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

# Summary

- A few years ago, we blindly applied mean-variance optimization to a set of capital market assumptions, and The Weird Portfolio was born.
- This portfolio is weird because it does not look like typical investor portfolios since it tilts heavily toward credit-based and alternative asset classes.
- Despite having weird allocations, the portfolio actually performed in line with the iShares Core Moderate Allocation ETF (AOM), which has entirely different holdings.
- By decomposing the investment universe of the strategies into their underlying independent risk factors, we explore how even different allocations can lead to closely shared risks.
- While mathematical exercise has its limitations, we believe that investors can learn a great deal about their portfolio performance by looking at the performance of the underlying risk factors and the portfolio’s exposure to those factors.

Back in August 2017, I joined Meb Faber on his podcast for a wide-ranging conversation on the market outlook, tactical asset allocation, and a variety of research commentaries we had recently written.

Early in the conversation, we discussed *Portfolios in Wonderland*, a presentation I had put together that highlighted the unique nature of the current market outlook versus prior periods, its implications for financial planning, and ideas for asset allocation that might increase an investor’s odds of achieving retirement success.

In particular, we highlighted JP Morgan’s capital market assumptions and blindly ran them through a mean-variance optimization. Unlike us, the optimizer has no attachment to a particular asset class and blindly seeks to maximize return for a stated risk target.

The resulting portfolio was could only be described as *weird.*

And thus The Weird Portfolio was born.

The idea behind The Weird Portfolio is to generate a portfolio that blindly follows the recommendations of a portfolio optimizer over time, with no ad hoc constraints or regard for tracking error. The ultimate question being, “if we did not care about the optics of our portfolio and had full confidence in our capital market assumptions, how might we invest?”

To achieve this goal, we employ intermediate-term (7-to-10 year) capital market assumptions from JP Morgan, BlackRock, and BNY Mellon.

For each set of capital market assumptions, we run several thousand 10-year return simulations, generating random monthly return samples using the provided expected return and covariance matrices. For a bit of spice, we also randomly shock the covariance matrix to appropriately reflect the time-varying, crashing nature of cross-asset correlations.

For each simulation generated, we construct the portfolio that maximizes return while having the same realized volatility profile as a 60/40 global equity / U.S. aggregate bond portfolio.

After generating the thousands of different portfolios, we average them together to create our final allocation profile.

It should be noted that this sort of stochastic optimization has a particular weakness. Namely, because the lowest possible weight is 0%, there is a potential upward bias in recommended allocations for small positions and a symmetric downward bias in larger positions.

Using this methodology, the target allocations for Q2 2019 are shown below.

By almost any standard, the allocations look rather odd. We can see almost no allocation to U.S. large-cap equities, a meaningful overweight towards credit-based assets, and large allocations to long-term U.S. Treasuries and gold.

While a couple years of data is not particularly meaningful, we thought it would be interesting to evaluate the performance of The Weird Portfolio to see if any insights could be gleaned. To track the performance, we allocate to low-cost ETFs that track each asset class. For alternatives, we utilize category index data from HFRI.

Below we plot the growth of $1 in the –Vanguard Balanced Index Fund (VBINX)–, the –iShares Core Moderate Allocation ETF (AOM)–, and –The Weird Portfolio–.

*Source: CSI Data and HFRI. Calculations by Newfound Research. Returns for The Weird Portfolio are backtested and hypothetical. Returns assume the reinvestment of all distributions. Returns are gross of all fees except for underlying ETF expense ratios. None of the strategies shown reflect any portfolio managed by Newfound Research and were constructed solely for demonstration purposes within this commentary. You cannot invest in an index.*

Well, this is a head scratcher. For all its *weirdness*, the performance of The Weird Portfolio really is not all that weird at all. What gives?

After all, the –iShares Core Moderate Allocation ETF (AOM)– has no exposure to gold or alternatives, its exposure to U.S. large-cap is 5.5x larger and credit exposures are largely non-existent.

We’ll attack this question two ways. The first is philosophically and the second is quantitatively.

From a philosophical perspective, we’ll let Harley Bassman do all the talking:

In a nutshell, all financial risk vectors are related. The shape of the Yield Curve, the level of Credit Spreads, the correlation of various points on the yield curve and the level of Implied Volatility should all move in tandem since the risk premium embedded in the Duration, Credit, and Convexity risk vectors should correlate in some grand manner.

…

A simpler explanation may be that the net carry (profit) across risk categories should equilibrate as ‘alpha seekers’ allocate capital across the various risky assets in search of excess return.

From a quantitative perspective, we can try to distill this by not looking at allocations to asset classes, but by looking at allocations to *eigen portfolios.*

What, pray tell, is an *eigen portfolio*?

The simple answer is that eigen portfolios give us a way of looking at our investment universe through the lens of statistical factors, not assets. The factors, in this case, are each created as a portfolio of the investments in our universe. Through a special mathematical process, we can ensure that the factors all have zero correlation to one another.

