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Straddles and Trend Following

By

On May 11, 2020

In Momentum, Portfolio Construction, Risk Management, Trend, Weekly Commentary

This post is available as a PDF download here.

Summary

  • The convex payoff profile of trend following strategies naturally lends itself to comparative analysis with option strategies. Unlike options, however, the payout of trend following is not guaranteed.
  • To compare and contrast the two approaches, we replicate simple trend following strategies with corresponding option straddle strategies.
  • While trend-following has no explicit up-front cost, it also bears the full brunt of any price reversals. The straddle-based approach, on the other hand, pays an explicit cost to insure against sudden and large reversals.
  • This transformation of whipsaw risk into an up-front option premium can be costly during strongly trending market environments where the option buyer would have been rewarded more for setting a higher deductible for their implicit insurance policy and paying a lower premium.
  • From 2005-2020, avoiding this upfront premium was beneficial. The sudden loss of equity markets in March 2020, however, allowed straddle-based approaches to make up for 15-years of relative underperformance in a single month.
  • Whether an investor wishes to avoid these up-front costs or pay them is ultimately a function of the risks they are willing to bear. As we like to say, “risk cannot be destroyed, only transformed.”

We often repeat the mantra that, “risk cannot be destroyed, only transformed.” While not being able to destroy risk seems like a limitation, the assertion that risk can be transformed is nearly limitless.

With a wide variety of investment options, investors have the ability to mold, shape, skew, and shift their risks to fit their preferences and investing requirements (e.g. cash flows, liquidity, growth, etc.).

The payoff profile of a strategy is a key way in which this transformation of risk manifests, and the profile of trend following is one example that we have written much on historically. The convex payoff of many long/short trend following strategies is evident from the historical payoff diagram.

Source: Newfound Research. Payoff Diversification (February 10th, 2020). Source: Kenneth French Data Library; Federal Reserve Bank of St. Louis. Calculations by Newfound Research. Returns are hypothetical and assume the reinvestment of all distributions. Returns are gross of all fees, including, but not limited to, management fees, transaction fees, and taxes. The 60/40 portfolio is comprised of a 60% allocation to broad U.S. equities and a 40% allocation to a constant maturity 10-Year U.S. Treasury index.  The momentum portfolio is rebalanced monthly and selects the asset with the highest prior 12-month returns whereas the buy-and-hold variation is allowed to drift over the 1-year period. The 10-Year U.S. Treasuries index is a constant maturity index calculated by assuming a 10-year bond is purchased at the beginning of every month and sold at the end of that month to purchase a new bond at par at the beginning of the next month. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses or sales charges. Past performance is not indicative of future results. 

This characteristic “V” shape in the diagram is reminiscent of an option straddle, where an investor buys a put and call option of the same maturity struck at the same price.  This position allows the investor to profit if the price of the underlying security moves significantly in either direction, but they pay for this opportunity in the option premiums.

Source: theoptionsguide.com

The similarity of these payoff profiles is no coincidence.  As we demonstrated in Trend – Convexity and Premium (February 11th, 2019), simple total return trend following signals coarsely approximate the delta of the straddle.  For those less familiar with the parlance of options, delta is the sensitivity in the value of the options to changes in the underlying stock.  For example, if delta is +1, then the value of the option position will match price changes in the underlying dollar-for-dollar.  If delta is -1, then the position will lose $1 for every dollar gained in the underlying and vice versa (i.e. the position is effectively short).

How does this connection arise?  Consider a naïve S&P 500 trend strategy that rebalances monthly and uses 12-month total returns as a trend signal, buying when prior returns are positive and shorting when prior returns are negative.  The key components of this strategy are today’s S&P 500 level and the level 12 months ago.

Now consider a strategy that buys a 1-month straddle with a strike equal to the level of the S&P 500 12 months ago.  When the current level is above the strike, the strategy’s delta will be positive and when the level is below the strike, the delta will be negative.  What we can see is that the sensitivity of our options trade to changes in the S&P 500 will match the sign of the trend strategy!

There are two key differences, however.  First, our trend strategy was designed to always be 100% long or 100% short, whereas the straddle’s sensitivity can vary between -100% and 100%.  Second, the trend strategy cannot change its exposure intramonth whereas the straddle will.  In fact, if price starts above the strike price (a positive trend) but ultimately ends below – so far as it is sufficiently far that we can make up for the premium paid for our options – the straddle can still profit!

In this commentary, we will compare and contrast the trend and option-based approaches for a variety of lookback horizons.

Methodology and Data

For this analysis, we will use the S&P 500 index for equity returns, the iShares Short-term U.S. Treasury Bond ETF (ticker: SHV) as the risk-free rate, and monthly options data on the S&P 500 (SPX options).

The long/short trend equity strategy looks at total returns of equities over a given number of months. If this return is positive, the strategy invests in equities for the following month. If the return is negative, the strategy shorts equities for the following month and earns the short-term Treasury rate on the cash. The strategy is rebalanced monthly on the third Friday of each month to coincide with the options expiration dates.

For the (semi-equivalent) straddle replication, at the end of each month we purchase a call option and a put option struck at the level of the S&P 500 at the beginning of the lookback window of the trend following strategy. We can also back out the strike price using the current trend signal value and S&P 500.  For example, if the trend signal is 25% and the S&P 500 is trading at $3000, we would set the strike of the options at $2400.

The options account is assumed to be fully cash collateralized. Any premium is paid on the options roll date, interest is earned on the remaining account balance, and the option payout is realized on the next roll date.

To value the options, we employ Black-Scholes pricing on an implied volatility surface derived from available out-of-the money options. Specifically, on a given day we fit a parabola to the implied variances versus log-moneyness (i.e. log(strike/price)) of the options for each time to maturity.

In prior research, we created straddle-derived trend-following models by purchasing S&P 500 exposure in proportion to the delta of the strategy.  To calculate delta, we had previously priced the options using 21-day realized volatility as a proxy for implied volatility.  This generally leads to over-pricing the options during crisis times and underpricing during more tame market environments, especially for deeper out of the money puts.  In this commentary we are actually purchasing the straddles and holding them for one month.

Source: Tiingo and DiscountOptionData.com. Calculations by Newfound Research.

