Tag: sequence risk

This post is available as a PDF download here.

Summary

The Perfect Withdrawal Rate (PWR) is the rate of regular portfolio withdrawals that leads to a zero balance over a given time frame.
4% is the commonly accepted lower bound for safe withdrawal rates, but this is only based on one realization of history and the actual risk investors take on by using this number may be uncertain.
Using simulation techniques, we aim to explore how different assumptions match the historical experience of retirement portfolios.
We find that simple assumptions commonly used in financial planning Monte Carlo simulations do not seem to reflect as much variation as we have seen in the historical PWR.
Including more stress testing and utilizing richer simulation methods may be necessary to successfully gauge that risk in a proposed PWR, especially as it pertains to the risk of failure in the financial plan.

Financial planning for retirement is a combination of art and science. The problem is highly multidimensional, requiring estimates of cash flows, investment returns and risk, taxation, life events, and behavioral effects. Reduction along the dimensions can simplify the analysis, but introduces consequences in the applicability and interpretation of the results. This is especially true for investors who are close to the line between success and failure.

One of the primary simplifying assumptions is the 4% rule. This heuristic was derived using worst-case historical data for portfolio withdrawals under a set of assumptions, such as constant inflation adjusted withdrawals, a fixed mix of stock and bonds, and a set time horizon.

Below we construct a monthly-rebalanced, fixed-mix 60/40 portfolio using the S&P 500 index for U.S. equities and the Dow Jones Corporate Bond index for U.S. bonds. Using historical data from 12/31/1940 through 12/31/2018, we can evaluate the margin for error the 4% rule has historically provided and how much opportunity for higher withdrawal rates was sacrificed in “better” market environments.

Source: Global Financial Data and Shiller Data Library. Calculations by Newfound Research. Returns are backtested and hypothetical. Past performance is not a guarantee of future results. Returns are gross of all fees. Returns assume the reinvestment of all distributions. 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.

But the history is only a single realization of the world. Risk is hard to gauge.

Perfect Withdrawal Rates

The formula (in plain English) for the perfect withdrawal rate (“PWR”) in a portfolio, assuming an ending value of zero, is relatively simple since it is just a function of portfolio returns:

The portfolio value in the numerator is the final value of the portfolio over the entire period, assuming no withdrawals. The sequence risk in the denominator is a term that accounts for both the order and magnitude of the returns.

Larger negative returns earlier on in the period increase the sequence risk term and therefore reduce the PWR.

From a calculation perspective, the final portfolio value in the equation is typically described (e.g. when using Monte Carlo techniques) as a log-normal random variable, i.e. the log-returns of the portfolio are assumed to be normally distributed. This type of random variable lends itself well to analytic solutions that do not require numerical simulations.

The sequence risk term, however, is not so friendly to closed-form methods. The path-dependent, additive structure of returns within the sequence risk term means that we must rely on numerical simulations.

To get a feel for some features of this equation, we can look at the PWR in the context of the historical portfolio return and volatility.

The relationship is difficult to pin down.

As we saw in the equation shown before, the –annualized return of the portfolio– does appear to impact the –PWR– (correlation of 0.51), but there are periods (e.g. those starting in the 1940s) that had higher PWRs with lower returns than in the 1960s. Therefore, investors beginning withdrawals in the 1960s must have had higher sequence risk.

Correlation between –annualized volatility– and –PWR– was slightly negative (-0.35).

The Risk in Withdrawal Rates

Since our goal is to assess the risk in the historical PWR with a focus on the sequence risk, we will use the technique of Brownian Bridges to match the return of all simulation paths to the historical return of the 60/40 portfolio over rolling 30-year periods. We will use the historical full-period volatility of the portfolio over the period for the simulation.

This is essentially a conditional PWR risk based on assuming we know the full-period return of the path beforehand.

To more explicitly describe the process, consider a given 30-year period. We begin by computing the full-period annualized return and volatility of the 60/40 portfolio over that period. We will then generate 10,000 simulations over this 30-year period but using the Brownian Bridge technique to ensure that all of the simulations have the exact same full-period annualized return and intrinsic volatility. In essence, this approach allows us to vary the path of portfolio returns without altering the final return. As PWR is a path-dependent metric, we should gain insight into the distribution of PWRs.

