,,,,,



14(15)


locBMlocPF

DKKDKK


BMRPFR

1)1)(1(1)1)(1(

Now we show that:

i i

ilocii



BMlocPFlocBMPFi


Remember that:

))(()(

)(

,,,

,,,

BMlocBMii

bmilocibmii

pfilocipfiii


curpfrcurpfwcur


iBMlocBMii

ibmilocibmii

ipfilocipfii

ii

curBMRcurbmwpfw

curbmrcurbmw

curpfrcurpfwcur

))((

)(

)(

,,,

,,,



ii bmwpfw


BMlocPFlocBMPFi

i

ibmilocibmii

ipfilocipfii

ii



)()( ,,,,,,



14(15)

Now we need to show that the excess return in DKK is equal to the sum of the allocation, the interaction, the selection and the currency effect. To do so, start by looking at the direct excess return in DKK:


locBMlocPF

DKKDKK


BMRPFR

1)1)(1(1)1)(1(

Now we show that:

i i

ilocii



BMlocPFlocBMPFi


Remember that:

))(()(

)(

,,,

,,,

BMlocBMii

bmilocibmii

pfilocipfiii


curpfrcurpfwcur


iBMlocBMii

ibmilocibmii

ipfilocipfii

ii

curBMRcurbmwpfw

curbmrcurbmw

curpfrcurpfwcur

))((

)(

)(

,,,

,,,



ii bmwpfw


BMlocPFlocBMPFi

i

ibmilocibmii

ipfilocipfii

ii


curbmrcurbmw

curpfrcurpfwcur

)(

)(

,,,

,,,


As stated, the effects cannot readily be aggregated over time. This is becau-se they are all expressed in percentage points.

There exists several alternative ways to aggregate percentage points over time. We do it by scaling excess log returns, thereby preserving signs and relative differences.

First, we find the daily excess return:

We then find the log excess return:

After that we find the relative difference between these. We define this as:

We multiply this factor on all the effects and then aggregate them over time.

Finally, we transform the effects back into the linear return world by dividing by k calculated over the full period:

So for example the final allocation effect is calculated as:



As stated, the effects cannot readily be aggregated over time. This is because they are all expressed in percentage points. There exists several alternative ways to aggregate percentage points over time. We do it by scaling excess log returns, thereby preserving signs and relative differences. First, we find the daily excess return:

DKKtDKKtDKKt BMRPFRexcess ,,, .


)1log()1log(log ,,, DKKtDKKtDKKt BMRPFRexcess .


t

tt excess

excessklog

.

We multiply this factor on all the effects and then aggregate them over time. Finally, we transform the effects back into the linear return world by dividing by k calculated over the full period:

tDKKt

tDKKt

t tDKKtDKKt

BMRPFR

BMRPFRk

))1(ln())1(ln(

)1()1(

,,

,,


k

kallocalloc t

tit

i

,

15(15)








t

tt excess

excessklog

.


tDKKt

tDKKt

t tDKKtDKKt

BMRPFR

BMRPFRk

))1(ln())1(ln(

)1()1(

,,

,,


k

kallocalloc t

tit

i

,

15(15)








t

tt excess

excessklog

.


tDKKt

tDKKt

t tDKKtDKKt

BMRPFR

BMRPFRk

))1(ln())1(ln(

)1()1(

,,

,,


k

kallocalloc t

tit

i

,

15(15)








t

tt excess

excessklog

.


tDKK,t

tDKK,t

t tDKK,tDKK,t

))BMR1(log())PFR1(log(

)BMR1()PFR1(k


k

kallocalloc t

tit

i

,

15(15)








t

tt excess

excessklog

.


tDKKt

tDKKt

t tDKKtDKKt

BMRPFR

BMRPFRk

))1(ln())1(ln(

)1()1(

,,

,,


k

kallocalloc t

tit

i

,

15(15)

Appendix 2: Aggregation over Time

equity performance attribution - seb group · as a practical illustration of the model, we focus on...

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