Return Attribution Analysis at Multiple Levels

Suppose you have a large fund like a university endowment. The fund sponsor decides to divide the fund into pieces (asset classes) and have each class managed by a specialist portfolio manager. In this case, you'll want to perform macro attribution analysis and micro attribution analysis to see how all of the decisions are playing out.

What part do you think is macro attribution?

You got it!

No, this isn't a part of performance to be measured. Macro attribution is about how the fund manager divides the capital into pieces.

Actually, this the micro attribution part. Macro attribution is about how the fund manager divides the capital into pieces.

These decisions are compared to some benchmark allocation. It might look something like this: | | Fund Weight | Fund Return | Benchmark Weight | Benchmark Return | |-----|:-----:|:-----:|:-----:|:-----:| | Small-cap Value | 40% | 4.50% | 30% | 4.70% | | Small-cap Growth | 20% | 3.80% | 30% | 3.90% | | Large-cap Total | 40% | -0.10% | 40% | -1.50% | | **Total** | **100%** | **2.52%** | **100%** | **1.98%** |

The macro analysis will start with the fund manager's decision to allocate to the three asset classes. You'll notice that small-cap value was overweighted. Was this a good choice?

You're right! And why?

Actually, it was. You may be focusing on the fact that the portfolio return there was less than the benchmark, but that's not the key to allocation effect. The benchmark return for small-cap value was greater than the overall portfolio return, and so there's a positive allocation contribution there. Here's the extended table with these allocation effects included:

Right again! The benchmark return for small-cap value was greater than the overall portfolio return, and so there's a positive allocation contribution there. Here's the extended table with these allocation effects included:

Not quite. Don't focus on that return difference, as that's not the key to allocation effect. The benchmark return for small-cap value was greater than the overall portfolio return, and so there's a positive allocation contribution there. Here's the extended table with these allocation effects included:

| | Fund Weight | Fund Return | Benchmark Weight | Benchmark Return | | Allocation Effect | |-----|:-----:|:-----:|:-----:|:-----:|:-----:|:-----:| | Small-cap Value | 40% | 4.50% | 30% | 4.70% | | 0.27% | | Small-cap Growth | 20% | 3.80% | 30% | 3.90% | | -0.19% | | Large-cap Total | 40% | -0.10% | 40% | -1.50% | | 0.00% | | **Total** | **100%** | **2.52%** | **100%** | **1.98%** | | **0.08%** | Each allocation effect is calculated as the weight difference multiplied by the benchmark asset class return beyond the total. For example, the small-cap value allocation effect is: >$$ (40 \% - 30 \%) \times (4.70 \% - 1.98 \%) = 0.27 \%$$.

Now turn to the return differences *within* each asset class to get at the selection effect. The small-cap value return is less than that of the benchmark. How is that the responsibility of the fund manager?

That's right! So these subtotals are still part of macro attribution. In the case of small-cap value, you can see underperformance there. Much as in the case of the Brinson-Hood-Beebower model, this difference is multiplied by the benchmark weight to arrive at the selection effect. >$$ 30 \% \times (4.50 \% - 4.70 \%) = -0.06 \% $$ What is the selection effect for small-cap growth?

Not quite; that's the allocation effect.

Actually, they generally don't. That responsibility was delegated to the portfolio managers.

Correct!

Not quite. It's the same calculation: just the portfolio weight multiplied by the return difference.

>$$ 30 \% \times (3.80 \% - 3.90 \%) = -0.03 \% $$ Then that column can be filled in. You'll also see the interaction effects here, calculated just as before: weighting difference multiplied by the return difference: | | Fund Weight | Fund Return | Benchmark Weight | Benchmark Return | | Allocation Effect | Selection Effect | Interaction Effect | |-----|:-----:|:-----:|:-----:|:-----:|:-----:|:-----:|:-----:|:-----:| | Small-cap Value | 40% | 4.50% | 30% | 4.70% | | 0.27% | -0.06% | -0.02% | | Small-cap Growth | 20% | 3.80% | 30% | 3.90% | | -0.19% | -0.03% | 0.01% | | Large-cap Total | 40% | -0.10% | 40% | -1.50% | | 0.00% | 0.56% | 0.00% | | **Total** | **100%** | **2.52%** | **100%** | **1.98%** | | **0.08%** | **0.47%** | **-0.01%** | The sum of these three effects in total is 0.54%, exactly the total return difference between the portfolio and the benchmark.

After macro analysis, micro analysis is performed using a similar process. There's a richness of flexibility: you can look at asset subclasses, sectors, country allocations, or however you want to break up the selected securities, doing the same for the benchmark. A micro analysis of that small-cap value portfolio might leave you with something like this: | Group | Portfolio Weight | Benchmark Weight | Portfolio Return | Benchmark Return | |-----|:-----:|:-----:|:-----:|:-----:| | A | 50% | 40% | 4.98% | 5.15% | | B | 20% | 30% | 3.36% | 2.84% | | C | 30% | 30% | 4.46% | 5.96% | | **Total** | **100%** | **100%** | **4.50%** | **4.70%** |

Now you can look more closely at where that 20-basis-point underperformance came from. With this grouping, which one seems to be the biggest problem?

Actually, this wasn't so bad. Sure, the portfolio return was below that of the benchmark, but there was a healthy return in Group A that was overweighted.

Actually, no; this group had the only positive contribution with a positive allocation effect and a positive selection effect. Returns were low, and the manager underweighted the group. Plus, selection led to returns above the benchmark. Excellent work by that manager!

That's it. Group A wasn't so bad. Sure, the portfolio return was below that of the benchmark, but there was a healthy return in Group A that was overweighted. Group B had the only positive contribution with a positive allocation effect and a positive selection effect. Returns were low, and the manager underweighted the group. Plus, selection led to returns above the benchmark. Excellent work by that manager! Group C had no allocation effect since the weighting was 30% for both the portfolio and the benchmark. But the selection effect was dismal. A full 150-basis-point underperformance, which when scaled by the weight, led to a -0.45% selection effect for that group. Here are the final values calculated as before: | Group | Portfolio Weight | Benchmark Weight | Portfolio Return | Benchmark Return | | Allocation Effect | Selection Effect | Interaction Effect | |-----|:-----:|:-----:|:-----:|:-----:|:-----:|:-----:|:-----:|:-----:| | A | 50% | 40% | 4.98% | 5.15% | | 0.05% | -0.07% | -0.02% | | B | 20% | 30% | 3.36% | 2.84% | | 0.19% | 0.16% | -0.05% | | C | 30% | 30% | 4.46% | 5.96% | | 0.00% | -0.45% | 0.00% | | **Total** | **100%** | **100%** | **4.50%** | **4.70%** | | **0.23%** | **-0.36%** | **-0.07%** |

To summarize: [[summary]]

How the fund manager divides the capital into pieces

How the portfolio managers perform relative to their benchmarks

How the markets behave over the time period measured

Yes

No

Because returns were above the fund average

Because the benchmark return outperformed the portfolio

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The fund manager chose to overweight that class

The fund manager chose the portfolio manager

The fund manager generally performs security selection

Other responses

-0.03

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Group A

Group B

Group C

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