Portfolio Navigation For DB Plans


Frank Sortino & Hal Forsey[1]

                          `Would you tell me, please, which way I ought to go from here?’                           `That depends a good deal on where you want to get to,’ said the Cat.                                                                                                             Lewis Carroll



Some people give advice on how to manage pension fund assets. Others focus on the liabilities. We focus on the link between the two; The Desired Target Return®. If you don’t know your DTR®, you don’t know how to get from where you are to where you need to be.  At any point in time the DTR is the return that must be earned on assets in order to return to a fully funded status within a designated time horizon.[i]  This can be viewed as a navigation problem.  Let’s assume the relevant actuarial statistics are as follows:

Table 1 00000000
PV of future benefits 60
Assets 60
Discount Rate 4.00%
Yearly Benefit 2.832
DTR 4.00%
PV of PV of
Year Assets total benefits annual benefits
0 60 59.99769493 2.832
1 59.568 59.45232273 2.723076923
2 59.11872 58.88513564 2.618343195
3 58.6514688 58.29526106 2.517637688
4 58.1655276 57.68179151 2.420805469
5 57.6601487 57.04378317 2.327697566



When setting up the plan the actuary assumed a discount rate of 4% on projected liabilities and a yearly benefit ($283.2M discounted to present value at the discount rate) in order to solve for the contribution schedule on this $6 billion dollar plan (add 8 zeros).  The plan is assumed to be fully funded at the top of the market in 2007, after the year 2000 high-tech sell off and the 9/11 attack on the twin towers.  Table 1 indicates a DTR of 4% would maintain the fully funded status for the next five years without any further contributions.

PMPT Portfolio Construction:

We recently asked a large institutional investment advisory firm to provide us with five asset allocations for portfolios with absolute returns of 4%, 6%, 8%, 10%, and 12%.[ii]  Each portfolio was constructed as described in a recent book.[iii]  Figure 1 shows the portfolio we constructed for their 8% absolute return strategy, given their manager data base.  We did not want to know the names of their active managers so they used a number for each category (e.g., LG – 20 is the 20th large growth manager).

Figure 1 (Absolute 8% return portfolio)

This portfolio may well have had only an 8% average using historic returns for the past few years but our methodology indicates the mean of their asset allocation using passive indexes is 9.5%.  When we include their active managers when they add value and ETFs when they don’t, the mean is 12.5%.  The DTR-alpha indicates their active managers could add 300 bp in any given year.  The Upside potential ratio indicates the actual portfolio with active managers has 30% more upside potential than downside risk (1.3) while a totally passive portfolio would have 20% more downside risk than upside potential (.8).  We believe this is useful information not contained in the Sortino ratio or Sharpe ratio.  We assume this is the portfolio the plan has had for some time and they simply rebalance each year to maintain this asset mix.

Portfolio Navigation

The Portfolio Navigation strategy begins with a DTR 4 portfolio because that is the internal return that discounts the liabilities to the present value of the assets. However, this portfolio does have the potential to earn 590 basis points more than the DTR in any given year.[iv]

Figure 2 traces the results for the 8% absolute strategy (AR-8) and the DTR-Portfolio Navigation strategy (black dashed line) beginning at the top of the market in May, 2007 when the S&P 500 was at 1425 on its way to a 50% decline by February of 2009.  We chose 8% as the bogey in Figure 2 because it is a popular return that actuaries assume will be earned on assets.  The assumed rate of return on assets does not figure in determining the present value of the liabilities but under FAS 87 it can affect what the firm declares as profits.


Figure 2 – Fully Funded

Actively Managed (DTR) vs an 8% Absolute return

As shown in Figure 2, whether one used Portfolio Navigation, an 8% absolute return strategy or simply bought the S&P ETF (SPY), the plan would have returned to a fully funded status in four years as indicated by the red dotted line that declines as benefits are paid each year. However, all happy endings are not the same.  The absolute return strategy was down 32% when the market finally bottomed while the DTR strategy was only down 11.7%.  Also, the DTR strategy is more than a billion dollars better off after four years.  How was this achieved?

In Figure 2 the DTR was calculated at the end of every quarter and when the asset value reached $5.77B the DTR increased to 6%. At that point the allocation to equity was increased from 30%, as given in the 4% portfolio, to 45% in the 6% portfolio.  Importantly, this change was not due to an economic forecast or some market timing strategy.  Based on the funding status, it was the return calculated to return to a fully funded status within a 5 year interval.  Five years is not a magic number that must be used in portfolio navigation.  We did so, so as not to be accused of making propitious changes with 20/20 hindsight.  We chose it before conducting the study and purposefully did not try other intervals.  In practice we would present the plan sponsor with other options.

Less than a year later the pension assets were down another $470 M and the DTR was calculated as 8% as shown in Figure 2. Again, in less than a year, the DTR was calculated to be back to 4%.  Would a pension fund have been willing to make such changes, buying as the market crashed and selling as the market recovered.  Well, that’s better than doing the opposite.  Of course, the pension committee would have to make that decision each time the DTR changed and they would want some evidence to support the decision.  This study is intended to provide that evidence.