Straddle vs. Trend Following

Below we plot the ratio of the equity curves for the straddle strategies versus their corresponding trend following strategies. When the line is increasing, the straddle strategy is out-performing, and when the line is decreasing the trend strategy is out-performing.

Source: Tiingo and DiscountOptionData.com. Calculations by Newfound Research.

We can see, generally, that trend following out-performed the explicit purchase of options for almost all lookback periods for the majority of the 15-year test period.

It is only with the most recent expiration – March 20, 2020 – that many of the straddle strategies came to out-perform their respective trend strategies.  With the straddle strategy, we pay an explicit premium to help insure our position against sudden and large intra-month price reversals.  This did not occur very frequently during the 15 year history, but was very valuable protection in March when the trend strategies were largely still long coming off markets hitting all-time-highs in late February.

Shorter-term lookbacks fared particularly well during that month, as the trend following strategy was in a long position on the February 2020 options expiry date, and the straddles set by the short-term lookback window were relatively cheap from a historical perspective.

Source: Tiingo and DiscountOptionData.com. Calculations by Newfound Research.

Note the curious case of the 14-month lookback.  Entering March, the S&P 500 was +45% over a 14-month lookback (almost perfectly anchored to December 2018 lows).  Therefore, the straddle was struck so deep in the money that it did not create any protection against the market’s sudden and large drawdown.

Prior to March 2020, only the 8- and 15-month lookback window strategies had outperformed their corresponding trend following strategies.  In both cases, it was just barely and just recently.

Another interesting point to note is that longer-term straddle strategies (lookbacks greater than 9 months) shared similar movements during many periods while shorter-term lookbacks (3-6 months) showed more dispersion over time.

Overall, many of the straddles exhibit more “crisis alpha” than their trend following counterparts.  This is an explicit risk we pay to hedge with the straddle approach and a fact we will discuss in more detail later on.

How Equity Movements Affect Straddles

Before we move into a discussion of how we can frame the straddle strategies, it will be helpful to revisit how straddles are affected by changing equity prices and how this effect changes with different lookback windows for the strategies.

Consider the delta of a straddle versus how far away price is from the strike (normalized by volatility).

Naively, we might consider that the longer our trend lookback window – and therefore the further back in time we set our strike price – the further away from the strike that price has had the opportunity to move. Consider two extremes: a strike set equal to the price of the S&P 500 10 years ago versus one set a day ago. We would expect that today’s price is much closer to that from a day ago than 10 years ago.

Therefore, for a longer lookback horizon we might expect that there is a greater chance that the straddle is currently deeper in the money, leading to a delta closer to +/- 1.  In the case of straddles struck at index levels more recently realized, it is more likely that price is close to at the money, leading to deltas closer to 0.

This also means that while the trend following strategy is taking a binary bet, the straddle is able to modulate exposure to equity moves when the trend is less pronounced. For example, if a 12-month trend signal is +1%, the trend model will retain a +1 exposure while the delta of the straddle may be closer to 0.

Source: Tiingo and DiscountOptionData.com. Calculations by Newfound Research.

Additionally, when the delta of a straddle is closer to zero, its gamma is higher.  Gamma reflects how quickly the straddle’s sensitivity to changes in the underlying asset – i.e. the delta – will change.  The trend strategy has no intra-month gamma, as once the position is set it remains static until the next rebalance.

As we generally expect the straddles struck longer ago to be deeper in the money than those struck more recently, we would also expect them to have lower gamma.

This also serves to nicely connect trend speed with the length of the lookback window. Shorter lookback windows are associated with trend models that change signals more rapidly while longer lookback windows are slower. Given that a total return trend signal can be thought of as the average of daily log returns, we would expect a longer lookback to react more slowly to recent changes than a shorter lookback because the longer lookback is averaging over more data.

But if we think of it through the lens of options – that the shorter lookback is coarsely replicating the delta of a straddle struck more recently – then the ideas of speed and gamma become linked.

Source: Tiingo and DiscountOptionData.com. Calculations by Newfound Research.

The Straddle Strategy as an Insurance Policy

One of the key differences between the trend strategy and the straddle is that the straddle has features that act as insurance against price reversals.  As an example, consider a case where the trend strategy has a positive signal.  To first replicate the payoff, the straddle strategy buys an in-the-money call option.  This is the first form of insurance, as the total amount this position can lose is the premium paid for the option, while the trend strategy can lose significantly more.

The straddle strategy goes one step further, though, and would also buy a put option.  So not only does it have a fixed loss on the call if price reverses course, but it can also profit if it reverses sufficiently.

One way to model the straddle strategies, then, is as insurance policies with varying deductibles. There is an up-front premium that is paid, and the strategy does not pay out until the deductible – the distance that the option is struck in the money – is met.

When the deductible is high – that is, when the trend is very strong in either direction – the premium for the insurance policy tends to be low.  On the other hand, a strategy that purchases at the money straddles would be equivalent to buying insurance with no deductible.

Source: Tiingo and DiscountOptionData.com. Calculations by Newfound Research.

On average, the 3-month straddle strategy pays annual premiums of about 14% for the benefit of only having to wait for a price reversal of 6% before protection kicks in. Toward the other end of the spectrum, the 12-month strategy has an annual average premium of under 6% with a 16% deductible.

We can also visualize how often each straddle strategy pays higher premiums by looking at the deltas of the straddles over time. When these values deviate significantly from +1 or -1, then the straddle is lowering its insurance deductible in favor of paying more in premium. When the delta is nearly +1 or -1, then the straddle is buying higher deductible insurance that will take a larger whipsaw to payout.

The charts below show the delta over time in the straddle strategies vs. the trend allocation for 3-, 6-, and 12-month lookback windows.

There is significant overlap, especially as trends get longer. The differences in the deltas in the 3-month straddle model highlight its tradeoff between lower deductibles and higher insurance premiums. However, this leads it to be more adaptive at capitalizing on equity moves in the opposite direction that lead to losses in the binary trend-following model.

Source: Tiingo and DiscountOptionData.com. Calculations by Newfound Research.

Source: Tiingo and DiscountOptionData.com. Calculations by Newfound Research.

Source: Tiingo and DiscountOptionData.com. Calculations by Newfound Research.

