Why Is The Sky Blue: Attribution and Relative Performance By: Gabriel PotterMBA, AIFA® 2016.02.16
Comedian Robin Williams’ recounts a conversation with his 3 year old son, Zachary:



Daddy, why is the sky blue?


Well because of the atmosphere.


Why is there atmosphere?


Well because we need to breathe.


Why do we need to breathe?


Why do you need to know?! … Ask Mommy. She’s omnipotent.  She knows everything.

-          Robin Williams, Live at the Met


Getting to the heart of questions

“Why is the sky blue?”  This is a classic, almost cliché question for parents, not because it’s difficult to answer, but rather because it  inevitably leads to increasingly deeper questions which ultimately defy simple explanations.  It might be tempting to say “just because” and leave it at that.  Instead, encouraging parents answer these potentially exhausting questions because young minds need to learn about their world.   We recognize the importance of fostering the naturally inquisitive tendencies we all have, and answering these questions ultimately gives us the motivation and ability to answer future questions for ourselves.  Going deeper into the root causes is important. 

Portfolio level performance and the market environment

The first quarter of 2016 isn’t over yet – it’s still early February at the time of writing – but the results have been poor for investors thus far.  We expect significant investigation during our next quarterly reviews as to the reasons why.  As part of our weblogs, weekly flash reports, monthly articles, and quarterly market reviews with clients, we at Westminster Consulting are trying to provide up-to-date context and information about the market environment.  Hopefully, this information prepares our readers and sets the groundwork for our client meetings where we may then dig deeper into their unique performance results and investment lineups.

Portfolio level attribution

Equity and fixed income market performance is a primary determinant of absolute returns, i.e. did you make or lose money.  That’s important, but nobody controls the market.  We only control how we interpret and react to it.  Instead, our duties as consultants is to try and select investment managers which can outperform on a relative basis, i.e. did this portfolio make more money (or defend more value from losses) than an appropriate benchmark.  We may then determine which of the underlying investments within the total portfolio contributed or detracted from relative performance.

To further this goal, we go through an attribution process at the portfolio level.  Put simply, we compare the investment returns to their appropriate index and weight the impact of each investment’s relative outperformance according to the weight of that investment within the portfolio. 

It’s a weighted average calculation.  It’s not complicated, but it’s easier to describe with an example. Let’s consider John Doe Computer’s (JDC) portfolio which uses two XYZ funds.  For this hypothetical example, let’s pretend the S&P 500 returned 10% over the past year.  Next, the XYZ Large Cap Core fund (XYZ-LCC) in JDC portfolio is up 15%.  So, the XYZ-LCC fund created 5% of relative outperformance vs. its benchmark.  This is an excellent result, but how much of that outperformance affects portfolio level outperformance?  If there was only one investment in the portfolio, the XYZ-LCC, then the calculation is easy:  the portfolio is outperforming its index by the full 5% (1.0 * 0.05 = 0.05).  However, in our example, there are actually two investments in the portfolio:  The XYZ-LCC and the XYZ Fixed Income (XYZ-FI) fund. The XYZ-LCC fund is only 30% of the total JDC portfolio.  Therefore, the benefit of the XYZ-LCC outperformance is 1.5% of contributed outperformance (0.3 * 0.05 = 0.015).  If the remaining 70% of the portfolio in the XYZ-FI fund happens to perform exactly as well as its index, then we can expect JDC’s total portfolio outperformance to its portfolio benchmark by 1.5%. 

Let’s make the JDC example slightly more complicated.  Let’s imagine the XYZ-FI performed at 5% in the past year while its benchmark, the Barclays Aggregate, returned 8%.  So, the XYZ-FI fund’s relative performance is -3%, but at 70% of the portfolio, it created -2.1% of impact to the portfolio relative return (0.7 * -0.03 = -0.021).  

Sum up the relative impacts (-2.1% + 1.5%) and you can expect the portfolio to underperform its benchmark by -0.6%.  Measured in absolute terms, JDC’s portfolio returned 8% ((0.7 * 0.05) + (0.3 * 0.15)) while its benchmark earned 8.6% ((0.7 * 0.08) + (0.3 * 0.10)), which perfectly corresponds to the predicted relative underperformance of -0.6%.

Three limitations of portfolio level attribution

By comparing the combined impacts of each underlying investment relative to its index, you can reasonably assert which investment managers most contributed or detracted to relative performance for a portfolio.  It is also logical to presume that the combined relative impact of each manager should equal the total difference between the portfolio return and the portfolio level benchmark.  Again, in the example above, the -0.6% of portfolio level underperformance can be calculated by figuring out total portfolio performance vs. its benchmark or by summing up the relative impacts of each underlying investment.

This assertion is true to a degree.  Weighted average analysis is acceptable for comparative, short term analysis, but there are limitations.  Occasionally, we will notice (or our clients will notice) that the sum of relative impacts does not equal the difference between year-to-date portfolio performance and benchmark performance and we need to figure out why.

There are three reasons for this.