Here is a more nuanced, quantitative answer. We can think of our NxN covariance matrix as an N-dimensional cloud of points. By performing an eigendecomposition, we can factorize the matrix into N linearly independent vectors. As each of these vectors will have a loading on each asset, we can think of them as portfolios (hence *eigen portfolios*). Furthermore, since the vectors are linearly independent, we know that they will have zero correlation to one another. Therefore, we can think of them as a set of basis portfolios that describe our investment universe.

Generally, we sort eigen portfolios by the proportion of variance they explain of our data. The first eigen portfolio will explain the most variance, the second the second most, et cetera. In most cases, there is a steep drop-off after the first several eigen portfolios, with 95% of the total variance being explained by just a handful of eigen portfolios in most asset class universes. These are often interpreted as the driving risk factors such as equity risk, interest rates, etc.

Note that with an N assets in our universe, there will always be N eigen portfolios. From a statistical perspective, not all of these eigen portfolios will necessarily be significant. Random matrix theory provides a number of ideas on identifying which eigen portfolios are meaningful and which are not, but we will leave that to another article on another day.

Let’s take a look at the weights of the first three eigen portfolios, which combined explained 80% of the cumulative variance.

While eigen portfolios are mathematically derived, it is sometimes possible to ascribe some economic intuition. For example, –Eigen Portfolio #1– has significant negative loadings on equities, credit exposures, and some alternatives. We might therefore interpret this as an equity beta factor. –Eigen Portfolio #2–, on the other hand, has slightly negative rate exposure, a significant positive loading on small-caps and a negative loading on gold. Finally, –Eigen Portfolio #3– has a significant loading on bonds and REITs, indicating that it is likely a duration factor of sorts.

Because these are portfolios, we can even go so far as to create their historical performance!

Note how –Eigen Portfolio #1– appears to be almost the mirror image of equity markets over the last 21 months. This makes sense, as that portfolio had significant *negative *weights towards equities.

Knowing that our eigen portfolios are independent from one another allows us to take one last step: we can examine our portfolios not as a set of asset classes, but rather as their implicit exposure to these eigen portfolios.

If we take this step for the –Vanguard Balanced Index Fund (VBINX)–, the –iShares Core Moderate Allocation ETF (AOM)–, and –The Weird Portfolio–, we see a very interesting result. Below we plot the loadings for the first five eigen portfolios.

We see that all three portfolios have significant negative weights on the first eigen portfolio (i.e. have *positive *exposure to equities) and positive weights to the third eigen portfolio. The biggest difference appears to be in the 2^{nd} eigen portfolio, where the –Vanguard Balanced Index Fund (VBINX)– retains a positive loading, the –iShares Core Moderate Allocation ETF (AOM)– has almost no loading, and –The Weird Portfolio– has a negative loading.

Unfortunately, the Eigen Portfolio #2 was one of the more difficult to interpret due to the significant weight spread between small-caps and gold, but it clearly provides a wedge between the –Vanguard Balanced Index Fund (VBINX)– and –The Weird Portfolio–. This may seem somewhat odd, as it implies a rather significant negative gold bias in the –Vanguard Balanced Index Fund (VBINX)–, but this bias is largely neutralized by the fourth eigen portfolio (not plotted) which has a heavy positive loading on gold, REITs, and U.S. small-caps with a large negative loading on emerging market equity. Taken together, these portfolios net out to negative emerging market exposure, which makes more economic sense since –Vanguard Balanced Index Fund (VBINX)– does not have any EM equity while the other two strategies do.

**Conclusion**

What is the takeaway to all of this analysis? We believe there are a handful worth noting.

First of all, extracting performance guidance from an asset allocation can be misleading. What looks weird on its face may exhibit little-to-no meaningful performance difference from more traditionally allocated portfolios in most environments. This is because what matters more than the asset allocation profile is the underlying risk factor profile. As we demonstrated in this commentary, while holdings may look meaningfully different, the embedded risk factors can still be quite similar.

Secondly, we should recognize that market environments can go through periods where certain risk factors are more important than others. As a naïve example, consider that stocks and bonds have largely exhibited negative correlations over the last several decades as economic growth shocks dominated market risk pricing. In prior decades, however, when inflation shocks were top of mine, stocks and bonds exhibited positive correlations. Over the time horizon evaluated, equity growth appears to be the dominant statistical risk factor, but that need not necessarily be the case going forward. The difference between the exposure of a standard 60/40 and The Weird Portfolio to the second eigen portfolio may manifest more significantly in the future.

Finally, we must acknowledge that 21 months is not a particularly meaningful horizon (despite this particular sample exhibiting some rather tumultuous periods), either from an economic regime perspective or a statistical perspective. Trying to draw too many conclusions from this small slice of history may be entirely misleading going forward.

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