Source: Tiingo and DiscountOptionData.com. Calculations by Newfound Research.

The chart below shows the annualized performance of the straddle strategies when they underperform trend following (premium) and the annualized performance of the straddle strategies when they outperform trend following (payout). As the lookback window increases, both of these figures generally decline in absolute value.

Source: Tiingo and DiscountOptionData.com. Calculations by Newfound Research.

Even though we saw previously that the 3-month straddle strategy had the highest annual premium, its overall payout when it outperforms trend following is substantial. The longer lookbacks do not provide as much of a buffer due to their higher deductible levels, despite their lower premiums.

When the naïve trend strategy is right, it captures the full price change with no up-front premium.  When it is wrong, however, it bears the full brunt of losses.

With the straddle strategy, the cost is paid up front for the benefit to not only protect against price reversals, but even potentially profit from them.

As a brief aside, a simpler options strategy with similar characteristics would be to buy only either a call option or put option depending on the trend signal. This strategy would not profit from a reversion of the trend, but it would cap losses. Comparing it to the straddle strategies highlights the cost and benefit of the added protection.

Source: Tiingo and DiscountOptionData.com. Calculations by Newfound Research.

Buying only puts or calls generally helped both of the strategies shown in the chart. This came in reduced premiums over a time period when trimming premiums whenever possible paid off, especially for the 12-month lookback strategy. However, there are some notable instances where the extra protection of the straddle was very helpful, e.g. August 2011 and late 2014 for the 3-month lookback strategy and March 2020 for both.

Despite the similarities between the options and trend strategies, this difference in when the payment is made – either up-front in the straddle strategy or after-the fact in whipsaw in the trend following strategy – ends up being the key differentiator.

The relative performance of the strategies shows that investors mostly benefitted over the past 15 years by bearing this risk of whipsaw and large, sudden price-reversals. However, as the final moths of data indicates, option strategies can provide benefits that option-like­ strategies cannot.

Ultimately, the choice between risks is up to investor preferences, and a diversified approach that pairs strategies different convex strategies such as trend following and options is likely most appropriate.

Conclusion

The convex payoff profile of trend following strategies naturally lends itself to comparative analysis with option strategies, which also have a convex payoff profile. In fact, we would argue – as we have many times in the past – that trend following strategies coarsely replicate the delta profile of option straddles.

In this commentary, we sought to make that connection more explicit by building option straddle strategies that correspond to a naïve trend following strategies of varying lookback lengths.

While the trend following approach has no explicit up-front cost, it risks bearing the full brunt of sudden and large price reversals.  With the straddle-based approach, an investor explicitly pays an up-front premium to insure against these risks.

When evaluated through the lens of an insurance policy, the straddle strategy dynamically adjusts its associated premium and deductible over time.  When trends are strong, for example, premiums paid tend to be lower, but the cost is a higher deductible.  Conversely, when trends are flat, the premium is much higher, but the deductible is much lower.

We found that over the 2005-2020 test period, the cost of the option premiums exceeded the cost of whipsaw in the trend strategies in almost all cases.  That is, until March 2020, when a significant and sudden market reversal allowed the straddle strategies to make up for 15 years of relative losses in a single month.

As we like to say: risk cannot be destroyed, only transformed.  In this case, the trend strategy was willing to bear the risk of large intra-month price reversals to avoid paying any up-front premium.  This was a benefit to the trend investor for 15 years.  And then it wasn’t.

By constructing straddle strategies, we believe that we can better measure the trade-offs of trend following versus the explicit cost of insurance.  While trend following may approximate the profile of a straddle, it sacrifices some of the intra-month insurance qualities to avoid an up-front premium.  Whether this risk trade-off is ultimately worth it depends upon the risks an investor is willing to bear.

One Hedge to Rule Them All

By

On March 30, 2020

In Craftsmanship, Portfolio Construction, Risk Management, Weekly Commentary

This post is available as a PDF download here.

Summary

  • About two years ago, we compared and contrasted different approaches to risk managing equity exposure; including fixed income, risk parity, managed futures, tactical equity, and options-based strategies.
  • Given the recent market events as the world navigates through the COVID-19 crisis, we revisit this analysis to see how these strategies would have fared over the past two years.
  • We find that all eight strategies studied have continued to successfully reduce risk, with two of the previously underperforming options-based strategies now jumping to the forefront of the pack.
  • Over time, performance of the risk management strategies still varies significantly both relative to the S&P 500 and compared to the other strategies. Generally, risk-managed strategies tend to behave like insurance, underperforming on the upside and outperforming on the downside.
  • Diversifying your diversifiers by blending a number of complementary risk-managed strategies together – even at random – can be a powerful method of improving long-term outcomes.

“The primary requirement of historical time is that inly one of the possible alternatives coming at you from the future can be actualized in the present where it will flow into the pat and remain forever after unalterable. You may sometimes have “another chance” and be able to make a different choice in some later present, but this can in no way change the choice you did in fact make in the first instance.”

– Dr. William G. Pollard, Prof. of Physics, Manhattan Project

23 trading days.

In a little over a month, the S&P 500 dropped nearly 35% from all-time highs in a sell-off that was one of the fastest in history. Many investors experienced the largest drawdowns their portfolios had seen since the Financial Crisis.

While the market currently sits in a drawdown closer to 25% (as of the time of this writing), the future remains could take any path. Following the relative calm in the market over the preceding year, we are now living through a historic time with the uncertainty and severity of the growing COVID-19 pandemic and its far-reaching ramifications.

However, as a firm that focuses on managing risk, we are used to not knowing the answers.

In the summer of 2018, we published a piece entitled The State of Risk Management where we examined the historical trade-offs in terms of returns during market downturns versus returns during calm market environments of a variety of risk management methods.

Since that time, especially with the benefit of hindsight, one might argue that risk management was unnecessary until this past month. While the S&P 500 experienced a 19% drawdown in Q4 of 2018, it quickly recovered and went on to post a gain of 32% in 2019, rewarding those who stayed the course (or, better yet, bought the dip).

Source: Tiingo. Returns are gross of all management fees, transaction fees, and taxes, but net of underlying fund fees. Total return series assumes the reinvestment of all distributions. Data through 3/27/2020.

