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Tag: tactical asset allocation

Failing Slow, Failing Fast, and Failing Very Fast

By

On April 9, 2018

In Risk Management, Sequence Risk, Weekly Commentary

This post is available as a PDF download here. 

Summary

  • For most investors, long-term “failure” means not meeting one’s financial objectives.
  • In the portfolio management context, failure comes in two flavors. “Slow” failure results from taking too little risk, while “fast” failure results from taking too much risk.  In his book, Red Blooded Risk, Aaron Brown summed up this idea nicely: “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.”
  • A third type of failure, failing very fast, occurs when we allow behavioral biases to compound the impact of market volatility (i.e. panicked selling near the bottom of a bear market).
  • In the aftermath of the global financial crisis, risk management was often used synonymously with risk reduction. In actuality, a sound risk management plan is not just about reducing risk, but rather about calibrating risk appropriately as a means of minimizing the risk of both slow and fast failure.

On the way back from a recent trip, I ran across a fascinating article in Vanity Fair: “The Clock is Ticking: Inside the Worst U.S. Maritime Disaster in Decades.”  The article details the saga of the SS El Faro, a U.S. flagged cargo ship that sunk in October 2015 at the hands of Hurricane Joaquin.  Quoting from the beginning of the article:

“In the darkness before dawn on Thursday, October 1, 2015, an American merchant captain named Michael Davidson sailed a 790-foot U.S.-flagged cargo ship, El Faro, into the eye wall of a Category 3 hurricane on the exposed windward side of the Bahama Islands.  El Faro means “the lighthouse” in Spanish.

 The hurricane, named Joaquin, was one of the heaviest to ever hit the Bahamas.  It overwhelmed and sank the ship.  Davidson and the 32 others aboard drowned. 

They had been headed from Jacksonville, Florida, on a weekly run to San Juan, Puerto Rico, carrying 391 containers and 294 trailers and cars.  The ship was 430 miles southwest of Miami in deep water when it went down.

Davidson was 53 and known as a stickler for safety.  He came from Windham, Maine, and left behind a wife and two college age daughters.  Neither his remains nor those of his shipmates were ever recovered. 

Disasters at sea do not get the public attention that aviation accidents do, in part because the sea swallows the evidence.  It has been reported that a major merchant ship goes down somewhere in the world every two or three days; most ships are sailing under flags of convenience, with underpaid crews and poor safety records. 

The El Faro tragedy attracted immediate attention for several reasons.  El Faro was a U.S.-flagged ship with a respected captain – and it should have been able to avoid the hurricane.  Why didn’t it?  Add to the mystery this sample fact: the sinking of the El Faro was the worst U.S. maritime disaster in three decades.”

From the beginning, Hurricane Joaquin was giving forecasters fits.  A National Hurricane Center release from September 29th said, “The track forecast remains highly uncertain, and if anything, the spread in the track model guidance is larger now beyond 48 hours…”  Joaquin was so hard to predict that FiveThirtyEight wrote an article about it.  The image below shows just how much variation there was in projected paths for the storm as of September 30th.

Davidson knew all of this.  Initially, he had two options.  The first option was the standard course: a 1,265-mile trip directly through open ocean toward San Juan.   The second was the safe play, a less direct route that would use a number of islands as protection from the storm.  This option would add 184 miles and six plus hours to the trip.

Davidson faced a classic risk management problem.  Should he risk failing fast or failing slow?

Failing fast would mean taking the standard course and suffering damage or disaster at the hands of the storm.  In this scenario – which tragically ended up playing out – Davidson paid the fatal price by taking too much risk.

Failing slow, on the other hand, would be playing it safe and taking the less direct route.  The risk here would be wasting the company’s time and money.  By comparison, this seems like the obvious choice.  However, the article suggests that Davidson may have been particularly sensitive to this risk as he had been gunning for a captain position on a new vessel that would soon replace El Faro on the Jacksonville to San Juan route.  In this scenario, Davidson would fail by taking too little risk.

This dichotomy between taking too little risk and failing slow and taking too much risk and failing fast is central to portfolio risk management.

Aaron Brown summed this idea up nicely in his book Red Blooded Risk, where he wrote, “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.”

Failing Slow

In the investing context, failing slow happens when portfolio returns are insufficient to generate the growth needed to meet one’s objectives.  No one event causes this type of failure.  Rather, it slowly builds over time.  Think death by a thousand papercuts or your home slowly being destroyed from the inside by termites.

Traditionally, this was probably the result of taking too little risk.  Oversized allocations to cash, which as an asset class has barely kept up with inflation over the last 90 years, are particularly likely to be a culprit in this respect.

Data Source: http://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/histretSP.html. Calculations by Newfound Research. Past performance does not guarantee future results.

 

Take your average 60% stock / 40% bond investor as an example.  Historically, such an investor would see a $100,000 investment grow to $1,494,003 over a 30-year horizon. Add a 5% cash allocation to that portfolio and the average end result drops to $1,406,935, an $87k cash drag.  Double the cash bucket to 10% and the average drag increases to nearly $170k.  This pattern continues as each additional 5% cash increment lowers ending wealth by approximately $80k.

Data Source: http://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/histretSP.html. Calculations by Newfound Research. Past performance does not guarantee future results.

 

Fortunately, there are ways to manage funds earmarked for near-term expenditures or as a safety net without carrying excessive amounts of cash.  For one example, see the Betterment article: Safety Net Funds: Why Traditional Advice Is Wrong.

Unfortunately, today’s investors face a more daunting problem.  Low returns may not be limited to cash.  Below, we present medium term (5 to 10 year) expected returns on U.S. equities, U.S. bonds, and a 60/40 blend from seven different firms/individuals.  The average expected return on the 60/40 portfolio is less than 1% per year after inflation.  Even if we exclude the outlier, GMO, the average expected return for the 60/40 is still only 1.3%.  Heck, even the most optimistic forecast from AQR is downright depressing relative to historical experience.

 

Expected return forecasts are the views of the listed firms, are uncertain, and should not be considered investment advice. Nominal returns are adjusted by subtracting 2.2% assumed inflation.

 

And the negativity is far from limited to U.S. markets.  For example, Research Affiliates forecasts a 5.7% real return for emerging market equities.  This is their highest projected return asset class and it still falls well short of historical experience for the U.S. equity markets, which have returned 6.5% after inflation over the last 90 years.

One immediate solution that may come to mind is just to take more risk.  For example, a 4% real return may still be technically achievable[1]. Assuming that Research Affiliates’ forecasts are relatively accurate, this still requires buying into and sticking with a portfolio that holds around 40% in emerging market securities, more than 20% in real assets/alternatives, and exactly 0% large-cap U.S. equity exposure[2].