The percentile bands for the simulations using this method are shown below with the actual PWR in each period overlaid.

From this chart, we see two items of note: The percentile bands in the distribution roughly track the historical return over each of the periods, and the actual PWR fluctuates into the left and right tails of the distribution rather frequently. Below we plot where the actual PWR actually falls within the simulated PWR distribution.

The actual PWR is below the 5^th percentile 12% of the time, below the 1^st percentile 4% of the time, above the 95^th percentile 11% of the time, and above the 99^th percentile 7% of the time. Had our model been more well calibrated, we would expect the percentiles to align; e.g. the PWR should be below the 5^th percentile 5% of the time and above the 99^th percentile 1% of the time.

This seems odd until we realize that our model for the portfolio returns was likely too simplistic. We are assuming Geometric Brownian Motion for the returns. And while we are fixing the return over the entire simulation path to match that of the actual portfolio, the path to get there is assumed to have constant volatility and independent returns from one month to the next.

In reality, returns do not always follow these rules. For example, the skew of the monthly returns over the entire history is -0.36 and the excess kurtosis is 1.30. This tendency toward larger magnitude returns and returns that are skewed to the left can obscure some of the risk that is inherent in the PWRs.

Additionally, returns are not totally independent. While this is good for trend following strategies, it can lead to an understatement of risk as we explored in our previous commentary on Accounting for Autocorrelation in Assessing Drawdown Risk.

Over the full period, monthly returns of lags 1, 4, and 5 exhibit autocorrelation that is significant at the 95% confidence level.

To incorporate some of these effects in our simulations, we must move beyond the simplistic assumption of normally distributed returns.

First, we will fit a skewed normal distribution to the rolling historical data and use that to draw our random variables for each period. This is essentially what was done in the previous section for the normally distributed returns.

Then, to account for some autocorrelation, we will use the same adjustment to volatility as we used in the previously reference commentary on autocorrelation risk. For positive autocorrelations (which we saw in the previous graphs), this results in a higher volatility for the simulations (typically around 10% – 25% higher).

The two graphs below show the same analysis as before under this modified framework.

The historical PWR now fall more within the bounds of our simulated results.

Additionally, the 5^th percentile band now shows that there were periods where a 4% withdrawal rule may not have made the cut.

Conclusion

Heuristics can be a great way to distill complex data into actionable insights, and the perfect withdrawal rate in retirement portfolios is no exception.

The 4% rule is a classic example where we may not be aware of the risk in using it. It is the commonly accepted lower bound for safe withdrawal rates, but this is only based on one realization of history.

The actual risk investors take on by using this number may be uncertain.

Using simulation techniques, we explored how different assumptions match the historical experience of retirement portfolios.

The simple assumptions (expected return and volatility) commonly used in financial planning Monte Carlo simulations do not seem to reflect as much variation as we have seen in the historical PWR. Therefore, relying on these assumptions can be risky for investors who are close to the “go-no-go” point; they do not have much room for failure and will be more likely to have to make cash flow adjustments in retirement.

Utilizing richer simulation methods (e.g. accounting for negative skew and autocorrelation like we did here or using a downside shocking method like we explored in A Shock to the Covariance System) may be necessary to successfully gauge that risk in a proposed PWR, especially as it pertains to the risk of failure in the financial plan.

Having a number to base planning calculations on makes life easier in the moment, but knowing the risk in using that number makes life easier going forward.

Drawdowns and Portfolio Longevity

By Corey Hoffstein

On January 22, 2019

In Risk Management, Sequence Risk

This post is available as a PDF download here.

Summary

While retirement planning is often performed with Monte Carlo simulations, investors only experience a single path.
Large or prolonged drawdowns early in retirement can have a significant impact upon the probability of success.
We explore this idea by simulation returns of a 60/40 portfolio and measuring the probability of portfolio failure based upon a quantitative measure of risk called the Ulcer Index.
We find that a high Ulcer Index reading early in an investor’s retirement can dramatically increase the probability of failure as well as decrease the expected longevity of a portfolio.

