*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.

- Calculate the

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.

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