This may work for those early in the accumulation phase, but it certainly would require quite a bit of intestinal fortitude.  For those nearing, or in, retirement, the problem is more daunting.  We’ve written quite a bit recently about the problems that low forward returns pose for retirement planning[3][4] and what can be done about it[5][6].

And obviously, one of the main side effects of taking more risk is increasing the portfolio’s exposure to large losses and fast failure, very much akin to Captain Davidson sailing way too close to the eye of the hurricane.

Failing Fast

At its core, failing fast in investing is about realizing large losses at the wrong time.  Think your house burning down or being leveled by a tornado instead of being destroyed slowly by termites.

Note that large losses are a necessary, but not sufficient condition for fast failure[7].  After all, for long-term investors, experiencing a bear market eventually is nearly inevitable.  For example, there has never been a 30-year period in the U.S. equity markets without at least one year-over-year loss of greater than 20%.  79% of historical 30-year periods have seen at least one year-over-year loss greater than 40%.

Fast failure is really about being unfortunate enough to realize a large loss at the wrong time.  This is called “sequence risk” and is particularly relevant for individuals nearing or in the early years of retirement.

We’ve used the following simple example of sequence risk before.  Consider three investments:

  • Portfolio A: -30% return in Year 1 and 6% returns for Years 2 to 30.
  • Portfolio B: 6% returns for Years 1 to 14, a -30% return in Year 15, and 6% returns for Years 16 to 30.
  • Portfolio C: 6% returns in Years 1 to 29 and a -30% return in Year 30.

Over the full 30-year period, all three investments have an identical geometric return of 4.54%.

Yet, the experience of investing in each of the three portfolios will be very different for a retiree taking withdrawals[8].  We see that Portfolio C fares the best, ending the 30-year period with 12% more wealth than it began with.  Portfolio B makes it through the period, ending with 61% of the starting wealth, but not without quite a bit more stress.  Portfolio A, however, ends in disaster, running out of money prematurely.

 

One way we can measure sequence risk is to compare historical returns from a particular investment with and without withdrawals.  The larger this gap, the more sequence risk was realized.

We see that sequence risk peaks in periods where large losses were realized early in the 10-year period.  To highlight a few periods:

  • The period ending in 2009 started with the tech bubble and ended with the global financial crisis.
  • The period ending in 1982 started with losses of 14.3% in 1973 and 25.9% in 1974.
  • The period ending in 1938 started off strong with a 43.8% return in 1928, but then suffered four consecutive annual losses as the Great Depression took hold.

Data Source: http://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/histretSP.html. Calculations by Newfound Research. Past performance does not guarantee future results.

 

A consequence of sequence risk is that asset classes or strategies with strong risk-adjusted returns, especially those that are able to successfully avoid large losses, can produce better outcomes than investments that may outperform them on a pure return basis.

For example, consider the period from August 2000, when the equity market peaked prior to the popping of the tech bubble, to March 2018.  Over this period, two common risk management tools – U.S. Treasuries (proxied by the Bloomberg Barclays 7-10 Year U.S. Treasury Index and iShares 7-10 Year U.S. Treasuries ETF “IEF”) and Managed Futures (proxied by the Salient Trend Index) – delivered essentially the same return as the S&P 500 (proxied by the SPDR S&P 500 ETF “SPY”).  Both risk management tools have significantly underperformed during the ongoing bull market (16.6% return from March 2009 to March 2018 for SPY compared to 3.1% for IEF and 0.7% for the Salient Trend Index).

Data Source: CSI, Salient. Calculations by Newfound Research. Past performance does not guarantee future results. Returns include no fees except underlying ETF fees. Returns include the reinvestment of dividends.

 

Yet, for investors withdrawing regularly from their portfolio, bonds and managed futures would have been far superior options over the last two decades.  The SPY-only investor would have less than $45k of their original $100k as of March 2018.  On the other hand, both the bond and managed futures investors would have growth their account balance by $34k and $29k, respectively.

Data Source: CSI, Salient. Calculations by Newfound Research. Past performance does not guarantee future results. Returns include no fees except underlying ETF fees. Returns include the reinvestment of dividends.

 

Failing Really Fast

Hurricanes are an unfortunate reality of sea travel.  Market crashes are an unfortunate reality of investing.  Both have the potential to do quite a bit of damage on their own.  However, what plays out over and over again in times of crisis is that human errors compound the situation.  These errors turn bad situations into disasters.  We go from failing fast to failing really fast.

In the case of El Faro, the list of errors can be broadly classified into two categories:

  1. Failures to adequately prepare ahead of time. For example, El Faro had two lifeboats, but they were not up to current code and were essentially worthless on a hobbled ship in the midst of a Category 4 hurricane.
  2. Poor decisions in the heat of the moment. Decision making in the midst of a crisis is very difficult.   The Coast Guard and NTSB put most of the blame on Davidson for poor decision making, failure to listen to the concerns of the crew, and relying on outdated weather information.

These same types of failures apply to investing.  Imagine the retiree that sells all of his equity exposure in early 2009 and sits out of the market for a few years during the first few years of the bull market or maybe the retiree that goes all-in on tech stocks in 2000 after finally getting frustrated with hearing how much money his friend had made off of Pets.com.  Taking a 50%+ loss on your equity exposure is bad, panicking and making rash decisions can throw your financial plans off track for good.

Compounding bad events with bad decisions is a recipe for fast failure.  Avoiding this fate means:

  1. Having a plan in place ahead of time.
  2. If you plan on actively making decisions during a crisis (instead of simply holding), systematize your process. Lay out ahead of time how you will react to various triggers.
  3. Sticking to your plan, even when it may feel a bit uncomfortable.
  4. Diversify, diversify, diversify.

On that last point, the benefits of diversifying your diversifiers cannot be overstated.

For example, take the following four common risk management techniques:

  1. Static allocation to fixed income (60% SPY / 40% IEF blend)
  2. Risk parity (Salient Risk Parity Index)
  3. Managed futures (Salient Trend Index)
  4. Tactical equity with trend-following (binary SPY or IEF depending on 10-month SPY return).

We see that a simple equal-weight blend of the four strategies delivers risk-adjusted returns that are in line with the best individual strategy.  In other words, the power of diversification is so significant that an equal-weight portfolio performs nearly the same as someone who had a crystal ball at the beginning of the period and could foresee which strategy would do the best.

Data Source: CSI, Salient, Bloomberg. Calculations by Newfound Research. Past performance does not guarantee future results. Returns include no fees except underlying ETF fees. Returns include the reinvestment of dividends. Blend is an equal-weight portfolio of the four strategies that is rebalanced on a monthly basis.

