*This post is available for download as a PDF here.*

**Summary**

- Determining the allocations of an investment strategy is often the first step in scenario analysis, sensitivity analysis, and stress testing.
- For a single fund or ETF, the allocations can be found on the provider’s website or in marketing materials. However, when analyzing a larger group of funds or using third-party software tools, simplifying assumptions are frequently employed.
- Balancing simplicity of the model with its applicability to the portfolio can lead to more robust results by avoiding the assumption that a particular investment strategy will behave like an average value.

In the investment industry, transparency is key. Obviously, any “edge” must be kept secret, but the process and holdings have to be transparent enough for investors to continue to have confidence in it.

With the proliferation of ETFs and mutual funds, which encompass multiple securities, knowing exactly what you own can sometimes be difficult.

If you do not know what an ETF (particularly an active ETF) or mutual fund holds, or more abstractly what factors influence its returns, how do you know how to utilize it within a portfolio?

How will it react if the market crashes, and how will it behave if interest rate increases really start to pick up?

These are questions that can be answered using scenario analysis, stress testing, and sensitivity analysis, and not surprisingly, there are many software tools to help with these task (e.g. BlackRock’s Aladdin, Riskalyze, RiXtrema, Axioma, MacroRIsk, HiddenLevers, etc.).

To keep things simple, many of these products use allocations on the front-end as the risk factors and leave the translation into factor exposures for the back-end that is ultimately displayed in the stress test results. However, how do *they* know what these strategies hold?

This is an important piece in determining what factors will significantly impact future performance.

**Methods to Determine Allocations **

The tools listed above vary in their transparency of process for determining allocations. At a high level, there are essentially three ways to determine what an ETF or mutual fund is holding:

- Look at what they are actually holding.
- Run a regression to determine the holdings.
- Make an assumption based on the strategy’s classification.

Each method comes with its own benefits and drawbacks, generally relating to its accuracy and ease of implementation on a broad scale.

**Look at the Actual Holdings **

Perhaps this is too obvious to state, but it is by far the most guaranteed way to get the answer.

Current holdings are often shown on the fund website, on many brokerage portals, and on research sites like Morningstar. Traditional ETFs report their holdings daily. And since the methodology is often transparent and index-based, it is generally possible to tell if the holdings are likely to change soon.

Since mutual funds often report holdings with a lag, generally monthly or at most quarterly, there may still be some uncertainty in the holdings, so understanding the flexibility that a manager has to alter holdings from day to day, week to week, month to month, etc. is extremely important.

Can they move 100% from equities to fixed income? Can they sell fully out of two sectors and buy two others?

If you still have questions about the process after combing through the info in marketing materials or from research providers, picking up the phone or sending an email to the company can often help.

The main downside of this is that it’s harder to evaluate many securities at once unless there is a quick way to summarize the data side-by-side.

Looking at sector exposures or factor exposures in equity products is a way to translate the data into an easily digestible format, and for broader portfolios and strategies, grouping securities by asset class is another way to compare different investments.

**Run a Regression to Determine the Holdings **

Any investment portfolio can be decomposed into a set of risk factor exposures plus the elusive “alpha”.

Typically, in the analysis of equity portfolios, we see risk factors like the excess market return, value, and momentum. However, it is perfectly acceptable to define our risk factors as the actual holdings that we think will describe the portfolio’s returns.

When we attempt to decompose returns based on holdings, our goal is to have a model specified such that we account for all sources of risk

This is a balancing act that requires some artfulness.

If you keep adding asset class exposures to the model, it will eventually yield a perfect fit…but it may be useless. With the common approach of using 36 months of data to fit these types of models, having 36 asset classes will lead to a model that looks like it fits the data perfectly.[1]

Because of this, some intuition into the portfolio and the underlying investment process is beneficial. If there is not emerging market exposure in a portfolio – based on the rules governing the investment universe or investment policy statement – then having emerging market equities in the model is not going to add any meaningful information.[2]

**The Downside of Regressions **

The downside of a regression based analysis is that it is not an exact science.

