13

Balanced attribution

13.1 INTRODUCTION

Consider a multi-currency portfolio with holdings in equity and fixed income investments from several different countries. The portfolio is managed as follows:

• First, an international asset allocation committee meets and decides the relative amounts to invest in different countries.
• For each country, a cash/equity/fixed income allocation decision is made.
• For the fixed income portions of the portfolio, the fund’s assets are invested in appropriate assets within each country and managed using fixed income strategies (carry, curve, credit).

Hopefully, value is being added at all three levels. However, assessing the value generated by each decision is very difficult without a full, multi-level attribution report.

The analysis for this type of portfolio is called balanced (or mixed) attribution, as it is used on a balanced portfolio, which is a portfolio containing two or more asset classes.

There are two contexts in which balanced attribution is required:

• A portfolio containing a mixture of fixed income and non–fixed income assets.
• A portfolio containing only fixed income assets, if they have been managed at least in part using asset allocation decisions.

13.2 CALCULATING BALANCED ATTRIBUTION

Balanced attribution requires a mixture of top-down Brinson attribution and bottom-up fixed income attribution tools. From Chapter 3, equations (3.1) and (3.17), the active return of a sector S against benchmark is given by the sum of the asset allocation return

and the stock selection return by

Asset allocation returns are calculated using sector-level weights and returns as usual. However, balanced attribution requires that stock selection returns be decomposed by fixed income risk.

Suppose that the portfolio and benchmark returns and of a sector are each given by the sum of carry and curve returns:

The stock selection return (13.2) can now be written

In general, the stock selection term becomes a sum of terms over each fixed income risk i:

Example

Consider the following portfolio (Table 13.1) and benchmark (Table 13.2). Fixed income returns have been decomposed into carry and curve returns with no residual.

Table 13.1 Portfolio weight and returns for balanced attribution

Table 13.2 Benchmark weight and returns for balanced attribution

Table 13.3 Portfolio performance contributions for balanced attribution

Table 13.4 Benchmark performance contributions for balanced attribution

From Tables 13.3 and 13.4, the active return of this portfolio over its benchmark is 3.4% − 0.5% = 2.9%.

This active return can be calculated using either Brinson attribution or mixed attribution. In the former case, the asset allocation and stock selection returns are given by (Table 13.5):

Table 13.5 Brinson attribution

In the latter case, the stock selection contribution returns are decomposed into return contributions generated by each source of fixed income return, shown in Table 13.6:

Table 13.6 Balanced attribution

In both cases the sum of the attribution contributions equals the overall active return, as expected.