Multi-asset attribution: weighting schemes, top-down and bottom-up, currencies and overlays

Advanced12 min read · updated 12 October 2026 · 15 sources

Multi-asset attribution explains the active return of a portfolio that combines equities, bonds, currencies and derivatives. The basic Brinson formulas are covered in the article performance attribution; this article is about practice: which weights do you use when futures shift the exposure? How do you separate the decision on an asset class from the selection within a region? And how do currencies and bonds fit into the same picture?

What it is about

A common question from practitioners is: there are several weighting schemes in attribution, but which ones actually exist? Behind this lies a real problem. The weighting scheme has to reconcile two views: the top-down decision on asset classes and regions and the bottom-up selection of individual securities, and it has to do so across different regions and types of investment. In a pure equity fund, the weight is simply the share of market value. In a mixed portfolio with futures, currency hedging and bonds of different durations, it no longer is.

At institutional firms, this is calculated by risk and attribution systems such as MSCI's BarraOne. MSCI calls its model the “Multi-Asset Class (MAC) Performance Attribution Model” and bases it on its factor model for multiple asset classes MSCI (2020). We could not find an attribution model called “MACS” in MSCI's public documentation; the abbreviation is used by some asset managers for multi-asset class strategies, i.e. for investment strategies, not for a calculation method. The ideas behind it can be explained independently of the vendor, along three questions: what counts as a weight? In what order are decisions measured? And which sources of return get a line of their own?

Weighting schemes at a glance

Whichever scheme you choose, the sum of the effects must match the actual return difference. Whatever is left over, often called the residual or timing effect, is a control figure. In the buy-and-hold calculation, according to the review by Bacon (2019), this residual can be substantial without necessarily being related to turnover; transaction-based calculations capture trading effects and costs at the security level. Monthly periods with weights at the start of the month are a widespread compromise.

Example: futures overlay with market value and exposure weights

A portfolio of $100 million holds 50% equities and 50% bonds. In addition, the manager buys equity index futures with a notional value of $10 million. This overlay raises the equity exposure to 60% without selling bonds. The benchmark consists of 60% equities and 40% bonds. Over the year, the equity index returns 8%, the portfolio's equities 9%, the bond index 2%, the portfolio's bonds 2.5% and the money market 2%. For simplicity, the future returns the index return minus the money market rate; we leave out the margin.

With market value weights, the future has almost no value; its gain ends up where the collateral sits, here in the bonds. Their return seemingly rises to (1.25 + 0.6) / 50 = 3.7%. With exposure weights, the future counts toward equities at its notional value, and a financing line of −10% at the money market rate balances the weights to 100%. Equities then have a weight of 60% and a return of (0.5 × 9 + 0.1 × 8) / 0.6 = 8.83%. The benchmark holds no financing; for this line, the portfolio return is therefore also used as the benchmark return.

For options, you use the delta-weighted exposure; for swaps, the notional value of the cash flow stream they replicate economically. Bacon (2019) describes how the Brinson decomposition can be extended to futures, options, swaps and short sales using notional holdings and returns.

Top-down and bottom-up

Where the interaction belongs depends on the decision process. In a top-down process, the committee first decides on asset classes, then on regions, and finally the managers pick the securities. Allocation is measured with benchmark returns, selection with the actual weights. The interaction then belongs to selection. In a bottom-up process, security selection comes first and the segment weights follow from it; selection is then measured with benchmark weights and the interaction is added to allocation. Bacon (2019) summarizes the literature as follows: bottom-up presupposes that security selection takes precedence; if selection follows a top-down allocation, it can be derived without interaction.

Two-level attribution: asset class first, then region

In a multi-level attribution, each decision is measured at its own level. An example with two asset classes and two regions in the equity portion:

If you calculate the same figures flat with three segments (Europe, USA, bonds) according to Brinson-Fachler, you get allocation of 0.32, selection of 0.20 and interaction of 0.09. The total is correct, but the allocation mixes two decisions: the equity overweight and the shift between regions. Calculated bottom-up, level 1 would give allocation of 0.53 and selection of 0.08. Only a hierarchy that follows the order of the actual process separates the decisions cleanly. Bacon (2019) describes multi-level models as a sequence of intermediate portfolios, each of which isolates exactly one decision.

Currencies: Karnosky and Singer

In an international portfolio, every foreign return has two parts: the return in the local market and the exchange rate movement. Karnosky and Singer (1994) split the local return into the local money market rate and a premium above it, and assign the interest rate differential to the currency. They then apply the Brinson logic twice: to the markets on the basis of the local premiums and to the currencies on the basis of currency returns including the interest rate differential. Ankrim and Hensel (1994) further split the currency effect into the forward premium from the interest rate differential and the unexpected exchange rate movement. More on the Karnosky-Singer model in the glossary.

This separation matters for the decision on the hedge ratio: the market premium rewards the choice of equity market, the currency line the choice of currency. The basics of the costs and benefits of hedging are covered in the article currency risk.

Bonds: income, yield curve, spread, selection

For bonds, sector weights are a poor fit, because returns depend mainly on interest rate changes and duration. Campisi (2000) breaks down the return of a bond portfolio into income, the Treasury effect from changes in government bond yields, the spread effect from changes in risk premiums and selection as the security-specific residual, each calculated against the benchmark (see Campisi model). Here, allocation decisions are better weighted by duration than by capital: if you hold more duration for the same capital, you carry more interest rate risk.