Consider a portfolio that is benchmarked to a 60/40 stock/bond blend. The equity portion is an equal blend of the S&P 500 index and the MSCI ACWI ex-US index, and the bond portion is based solely on the Barclays Aggregate Bond index. The manager is able to add 100bps annually to the performance of this blend with a tracking error of 3% (information ratio of 0.33).

The issue is that we only know beforehand that the strategy is “balanced”: it holds some amount of equities and some amount of fixed income, with possibly time-varying allocations.

If we run a rolling 36-month regression using the S&P 500 and the Barclays Aggregate as our predictors, the results can look unstable, especially for the lower volatility bond.

*Rolling 36-month Stock and Bond Exposure for a Hypothetical Balanced Strategy**Source: MSCI and Morningstar. Calculations by Newfound Research. Results are purely hypothetical and do not represent any Newfound strategy.*

Our perceived equity exposure ranges from 0.48 to 0.73 over time while our perceived bond exposure ranges from 0.21 to 0.74. If we had the entire period of data at our fingertips, we would estimate equity exposure of 0.60 and bond exposure of 0.55 – much closer to the true underlying exposure. However, this improved accuracy requires 17 years of data, which is unfeasible for many of today’s strategies.

What if we decide on a more accurate model to calculate the strategy’s actual holdings?

We can add the MSCI ACWI ex-US index to the model and see what changes.

*Rolling 36-month Stock and Bond Exposure for a Hypothetical Balanced Strategy*

*Source: MSCI and Morningstar. Calculations by Newfound Research. Results are purely hypothetical and do not represent any Newfound strategy.*

Despite the accurately specified model, we are now often supposedly trading U.S. equity exposure for international equity exposure over time.

*Exposure Statistics for a Hypothetical Balanced Strategy*

Barclays Agg. Exposure | S&P 500 Exposure | MSCI ACWI ex-US Exposure | Total Equity Exposure | |

Maximum Rolling Value | 0.63 | 0.45 | 0.44 | 0.71 |

Minimum Rolling Value | 0.07 | 0.07 | 0.13 | 0.49 |

Full Period Value | 0.41 | 0.31 | 0.27 | 0.59 |

*Source: MSCI and Morningstar. Calculations by Newfound Research. Results are purely hypothetical and do not represent any Newfound strategy.*

In this example, it is entirely possible that the manager’s information ratio is attributable to shifting between the sleeves, especially since asset allocation is generally a much more influential process in generating investment returns than is security selection. But since this example is contrived, we are assuming that the sleeve allocations remain fixed over time.

If our goal is to use the allocations to do a simple stress test, we could say, “if equities drop 20%, how will our portfolio react?”

Assuming that bonds remain approximately unchanged, this yields a portfolio decline of either 10% or 14% for an assumed equity exposure of 0.5 and 0.7, respectively, and a decline of 12% for the true equity exposure of 0.6.

An error of 2% in absolute terms is not large, but it still represents uncertainty that can compound with the tracking error of the strategy. If an investor is anchored to a maximum drop under a stressful market scenario, quickly seeing losses mount beyond this reference point can lead to an emotional decision, locking in the loss.

If the manager had even less tracking error (i.e. was more of a closet indexer), then having a poorly specified model can still lead to these types of scenarios using regression based allocation estimates. It is beneficial to rely on as much information about the holdings as is available when specifying our model.

**Make an Assumption Based on the Strategy’s Classification **

The final method is to assume a set allocations for a strategy based on its classification, which can be tied to the strategy’s name, benchmark, or category (e.g. Morningstar, Lipper, etc.).

This is the route that BlackRock Aladdin uses for mutual funds in its scenario analyzer.[3]

For example, all funds within the 30%-50% Allocation to Equity category are represented by the following allocations:

*Source: BlackRock. As of October 2017.*

If we run our regression based analysis from the previous section, using these indices as our model variables, we find that the models generally fit well for the 116 funds (lowest fee share class). This is expected since these strategies maintain relatively statics asset class allocations.

*Adjusted R-squared Histogram for Regression-based Allocation Analysis – 30%-50% Allocation to Equity Category*

*Source: MSCI and Morningstar. Calculations by Newfound Research. Past performance is not a guarantee of future results.*

There is still a decent amount of variation in the exposures of the individual funds to the different asset classes, especially in U.S. and international bonds.

