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

# Summary

- Value and momentum equities exhibited significant performance last week raising short-term questions about factor crowding and long-term questions about appropriate factor diversification.
- We explore the idea of appropriate factor diversification through the lens of a retiring investor, asking the question, “are all equity styles appropriate at all points in an investor’s lifecycle?”
- Using a backwards induction method, we simulate portfolio decisions are derive optimal portfolios based upon an investor’s age and net-worth relative to their desired spending level.
- We find that portfolios are split into four distinct zones – the zone of safety, the cone of balance, the triangle of growth, and the twilight zone – each representing a distinct asset allocation.

Calm headline returns last week belie a tumultuous undercurrent in factor equities. Specifically, value and momentum equities both performed a rapid turnaround relative to recent performance. When all was said and done, the rotation between the two factors resulted in a weekly performance spread of over 900 basis points.

*Source: CSI Data; Calculations by Newfound Research. Results assume the reinvestment of all distributions. Results are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Past performance is not an indicator of future results. *

This abrupt course correction raised eyebrows throughout the quant world. Some took to measuring the historical rarity of the event. Others opined about the impact of factor crowding and the potential ensuing risks to portfolio construction. Many reminisced about the 2007 quant quake and wondered, “who blew up this time?”

There were those who swore these tea leaves prophesized doom and gloom and those who crossed their fingers that value might finally be making a comeback, but the majority simply shrugged and said, “stay the course.” Which, barring truly unusual circumstances, tends to be the prudent course of action.

It was, ironically, a particularly bad week for us to publish a research note that used a momentum / low-volatility portfolio barbell as a core example^{1}, as low-volatility equities and momentum moved in directional lockstep with one another all week.

*Source: CSI Data; Calculations by Newfound Research. Results assume the reinvestment of all distributions. Results are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Past performance is not an indicator of future results. *

When quants talk about factor crowding, there are really two types of crowding that can occur:

- The first occurs when too many investors crowd into the same trade. The most common way to measure this type of crowding is by looking at valuation spreads between the two legs of the trade. For example, crowding into growth stocks may cause value spreads between growth and value equities to widen to a historically unusual level (e.g. the dot-com era). Similarly, crowding into value stocks would lead to an unusually compressed spread in relative valuation between value and growth stocks.
- The second is when multiple factors crowd into the same trade. This can occur when multiple factors – especially when implemented in an unconstrained fashion – identify the same securities as being attractive. For example, if low-volatility stocks are out-performing their peers, momentum portfolios may rotate into these winners. This can cause two sets of investors to rotate into the same securities, causing crowding.

The latter form of crowding can be measured through holdings-based analysis (e.g. determining positional overlaps) or statistical analysis (e.g. correlation-based).

Below we plot the rolling correlation between residual momentum style returns with other popular factors. We can see that while momentum has historically had a relatively high correlation with **–growth–**, its correlation with **–low volatility–** is significantly time-varying. Prior to this week, the correlation between momentum and low volatility had climbed from -0.3 to north of 0.5 in 2019.

(Note that the above graph is available and updated daily on our Equity Style Dashboard.)

As proponents of style-based investing, we ask ourselves: what to do? Should we dynamically adjust our allocation to factors based upon crowding risk? If so, is the goal better performance (avoid highly crowded, and therefore lower return styles) or better risk management (maintain more consistent diversification across our style bets)?

In this pursuit, do we risk chasing signal only to realize noise?

These are non-trivial questions and their answers have important ramifications for portfolio design. While we believe these are questions worth exploring further, we want to start with perhaps one that is more trivial: are all styles even appropriate for all investors?

**Factors and Financial Planning**

This is not a new question for us. In June 2017 we wrote *Factors & Financial Planning*, employing capital market assumptions for stocks, bonds, and a variety of equity styles to construct different risk-based portfolios. We found that for growth-based investors, a barbell of value and momentum was preferred while for more conservative investors, a more diversified split of factors was prudent.

In our July 2018 note *The New Glide Path*we explored the use of trend equity strategies in designing a multi-asset glide path. Our process followed a backwards induction framework similar to Gordon Irlam’s article *Portfolio Size Matters*(Journal of Portfolio Finance, Vol 13 Issue 2). The general process was:

- Starting at age 100, assume a success rate of 100% for all wealth levels except for $0, which has a 0% success rate.
- Move back in time T years and generate N real return simulations.
- For each possible wealth level and each possible portfolio configuration of our assets, use the N simulations to generate N possible future wealth levels, subtracting the real annual spend level.
- For a given simulation, use standard mortality tables to determine if the investor died during the year. If he did, set the success rate to 100% for that simulation. Otherwise, set the success rate to the success rate of the wealth bucket the simulation falls into at T+1.
- For the given portfolio configuration, set the success rate as the average success rate across all simulations.
- For the given wealth level, select the portfolio configuration that maximizes success rate. If multiple portfolios guarantee success, choose the most conservative portfolio. If multiple portfolios maximize the success rate, average them together.
- Return to step 2.

To quote *The New Glide Path*:

By working backwards, we can tackle what would be an otherwise computationally intractable problem. In effect, we are saying, “if we know the optimal decision at time T+1, we can use that knowledge to guide our decision at time T.”

This methodology also allows us to recognize that the relative wealth level to spending level is important. For example, having $2,000,000 at age 70 with a $40,000 real spending rate is very different than having $500,000, and we would expect that the optimal allocation would different.

Consider the two extremes. The first extreme is we have an excess of wealth. In this case, since we are optimizing to maximize the probability of success, the result will be to take no risk and hold a significant amount of T-Bills. If, however, we had optimized to acknowledge a desire to bequeath wealth to the next generation, you would likely see the opposite extreme: with little risk of failure, you can load up on stocks and to try to maximize growth.