Introduction

At Newfound we often say, “while other asset managers focus on alpha, our first focus is on risk.”

Not that there is anything wrong with the pursuit of alpha. We’d argue that the pursuit of alpha is actually a necessary component for well-functioning financial markets.

It’s simply that we have never met a financial advisor who has built a financial plan that assumed any sort of alpha. Alpha is great if we can harvest it, but the empirical evidence suggesting how difficult that can be (both for the manager net-of-fees as well as the investor behaviorally) would make the presumption of achieving alpha rather bold.

Furthermore, alpha is a zero-sum game: we can’t all plan for it.

Risk, however, is a crucial element of every investor’s plan. Bearing too little risk can lead to a portfolio that “fails slowly,” falling short of achieving the escape velocity required to outpace inflation. Bearing too much risk, however, can lead to sudden and catastrophic ruin: a case of “failing fast.”

When investors hit retirement, the usual portfolio math changes. While we’re taught in Finance 101 that the order of returns does not matter, the introduction of portfolio withdrawals makes the order of returns a large determinant of plan success. This phenomenon is known as “sequence risk” and it peaks in the years just before and after retirement.

Typically, we look at returns through the lens of the investment. In retirement, however, what really matters is the returns of the investor.

We’re often told that our primitive brain, trained on the African veldt, is unsuited for investing. Yet our brain seems to understand quite well that we do not get to live our lives as the average of a Monte Carlo simulation.

If we lose our arm to a lion because we did not flee when we heard a rustle in the bushes, we do not end up with half of an arm because of all the other parallel universes where we did flee. On the timeline we live, the situation is binary.

As investors, the same is true. We live but a single path and there are very real, very permanent knock-out conditions we need to be aware of. Prolonged and significant drawdowns during the first years of retirement rank among the most dangerous.

Drawdowns and the Risk of Ruin

A retirement plan typically establishes a safe withdrawal rate. This is the amount of inflation-adjusted money an investor can withdraw from their portfolio every year and still retain a sufficiently high probability that they will not run out of money before they die.

A well-established (albeit controversial) rule is that 4% of an investor’s portfolio level at retirement is usually an appropriate withdrawal amount. For example, if an investor retires with a $1,000,000 portfolio, they can theoretically safely withdraw $40,000 a year. Another way to think of this is that the portfolio reflects 25 years of spending assuming growth matches inflation.

The problem with portfolio drawdowns is that the withdrawal rate now reflects a larger proportion of capital unless it is commensurately adjusted downward. For example, if the portfolio falls to $700,000, a $40,000 withdrawal is now 5.7% of capital and the portfolio reflects just 17.5 years of spending units.

Even shallow, prolonged drawdowns can have a damaging effect. If the portfolio falls to $900,000 and stays stagnant for the next five years, the $40,000 withdrawals grow from representing 4% of the portfolio to nearly 5.5% of the portfolio. If we do not adjust the withdrawal, at five years into retirement we have gone from 25 spending units to 18.5, losing a year and a half of portfolio longevity.

As sudden and steep drawdowns can be just as damaging as shallow and prolonged ones, we prefer to use a quantitative measure known as the Ulcer Index to measure this risk. Specifically, the Ulcer Index is calculated as the root mean square of monthly drawdowns, capturing both severity and duration simultaneously.

In an effort to demonstrate the damaging impact of drawdowns early in retirement, we will run the following experiment:

Generate 250,000 simulations, each block-bootstrapped from monthly real U.S. equity and real U.S. 5-year Treasury bond returns from 1918 – 2018.
Assume a 65 year old investor with a $1,000,000 starting portfolio and a fixed real $3,333 withdrawal monthly ($40,000 annual).
Assume the investor holds a 60/40 portfolio at all times.
For each simulation:
- Calculate the Ulcer Index of the first five years of portfolio returns (ignoring withdrawals).
- Determine how many years until the portfolio runs out of money.