 

Achieving Risk Ignition

In the wake of the tech bubble and the global financial crisis, lots of attention has (rightly) been given to portfolio risk management.  Too often, however, we see risk management used as a synonym for risk reduction.  Instead, we believe that risk management is ultimately taking the right amount of risk, not too little or too much.  We call this achieving risk ignition[9] (a phrase we stole from Aaron Brown), where we harness the power of risk to achieve our objectives.

In our opinion, a key part of achieving risk ignition is utilizing changes that can dynamically adapt the amount of risk in the portfolio to any given market environment.

As an example, take an investor that wants to target 10% volatility using a stock/bond mix.  Using historical data going back to the 1980s, this would require holding 55% in stocks and 45% in bonds.  Yet, our research shows that 20% of that bond position is held simply to offset the worst 3 years of equity returns. With 10-year Treasuries yielding only 2.8%, the cost of re-allocating this 20% of the portfolio from stocks to bonds just to protect against market crashes is significant.

This is why we advocate using tactical asset allocation as a pivot around a strategic asset allocation core.  Let’s continue to use the 55/45 stock/bond blend as a starting point.  We can take 30% of the portfolio and put it into a tactical strategy that has the flexibility to move between 100% stocks and 100% bonds.  We fund this allocation by taking half of the capital (15%) from stocks and the other half from bonds.  Now our portfolio has 40% in stocks, 30% in bonds, and 30% in tactical.  When the market is trending upwards, the tactical strategy will likely be fully invested and the entire portfolio will be tilted 70/30 towards stocks, taking advantage of the equity market tailwinds.  When trends turn negative, the tactical strategy will re-allocate towards bonds and in the most extreme configuration tilt the entire portfolio to a 40/60 stock/bond mix.

In this manner, we can use a dynamic strategy to dial the overall portfolio’s risk up and down as market risk ebbs and flows.

Summary

For most investors, failure means not meeting one’s financial objectives.  In the portfolio management context, failure comes in two flavors: slow failure results from taking too little risk and fast failure results from taking too much risk.

While slow failure has typically resulted from allocating too conservatively or holding excessive cash balances, the current low return environment means that even investors doing everything by the book may not be able to achieve the growth necessary to meet their goals.

Fast failure, on the other hand, is always a reality for investors.  Market crashes will happen eventually.  The biggest risk for investors is that they are unlucky enough to experience a market crash at the wrong time.  We call this sequence risk.

A robust risk management strategy should seek to manage the risk of both slow failure and fast failure.  This means not simply seeking to minimize risk, but rather calibrating it to both the objective and the market environment.

 

 

[1] Using Research Affiliates’ asset allocation tool, the efficient portfolio that delivers an expected real return of 4% means taking on estimated annualized volatility of 12%.  This portfolio has more than double the volatility of a 40% U.S. large-cap / 60% intermediate Treasuries portfolio, which not coincidently returned 4% after inflation going back to the 1920s.

[2] The exact allocations are 0.5% U.S. small-cap, 14.1% foreign developed equities, 24.6% emerging market equities, 12.0% long-term Treasuries, 5.0% intermediate-term Treasuries, 0.8% high yield, 4.5% bank loans, 2.5% emerging market bonds (USD), 8.1% emerging market bonds (local currency), 4.4% emerging market currencies, 3.2% REITs, 8.6% U.S. commercial real estate, 4.2% commodities, and 7.5% private equity.

[3] https://blog.thinknewfound.com/2017/08/impact-high-equity-valuations-safe-retirement-withdrawal-rates/

[4] https://blog.thinknewfound.com/2017/09/butterfly-effect-retirement-planning/

[5] https://blog.thinknewfound.com/2017/09/addressing-low-return-forecasts-retirement-tactical-allocation/

[6] https://blog.thinknewfound.com/2017/12/no-silver-bullets-8-ideas-financial-planning-low-return-environment/

[7] Obviously, there are scenarios where large losses alone can be devastating.  One example are losses that are permanent or take an investment’s value to zero or negative (e.g. investments that use leverage).  Another are large losses that occur in portfolios that are meant to fund short-term objectives/liabilities.

[8] We assume 4% withdrawals increased for 2% annual inflation.

[9] https://blog.thinknewfound.com/2015/09/achieving-risk-ignition/

Addressing Low Return Forecasts in Retirement with Tactical Allocation

By

On September 25, 2017

In Risk Management, Sequence Risk, Weekly Commentary

This post is available for download as a PDF here.

Summary­­

  • The current return expectations for core U.S. equities and bonds paint a grim picture for the success of the 4% rule in retirement portfolios.
  • While varying the allocation to equities throughout the retirement horizon can provide better results, employing tactical strategies to systematically allocate to equities can more effectively reduce the risk that the sequence of market returns is unfavorable to a portfolio.
  • When a tactical strategy is combined with other incremental planning and portfolio improvements, such as prudent diversification, more accurate spending assessments, tax efficient asset location, and fee-conscious investing, a modest allocation can greatly boost likely retirement success and comfort.

Over the past few weeks, we have written a number of posts on retirement withdrawal planning.

The first was about the potential impact that high core asset valuations – and the associated muted forward return expectations – may have on retirement.

The second was about the surprisingly large impact that small changes in assumptions can have on retirement success, akin to the Butterfly Effect in chaos theory. Retirement portfolios can be very sensitive to assumed long-term average returns and assumptions about how a retiree’s spending will evolve over time.

In the first post, we presented a visualization like the following:

Historical Wealth Paths for a 4% Withdrawal Rate and 60/40 Stock/Bond Allocation
Source: Shiller Data Library.  Calculations by Newfound Research. Analysis uses real returns and assumes the reinvestment of dividends.  Returns are hypothetical index returns and are gross of all fees and expenses.  Results may differ slightly from similar studies due to the data sources and calculation methodologies used for stock and bond returns.

 

The horizontal (x-axis) represents the year when retirement starts.  The vertical (y-axis) represents the years post-retirement.  The coloring of each cell represents the savings balance at a given point in time.  The meaning of each color as follows:

  • Green: Current account value greater than or equal to initial account value (e.g. an investor starting retirement with $1,000,000 has a current account balance that is at least $1,000,000).
  • Yellow: Current account value is between 75% and 100% of initial account value
  • Orange: Current account value is between 50% and 75% of the initial account value.
  • Red: Current account value is between 25% and 50% of the initial account value.
  • Dark Red: Current account value is between 0% and 25% of initial account value.
  • Black: Current account value is zero; the investor has run out of money.

We then recreated the visualization, but with one key modification: we adjusted the historical stock and bond returns downward so that the long-term averages are in line with realistic future return expectations[1] given current valuation levels.  We did this by subtracting the difference between the actual average log return and the forward-looking long return from each year’s return.  With this technique, we capture the effect of subdued average returns while retaining realistic behavior for shorter-term returns.