With the future poised to follow a variety of uncertain paths, we think it is a prudent time to check in on some of the more popular ways to manage risk and see how they are handling the current events.

The Updated Historical Track Record

For risk management, we examine eight strategies that roughly fit into four categories:

  • Diversification Strategies: strategic 60/40 stock/bond mix1and risk parity2
  • Options Strategies: equity collar3, protective put4, and put-write5,6
  • Equity Strategies: long-only defensive equity that blends a minimum volatility strategy7, a quality strategy8, and a dividend growth strategy9 in equal weights
  • Trend-Following Strategies: managed futures10 and tactical equity11

Index data was used prior to fund inception when necessary, and the common inception data is December 1997.

The following charts show the return and risk characteristics of the strategies over the entire historical period. Previously, we had used maximum drawdown as a measure of risk but have now switched to using the ulcer index to quantify both the duration and severity of drawdowns.

Data Source: CBOE, Tiingo, S&P. Calculations by Newfound Research. Past performance does not guarantee future results. All returns are hypothetical index returns. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses, sales charges, or trading expenses. Index returns include the reinvestment of dividends. No index is meant to measure any strategy that is or ever has been managed by Newfound Research. Data is from December 1997 to 3/27/2020.

Data Source: CBOE, Tiingo, S&P. Calculations by Newfound Research. Past performance does not guarantee future results. All returns are hypothetical index returns. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses, sales charges, or trading expenses. Index returns include the reinvestment of dividends. No index is meant to measure any strategy that is or ever has been managed by Newfound Research. Data is from December 1997 to 3/27/2020.

Relative to when we previously presented these statistics (as of July 2018), the most notable changes are that the 95-100 Collar index and Risk Parity have improved and that Managed Futures moved into the top-performing spot up from the middle of the pack. Trend Equity dropped slightly in the rankings, which is partially attributable to our switching over to using the Newfound Trend Equity Index, which includes exposure to small- and mid-cap companies and invests in cash rather than corporate bonds for the defensive position.

Six of the eight strategies still exhibit strong risk-adjusted performance relative to the S&P over the entire time period.

But as we also showed in 2018, the dispersion in strategy performance is significant.

Data Source: CBOE, Tiingo, S&P. Calculations by Newfound Research. Past performance does not guarantee future results. All returns are hypothetical index returns. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses, sales charges, or trading expenses. Index returns include the reinvestment of dividends. No index is meant to measure any strategy that is or ever has been managed by Newfound Research. Data is from December 1997 to 3/27/2020.

This chart also highlights the current trailing one-year performance for each strategy as of 3/27/2020.

Both the 95-110 Collar and the 5% Put Protection indices are in the top 10% of their historical one-year returns, with the put protection index forging new maximum territory. Trend equity and defensive equity have exhibited returns closer to their median levels, while managed futures, strategic diversification with bonds, and risk parity have had returns above their medians.

When we examine the current market environment, this makes sense. Many options were relatively cheap (i.e. implied volatility was low) heading into and early in February, and the option rollover date was close to when the drawdown began (positive timing luck). Equity trends were also very strong coming out of 2019.

With the sharp reversal in equity prices, option strategies provided a strong static hedge that any investors had been paying premiums for through the previous years of bull market returns.

Trend equity strategies were slower to act as trends took time to reverse before cash was introduced into the portfolio, and managed futures were eventually able to capitalize on short positions and diversification once these trends were established.

Zooming in more granularly, we can see the trade-offs between the hedging performance of each strategy in down markets and the premiums paid through negative returns in up-markets. This chart shows the returns relative to the S&P 500 (SPY). When the lines are increasing (decreasing), the hedge is outperforming (underperforming). A flatter line during periods of calm markets indicates lower premiums if we think of these strategies as insurance policies.

Data Source: CBOE, Tiingo, S&P. Calculations by Newfound Research. Past performance does not guarantee future results. All returns are hypothetical index returns. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses, sales charges, or trading expenses. Index returns include the reinvestment of dividends. No index is meant to measure any strategy that is or ever has been managed by Newfound Research. Data is through 3/27/2020.

All eight strategies have provided hedging in both Q4 2018 and the current downturn. The -95-100 Collar- provided some of the lowest premiums. -Trend Equity- also provided low premiums but had a slower time getting back in the market after the hedging period in 2018.

-Managed Futures- have provided some of the best hedging through both down periods but had the highest premium during the strong market of 2019.

With the continued dispersion in performance, especially with the “new” market crisis, this highlights the importance of diversification.

Diversifying Your Diversifiers

Not every risk management strategy will perfectly hedge every downturn while also having a low cost during up markets.

We see the power of diversifying your diversifiers when we test simple equal-weight blends of the risk management strategies. In our 2018 update, we had used an equal weight blend of all eight strategies and a blend of the six strategies that had historical Sharpe ratios above the S&P 500. This latter selection was admittedly biased with hindsight. The two excluded strategies – the 95-110 Collar and the 5% Put Protection indices – were some of the best performing over the period from August 2018 to March 2020!

Our own biases notwithstanding, we still include both blends for comparison.

Both blends have higher Sharpe ratios than 6 of the 8 individual strategies and higher excess return to ulcer index ratios than all of the eight individual strategies.

This is a very powerful result, indicating that naïve diversification is nearly as good as being able to pick the best individual strategies with perfect foresight.

Data Source: CBOE, Tiingo, S&P. Calculations by Newfound Research. Past performance does not guarantee future results. All returns are hypothetical index returns. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses, sales charges, or trading expenses. Index returns include the reinvestment of dividends. No index is meant to measure any strategy that is or ever has been managed by Newfound Research. Data is through 3/27/2020.

But holding eight – or even six – strategies can be daunting, especially for more aggressive investors who may only want to allocate a small portion of their portfolio to a risk management sleeve.

How much diversification is enough?

The following charts show the distribution of risk-adjusted returns from randomly choosing any number of the 8 strategies and holding them in equal weight.

As is to be expected, the cost of choosing the “wrong” blend of strategies decreases as the number of strategies held increases. The potential benefits initially increase and then back off as the luck of choosing the “right” strategy blend is reduced through holding a greater number of strategies.

Both charts show the distributions converging for the single choice for an 8-strategy portfolio.