Based upon this data, below we plot the probability of failure – i.e. the probability we run out of money before we die – given an assumed age of death as well as the Ulcer Index realized by the portfolio in the first five years of retirement.

As an example of how to read this graph, consider the darkest blue line in the middle of the graph, which reflects an assumed age of death of 84. Along the x-axis are different bins of Ulcer Index levels, with lower numbers reflecting fewer and less severe drawdowns, while higher numbers reflect steeper and more frequent ones.

As we trace the line, we can see that the probability of failure – i.e. running out of money before death – increases dramatically as the Ulcer Index increases. While for shallow and infrequent drawdowns the probability of failure is <5%, we can see that the probability approaches 50% for more severe, frequent losses.

Beyond the binary question of failure, it is also important to consider when a portfolio runs out of money relative to when we die. Below we plot how many years prior to death a portfolio runs out of money, on average, based upon the Ulcer Index.

Once again using the darkest blue line as an example, we can see that for most minor-to-moderate Ulcer Index levels, the portfolio would only run out of money a year or two before we die in the case of failure. For more extreme losses, however, the portfolio can run out of money a full decade before we kick the bucket.

It is worth stressing here that these Ulcer Index readings are derived using simulations based upon prior realized U.S. equity and fixed income returns. In other words, while improbable (see the histogram below), extreme readings are not impossible.

It is worth further acknowledging that U.S. assets have experienced some of the highest realized risk premia in the world, and more conservative estimates may put a higher probability mass on more extreme Ulcer Index readings.

Conclusion

For early retirees, large or prolonged drawdowns early in retirement can have a significant impact on the probability of success.

In this commentary, we capture both the depth and duration of drawdowns using a single metric known as the Ulcer Index. We simulate 250,000 possible return paths for a 60/40 portfolio and calculate the Ulcer Index in the first five years of returns. We then plot the probability of failure as well as expected portfolio longevity conditional upon the Ulcer Index level realized.

We clearly see a positive relationship between failure and Ulcer Index, with larger and more prolonged drawdowns earlier in retirement leading to a higher probability of failure. This phenomenon is precisely why investors tend to de-risk their portfolios over time.

While the right risk profile and a well-diversified portfolio make for a strong foundation, we believe that investors should also consider expanding their investment palette to include alternative assets and style premia that may be more defensive oriented in nature. For example, defensive equities (e.g. low-volatility and quality approaches) have historically demonstrated an ability to reduce drawdown risk. Diversified, multi-asset style premia also tend to exhibit low correlation to traditional risk factors and a low intrinsic style premia.

Here at Newfound, we focus on trend equity strategies, which seek to overlay trend-following approaches on top of equity exposures in an effort to reduce left-tail risk and create a higher quality of return profile.

However, an investor chooses to build their portfolio, however, it should be risk that is on the forefront of their mind.

The New Glide Path

By Corey Hoffstein

On July 2, 2018

In Portfolio Construction, Risk Management, Sequence Risk, Weekly Commentary

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.

Risk Ignition with Trend Following

By Corey Hoffstein

On April 23, 2018

In Risk & Style Premia, Risk Management, Trend, Weekly Commentary

This post is available as a PDF download here.

Summary

While investors are often concerned about catastrophic risks, failing to allocate enough to risky assets can lead investors to “fail slowly” by not maintaining pace with inflation or supporting withdrawal rates.
Historically, bonds have acted as the primary means of managing risk.However, historical evidence suggests that investors may carry around a significant allocation to fixed income only to offset the tail risks of a few bad years in equities.
Going forward, maintaining a large, static allocation to fixed income may represent a significant opportunity cost for investors.
Trend following strategies have historically demonstrated the ability to significantly reduce downside risk, though often give up exposure to the best performing years as well.
Despite reducing upside capture, trend following strategies may represent a beneficial diversifier for conservative portfolios going forward, potentially allowing investors to more fully participate with equity market growth without necessarily fully exposing themselves to equity market risk.