 

Historical Wealth Paths for a 4% Withdrawal Rate and 60/40 Stock/Bond Allocation with Current Return Expectations

Source: Shiller Data Library.  Calculations by Newfound Research. Analysis uses real returns and assumes the reinvestment of dividends.  Returns are hypothetical index returns and are gross of all fees and expenses.  Results may differ slightly from similar studies due to the data sources and calculation methodologies used for stock and bond returns.

 

One downside of the above visualizations is that they only consider one withdrawal rate / portfolio composition combination.  If we want the see results for withdrawal rates ranging from 1% to 10% in 1% increments and portfolio combinations ranging from 0/100 stocks/bonds to 100/0 stocks/bonds in 20% increments, we would need sixty graphs!

To distill things a bit more, we looked at the historical “success” of various investment and withdrawal strategies.  We evaluated success on three metrics:

  1. Absolute Success Rate (“ASR”): The historical probability that an individual or couple will not run out of money before their retirement horizon ends.
  2. Comfortable Success Rate (“CSR”): The historical probability that an individual or couple will have at least the same amount of money, in real terms, at the end of their retirement horizon compared to what they started with.
  3. Ulcer Index (“UI”): The average pain of the wealth path over the retirement horizon where pain is measured as the severity and duration of wealth drawdowns relative to starting wealth. [2]

As a quick refresher, below we present the ASR for various withdrawal rate / risk profile combinations over a 30-year retirement horizon first using historical returns and then using historical returns adjusted to reflect current valuation levels.  The CSR and Ulcer Index table illustrated similar effects.

Absolute Success Rate for Various Combinations of Withdrawal Rate and Portfolio Composition – 30 Yr. Horizon

Absolute Success Rate for Various Combinations of Withdrawal Rate and Portfolio Composition with Average Stock and Bond Returns Equal to Current Expectations – 30 Yr. Horizon

Source: Shiller Data Library.  Calculations by Newfound Research.  Analysis uses real returns and assumes the reinvestment of dividends.  Returns are hypothetical index returns and are gross of all fees and expenses.  Results may differ slightly from similar studies due to the data sources and calculation methodologies used for stock and bond returns.

 

Overall, our analysis suggested that retirement withdrawal rates that were once safe may now deliver success rates that are no better – or even worse – than a coin flip.

The combined conclusion of these two posts is that the near future looks pretty grim for retirees and that an assumption that is slightly off can make the outcome even worse.

Now, we are going to explore a topic that can both mitigate low growth expectations and adapt a retirement portfolio to reduce the risk of a bad planning assumption. But first, some history.

 

How the 4% Rule Started

In 1994, Larry Bierwirth proposed the 4% rule, and William Bengen expanded on the research in the same year.[3], [4]

In the original research, the 4% rule was derived assuming that the investor held a 50/50 stock/bond portfolio, rebalanced annually, withdrew a certain percentage of the initial balance, and increased withdrawals in line with inflation. 4% is the highest percentage that could be withdrawn without ever running out of money over an historical 30-year retirement horizon.

Graphically, the 4% rule is the minimum value shown below.

Maximum Inflation Indexed Withdrawal to Deplete a 60/40 Portfolio Over a 30 Yr. Horizon

Source: Shiller Data Library.  Calculations by Newfound Research.  Analysis uses real returns and assumes the reinvestment of dividends.  Returns are hypothetical index returns and are gross of all fees and expenses.  Results may differ slightly from similar studies due to the data sources and calculation methodologies used for stock and bond returns.

 

Since its publication, the rule has become common knowledge to nearly all people in the field of finance and many people outside it. While it is a good rule-of-thumb and starting point for retirement analysis, we have two major issues with its broad application:

  1. It assumes that not running out of money is the only goal in retirement without considering implications of ending surpluses, return paths that differ from historical values, or evolving spending needs.
  2. It provides a false sense of security: just because 4% withdrawals never ran out of money in the past, that is not a 100% guarantee that they won’t in the future.

 

For example, if we adjust the stock and bond historical returns using the estimates from Research Affiliates (discussed previously) and replicate the analysis Bengen-style, the safe withdrawal rate is a paltry 2.6%.

 

Maximum Inflation Indexed Withdrawal to Deplete a 60/40 Portfolio Over a 30 Yr. Horizon using Current Return Estimates

Source: Shiller Data Library and Research Affiliates.  Calculations by Newfound Research.  Analysis uses real returns and assumes the reinvestment of dividends.  Returns are hypothetical index returns and are gross of all fees and expenses.  Results may differ slightly from similar studies due to the data sources and calculation methodologies used for stock and bond returns.

 

While this paints a grim picture for retirement planning, it’s not likely how one would plan their financial future. If you were to base your retirement planning solely on this figure, you would have to save 54% more for retirement to generate the same amount of annual income as with the 4% rule, holding everything else constant.

In reality, even with the low estimates of forward returns, many of the scenarios had safe withdrawal rates closer to 4%. By putting a multi-faceted plan in place to reduce the risk of the “bad” scenarios, investors can hope for the best while still planning for the worst.

One aspect of a retirement plan can be a time-varying asset allocation scheme.

 

Temporal Risk in Retirement

Conventional wisdom says that equity risk should be reduced as one progresses through retirement. This is what is employed in many “through”-type target date funds that adjust equity exposure beyond the retirement age.

If we heed the “own your age in bonds” rule, then a retiree would decrease their equity exposure from 35% at age 65 to 5% at the end of a 30-year plan horizon.

Unfortunately, this thinking is flawed.

When a newly-minted retiree begins retirement, their success is highly dependent on their first few years of returns because that is when their account values are the largest. As they make withdrawals and are reducing their account values, the impact of a large drawdown in dollar terms is not nearly as large.  This is known as sequence risk.

As a simple example, consider three portfolio paths:

  • Portfolio A: -30% return in Year 1 and 6% returns for every year from Year 2 – Year 30.
  • Portfolio B: 6% returns for every year except for Year 15, in which there is a -30% return.
  • Portfolio C: 6% returns for every year from Year 1 – Year 29 and a -30% return in Year 30.

These returns work about to the expected returns on a 60/40 portfolio using Research Affiliates’ Yield & Growth expectations, and the drawdown is approximately in line with the drawdown on a 60/40 portfolio over the past decade.  We will assume 4% annual withdrawals and 2% annual inflation with the withdrawals indexed to inflation.

 

3 Portfolios with Identical Annualized Returns that Occur in Different Orders

Portfolio C fares the best, ending the 30-year period with 12% more wealth than it began with. Portfolio B makes it through, not as comfortably as Portfolio C but still with 61% of its starting wealth. Portfolio A, however, starts off stressful for the retiree and runs out of money in year 27.