Data Source: CBOE, Tiingo, S&P. Calculations by Newfound Research. Past performance does not guarantee future results. All returns are hypothetical index returns. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses, sales charges, or trading expenses. Index returns include the reinvestment of dividends. No index is meant to measure any strategy that is or ever has been managed by Newfound Research. Data is through 3/27/2020.

Data Source: CBOE, Tiingo, S&P. Calculations by Newfound Research. Past performance does not guarantee future results. All returns are hypothetical index returns. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses, sales charges, or trading expenses. Index returns include the reinvestment of dividends. No index is meant to measure any strategy that is or ever has been managed by Newfound Research. Data is through 3/27/2020.

Even holding 3 or 4 of the eight risk management strategies, chosen at random, leads to robust results, in general, with narrowed bands in the distribution (e.g. 25th to 75th percentiles).

Blending strategies from each of the different categories – static diversification, options, equity, and trend-following – can further reduce concentration risk verses selection at random and ensure that a variety of risk factors within the hedging strategies (e.g. interest rates from bonds, volatility from options, beta from equity, and whipsaw from trend-following) are mitigated.

Conclusion

We’ve said it many times before: There is no holy grail when it comes to risk management. While finding the perfect hedge that beats all others in every environment is enticing, it is impossible via the simple fact that risk cannot be destroyed, only transformed.

In an uncertain world where we cannot predict exactly what the next crisis will look like – or even what the current crisis will look like after today – diversifying your diversifiers by combining a number of complementary risk-managed strategies may be a prudent course of action.

We believe that this type of balanced approach has the potential to deliver compelling results over a full market cycle while managing the idiosyncratic risk of any one manager or strategy.

Diversification can also help to increase the odds of an investor sticking with their risk management plan as the short-term performance lows won’t be quite as low as they would be with a single strategy (conversely, the highs won’t be as high either).

Developing a plan and sticking with it is the most important first step in risk management. It is obviously desirable to keep premiums in strong markets as low as possible while having efficient hedges in down markets, but simple diversification can go a long way to provide a robust results.

Risk management is, by definition, required to be in place before risks are realized. Even when the market is currently down, risks in the future are still present. Therefore, we must periodically ask ourselves, “What risks are we willing to bear?”

One potential path has been locked into history, but the next time potential risks become reality – and they inevitably will – we must be comfortable with our answer.

Diversification with Portable Beta

By

On February 18, 2020

In Craftsmanship, Portfolio Construction, Risk & Style Premia, Risk Management, Weekly Commentary

This post is available as a PDF download here.

Summary

  • A long/flat tactical equity strategy with a portable beta bond overlay – a tactical 90/60 portfolio – has many moving parts that can make attribution and analysis difficult.
  • By decomposing the strategy into its passive holdings (a 50/50 stock/bond portfolio and U.S. Treasury futures) and active long/short overlays (trend equity, bond carry, bond momentum, and bond value), we can explore the historical performance of each component and diversification benefits across each piece of the strategy.
  • Using a mean-variance framework, we are also able to construct an efficient frontier of the strategy components and assess the differences between the optimal portfolio and the tactical 90/60.
  • We find that the tactical 90/60 is relatively close to the optimal portfolio for its volatility level and that its drawdown risk profile is close to that of an unlevered 60/40 portfolio.
  • By utilizing a modest amount of leverage and pairing it will risk management in both equities and bonds, investors may be able to pursue capital efficiency and maximize portfolio returns while simultaneously managing risk.

Portable beta strategies seek to enhance returns by overlaying an existing portfolio strategy with complementary exposure to diversifying asset classes and strategies. In overlaying exposure on an existing portfolio strategy, portable beta strategies seek to make every invested dollar work harder. This idea can create “capital efficiency” for investors, freeing up dollars in an investor’s portfolio to invest in other asset classes or investment opportunities.

At Newfound, we focus on managing risk. Trend following – or absolute momentum – is a key approach we employ do this, especially in equities. Trend equity strategies are a class of strategies that aim to harvest the long-term benefits of the equity risk premium while managing downside risk through the application of trend following.

We wrote previously how a trend equity strategy can be decomposed into passive and active components in order to isolate different contributors to performance. There is more than one way to do this, but in the most symmetric formulation, a “long/flat” trend equity strategy (one that that either holds equities or cash; i.e. does not short equities) can be thought of as a 100% passive allocation to a 50/50 portfolio of stocks and cash plus a 50% overlay allocation to a long/short trend equity strategy that can move between fully short and fully long equities. This overlay component is portable beta.

We have also written previously about how a portable beta overlay of bonds can be beneficial to trend equity strategies – or even passive equity investments, for that matter. For example, 95% of a portfolio could be invested in a trend equity strategy, and the remaining 5% could be set aside as collateral to initiate a 60% overlay to 10-year U.S. Treasury futures. This approximates a 60/40 portfolio that is leveraged by 50%

Source: Newfound. Allocations are hypothetical and for illustrative purposes only.

Since this bond investment introduces interest rate risk, we have proposed ways to manage risk in this specific sleeve using factors such as value, carry, and momentum. By treating these factors as fully tactical long/short portfolios themselves, if we hold them in equal weight, we can also break down the tactical U.S. Treasury futures overlay into active and passive components, with a 30% passive position in U.S. Treasury futures and 10% in each of the factor-based strategies.

Source: Newfound. Allocations are hypothetical and for illustrative purposes only.

When each overlay is fully invested, the portfolio will hold 95% stocks, 5% cash, and 60% U.S. Treasury futures. When all the overlays are fully short, the strategy will be fully invested in cash with no bond overlay position.

While the strategy has not changed at all with this slicing and dicing, we now have a framework to explore the historical contributions of the active and passive components and the potential diversification benefits that they offer.

Diversification Among Components

For the passive portfolio 50/50 stock/cash, we will use a blend of the Vanguard Total U.S. stock market ETF (VTI) and the iShares Short-term Treasury Bond ETF (SHV) with Kenneth French data for market returns and the risk-free rate prior to ETF inception.

For the active L/S Trend Equity portfolio, we will use a long/short version of the Newfound U.S. Trend Equity Index.