In our recent commentary Failing Slow, Failing Fast, and Failing Very Fast, we re-introduced the idea of “risk ignition,” a phrase we first read in Aaron Brown’s book Red Blooded Risk. To quote the book on the core concept of the idea,

“Taking less risk than is optimal is not safer; it just locks in a worse outcome. Taking more risk than is optimal also results in a worse outcome, and often leads to complete disaster.”

Risk ignition is about taking sufficient risk to promote growth, but not so much risk as to create a high probability of catastrophe.

Traditionally, financial planners have tried to find the balance of risk in the intersection of an investor’s tolerance for risk and their capacity to bear it. The former addresses the investor’s personal preferences while the latter addresses their financial requirements.

What capacity fails to capture, in our opinion, is an investor’s need to take risk. It would be difficult to make the argument that a recent retiree with $1,000,000 saved and a planned 4% inflation-adjusted withdrawal rate should ever be allocated to 100% fixed income in the current interest rate environment, no matter what his risk tolerance is. Bearing too little risk is precisely how investors end up failing slowly.

The simple fact is that earning a return above the risk-free rate requires bearing risk. It is why, after all, the excess annualized return that equities earn is known as the “equity risk premium.” Emphasis on the “risk premium” part.

As more and more Baby Boomers retire, prevailing low interest rates mean that traditionally allocated conservative portfolios may no longer offer enough upside to address longevity risk. However, blindly moving these investors into riskier profiles (which may very well be above their risk tolerance anyway) may be equally imprudent, as higher portfolio volatility increases sensitivity to sequence risk when an investor begins taking distributions.

This is where we believe that tactical strategies can play an important role.

Holding Bonds for Insurance

In the simplest asset allocation framework, investors balance their desire to pursue growth with their tolerance (and even capacity) for risk by blending stocks and bonds. More conservative investors tend to hold a larger proportion of fixed income instruments, preferring their defined cash flows and maturity dates, while growth investors tilt more heavily towards equities. Stocks fight the risk of lost purchasing power (i.e. inflation) while bonds fight the risk of capital loss.

The blend between equities and bonds will ultimately be determined by balancing exposure to these two risks.

But why not simply hold just stocks? A trivial question, but one worth acknowledging. The answer is found in the graph below, where we plot the distribution fitting the annual returns of a broad U.S. equity index from 1962 to 2017. What we see is a large negative skew, which implies that the left tail of the distribution is much larger than the right. In plain English: every once in a while, stocks crash. Hard.

Source: Kenneth French Data Library. Calculations by Newfound Research. Returns are gross of all fees, including transaction fees, taxes, and any management fees. Returns assume the reinvestment of all distributions. Past performance is not a guarantee of future results.

The large left tail implies a drawdown risk that investors with short time horizons, or who are currently taking distributions from their portfolios, may not be able to bear. This is evident by plotting the realized excess return of different stock / bond[1] mixes versus their respective realized volatility profiles. We can see that volatility is largely driven by the equity allocation in the portfolio.

This left tail, and long-term equity realized equity volatility in general, is driven by just a few outlier events. To demonstrate, we will remove the worst performing years for U.S. equities from the dataset. For the sake of fairness, we’ll also drop an equal number of best years (acknowledging that the best years often follow the worse, and vice versa). Despite losing the best years, the worst years are so bad that we still see a tremendous shift up-and-to-the-left in the realized frontier, indicating higher realized returns with less risk.

Consider that the Sharpe optimal portfolio moves from the 50% stocks / 50% bonds mixture when the full data set is used to an 80% stock / 20% bond split when the best and worst three years are dropped.

Note that in the full-sample frontier, achieving a long-term annualized volatility of 10% requires holding somewhere between 40-50% of our portfolio in 10-year U.S. Treasuries. When we drop the best and worst 3 years of equity returns, the same risk level can be achieved with just a 20-30% allocation to bonds.

If we go so far as to drop the best and worst five years? We would only need 10% of our portfolio in bonds to hit that long-term volatility target.