Sequence risk is a big issue that retirement portfolios face, so how does one combat it with dynamic allocations?

 

The Rising Glide Path in Retirement

Kitces and Pfau (2012) proposed the rising glide path in retirement as a method to reduce sequence risk.[5]  They argued that since retirement portfolios are most exposed to market risk at the beginning of the retirement period, they should start with the lowest equity risk and ramp up as retirement progresses.

Based on Monte Carlo simulations using both capital market assumptions in line with historical values and reduced return assumptions for the current environment, the paper showed that investors can maximize their success rate and minimize their shortfall in bad (5th percentile) scenarios by starting with equity allocations of between 20% and 40% and increasing to 60% to 80% equity allocations through retirement.

We can replicate their analysis using the reduced historical return data, using the same metrics from before (ASR, CSR, and the Ulcer Index) to measure success, comfort, and stress, respectively.

 

Absolute Success Rate for Various Equity Glide Paths with Average Stock and Bond Returns Equal to Current Expectations – 30 Yr. Horizon with a 4% Initial Withdrawal Rate

Comfortable Success Rate for Various Equity Glide Paths with Average Stock and Bond Returns Equal to Current Expectations – 30 Yr. Horizon with a 4% Initial Withdrawal Rate

Ulcer Index for Various Equity Glide Paths with Average Stock and Bond Returns Equal to Current Expectations – 30 Yr. Horizon with a 4% Initial Withdrawal Rate

Source: Shiller Data Library and Research Affiliates.  Calculations by Newfound Research.  Analysis uses real returns and assumes the reinvestment of dividends.  Returns are hypothetical index returns and are gross of all fees and expenses.  Results may differ slightly from similar studies due to the data sources and calculation methodologies used for stock and bond returns.

 

Note that the main diagonal in the chart represents static allocations, above the main diagonal represents the decreasing glide paths, and below the main diagonal represents increasing glide paths.

Since these returns are derived from the historical returns for stocks and bonds (again, accounting for a depressed forward outlook), they capture both the sequence of returns and shifting correlations between stocks and bonds better than Monte Carlo simulation. On the other hand, the sample size is limited, i.e. we only have about 4 non-overlapping 30 year periods.

Nevertheless, these data show that there was not a huge benefit or detriment to using either an increasing or decreasing equity glide path in retirement based on these metrics. If we instead look at minimizing expected shortfall in the bottom 10% of scenarios, similar to Kitces and Pfau, we find that a glide path starting at 40% rising to around 80% performs the best.

However, it will still be tough to rest easy with a plan that has an ASR of around 60 and a CSR of around 30 and an expected shortfall of 10 years of income.

With these unconvincing results, what can investors do to improve their retirement outcomes through prudent asset allocation?

 

Beyond a Static Glide Path

There is no reason to constrain portfolios to static glide paths. We have said before that the risk of a static allocation varies considerably over time. Simply dictating an equity allocation based on your age does not always make sense regardless of whether that allocation is increasing or decreasing.

If the market has a large drawdown, an investor should want to avoid this regardless of where they are in the retirement journey. Missing drawdowns is always beneficial as long as enough upside is subsequently realized.

In recent papers, Clare et al. (2017 and 2017) showed that trend following can boost safe withdrawal rates in retirement portfolios by managing sequence risk. [6],[7]

The million-dollar question is, “how tactical should we be?”

The following charts show the ASR, CSR, and Ulcer index values for static allocations to stocks, bonds, and a simple tactical strategy that invests in stocks when they are above their 10-month simple moving average (SMA) and in bonds otherwise.

The charts are organized by the minimum and maximum equity exposures along the rows and columns. The charts are symmetric across the main diagonal so that they can be compared to both increasing and decreasing equity glide paths.

The equity allocation is the minimum of the row and column headings, the tactical strategy allocation is the absolute difference between the headings, and the bond allocation is what’s needed to bring the total allocation to 100%.

For example, the 20% and 50% column is a portfolio of 20% equities, 30% tactical strategy, and 50% bonds. It has an ASR of 75, a CSR of 40, and an Ulcer index of 22.

 

Absolute Success Rate for Various Tactical Allocation Bounds Paths with Average Stock and Bond Returns Equal to Current Expectations – 30 Yr. Horizon with a 4% Initial Withdrawal Rate

Comfortable Success Rate for Various Tactical Allocation Bounds with Average Stock and Bond Returns Equal to Current Expectations – 30 Yr. Horizon with a 4% Initial Withdrawal Rate

Ulcer Index for Various Tactical Allocation Bounds with Average Stock and Bond Returns Equal to Current Expectations – 30 Yr. Horizon with a 4% Initial Withdrawal Rate

Source: Shiller Data Library and Research Affiliates.  Calculations by Newfound Research.  Analysis uses real returns and assumes the reinvestment of dividends.  Returns are hypothetical index returns and are gross of all fees and expenses.  Results may differ slightly from similar studies due to the data sources and calculation methodologies used for stock and bond returns.

 

These charts show that being tactical is extremely beneficial under these muted return expectations and that being highly tactical is even better than being moderately tactical.

So, what’s stopping us from going whole hog with the 100% tactical portfolio?

Well, this is a case where a tactical strategy can reduce the risk of not making it through the 30-year retirement at the risk of greatly increasing the ending wealth. It may sound counterintuitive to say that ending with too much extra money is a risk, but when our goal is to make it through retirement comfortably, taking undue risks come at a cost.

For instance, we know that while the tactical strategy may perform well over a 30-year time horizon, it can go through periods of significant underperformance in the short-term, which can lead to stress and questioning of the investment plan. For example, in 1939 and 1940, the tactical strategy underperformed a 50/50 portfolio by 16% and 11%, respectively.

These times can be trying for investors, especially those who check their portfolios frequently.[8] Even the best-laid plan is not worth much if it cannot be adhered to.

Being tactical enough to manage the risk of having to make a major adjustment in retirement while keeping whipsaw, tracking error, and the cost of surpluses in check is key.

 

Sizing a Tactical Sleeve

If the goal is having the smallest tactical sleeve to boost the ASR and CSR and reduce the Ulcer index to acceptable levels in a low expected return environment, we can turn back to the expected shortfall in the bad (10th percentile) scenarios to determine how large of a tactical sleeve to should include in the portfolio. The analysis in the previous section showed that being tactical could yield ASRs and CSRs in the 80s and 90s (dark green).  This, however, requires a tactical sleeve between 50% and 70%, depending on the static equity allocation.

Thankfully, we do not have to put the entire burden on being tactical: we can diversify our approaches.  In the previous commentaries mentioned earlier, we covered a number of topics that can improve retirement results in a low expected return environment.