The passive 10-year U.S. Treasury futures is the continuous futures contract with a proxy of the 10-year constant maturity Treasury index minus the cash index used before inception (January 2000). The active long/short bond factors can be found on the U.S. Treasuries section of our quantitative signals dashboard, which is updated frequently.

All data starts at the common inception point in May 1957.

As a technical side note, we must acknowledge that a constant maturity 10-year U.S. Treasury index minus a cash index will not precisely match the returns of 10-year U.S. Treasury futures. The specification of the futures contracts state that the seller of such a contract has the right to deliver any U.S. Treasury bond with maturity between 6.5 and 10 years. In other words, buyers of this contract are implicitly selling an option, knowing that the seller of the contract will likely choose the cheapest bond to deliver upon maturity (referred to as the “cheapest to deliver”). Based upon the specification and current interest rate levels, that current cheapest to deliver bond tends to have a maturity of 6.5 years.

This has a few implications. First, when you buy U.S. Treasury futures, you are selling optionality. Finance 101 will teach you that optionality has value, and therefore you would expect to earn some premium for selling it. Second, the duration profile between our proxy index and 10-year U.S. Treasury futures has meaningfully diverged in the recent decade. Finally, the roll yield harvested by the index and the futures will also diverge, which can have a non-trivial impact upon returns.

Nevertheless, we believe that for the purposes of this study, the proxy index is sufficient for broad, directional attribution and understanding.

Source: Kenneth French Data Library, Federal Reserve Bank of St. Louis, Tiingo, Stevens Futures. Calculations by Newfound Research. Data is from May 1957 to January 2020. Returns are hypothetical and assume the reinvestment of all distributions. Returns are gross of all fees, including, but not limited to, management fees, transaction fees, and taxes. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses or sales charges. Past performance is not indicative of future results. 

The 50/50 Stock/Cash portfolio is the only long-only holding. While the returns are lower for all the other strategies, we must keep in mind that they are all overlays that can add to the 50/50 portfolio rather than simply de-risk and cannibalize its return.

This is especially true since these overlay strategies have exhibited low correlation to the 50/50 portfolio.

The table below shows the full period correlation of monthly returns for all the portfolio components. The equity and bond sub-correlation matrices are outlined to highlight the internal diversification.

Source: Kenneth French Data Library, Federal Reserve Bank of St. Louis, Tiingo, Stevens Futures. Calculations by Newfound Research. Data is from May 1957 to January 2020. Returns are hypothetical and assume the reinvestment of all distributions. Returns are gross of all fees, including, but not limited to, management fees, transaction fees, and taxes. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses or sales charges. Past performance is not indicative of future results. 

Not only do all of the overlays have low correlation to the 50/50 portfolio, but they generally exhibit low cross-correlations. Of the overlays, the L/S bond carry and L/S bond momentum strategies have the highest correlation (0.57), and the L/S bond carry and passive bond overlay have the next highest correlation (0.47).

The bond strategies have also exhibited low correlation to the equity strategies. This results in good performance, both absolute and risk-adjusted, relative to a benchmark 60/40 portfolio and a benchmark passive 90/60 portfolio.

Source: Kenneth French Data Library, Federal Reserve Bank of St. Louis, Tiingo, Stevens Futures. Calculations by Newfound Research. Data is from May 1957 to January 2020. Returns are hypothetical and assume the reinvestment of all distributions. Returns are gross of all fees, including, but not limited to, management fees, transaction fees, and taxes. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses or sales charges. Past performance is not indicative of future results. 

Finding the Optimal Blend

Up to this point, we have only considered the fixed allocations to each of the active and passive strategies outlined at the beginning. But these may not be the optimal holdings.

Using a block-bootstrap method to simulate returns, we can utilize mean-variance optimization to determine the optimal portfolios for given volatility levels.1 This yields a resampled historical realized efficient frontier.

Source: Kenneth French Data Library, Federal Reserve Bank of St. Louis, Tiingo, Stevens Futures. Calculations by Newfound Research. Data is from May 1957 to January 2020. Returns are hypothetical and assume the reinvestment of all distributions. Returns are gross of all fees, including, but not limited to, management fees, transaction fees, and taxes. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses or sales charges. Past performance is not indicative of future results. 

Plotting the benchmark 60/40, benchmark 90/60, and the tactical 90/60 on this efficient frontier, we see that the tactical 90/60 lies very close to the frontier at about 11.5% volatility. The allocations for the frontier are shown below.

 

Source: Kenneth French Data Library, Federal Reserve Bank of St. Louis, Tiingo, Stevens Futures. Calculations by Newfound Research. Data is from May 1957 to January 2020. Returns are hypothetical and assume the reinvestment of all distributions. Returns are gross of all fees, including, but not limited to, management fees, transaction fees, and taxes. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses or sales charges. Past performance is not indicative of future results. 

As expected, the lower volatility portfolios hold more cash and the high volatility portfolios hold more equity. For the 9% volatility level, these two allocations match, leading to the full allocation to a 50/50 stock/cash blend as in the tactical 90/60.

The passive allocation to the Treasury futures peaks at about 60%, while the L/S bond factor allocations are generally between 5% and 20% with more emphasis on Value and typically equal emphasis on Carry and Momentum.

The allocations in the point along the efficient frontier that matches the tactical 90/60 portfolio’s volatility are shown below.

Source: Kenneth French Data Library, Federal Reserve Bank of St. Louis, Tiingo, Stevens Futures. Calculations by Newfound Research. Data is from May 1957 to January 2020. Returns are hypothetical and assume the reinvestment of all distributions. Returns are gross of all fees, including, but not limited to, management fees, transaction fees, and taxes. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses or sales charges. Past performance is not indicative of future results. 

In this portfolio, we see a higher allocation to passive equities, a smaller position in the tactical equity L/S, and a larger position in passive Treasury futures. However, given the resampled nature of the process, these allocations are not wildly far away from the tactical 90/60.

The differences in the allocations are borne out in the Ulcer Index risk metric, which quantifies the severity and duration of drawdowns.