One interpretation of this data is that investors carry a very significant allocation to bonds in their portfolio simply in effort to hedge the left-tail risks of equities. For a “balanced” investor (i.e. one around the 10% volatility level of a 60/40 portfolio), the worst three years of equity returns increases the recommended allocation to bonds by 20-30%!

Why is this important? Consider that forward bond forecasts heavily rely on current interest rates. Despite the recent increase in the short-end of the U.S. Treasury yield curve, intermediate term rates remain well-below long-term averages. This has two major implications:

If a bear market were to emerge, bonds may not provide the same protection they did in prior bear environments. (See our commentary Bond Returns: Don’t Be Jealous, Be Worried)
The opportunity cost for holding bonds versus equities may be quite elevated (if the term premium has eroded while the equity risk premium has remained constant).

Enter trend following.

Cutting the Tails with Trend Following

At its simplest, trend following says to remain invested while an investment is still appreciating in value and divest (or, potentially, even short) when an investment begins to depreciate.

(Since we’ve written at length about trend following in the past, we’ll spare the details in this commentary. For those keen on learning more about the history and theory of trend following, we would recommend our commentaries Two Centuries of Momentum and Protect and Participate: Managing Drawdowns with Trend Following.)

How, exactly, trend is measured is part of the art. The science, however, largely remains the same: trend following has a long, documented trail of empirical evidence suggesting that it may be an effective means of reducing drawdown risk in a variety of asset classes around the globe.

We can see in the example below that trend following applied to U.S. equities over the last 50+ years is no exception.

(In this example, we have applied a simple price-minus-moving-average trend following strategy. When price is above the 200-day moving average, we invest in broad U.S. equities. When price falls below the 200-day moving average, we divest into the risk-free asset. The model is evaluated daily after market close and trades are assumed to be executed at the close of the following day.)

Source: Kenneth French Data Library and Federal Reserve of St. Louis. Calculations by Newfound Research. Returns are gross of all fees, including transaction fees, taxes, and any management fees. Returns assume the reinvestment of all distributions. Past performance is not a guarantee of future results.

While the long-term equity curve tells part of the story – nearly matching long-term returns while avoiding many of the deepest – we believe that a more nuanced conversation can be had by looking at the joint distribution of annual returns between U.S. equities and the trend following strategy.

Source: Kenneth French Data Library. Calculations by Newfound Research. Scatter plot shows the joint distribution of annual returns from 1962 to 2017 for a broad U.S. equity index and a trend following strategy. Returns are gross of all fees, including transaction fees, taxes, and any management fees. Returns assume the reinvestment of all distributions. Past performance is not a guarantee of future results.

We can see that when U.S. equity returns are positive, the trend following strategy tends to have positive returns as well (albeit slightly lower ones). When returns are near zero, the trend following strategy has slightly negative returns. And when U.S. equity returns are highly negative, the trend following strategy significantly limits these returns.

In many ways, one might argue that the return profile of a trend following strategy mirrors that of a long call option (or, alternatively, index plus a long put option). The strategy has historically offered protection against large drawdowns, but there is a “premium” that is paid in the form of whipsaw.

We can also see this by plotting the annual return distribution of U.S. equities with the distribution of the trend strategy superimposed on top.

The trend strategy exhibits significantly less skew than U.S. equities, but loses exposure in both tails. This means that while trend following has historically been able to reduce exposure to significant losses, it has also meant giving up the significant gains. This makes sense, as many of the market’s best years come off the heels of the worst, when trend following may be slower to reinvest.

In fact, we can see that as we cut off the best and worst years, the distribution of equity returns converges upon the distribution of the trend following strategy.

Our earlier analysis of changes to the realized efficient frontier when the best and worst years are dropped indicates that the return profile of trend following may be of significant benefit to investors. Specifically, conservative investors may be able to hold a larger allocation to trend following than naked equities. This allows them to tilt their exposure towards equities in positive trending periods without necessarily invoking a greater level of portfolio volatility and drawdown due to the negative skew equities exhibit.

