Performance attribution: Numerical illustration

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來自 Rice University 的課程

Investment Strategies and Portfolio Analysis

108 個評分

Rice University

Investment Strategies and Portfolio Analysis

108 個評分

課程 4（共 5 門，Specialization Investment and Portfolio Management）

In this course, you will learn about latest investment strategies and performance evaluation. You will start by learning portfolio performance measures and discuss best practices in portfolio performance evaluation. You will explore different evaluation techniques such as style analysis and attribution analysis and apply them to evaluate different investment strategies. Special emphasis will be given to recent financial market innovations and current investment trends. After this course, learners will be able to: • Describe performance measurement measures • Evaluate portfolio performance • Describe and contrast different investment strategies • Propose investment strategy solutions

從本節課中

Performance evaluation: Style analysis and performance attribution

In this module, you are going to learn to use two analytical tools that are widely used in practice to evaluate what the portfolio performance can be attributed to. You will first learn about style analysis. Then, you will learn about attribution analysis, which has become a crucial component in internal evaluation system of investment managers and institutional clients in the industry. Focus will be placed on the practical applications.

Performance attribution7:25

Performance attribution: Numerical illustration7:21

與講師見面

Arzu Ozoguz
Finance Faculty
Jones Graduate School of Business

Okay, so let me now show you how this works with an example, right?

And it's going to become clear, all right?

So suppose we have an equity fund, Portfolio P, all right,

that invest in large cap, mid cap, and small cap stocks, all right?

And its benchmark, right, consists of 40%

invested in Large Cap, 35% invested in Mid Cap and

25% invested in Small Cap, right?

Now, on the other hand, our portfolio, right,

our Portfolio P has different ways across these segments, right?

It overweighs the large cap, right?

50% in large cap.

And it underweighs the small cap and the small cap segments, right?

Now the total return on our portfolio P is 16.9%.

Versus the total return on the benchmark is 14.2%, right?

Basically, portfolio P outperforms the benchmark by a difference of 2.7%, right?

Now the question I want to answer is, where is this difference coming from?

Is is coming from the allocation decision, right?

The fact that Portfolio P has different weights across

the three segments or is it due to security selection, okay?

All right, so let's see how this works.

Okay, so first I'm going to focus on the asset allocation piece.

Remember the asset allocation piece, it compares the active

weight the difference in the weights across the segments,

times the return that comes from that segment based on the benchmark, all right?

Okay, so let me start by looking at contribution from

the asset allocation, all right?

Remember from our expression, what is the asset allocation?

The contribution from the asset allocation?

Well, we're going to compare the actual portfolio weight with the benchmark

weight, all right?

Times how the benchmark segment performed.

Right, so let's see how our portfolio p differs from the benchmark.

Right, so what is the active weight?

Well, it is the active weighting decision by the manager, right.

We have overweighted the large cap relative to the benchmark so

the active weight is 10%.

Times how the benchmark did in that segment, all right.

So that gives us an attribution of 1.5%.

What about the Mid Cap?

Well, the Mid Cap has an active weight of -5%, right?

It's lower than the benchmark.

Times how that segment performed in the benchmark, right?

That gives us a -0.6%.

All right, finally, what is the asset allocation to the small cap?

Again, we have an active weight of -5%.

Right, multiply that so it's an attribution of -0.8%, all right?

Now, if you add all of those up, right,

you're going to find that this is 0.1%.

All right, so of this return difference in the portfolio and

the benchmark, 0.1% is attributable to the asset allocation or

the active weight decisions of the portfolio manager, right?

Now let's look at the security selection contribution, right?

The contribution from the selection.

Now again, let me refer back to this equation, right?

What are we trying to do now?

Well, how much weight did we put in the portfolio to that segment?

Times how much did our selection, how much better that our or

worst that our selection do, right?

What is the return difference between the securities that

we picked versus the benchmark, right?

So let's do that, all right?

So now, I'm comparing what?

Well, what is the excess performance

between the securities in the chosen portfolio versus the benchmark?

Well, the excess performance is 3%.

How much did we allocate, how much weight did we allocate?

Well, we allocated 50%.

So this times 3%, that gives me 1.5%, right?

What about the Mid Cap?

Well, the Mid Cap securities that we picked outperformed by 9% but

we allocated 30% of the portfolio to this segment.

So the attribution from this segment is 2.7%, all right?

The securities in this Small Cap segment

underperformed by 8% times the weight

allocated to the Small Cap, right?

That gives us 1.6%.

Now if I add those up, I will get 2.6%, right?

So what does that mean?

Well, that means of the 2.7% return difference between

the portfolio return and the benchmark,

2.6% of that can be attributed to security selection, all right?

So now we will put everything together, all right?

Basically, what we were trying to do is understand where this 2.7%

difference comes from, right?

And what we see is 0.1% of this difference is

attributable to asset allocation, right?

It's the contribution from asset allocation decisions, right?

Ultimately the different weightings of the different asset classes, right?

And 2.6% of this difference can be attributed to security selection right?

That is the particular securities chosen within each asset

class has contributed 2.6% to the difference, right?

You can see how meaningful and how informative this analysis can be.

All right, so performance attribution, right,

helps us decompose a portfolio's return to the exact sources its gains, right?

Style or its asset allocation versus security selection, right?

And therefore it provides an additional tool to evaluate

the effectiveness of a portfolio manager's stock selection skill.

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