Source: Kenneth French Data Library, Federal Reserve Bank of St. Louis, Tiingo, Stevens Futures. Calculations by Newfound Research. Data is from May 1957 to January 2020. Returns are hypothetical and assume the reinvestment of all distributions. Returns are gross of all fees, including, but not limited to, management fees, transaction fees, and taxes. You cannot invest directly in an index and unmanaged index returns do not reflect any fees, expenses or sales charges. Past performance is not indicative of future results. 

The efficient frontier portfolio has a lower Ulcer Index than that of the tactical 90/60 even though their returns and volatility are similar. However, the Ulcer index of the tactical 90/60 is very close to that of the benchmark 60/40.

These differences are likely due to the larger allocation to the tactical equity long/short which can experience whipsaws (e.g. in October 1987), the lower allocation to passive U.S. equities, and the lower allocation to the Treasury overlay.

In an uncertain future, there can be significant risk in relying too much on the past, but having this framework can be useful for gaining a deeper understanding of which market environments benefit or hurt each component within the portfolio and how they diversify each other when held together.

Conclusion

In this research note, we explored diversification in a long/flat tactical equity strategy with a portable beta bond overlay. By decomposing the strategy into its passive holdings (50/50 stock/bond portfolio and U.S. Treasury futures) and active long/short overlays (trend equity, bond carry, bond momentum, and bond value), we found that each of the overlays has historically exhibited low correlation to the passive portfolios and low cross-correlations to each other. Combining all of these strategies using a tactical 90/60 portfolio has led to strong performance on both an absolute and risk-adjusted basis.

Using these strategy components, we constructed an efficient frontier of portfolios and also found that the “intuitive” tactical 90/60 portfolio that we have used in much of our portable beta research is close to the optimal portfolio for its volatility level. While this does not guarantee that this portfolio will be optimal over any given time period, it does provide evidence for the robustness of the multi-factor risk-managed approach.

Utilizing portable beta strategies can be an effective way for investors to pursue capital efficiency and maximize portfolio returns while simultaneously managing risk. While leverage can introduce risks of its own, relying on diversification and robust risk-management methods (e.g. trend following) can mitigate the risk of large losses.

The fear of using leverage and derivatives may be an uphill battle for investors, and there are a few operational burdens to overcome, but when used appropriately, these tools can make portfolios work harder and lead to more flexibility for allocating to additional opportunities.

If you are interested in learning how Newfound applies the concepts of tactical portable beta to its mandates, please reach out (info@thinknewfound.com).

Dynamic Spending in Retirement Monte Carlo

By

On July 15, 2019

In Risk Management, Sequence Risk, Weekly Commentary

This post is available as a PDF download here.

Summary­

  • Many retirement planning analyses rely on Monte Carlo simulations with static assumptions for withdrawals.
  • Incorporating dynamic spending rules can more closely align the simulations with how investors would likely behave during times when the plan looked like it was on a path to failure.
  • Even a modest reduction in withdrawals (e.g. 10%) can have a meaningful impact on reducing failure rates, nearly cutting it in half in a sample simulation.
  • Combining dynamic spending rules with other marginal improvements, such as supplemental income and active risk management, can lead to more robust retirement plans and give investors a better understanding of the variables that are within their realm of control.

Monte Carlo simulations are a prevalent tool in financial planning, especially pertaining to retirement success calculations.

Under a typical framework of normally distributed portfolio returns and constant inflation-adjusted withdrawals, calculating the success of a given retirement portfolio is straightforward. But as with most tools in finance, the art lies both in the assumptions that go into the calculation and in the proper interpretation of the result.

If a client is told they have a 10% chance of running out of money over their projected retirement horizon, what does that mean for them?

They cannot make 9 copies of themselves to live out separate lives, with one copy (hopefully not the original) unfortunately burning through the account prematurely.

They also cannot create 9 parallel universes and ensure they do not choose whichever one does not work out.

We wrote previously how investors follow a single path (You Are Not a Monte-Carlo Simulation). If that path hits zero, the other hypothetical simulation paths don’t mean a thing.

A simulation path is only as valuable as the assumptions that go into creating it, and fortunately, we can make our simulations align more closely with investor behavior.

The best way to interpret the 10% failure rate is to think of it as a 10% chance of having to make an adjustment before it hits zero. Rarely would an investor stand by while their account went to zero. There are circumstances that are entirely out of investor control, but to the extent that there was something they could do to prevent that event, they would most likely do it.

Derek Tharp, on Michael Kitces’ blog, wrote a post a few years ago weighing the relative benefit of implementing small but permanent adjustments vs. large but temporary adjustments to retirement withdrawals and found that making small adjustments and leaving them in place led to greater likelihoods of success over retirement horizons (Dynamic Retirement Spending Adjustments: Small-But-Permanent Vs Large-But-Temporary).

In this week’s commentary, we want to dig a little deeper into some simple path dependent modifications that we can make to retirement Monte-Carlo simulations with the hope of creating a more robust toolset for financial planning.

The Initial Plan

Suppose an investor is 65 and holds a moderate portfolio of 60% U.S. stocks and 40% U.S. Treasuries. From 1871 until mid-2019, this portfolio would have returned an inflation-adjusted 5.1% per year with 10.6% volatility according to Global Financial Data.

Sticking with the rule-of-thumb 4% annual withdrawal of the initial portfolio balance and assuming a 30-year retirement horizon, this yields a predicted failure rate of 8% (plus or minus about 50 bps).

The financial plan is complete.

If you start with $1,000,000, simply withdraw $3,333/month and you should be fine 92% of the time.

But what if the portfolio drops 5% in the first month? (It almost did that in October 2018).

The projected failure rate over the next 29 years and 11 months has gone up to 11%. That violates a 10% threshold that may have been a target in the planning process.

Or what if it drops 30% in the first 6 months, like it would have in the second half of 1931?

Now the project failure rate is a staggering 46%. Retirement success has been reduced to a coin flip.

Admittedly, these are trying scenarios, but these numbers are a key driver for financial planning. If we can better understand the risks and spell out a course of action beforehand, then the risk of making a rash emotion-driven decision can be mitigated.

Aligning the Plan with Reality

When the market environment is challenging, investors can benefit by being flexible. The initial financial plan does not have to be jettisoned; agreed upon actions within it are implemented.