Modern systems break things down more finely. Bacon (2019) lists carry, yield curve effects (parallel shift, twist, curvature), spread, selection, trading and currency as typical building blocks; fixed income attribution usually remains arithmetic. The fixed income attribution in BarraOne reports, among other things, income, paydowns, roll-down, term structure, inflation, spread and currency MSCI (2020). The basics of bond mathematics are covered in duration, yield curve and bond mathematics.

Factor-based attribution with risk models

A risk model describes each position by its exposures to factors: countries, industries and styles for equities, the yield curve, spreads and inflation for bonds, plus currencies and commodities. Factor attribution calculates the active return as the sum of active exposure times factor return plus a specific residual Grinold and Kahn (2000). The advantage for mixed portfolios: all asset classes speak the same language, and the return attribution matches the risk decomposition.

The MAC model in BarraOne attributes returns to factors from equities, bonds and commodities, consistent with the risk reports. In addition, MSCI offers a Brinson-Fachler attribution for top-down allocation, an asset selection attribution for bottom-up selection, a currency attribution, a dedicated fixed income attribution and an attribution across several portfolio levels for nested structures of asset classes, strategies and managers MSCI (2020). Roth and Sharp (2015) describe how MSCI adapts standard tools for multi-asset portfolios to show the effect of capital allocation between and within asset classes. How exactly the weights are formed is not disclosed in these public documents.

Brinson and factors answer different questions: Brinson, which decision had an effect; factor attribution, which risk was rewarded. A multi-asset report therefore often shows both: the committee's decisions according to Brinson and, below them, the factors through which they worked.

Linking and geometric attribution

Monthly effects do not add up to the excess return for the year; how the Carino and Menchero methods solve this is shown in the article performance attribution. Bacon (2019) distinguishes smoothing methods, which distribute the difference across the periods after the fact (logarithmically according to Cariño (1999) or optimized according to Menchero (2000)), from linking methods such as that of the French working group GRAP and that of Frongello (2002); the last two deliver the same results but depend on the order of the periods. Menchero (2004) provides a guide to the properties a method should satisfy.

The alternative is geometric attribution: the excess return (1 + R) / (1 + B) − 1 links across periods without a residual and can be converted between currencies. According to Bacon (2019), that is exactly what speaks in its favor; Menchero (2005) shows how to adjust pure geometric effects as little as possible so that they add up without a residual.

Advanced

• Options in the overlay: the exposure is delta times the underlying and changes with the price. For a monthly attribution, the delta at the start of the month is often sufficient; the remainder from gamma and time value is shown as a separate line.
• Negative weights: the formulas cope with short sales and financing lines, but readers do not always. The allocation of the financing line (+0.36 in the example) is not a gain, but the offsetting entry to the bond overweight.
• Duration weights: instead of capital shares, you use each segment's contribution to duration, i.e. weight times duration divided by total duration. Allocation then measures the maturity decision, and selection measures the choice of securities for a given interest rate risk.
• Order of levels: whether you decompose first by asset class and then by region or the other way round changes the effects. The order should follow the decision process; otherwise, the attribution measures decisions that nobody made.
• Interaction: whether to show it separately or to allocate it is disputed in the literature, as Bacon (2019) shows. What matters is to state the convention in the report and to stick to it.

What research shows

The foundation remains the decomposition of Brinson et al. (1986) and Brinson and Fachler (1985). Karnosky and Singer (1994) showed that a multi-currency portfolio is managed suboptimally if currency decisions are not made independently of market decisions, and provided the framework for measuring the two separately. For bonds, Campisi (2000) names five differences from equities: fixed maturity, a fixed payment promise, lower liquidity, interest rate changes as the most important return driver, and very uniform pricing that leaves little room for selection.

A literature of its own has developed on linking; Menchero (2004) sets out requirements and compares the methods. Bacon (2019) gives an overview of the development from the first models through currencies, bonds and derivatives to geometric attribution, and Bacon (2008) is a handbook with formulas.

Limitations

• Data: exposure weights and transaction-based calculations require complete holdings, transaction and derivatives data. For funds, these are often missing.
• Conventions: how a swap, an option or the margin is booked is a choice. Two systems can show different effects for the same portfolio.
• Hierarchy: the levels must match the process. A hierarchy chosen after the fact explains the past but does not measure any decision.
• Factor models: a factor attribution is only as good as the model; factors it does not know end up in the specific residual.
• Luck or skill: even a clean decomposition does not prove skill. A year of positive selection is an observation, not a statistic.

How Portfolio Lab calculates

The Risk page calculates the Brinson-Fachler decomposition monthly against a benchmark: another portfolio from your grid or a single security. The weights used are the actual market value weights of a backtest without costs and without leverage at the start of each month, after drift and the chosen rebalancing; within the month, this is a buy-and-hold calculation. These portfolios have no futures overlays, so market value and exposure are the same here. Segments can be the positions, the asset classes (default) or asset class and main category combined; each position counts as a whole toward one segment, and the app does not calculate a step-by-step two-level decomposition as above. If the benchmark does not hold a segment, the deviation counts as allocation.

There is no separate currency attribution: all returns are calculated in the base currency, and exchange rate effects are contained in allocation and selection. The monthly effects are linked using Carino (default) or Menchero, for the whole period, per calendar year and cumulatively; at least 12 common months are required. In addition, the factor attribution breaks down the portfolio's excess return in US dollars into factor contributions, alpha and residual, statically over the period and on a rolling basis with loadings from 24 to 120 months before each month (default 36), with Newey-West t-statistics. More in the risk and attribution methodology.

This article explains a method; it is not investment or tax advice. Worked examples are simplified and rounded. All terms in the glossary.