*Fund Exposure Statistics for Regression-based Allocation Analysis – 30%-50% Allocation to Equity Category*

U.S. Equity | Int'l Equity | U.S. Bond | Int'l Bond | |

Average Fund Exposure | 0.33 | 0.12 | 0.65 | -0.22 |

Assumed Fund Exposure | 0.28 | 0.09 | 0.49 | 0.07 |

Maximum Fund Exposure | 0.59 | 0.42 | 2.09 | 0.35 |

Minimum Fund Exposure | 0.08 | -0.12 | 0.06 | -0.91 |

% of Funds with Significant Exposure | 95% | 72% | 85% | 23% |

Average Significant Exposure | 0.34 | 0.14 | 0.71 | -0.35 |

* **Source: MSCI, BlackRock and Morningstar. Calculations by Newfound Research. Past performance is not a guarantee of future results.*

While the average fund exposures are close to the assumed values, the individual funds are further away. If we treat the exposures as portfolios, we would need to have a 34% average turnover to get to the assumed allocations, and only a little over 20% of the funds could get there with less than 20% turnover.

Moving to a more fluid category – Tactical Allocation – we see as similar setup for assumed allocations:

*Source: BlackRock. As of October 2017.*

If we run our regression based analysis from the previous section, using these indices as our model variables, we find that the fit for the 93 funds (again using the lowest fee share class) was much looser than for the more static allocation category of funds.

*Adjusted R-squared Histogram for Regression-based Allocation Analysis – Tactical Allocation Category*

*Source: MSCI and Morningstar. Calculations by Newfound Research. Past performance is not a guarantee of future results.*

The average exposures are further from the assumed values now, especially for bonds. The maximum and minimum fund exposures also span a much larger range, even for the equity allocations.

*Fund Exposure Statistics for Regression-based Allocation Analysis – Tactical Allocation Category*

U.S. Equity | Int'l Equity | U.S. Bond | Int'l Bond | |

Average Fund Exposure | 0.41 | 0.09 | 0.47 | 0.00 |

Assumed Fund Exposure | 0.36 | 0.11 | 0.28 | 0.09 |

Maximum Fund Exposure | 1.40 | 0.49 | 3.35 | 2.36 |

Minimum Fund Exposure | -0.33 | -0.30 | -1.65 | -2.02 |

% of Funds with Significant Exposure | 71% | 34% | 34% | 6% |

Average Significant Exposure | 0.53 | 0.23 | 1.12 | -0.73 |

* **Source: MSCI, BlackRock and Morningstar. Calculations by Newfound Research. Past performance is not a guarantee of future results.*

Again, if we treat the exposures as portfolios, we would now need to have a 76% average turnover to get to the assumed allocations, and only 4 funds could get there with less than 20% turnover.

Averages are often misleading[4], and there can be a lot of risk treating a single product as “average” when we cannot take advantage of the Law of Large Numbers.

**Conclusion**

As we have said before, all models are wrong, and some models are useful. The goal is not perfection; rather, we strive to balance simplicity and applicability by having robust, parsimonious models.

While it may be nice to back out what the allocations are, we ultimately have to decide what we care most about with a given analysis.

Holdings are great for implementing a replication strategy and illustrating a similar portfolio, but by introducing an auxiliary step in determining the sensitivity to underlying risk factors, which is often the end goal, we possibly have unnecessary sources of uncertainty. Not only do we have error in what the allocation are, but we also have error in how those allocations are affected by changes in the risk factors, such as interest rate increases, tightening credit spreads, CAPE ratio changes, and VIX movements.

[1] As long as the asset classes are not linearly dependent.

[2] This is not to say that the other asset classes (e.g. foreign developed equities) are not sensitive to emerging market equity returns. For this analysis, we assume that that sensitivity would already be captured by including foreign developed exposure in the model.

[3] https://www.blackrock.com/tools/scenario-tester

[4] https://blog.thinknewfound.com/2017/09/the-lie-of-averages/

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