One of the simplest – and most impactful – modifications to make is an adjustment to spending. For instance, an investor might decide at the outset to scale back spending by a set amount when the probably of failure crosses a threshold.Source: Global Financial Data. Calculations by Newfound.

This reduction in spending would increase the probability of success going forward through the remainder of the retirement horizon.

And if we knew that this spending cut would likely happen if it was necessary, then we can quantify it as a rule in the initial Monte Carlo simulation used for financial planning.

Graphically, we can visualize this process by looking at the probabilities of failure for varying asset levels over time. For example, at 10 years after retirement, the orange line indicates that a portfolio value ~80% of the initial value would have about a 5% failure rate.

Source: Global Financial Data. Calculations by Newfound.

As long as the portfolio value remains above a given line, no adjustment would be needed based on a standard Monte Carlo analysis. Once a line is crossed, the probability of success is below that threshold.

This chart presents a good illustration of sequence risk: the lines are flatter initially after retirement and the slope progressively steepens as the time progresses. A large drawdown initially puts the portfolio below the threshold for making and adjustment.

For instance, at 5 years, the portfolio has more than a 10% failure rate if the value is below 86%. Assuming zero real returns, withdrawals alone would have reduced the value to 80%. Positive returns over this short time period would be necessary to feel secure in the plan.

Looking under the hood along the individual paths used for the Monte Carlo simulation, at 5 years, a quarter of them would be in a state requiring an adjustment to spending at this 10% failure level.

Source: Global Financial Data. Calculations by Newfound.

This belies the fact that some of the paths that would have crossed this 10% failure threshold prior to the 5-year mark improved before the 5-year mark was hit. 75% of the paths were below this 10% failure rate at some point prior to the 5-year mark. Without more appropriate expectations of a what these simulations mean, under this model, most investors would have felt like their plan’s failure rate was uncomfortable at some point in the first 5 years after retirement!

Dynamic Spending Rules

If the goal is ultimately not to run out of funds in retirement, the first spending adjustment case can substantially improve those chances (aside from a large negative return in the final periods prior to the last withdrawals).

Each month, we will compare the portfolio value to the 90% success value. If the portfolio is below that cutoff, we will size the withdrawal to hit improve the odds of success back to that level, if possible.

The benefit of this approach is greatly improved success along the different paths. The cost is forgone income.

But this can mean forgoing a lot of income over the life of the portfolio in a particularly bad state of the world. The worst case in terms of this total forgone income is shown below.

Source: Global Financial Data. Calculations by Newfound.

The portfolio gives up withdrawals totaling 74%, nearly 19 years’ worth. Most of this is given up in consecutive periods during the prolonged drawdown that occurs shortly after retirement.

This is an extreme case that illustrates how large of income adjustments could be required to ensure success under a Monte Carlo framework.

The median case foregoes 9 months of total income over the portfolio horizon, and the worst 5% of cases all give up 30% (7.5 years) of income based off the initial portfolio value.

That is still a bit extreme in terms of potential cutbacks.

As a more realistic scenario that is easier on the pocketbook, we will limit the total annual cutback to 30% of the withdrawal in the following manner:

  • If the current chance of failure is greater than 20%, cut spending by 30%. This equates to reducing the annual withdrawal by $12,000 assuming a $1,000,000 initial balance.
  • If the current chance of failure is between 15% and 20%, cut spending by 20%. This equates to reducing the annual withdrawal by $8,000 assuming a $1,000,000 initial balance.
  • If the current chance of failure is between 10% and 15%, cut spending by 10%. This equates to reducing the annual withdrawal by $4,000 assuming a $1,000,000 initial balance.

These rules still increase the success rate to 99% but substantially reduce the amount of reductions in income.

Looking again at the worst-case scenario, we see that this case still “fails” (even though it lasts another 4.5 years) but that its reduction in come is now less than half of what it was in the extreme cutback case. This pattern is in line with the “lower for longer” reductions that Derek had looked at in the blog post.

Source: Global Financial Data. Calculations by Newfound.

On the 66% of sample paths where there was a cut in spending at some point, the average total cut amounted to 5% of the portfolio (a little over a year of withdrawals spread over the life of the portfolio).

Even moving to an even less extreme reduction regime where only 10% cuts are ever made if the probability of failure increases above 10%, the average reduction in the 66% of cases that required cuts was about 9 months of withdrawals over the 30-year period.

In these scenarios, the failure rate is reduced to 5% (from 8% with no dynamic spending rules).

Source: Global Financial Data. Calculations by Newfound.

Conclusion

Retirement simulations can be a powerful planning tool, but they are only as good as their inputs and assumptions. Making them align as closes with reality as possible can be a way to quantify the impact of dynamic spending rules in retirement.

While the magnitude of spending reductions necessary to guarantee success of a retirement plan in all potential states of the world is prohibitive. However, small modifications to spending can have a large impact on success.

For example, reducing withdrawal by 10% when the forecasted failure rate increases above 10% nearly cut the failure rate of the entire plan in half.

But dynamic spending rules do not exist in a vacuum; they can be paired with other marginal improvements to boost the likelihood of success:

  • Seek out higher returns – small increases in portfolio returns can have a significant impact over the 30 -ear planning horizon.
  • Supplement income – having supplements to income, even small ones, can offset spending during any market environment, improving the success rate of the financial plan.
  • Actively manage risk – managing risk, especially early in retirement is a key factor to now having to reduce withdrawals in retirement.
  • Plan for more flexibility – having the ability to reduce spending when necessary reduces the need to rely on the portfolio balance when the previous factors are not working.

While failure is certainly possible for investors, a “too big to fail” mentality is much more in line with the reality of retirement.

Even if absolute failure is unlikely, adjustments will likely be a requirement. These can be built into the retirement planning process and can shed light on stress testing scenarios and sensitivity.

From a retirement planning perspective, flexibility is simply another form of risk management.

The Path-Dependent Nature of Perfect Withdrawal Rates

By

On April 22, 2019

In Risk Management, Sequence Risk, Weekly Commentary

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.

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.

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.

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.

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.

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.

The actual PWR is below the 5th percentile 12% of the time, below the 1st percentile 4% of the time, above the 95th percentile 11% of the time, and above the 99th 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 5th percentile 5% of the time and above the 99th 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.

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.

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.

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.

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

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

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.

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.

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