  • Thoroughly examine and define planning factors such as taxes and the evolution of spending throughout retirement.
  • Be strategic, not static: Have a thoughtful, forward-looking outlook when developing a strategic asset allocation. This means having a willingness to diversify U.S. stocks and bonds with the ever-expanding palette of complementary asset classes and strategies.
  • Utilize a hybrid active/passive approach for core exposures given the increasing availability of evidence-based, factor-driven investment strategies.
  • Be fee-conscious, not fee-centric. For many exposures (e.g. passive and long-only core stock and bond exposure), minimizing cost is certainly appropriate. However, do not let cost considerations preclude the consideration of strategies or asset classes that can bring unique return generating or risk mitigating characteristics to the portfolio.
  • Look beyond fixed income for risk management given low interest rates.
  • Recognize that the whole can be more than the sum of its parts by embracing not only asset class diversification, but also strategy/process diversification.

While each modification might only result in a small, incremental improvement in retirement outcomes, the compounding effect can be very beneficial.

The chart below shows the required tactical sleeve size needed to minimize shortfalls/surpluses for a given improvement in the annual returns (0bp through 150bps).

 

Tactical Allocation Strategy Size Needed to Minimize 10% Expected Shortfall/Surplus with Average Stock and Bond Returns Equal to Current Expectations for a Range of Annualized Return Improvements  – 30 Yr. Horizon with a 4% Initial Withdrawal Rate

Source: Shiller Data Library and Research Affiliates.  Calculations by Newfound Research.  Analysis uses real returns and assumes the reinvestment of dividends.  Returns are hypothetical index returns and are gross of all fees and expenses.  Results may differ slightly from similar studies due to the data sources and calculation methodologies used for stock and bond returns.

 

For a return improvement of 125bps per year over the current forecasts for static U.S. equity and bond portfolios, with a static equity allocation of 50%, including a tactical sleeve of 20% would minimize the shortfall/surplus.

This portfolio essentially pivots around a static 60/40 portfolio, and we can compare the two, giving the same 125bps bonus to the returns for the static 60/40 portfolio.

 

Comparison of a Tactical Allocation Enhanced Portfolio with a Static 60/40 Portfolio with Average Stock and Bond Returns Equal to Current Expectations + 125bps per year   – 30 Yr. Horizon with a 4% Initial Withdrawal Rate

Source: Shiller Data Library and Research Affiliates.  Calculations by Newfound Research.  Analysis uses real returns and assumes the reinvestment of dividends.  Returns are hypothetical index returns and are gross of all fees and expenses.  Results may differ slightly from similar studies due to the data sources and calculation methodologies used for stock and bond returns.

 

In addition to the much more favorable statistics, the tactically enhanced portfolio only has a downside tracking error of 1.1% to the static 60/40 portfolio.

 

Conclusion: Being Dynamic in Retirement

From this historical analysis, high valuations of core assets in the U.S. suggest a grim outlook for the 4% rule. Predetermined dynamic allocation paths through retirement can help somewhat, but merely specifying an equity allocation based on one’s age loses sight of the changing risk a given market environment.

The sequence of market returns can have a large impact on retirement portfolios. If a drawdown happens early in retirement, subsequent returns may not be enough to provide the tailwind that they have in the past.

Investors who are able to be fee/expense/tax-conscious and adhere to prudent diversification may be able to incrementally improve their retirement outlook to the point where a modest allocation to a sleeve of tactical investment strategies can get their portfolio back to a comfortable success rate.

Striking a balance between shortfall/surplus risk and the expected experience during the retirement period along with a thorough assessment of risk tolerance in terms of maximum and minimum equity exposure can help dictate how flexible a portfolio should be.

In our QuBe Model Portfolios, we pair allocations to tactically managed solutions with systematic, factor based strategies to implement these ideas.

While long-term capital market assumptions are a valuable input in an investment process, adapting to shorter-term market movements to reduce sequence risk may be a crucial way to combat market environments where the low return expectations come to fruition.

[1] Specifically, we use the “Yield & Growth” capital market assumptions from Research Affiliates.  These capital market assumptions assume that there is no valuation mean reversion (i.e. valuations stay the same going forward).  The adjusted average nominal returns for U.S. equities and 10-year U.S. Treasuries are 5.3% and 3.1%, respectively, compared to the historical values of 9.0% and 5.3%.

[2] Normally, the Ulcer Index would be measured using true drawdown from peak, however, we believe that using starting wealth as the reference point may lead to a more accurate gauge of pain.

[3] Bierwirth, Larry. 1994. Investing for Retirement: Using the Past to Model the Future. Journal of Financial Planning, Vol. 7, no. 1 (January): 14-24.

[4] Bengen, William P. 1994. “Determining Withdrawal Rates Using Historical Data.” Journal of Financial Planning, vol. 7, no. 4 (October): 171-180.

[5] Pfau, Wade D. and Kitces, Michael E., Reducing Retirement Risk with a Rising Equity Glide-Path (September 12, 2013). Available at SSRN: https://ssrn.com/abstract=2324930

[6] Clare, A. and Seaton, J. and Smith, P. N. and Thomas, S. (2017). Can Sustainable Withdrawal Rates Be Enhanced by Trend Following? Available at SSRN: https://ssrn.com/abstract=3019089

[7] Clare, A. and Seaton, J. and Smith, P. N. and Thomas, S. (2017) Reducing Sequence Risk Using Trend Following and the CAPE Ratio. Financial Analysts Journal, Forthcoming. Available at SSRN: https://ssrn.com/abstract=2764933

[8] https://blog.thinknewfound.com/2017/03/visualizing-anxiety-active-strategies/

Combining Tactical Views with Black-Litterman and Entropy Pooling

By

On July 17, 2017

In Portfolio Construction, Weekly Commentary

This post is available as a PDF download here. 

Summary­­

  • In last week’s commentary, we outline a number of problems faced by tactical asset allocators in actually implementing their views.
  • This week, we explore popular methods for translating a combination of strategic views and tactical views into a single, comprehensive set of views that can be used as the foundation of portfolio construction.
  • We explore Black-Litterman, which can be used to implement views on returns as well as the more recently introduced Entropy Pooling methodology of Meucci, which allows for more flexible views.
  • For practitioners looking to implement tactical views into a number of portfolios in a coherent manner, the creation of posterior capital market assumptions via these methods may be an attractive process.

Note: Last week’s commentary was fairly qualitative – and hopefully applicable for practitioners and non-practitioners alike.  This week’s is going to be a bit wonkier and is primarily aimed at those looking to express tactical views in an asset allocation framework.  We’ll try to keep the equations to a minimum, but if the question, “how do I create a posterior joint return distribution from a prior and a rank view of expected asset class returns?” has never crossed your mind, this might be a good week to skip.

