0:32

In this example, I have the benchmark composition and the fund composition.

Â I've chosen a very simple example, where there are only three sectors, and

Â we can think of this fund as being completely invested in stocks.

Â Okay, so there are three categories of stocks, three industrial sectors that

Â the fund is active in, which I've labeled technology, financials, and biotech.

Â The benchmark has 30% invested in technology, 30% in financials, and

Â 40% in biotech.

Â Whereas the actively managed fund has an overweight in technology,

Â 35 versus 30, underweight in financials, 25 instead of 30,

Â and identical allocation in biotech, okay?

Â So to be able to distinguish the performance contribution

Â of stock selection and asset allocation, we must use some information.

Â The portfolio weights is one aspect.

Â The other aspect, of course,

Â is the performance of the various sectors in the benchmark and in the fund.

Â And this is the information we have in this next slide.

Â So here you see that the technology stock in the benchmark had a performance of 8%,

Â financials, 5%, biotech, 7%.

Â Whereas in the actively managed fund, where, remember,

Â the choice of securities within the technology sector can be

Â very different from the technology sector in the benchmark.

Â Here, in my example, the fund has a 1% excess performance in technology,

Â 1% excess performance in financial, and an equivalent performance in biotech, okay?

Â So let's first compute the overall excess return generated by this

Â actively managed fund.

Â We see that the fund does better in technology and

Â financial and just as well in biotech.

Â So the excess return is going to be positive.

Â So let's compute it explicitly.

Â So what we call the total active return is the difference between the fund

Â performance and the benchmark performance.

Â Each of these performances are computed as weighted average of the performance of

Â each of the individual sectors.

Â So for the fund, the second bullet point here, we have 35% in the first sector,

Â we generate a 9% return, 30% at 6% performance, and

Â the remaining 40% invested in the third sector with the performance of 7%.

Â The total return is 7.45%, whereas the performance of the benchmark is 6.7%.

Â The difference between the two is a little bit less than 1%,

Â 75 basis points to be precise.

Â Now we're going to decompose the 75 basis points between asset allocation effect and

Â stock selection effect.

Â 3:19

The way we measure the asset allocation effect is by looking at the differences in

Â weights.

Â Did we over allocate in technology, under allocate in technology?

Â But to see whether this distinction between the allocation and

Â the fund and the benchmark is the source of performance,

Â we're going to multiply this weight difference by the benchmark performance,

Â to see if just over weighting one particular sector yields an excess return.

Â In particular, in my example, we see here that if we over weight the technology

Â sector, even if we select exactly the same stocks than the benchmark,

Â the fund is going to over perform because the technology sector

Â has a slightly higher return than the other sectors.

Â 4:13

We can measure something very similar when looking at the stock selection effect

Â by looking at the benchmark weight multiplied by the performance differences.

Â This time, what we're doing is looking at the asset allocation in the benchmark and

Â looking at the excess performance generated by the correct selection of

Â securities within each sector.

Â And to measure that, we just look at the differences in performance

Â between the fund and the benchmark, in each of the sector.

Â For example in the technology sector, we have an excess return of 1%,

Â in the financials, an excess return of 1%, and in the biotech, no excess return.

Â We weight all these excess returns by the benchmark weight

Â to obtain the overall stock selection effect.

Â In this case, we obtain 60 basis point, a little bit less than a percent,

Â almost half a percent, actually.

Â 5:05

Finally, the performance attribution must also take into account

Â the interaction terms.

Â So what are these interaction terms?

Â We're going to look at the weight difference and the performance difference.

Â Again, we could overweight a particular sector,

Â which performs better than the others.

Â This is the case for technology.

Â But we could poorly select the securities within that sector,

Â creating an overall underperformance in terms of interaction.

Â So we're going to look at the product of weight differences and

Â performance differences.

Â And here in my example, there is a positive interaction term in technology.

Â We overweight a sector in which we have a very large performance larger

Â than the benchmarks, so this creates a positive interaction.

Â But there is a negative interaction terms for financials.

Â Why?

Â Because we have an over-performance, we select the securities in financial in

Â a good way in the activity managed fund, but we underweight solely that sector.

Â So this creates an overall negative interaction effect.

Â 6:09

The sum of the technology and financial effect,

Â given that the biotech effect is 0, the sum of the two cancel out, and

Â we have 0 basis point coming from the interaction.

Â So to summarize, in this example, we have a contribution coming from the asset

Â allocation decision of 20%, stock selection of 80%.

Â Out of the total over performance, 80% of the performance comes from the ability

Â of the fund manager to select the correct stock within a sector.

Â 6:42

The performance attribution approach that we have just presented is called

Â the return decomposition.

Â It's not the only way that we can address that problem, there are other approaches.

Â I'm listing here two of these alternative approaches.

Â One is called the risk factor analysis,

Â where instead of looking at the overall performance in terms of return,

Â we decompose it into exposure to different risk factors.

Â This requires a preliminary statistical analysis.

Â Another approach is to look at a style analysis,

Â where we decompose the return contribution into the exposure to different

Â management styles, such as momentum, contrarian strategies, and so on.

Â These two approaches are complementary to the methodology we have discussed here,

Â but the return the composition approach is the first one that was developed

Â to analyze the performance attribution.

Â Thank you.

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Â