In the table below, we find the optimal mix of stocks, bonds, and the trend strategy that would have maximized excess annualized return for the same level of volatility of a given stock/bond blend.

Target	U.S. Equities	10-Year Treasury Index	Trend Strategy
0/100	7.4%	34.7%	58.0%
10/90	9.7%	48.4%	41.9%
20/80	11.5%	59.5%	29.0%
30/70	10.9%	56.4%	32.7%
40/60	8.9%	43.8%	47.3%
50/50	6.6%	29.9%	63.6%
60/40	37.2%	25.0%	37.8%
70/30	45.4%	14.0%	40.7%
80/20	53.9%	3.1%	43.1%
90/10	75.9%	0.0%	24.1%
100/0	100.0%	0.0%	0.0%

We can see that across the board, the optimal portfolio would have had a significant allocation to the trend following strategy. Below, we plot excess annualized return versus volatility for each of these portfolios (in orange) as well as the target mixes (in blue).

In all but the most aggressive cases (where trend following simply was not volatile enough to match the required volatility of the benchmark allocation), trend following creates a lift in excess annualized return. This is because trend following has historically allowed investors to simultaneously decrease overall portfolio risk in negative trending environments and increaseexposure to equities in positive trending ones.

Consider, for example, the optimal mixture that targets the same risk profile of the 30/70 stock/bond blend. The portfolio holds 9.7% in stocks, 48.4% in bonds and 41.9% in the trend strategy. This means that in years where stocks are exhibiting a positive trend, the portfolio is a near 50/50 stock/bond split. In years where stocks are exhibiting a negative trend, the portfolio tilts towards a 10/90 split. Trend following allows the portfolio to both be far more aggressive as well as far more defensive than the static benchmark.

Used in this manner, even if the trend following strategy underperforms stocks in positive trending years, so long as it outperforms bonds, it can add value in the context of the overall portfolio! While bonds have, historically, acted as a static insurance policy, trend following acts in a far more dynamic capacity, allowing investors to try to maximize their exposure to the equity risk premium.

Conclusion

Historically, stocks and bonds have acted as the building blocks of asset allocation. Investors pursuing a growth mandate have tilted towards stocks, while those focused on capital preservation have tilted more heavily towards bonds.

For conservative investors, the need to employ a large bond position is mainly driven by the negative skew exhibited by equity returns. However, this means that investors are significantly under-allocated to equities, and therefore sacrifice significant growth potential, during non-volatile years.

With low forecasted returns in fixed income, the significant allocation to bonds carried around by most conservative investors may represent a significant opportunity cost, heightening the risk offailing slow.

Trend following strategies, however, offer a simple alternative. The return profile of these strategies has historically mimicked that of a call option: meaningful upside participation with limited downside exposure. While not contractually guaranteed, this dynamic exposure may offer investors a way to reduce their allocation to fixed income without necessarily increasing their exposure to left-tail equity risk.

[1] We use a constant maturity 10-year U.S. Treasury index for bonds.

The Research Library of Newfound Research

Tag: sequence risk

The Path-Dependent Nature of Perfect Withdrawal Rates

Summary

Perfect Withdrawal Rates

The Risk in Withdrawal Rates

Conclusion

Drawdowns and Portfolio Longevity

Summary

Introduction

Drawdowns and the Risk of Ruin

Conclusion

The New Glide Path

Summary

Building a New Glidepath

The Results

Conclusion

Risk Ignition with Trend Following

Summary

Holding Bonds for Insurance

Cutting the Tails with Trend Following

Conclusion

Tag: sequence risk

The Path-Dependent Nature of Perfect Withdrawal Rates

Summary

Perfect Withdrawal Rates

The Risk in Withdrawal Rates

Conclusion

Drawdowns and Portfolio Longevity

Summary­

Introduction

Drawdowns and the Risk of Ruin

Conclusion

The New Glide Path

Summary­

Building a New Glidepath

The Results

Conclusion

Risk Ignition with Trend Following

Summary­

Holding Bonds for Insurance

Cutting the Tails with Trend Following

Conclusion

Summary

Summary

Summary