The second extreme is having a significant dearth of wealth. In this case, we would expect to see the optimizer recommend a significant amount of stocks, since the safer assets will likely guarantee failure while the risky assets provide a lottery’s chance of success.

In this note, we employ the process utilized in *The New Glide Path *but use an investment universe that includes a number of U.S. equity styles. Specifically, our investment universe will consist of:

- Equities: U.S. Total Market, EAFE + Canada.
- Bonds: 1-year US Treasuries, 10-year U.S. Treasuries.
- Long-Only Styles: Value, Size, Momentum, Low-Volatility.

*Source: MSCI; Global Financial Data; Calculations by Newfound Research. Results assume the reinvestment of all distributions. Results are gross of all fees, including, but not limited to, manager fees, transaction costs, and taxes. Past performance is not an indicator of future results. *

As a technical side note, we should note that generating all possible portfolio variations of these 8 assets would be computationally taxing, as would be an optimization-based approach. Therefore, we assume that each asset’s allocation is one of the following values: 0%, 10%, 20%, 40%, 60%, 80%, or 100%. We also assume that portfolios all sum to 100%. While this leads to rather coarsely defined portfolios, the objective of our search is not precision, but rather directional guidance as to whether certain factors should be preferred at different points in an investor’s lifecycle. These choices lead to 4,803 possible portfolio configurations.

Before we present our results, we should offer a few words of caution on reading too deeply into them.

- The joint dataset only goes back to 1997, severely biasing the test towards results realized over the last 20 years. Knowing that value has struggled, for example, we would expect value to be under-represented in our results. Further, being a low and stable inflation regime, we might see a larger representation of fixed income assets.
- A large proportion of the style data is backtested and therefore suffers all the usual risks of backtested results. Specifically, we risk that these results are overstated (and potentially in dramatic fashion), which may lead to an over-emphasis on certain factors.

With those risks in mind, results of our test are depicted graphically below. We will use the 1-year U.S. Treasury results as an example of how to read the graphs.

Each cell represents the optimal portfolio’s allocation to 1-year U.S. Treasuries.

Along the bottom axis we have the investor’s age.

The vertical axis represents “relative spending units”: i.e. how much wealth an investor has relative to the amount they would like to spend each year in real terms. For example, if an investor has $1,000,000 and would like to spend $40,000, they have 25 relative spending units.

We can see that for high relative spending units, the investor can hold a significant proportion of their wealth in short-term U.S. Treasuries (bearing in mind our note above about understated inflation risk). This is because the investor is more likely to die before they out-spend their wealth. On the other hand, we can see no short-term U.S. Treasury allocation for lower relative spending units earlier in an investor’s life, signaling the importance of growing assets in that time frame.

Evaluating all the assets we can see:

- The upper right half of the graph largely represents the “zone of safety” where an investor has a sufficient amount of wealth relative to their spending plan that they can invest very conservatively and still succeed. Numerically, if relative spending units exceed -1.25 x Age + 142.5, the investor is generally very safe.
- Below the “zone of safety” is the “cone of balance.”The cone is largest for the early retiree, likely representing the need to balance growth and capital preservation and declines in size as they age. Allocations to 10-year U.S. Treasuries are approximately 40-60% in this range. Equities within this range are largely a mixture between value and momentum.
- Below the “cone of balance” is the “triangle of growth.” Early retirees with insufficient relative spending units need to focus on growing their capital (or decreasing their spending, thereby increasing their relative spending units) to avoid running out of money later.
- Finally, below the “triangle of growth” is the “twilight zone.” This is a zone where investors need to both desperately growth their capital while simultaneously desperately avoiding losses. We can see that early in the zone, preservation is preferred. However, once deep in the zone – where an investor is guaranteed to withdraw the remainder of their capital – the strategy piles in on equities as a last ditch effort to grow.
- Most curiously, at least to us, is that minimum volatility securities fail to make a showing in this test. This may be due to several facts: (1) insufficient data; (2) poor test design; or (3) the specification of the minimum volatility portfolio we employed. Or, conversely, it may actually indicate that U.S. Treasury bonds were a better vehicle when total portfolio construction was considered.

**Conclusion**

In this research note, we ask the question, “should all equity styles be considered equally by investors in all stages of their lifecycle?” While we specifically focused on individual retirees, we believe this analysis extends naturally to pensions and other liability-driven institutions.

To explore this question, we designed a test that sought to maximize an individual investor’s likelihood of achieving success in retirement, where success is (rather morbidly) defined as dying before running out of money.

The result of this test identified four critical zones:

- “Zone of Safety”: Investors have sufficient capital to meet withdrawal needs and can invest as conservatively as they wish.
- “Cone of Balance”: Investors likely have sufficient savings to retire but need to balance both long-term growth objectives with capital preservation. Here we found that 10-year U.S. Treasuries were balanced with value and momentum equities.
- “Triangle of Growth”: Investors in this zone will outspend their net worth unless they grow their assets, so the portfolio tilts heavily towards momentum equities.
- “Twilight Zone”: Investors in this zone have so few assets that they must protect them at all cost. However, if assets dwindle too far, the portfolio swings wildly back towards equities, as a bet on growth is the only opportunity for avoiding failure.

We should stress that the results of our study are specific to our study design and that alternative designs may lead to different conclusions. However, we believe that the general conclusions do line up well with our intuition and highlight that not all investment styles may necessarily be appropriate for investors at all points in their investment lifecycle.

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