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

# Summary

- In practice, investors and institutions alike have spending patterns that makes the sequence of market returns a relevant risk factor.
- All else held equal, investors would prefer to make contributions before large returns and withdrawals before large declines.
- For retirees making constant withdrawals, sustained declines in portfolio value represent a significant risk. Trend-following has demonstrated historical success in helping reduce the risk these types of losses.
- Traditionally, stock/bond glide paths have been used to control sequence risk. However, trend-following may be able to serve as a valuable hybrid between equities and bonds and provide a means to diversify our diversifiers.
- Using backward induction and a number of simplifying assumptions, we generate a glide path based upon investor age and level of wealth.
- We find that trend-following receives a significant allocation – largely in lieu of equity exposure – for investors early in retirement and whose initial consumption rate closely reflects the 4% level.

In past commentaries, we have written at length about investor sequence risk. Summarized simply, sequence risk is the sensitivity of investor goals to the sequence of market returns. In finance, we traditionally assume the sequence of returns does not matter. However, for investors and institutions that are constantly making contributions and withdrawals, the sequence can be incredibly important.

Consider for example, an investor who retires with $1,000,000 and uses the traditional 4% spending rule to allocate a $40,000 annual withdrawal to themselves. Suddenly, in the first year, their portfolio craters to $500,000. That $40,000 no longer represents just 4%, but now it represents 8%.

Significant drawdowns and fixed withdrawals mix like oil and water.

Sequence risk is the exact reason why traditional glide paths have investors de-risk their portfolios over time from growth-focused, higher volatility assets like equities to traditionally less volatile assets, like short-duration investment grade fixed income.

Bonds, however, are not the only way investors can manage risk. There are a variety of other methods, and frequent readers will know that we are strong advocates for the incorporation of trend-following techniques.

But how much trend-following should investors use? And when?

That is exactly what this commentary aims to explore.

**Building a New Glidepath**

In many ways, this is a very open-ended question. As a starting point, we will create some constraints that simplify our approach:

- The assets we will be limited to are broad U.S. equities, a trend-following strategy applied to U.S. equities, a 10-year U.S. Treasury index, and a U.S. Treasury Bill index.
- In any simulations we perform, we will use resampled historical returns.
- We assume an annual spend rate of $40,000 growing at 3.5% per year (the historical rate of annualized inflation over the period).
- We assume our investor retires at 60.
- We assume a male investor and use the Social Security Administration’s 2014 Actuarial Life Table to estimate the probability of death.

*Source: St. Louis Federal Reserve and Kenneth French Database. Past performance is hypothetical and backtested. Trend Strategy is a simple 200-day moving average cross-over strategy that invests in U.S. equities when the price of U.S. equities is above its 200-day moving average and in U.S. T-Bills otherwise. Returns are gross of all fees and assume the reinvestment of all dividends. None of the equity curves presented here represent a strategy managed by Newfound Research. *

To generate our glide path, we will use a process of backwards induction similar to that proposed by Gordon Irlam in his article *Portfolio Size Matters *(Journal of Personal Finance, Vol 13 Issue 2). The process works thusly:

- 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 1 year and generate 10,000 1-year return simulations.
- For each possible wealth level and each possible portfolio configuration of the four assets, use the 10,000 simulations to generate 10,000 possible future wealth levels, subtracting the inflation-adjusted annual spend.
- 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.
- Return to step 2.

As a technical side-note, we should mention that exploring all possible portfolio configurations is a computationally taxing exercise, as would be an optimization-based approach. To circumvent this, we employ a quasi-random low-discrepancy sequence generator known as a Sobol sequence. This process allows us to generate 100 samples that efficiently span the space of a 4-dimensional unit hypercube. We can then normalize these samples and use them as our sample allocations.

If that all sounded like gibberish, the main thrust is this: we’re not really checking every single portfolio configuration, but trying to use a large enough sample to capture most of them.

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.

**The Results**

To plot the results both over time as well as over the different wealth levels, we have to plot each asset individually, which we do below. As an example of how to read these graphs, below we can see that in the table for U.S. equities, at age 74 and a $1,600,000 wealth level, the glide path would recommend an 11% allocation to U.S. equities.

A few features we can identify:

- When there is little chance of success, the glide path tilts towards equities as a potential lottery ticket.
- When there is a near guarantee of success, the glide path completely de-risks.
- While we would expect a smooth transition in these glide paths, there are a few artifacts in the table (e.g. U.S. equities with $200,000 wealth at age 78). This may be due to a particular set of return samples that cascade through the tables. Or, because the trend following strategy can exhibit nearly identical returns to U.S. equities over a number of periods, we can see periods where the trend strategy received weight instead of equities (e.g. $400,000 wealth level at age 96 or $200,000 at 70).

Ignoring the data artifacts, we can broadly see that trend following seems to receive a fairly healthy weight in the earlier years of retirement and at wealth levels where capital preservation is critical, but growth cannot be entirely sacrificed. For example, we can see that an investor with $1,000,000 at age 60 would allocate approximately 30% of their portfolio to a trend following strategy.

Note that the initially assumed $40,000 consumption level aligns with the generally recommended 4% withdrawal assumption. In other words, the levels here are less important than their size relative to desired spending.

It is also worth pointing out again that this analysis uses historical returns. Hence, we see a large allocation to T-Bills which, once upon a time, offered a reasonable rate of return. This may not be the case going forward.

**Conclusion**

Financial theory generally assumes that the order of returns is not important to investors. Any investor contributing or withdrawing from their investment portfolio, however, is dramatically affected by the order of returns. It is much better to save before a large gain or spend before a large loss.

For investors in retirement who are making frequent and consistent withdrawals from their portfolios, sequence manifests itself in the presence of large and prolonged drawdowns. Strategies that can help avoid these losses are, therefore, potentially very valuable.

This is the basis of the traditional glidepath. By de-risking the portfolio over time, investors become less sensitive to sequence risk. However, as bond yields remain low and investor life expectancy increases, investors may need to rely more heavily on higher volatility growth assets to avoid running out of money.

To explore these concepts, we have built our own glide path using four assets: broad U.S. equities, 10-year U.S. Treasuries, U.S. T-Bills, and a trend following strategy. Not surprisingly, we find that trend following commands a significant allocation, particularly in the years and wealth levels where sequence risk is highest, and often is allocated to in lieu of equities themselves.

Beyond recognizing the potential value-add of trend following, however, an important second takeaway may be that there is room for significant value-add in going beyond traditional target-date-based glide paths for investors.

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