The first limitation:  snapshot analysis

First, weighted average analysis is based on a snapshot in time and presumes the weights of the investments at the end of the period were held constant during the entire return period.  In reality, the underlying weights of investments are constantly in flux.  Those weights actually change during the return period, and it will have an impact on performance comparisons.  In our investment level net performance calculation – the vertical bar charts we provide in every quarterly review – the accurately update the weights of the underlying portfolio on a more granular basis, usually monthly. 

The second limitation:  compounding

Weighted average calculations are based on a single time period of calculation; therefore there is no possibility of compounding results over multiple time periods.  There is an eccentricity in the math in which net-positives will not offset net negatives due to compounding.  For example, imagine you have $100 invested in XYZ Small Cap Fund.  In the first quarter, small caps rally and return 50% to investors – now you have $150 in the fund.  In the second quarter, the rally ends and small caps plummet a full 50% - now you have $75. 

If you think of performance returns as a weighted average calculation, you’d be tempted to compute returns a single time period as if performance were equally affecting multiple pools of money.  So, you might (wrongly) think that a +50% return and a -50% loss should offset to 0%, and that you should leave the investment with $100, right where you started.  Reality is more complicated.  We’re dealing with a single pool of money in two different time periods.  So, in reality, you start with $100, go to $150 and then end with $75 – a 25% loss due to compounding. 

Since weighted average calculations do not account for compounding, the differences between reality and weighted average calculations get worse as the degree of returns get’s bigger.  We’ve shown that a 50% and -50% return series creates a -25% level error.  By comparison, a 20% and -20% return creates a modest -4% error.  (You start with $100, go up to $120, and then fall to $96.)  Thankfully, most market environments aren’t as drastic as 50% rallies and losses, but over time, these small differences become subject to further compounding errors.  For these reasons, attribution analyses are most useful in short time periods and in low volatility market environments. 

The third limitation:  sum-of-parts benchmarking

Another limitation involves the comparability of the blended benchmark and the portfolio.  In our JDC example, there are two investments - a large cap core fund and a bond fund.  There are also two corresponding benchmarks – the S&P 500 and the Barclays Aggregate.  In this case, we can make a fairly precise sum-of-parts benchmark which perfectly corresponds to those investments. 

However, some benchmarks aren’t perfect sum-of-parts representations of the underlying investments.  For instance, some foundations use a broad market benchmark (e.g. 50% S&P 500 / 30% Barclays Aggregate / 20% MSCI EAFE), but there may be a dozen underlying investments which only partially correspond to these benchmarks.

There can be a variety of reasons to use a broad market benchmark rather than a sum-of-parts benchmark which perfectly corresponds to each underlying investment.  A broad market benchmark is static and unchanging.  It represents a consistent strategic target.  It’s easier to understand, replicate, and double-check.  A sum-of-parts index must be updated as often as the underlying weights in the portfolio change.

Sum-of-parts benchmarks may be impractical because some of the underlying investments use specious or marginally relevant index benchmarks.  Similarly, some alternative investments use problematic benchmarks, such as a cash-plus benchmark.  To explain, imagine a hedge fund with a target rate of return of T-Bills + 3%.  In other words, this hedge fund is trying to generate as much as cash, plus a few percentage points of return (e.g. T-Bills + 3%).  As a return target, this is useful as it gives investors a sense of how aggressive the hedge fund is likely to get in pursuit of its goal.  As a component in a sum-of-parts benchmark, it’s a terrible idea. 

As a rule, we don’t like T-Bill + % benchmarks because it presumes pure alpha out of nothing, and makes combined risk-adjusted returns impossible to figure out accurately.  T-Bills + % benchmarks would be acceptable if we only focused on target returns.  However, we often use benchmarks to determine other sorts of risk and risk-adjusted return metrics such as Sharpe Ratio, Alpha, or Standard Deviation, and we would get unrealistic targets if we hoped to achieve additional returns without any additional risk.  So, we might include the T-Bill +3% benchmark in our reports but our underlying sum-of-parts benchmark may use a peer based index, such as a conservative Hedge Fund of Funds Composite Index, as the underlying index.

In short, portfolio level attribution is designed to evaluate who the relative winners and losers are on a comparative basis, quarter-to-quarter, but it is not always an accurate reflection of combined performance vs. benchmarks.  In our reports, the investment calculated performance (i.e. the vertical bar-charts page) reflects the true, net of fees combined performance.

The next step:  investment level attribution

By now, you should have an understanding of portfolio level attribution.  However, we have simply declared outperforming and underperforming investments.  We completely passed over the reasons for investment level outperformance or underperformance.  How did XYZ-LCC get 15% during the year while the S&P was only up 10%?  What did the XYX managers do differently from the index to generate so much more return?  Next month, we will look one level deeper.  We will discuss investment level attribution.

Gabriel Potter

Gabriel is a Senior Investment Research Associate at Westminster Consulting, where he is responsible for designing strategic asset allocations and conducts proprietary market research.

An avid writer, Gabriel manages the firm’s blog and has been published in the Journal of Compensation and Benefits,...

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