In last week’s commentary, we touched upon some of the important details that can make the actual implementation and management of tactical asset allocation a difficult proposition.[1]  Specifically, we noted that:

  1. Establishing consistent measures across assets is hard (e.g. “what is fair value for a bond index and how does it compare to equities?”);
  2. There often are fewer bets being made, so position sizing is critical;
  3. Cross-asset dynamics create changing risk profiles for bets placed.
  4. Tactical decisions often explicitly forego diversification, increasing the hurdle rate.

We’ll even add a fifth, sixth, and seventh:

  1. Many attractive style premia (e.g. momentum, value, carry, and trend) trades require leverage or shorting. Many other tactical views (e.g. change in yield curve curvature or change in credit spreads) can require leverage and shorting to neutralize latent risk factors and allocate risk properly.
  2. Combining (potentially conflicting) tactical views is not always straight forward.
  3. Incorporating tactical views into a preexisting policy portfolio – which may include long-term strategic views or constraints – is not obvious.

This week, we want to address how points #2-7 can be addressed with a single comprehensive framework.[2]

What is Tactical Asset Allocation?

As we hinted in last week’s commentary, we’re currently smack dab in the middle of writing a book on systematic tactical asset allocation.

When we sat down to write, we thought we’d start at an obvious beginning: defining “what is tactical asset allocation?”

Or, at least, that was the plan.

As soon as we sat down to write, we got a case of serious writer’s block.  Which, candidly, gave us deep pause.  After all, if we struggled to even write down a succinct definition for what tactical asset allocation is, how in the world are we qualified to write a book about it?

Fortunately, we were eventually able to put digital ink to digital paper.  While our editor would not let us get away with a two sentence chapter, our thesis can be more or less boiled down to:

Strategic asset allocation is the policy you would choose if you thought risk premia were constant; tactical asset allocation is the changes you would make if you believe risk premia are time-varying.[3]

We bring this up because it provides us a mental framework for thinking about how to address problems #2 – 7.

Specifically, given prior market views (e.g. expected returns and covariances) that serve as the foundation to our strategic asset allocation, can our tactical views be used to create a posterior view that can then serve as the basis of our portfolio construction process? 

Enter Black-Litterman

Fortunately, we’re not the first to consider this question.  We missed that boat by about 27 years or so.

In 1990, Fischer Black and Robert Litterman developed the Black-Litterman model while working at Goldman Sachs. The model provides asset allocators with a framework to embed opinions and views about asset class returns into a prior set of return assumptions to arrive at a bespoke asset allocation.

Part of what makes the Black-Litterman model unique is that it does not ask the allocator to necessarily come up with a prior set of expected returns.  Rather, it relies on equilibrium returns – or the “market clearing returns” – that serve as a neutral starting point.  To find these returns, a reverse optimization method is utilized.

Here, R is our set of equilibrium returns, c is a risk aversion coefficient, S is the covariance matrix of assets, and w is the market-capitalization weights of those assets.

The notion is that in the absence of explicit views, investors should hold the market-capitalization weighted portfolio (or the “market portfolio”).  Hence, the return views implied by the market-capitalization weights should be our starting point.

Going about actually calculating the global market portfolio weights is no small feat.  Plenty of ink has been spilled on the topic.[4]  For the sake of brevity, we’re going to conveniently ignore this step and just assume we have a starting set of expected returns.

The idea behind Black-Litterman is to then use a Bayesian approach to combine our subjective views with these prior equilibrium views to create a posterior set of capital market assumptions.

Specifically, Black-Litterman gives us the flexibility to define:

  • Absolute asset class return views (e.g. “I expect U.S. equities to return 4%”)
  • Relative asset class return views (e.g. “I expect international equities to outperform U.S. equities by 2%”)
  • The confidence in our views

Implementing Black-Litterman

We implement the Black-Litterman approach by constructing a number of special matrices.

  • P: Our “pick matrix.” Each row tells us which asset classes we are expressing a view on.  We can think of each row as a portfolio.
  • Q: Our “view vector.” Each row tells us what our return view is for the corresponding row in the pick matrix.
  • O: Our “error matrix.” A diagonal matrix that represents the uncertainty in each of our views.

Given these matrices, our posterior set of expected returns is:

If you don’t know matrix math, this might be a bit daunting.

At the highest level, our results will be a weighted average of our prior expected returns (R) and our views (Q).  How do compute the weights?  Let’s walk through it.

  • t is a scalar. Generally, small.  We’ll come back to this in a moment.
  • S is the prior covariance matrix. Now, the covariance matrix represents the scale of our return distribution: i.e. how far away from the expectation that we believe our realized returns could fall. What we need, however, is some measure of uncertainty of our actual expected returns.  g. If our extracted equilibrium expected returns for stocks is 5%, how certain are we it isn’t actually supposed to be 4.9% or 5.1%? This is where t comes back.  We use a small t (generally between 0.01 and 0.05) to scale S to create our uncertainty estimate around the expected return. (tS)-1, therefore, is our certainty, or confidence, in our prior equilibrium returns.
  • If O is the uncertainty in our view on that portfolio, O-1 can be thought of as our certainty, or confidence, in each view.
    Each row of P is the portfolio corresponding to our view. P’O-1P, therefore, can be thought of as the transformation that turns view uncertainty into asset class return certainty.
  • Using our prior intuition of (tS)-1, (tS)-1R can be thought of as certainty-scaled prior expected returns.
  • Q represents our views (a vector of returns). O-1Q, therefore, can be thought of as certainty-scaled P’O-1Q takes each certainty-scaled view and translates it into cumulative asset-class views, scaled for the certainty of each view.

With this interpretation, the second term – (tS)-1R + P’O-1Q – is a weighted average of our prior expected returns and our views.  The problem is that we need the sum of the weights to be equal to 1.  To achieve this, we need to normalize.

That’s where the first term comes in.  (tS)-1 + P’O-1P is the sum of our weights.  Multiplying the second term by ((tS)-1 + P’O-1P)-1 is effectively like dividing by the sum of weights, which normalizes our values.

Similar math has been derived for the posterior covariance matrix as well, but for the sake of brevity, we’re going to skip it.  A Step- by-Step Guide to Black-Litterman by Thomas Idzorek is an excellent resource for those looking for a deeper dive.

Black-Litterman as a Solution to Tactical Asset Allocation Problems

So how does Black-Litterman help us address problems #2-7 with tactical asset allocation?

Let’s consider a very simple example.  Let’s assume we want to build a long-only bond portfolio blending short-, intermediate-, and long-term bonds.

For convenience, we’re going to make a number of assumptions:

  1. Constant durations of 2, 5, and 10 for each of the bond portfolios.
  2. Use current yield-to-worst of SHY, IEI, and IEF ETFs as forward expected returns. Use prior 60 months of returns to construct the covariance matrix.

This gives us a prior expected return of:

E[R]
SHY1.38%
IEI1.85%
IEF2.26%

And a prior covariance matrix,

SHYIEIIEF
SHY0.000050.0001770.000297
IEI0.0001770.0007990.001448
IEF0.0002970.0014480.002795

In this example, we want to express a view that the curvature of the yield curve is going to change.  We define the curvature as:

Increasing curvature implies the 5-year rate will go up and/or the 2-year and 10-year rates will go down.  Decreasing curvature implies the opposite.

To implement this trade with bonds, however, we want to neutralize duration exposure to limit our exposure to changes in yield curve level and slope.  The portfolio we will use to implement our curvature views is the following:

We also need to note that bond returns have an inverse relationship with rate change.  Thus, to implement an increasing curvature trade, we would want to short the 5-year bond and go long the 2- and 10-year bonds.

Let’s now assume we have a view that the curvature of the yield curve is going to increase by 50bps over the next year.  We take no specific view as to how this curvature increase will unfold (i.e. the 5-year rate rising by 50bps, the 5-year rate rising by 25bps and each of the 2-year and 10-year rates falling by 25bps, etc.).  This implies that the curvature bond portfolio return has an expected return of negative 5%.

Implementing this trade in the Black-Litterman framework, and assuming a 50% certainty of our trade, we end up with a posterior distribution of:

E[R]
SHY1.34%
IEI1.68%
IEF1.97%

And a posterior ovariance matrix,

SHYIEIIEF
SHY0.0000490.0001820.000304
IEI0.0001820.0008190.001483
IEF0.0003040.0014830.002864

We can see that while the expected return for SHY did not change much, the expected return for IEF dropped by 0.29%.

The use of this model, then, is that we can explicitly use views about trades we might not be able to make (due to leverage or shorting constraints) to alter our capital market assumptions, and then use our capital market assumptions to build our portfolio.

For global tactical style premia – like value, momentum, carry, and trend – we need to explicitly implement the trades.  With Black-Litterman, we can implement them as views, create a posterior return distribution, and use that distribution to create a portfolio that still satisfies our policy constraints.

The Limitations of Black-Litterman

Black-Litterman is a hugely powerful tool.  It does, however, have a number of limitations.  Most glaringly,

  • Returns are assumed to be normally distributed.
  • Expressed views can only be on returns.

To highlight the latter limitation, consider a momentum portfolio that ranks asset classes based on prior returns.  The expectation with such a strategy is that each asset class will outperform the asset class ranked below it.  A rank view, however, is inexpressible in a Black-Litterman framework.

Enter Flexible Views with Entropy Pooling

While a massive step forward for those looking to incorporate a variety of views, the Black-Litterman approach remains limited.

In a paper titled Fully Flexible Views: Theory and Practice[5], Attilio Meucci introduced the idea of leveraging entropy pooling to incorporate almost any view a practitioner could imagine.  Some examples include,

  • A prior that need not be normally distributed – or even be returns at all.
  • Non-linear functions and factors.
  • Views on the return distribution, expected returns, median returns, return ranks, volatilities, correlations, and even tail behavior.

Sounds great!  How does it work?

The basic concept is to use the prior distribution to create a large number of simulations.  By definition, each of these simulations occurs with equal probability.

The probability of each scenario is then adjusted such that all views are satisfied.  As there may be a number of such solutions, the optimal solution is the one that minimizes the relative entropy between the new distribution and the prior distribution.

How is this helpful?  Consider the rank problem we discussed in the last section.  To implement this with Meucci’s entropy pooling, we merely need to adjust the probabilities until the following view is satisfied:

Again, our views need not be returns based.  For example, we could say that we believe the volatility of asset A will be higher than asset B.  We would then just adjust the probabilities of the simulations until that is the case.

Of course, the accuracy of our solution will depend on whether we have enough simulations to accurately capture the distribution.  A naïve numerical implementation that seeks to optimize over the probabilities would be intractable.  Fortunately, Meucci shows that the problem can be re-written such that the number of variables is equal to the number of views.[6]

A Simple Entropy Pooling Example

To see entropy-pooling in play, let’s consider a simple example.  We’re going to use J.P. Morgan’s 2017 capital market assumptions as our inputs.

In this toy example, we’re going to have the following view: we expect high yield bonds to outperform US small-caps, US small-caps to outperform intermediate-term US Treasuries, intermediate-term US Treasuries will outperform REITs, and REITs will outperform gold.  Exactly how much we expect them to outperform by is unknown.  So, this is a rank view.

We will also assume that we are 100% confident in our view.

The prior, and resulting posterior expected returns are plotted below.

We can see that our rank views were respected in the posterior.  That said, since the optimizer seeks a posterior that is as “close” as possible to the prior, we find that the expected returns of intermediate-term US Treasuries, REITs, and gold are all equal at 3%.

Nevertheless, we can see how our views altered the structure of other expected returns.  For example, our view on US small-caps significantly altered the expected returns of other equity exposures.  Furthermore, for high yield to outperform US small-caps, asset class expectations were lowered across the board.

Conclusion

Tactical views in multi-asset portfolios can be difficult to implement for a variety of reasons.  In this commentary, we show how methods like Black-Litterman and Entropy Pooling can be utilized by asset allocators to express a variety of views and incorporate these views in a cohesive manner.

Once the views have been translated back into capital market assumptions, these assumptions can be leveraged to construct a variety of portfolios based upon policy constraints.  In this manner, the same tactical views can be embedded consistently across a variety of portfolios while still acknowledging the unique objectives of each portfolio constructed.

[1] https://blog.thinknewfound.com/2017/07/four-important-details-tactical-asset-allocation/

[2] For clarity, we’re using “addressed” here in the loose sense of the word.  As in, “this is one potential solution to the problem.”  As is frequently the case, the solution comes with its own set of assumptions and embedded problems.  As always, there is no holy grail.

[3] By risk premia, we mean things like the Equity Risk Premium, the Bond Risk Premium (i.e. the Term Premium), the Credit Risk Premium, the Liquidity Risk Premium, et cetera.  Active Premia – like relative value – confuse this notion a bit, so we’re going to conveniently ignore them for this discussion.

[4] For example, see: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2352932

[5] https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1213325

[6] Those looking to implement can find Meucci’s MatLab code (https://www.mathworks.com/matlabcentral/fileexchange/21307-fully-flexible-views-and-stress-testing) and public R code (https://r-forge.r-project.org/scm/viewvc.php/pkg/Meucci/R/EntropyProg.R?view=markup&root=returnanalytics) available.  We have a Python version we can likely open-source if there is enough interest.

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