The Underfunded Case

What if the pension plan was underfunded at the beginning of this study? Figure 3 illustrates the results if the plan had a shortfall in May of 2007.  All the statistics in Table 1 were kept constant except the pension assets were assumed to be $5.37 B.  In this example the plan would return to fully funded status if it earned 6% for the next 5 years.  This time we compare Portfolio Navigation (black dashed line) to absolute return strategies of 4%, 6%, 8%, 10% and 12%.  All absolute strategies are rebalanced annually.  The DTR- Portfolio Navigation strategy begins with a DTR of 6% and changes three times over the next four years.

After four years none of the strategies has succeeded in returning to a fully funded status. Portfolio Navigation does not guarantee success anymore than navigation aids for air travel guaranty one will reach their destination.  In both cases it is a matter of improving your odds of success.  Navigation has steadily improved over the decades to become a reliable science.[v]  We are a long way from that level of reliability. What if the market never recovered?  What if the airplane crashes?  Risk is situation specific.  The way one should measure the risk of flying is not appropriate for measuring the risk of investing in financial markets. We have set forward in books and papers what we believe to be an improvement in the way to calculate risk and reward when investing.  This paper describes a way to use these improvements as tools to navigate from where a pension plan’s assets are to where they need to be over a prescribed time horizon.


[1] Frank Sortino is Professor Emeritus in Finance and Hal Forsey is Professor Emeritus in Mathematics from San Francisco State University, California.

Figure 3 – Under Funded

                                       (DTR® vs Absolute Return Strategies)

The reason the DTR strategy stays at 8% for the last two years is that time is running out in the initial 5 year horizon. Of course the pension committee could decide to reset the time horizon to 3 years or more in May of 2011.  The operative questions are: as fiduciaries, do they know how much risk they will be taking to get from where they are ($5.58 B) to where they want to be ($5.7 B) in just one more year?  Is that too much risk? Should they start making contributions and/or increase the time horizon?  These are questions that have an answer, if you have the right tools.

Throughout this study we have assumed the goal was to fund the plan within the cost constraints provided by the actuary. The investment objective then became, maximize the potential to exceed the DTR relative to the risk of falling below the DTR.  What if the goal was to maximize the excess return of the assets over the current costs in order to increase earnings?  Even so, there is still some return that must be earned in order to accomplish that goal and the investment objective remains the same.  It is simply another application of Portfolio Navigation for another Desired Target Return®.







  • Constructing a portfolio around the assumed actuarial return on assets ignores the link between pension assets and pension liabilities.       Therefore, constructing a portfolio around that link, the DTR®, makes more sense. Likewise, the mean and standard deviation and beta are also unrelated to the link between assets and liabilities.
  • Absolute return strategies come in many forms. Some attempt to minimize the risk of falling below a specific return that may or may not be related to the funding ratio and totally ignore the upside potential. We have written our opinions about this subject on our blog, pmpt.me (see, “Absolute Nonsense”).
  • Portfolio navigation outperformed a wide range of absolute return strategies with less downside risk during one of the worst stock market periods in our history.
  • It also outperformed all absolute return strategies when the plan was underfunded and began with a 6% DTR or 8% DTR (available on our website download folder).
  • Maintaining the same asset mix by rebalancing may have been appropriate in bygone years, but not in today’s volatile markets. In the last twelve years we have witnessed three major disruptions in the financial markets and we are still suffering from the last one. We believe it is time to find a new way to reach your destination. This study offers a way to accomplish this with less risk in a manner that is understandable.

[i] This could be calculated by any actuarial firm as the internal rate of return that discounts the projected liability stream to present value.  All we are using in this study is the statistics shown in Table 1.

[ii] These are the asset allocations provided:

[iii] “The Sortino Framework for Constructing Portfolios,” Elsevier Publishing 2010 (see Amazon.com).




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Defining Risk Video

Many people are talking about risk in a way that has nothing to do with what is at stake.  The myRA  bond introduced by President Obama at his state of the union address is the latest example.  This 3 minute video is my explanation of what is at stake. The 2nd video is a 4 minute video on Portfolio Navigation.  The 3rd video is an interview with the former CEO of The City and County of San Francisco Retirement System and an interview with professor Sam Savage of Stanford University.  The full 30 minute video that covers the research findings of the past 30 years is available at the KMVT link below the interview video.


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Portfolio Navigation Update

Dr. Frank Sortino discusses a better way to make asset allocation changes than either rebalancing or LDI. (SEE Also November 2012 under Archives)

This is a 5 minute clip from a 30 minute video produced at KMVT Studios in Silicon Valley. (For the full video0 (Click on  KMVT Channel.)

Isn’t this just like…(insert phrase) is what we often say when someone describes something new to us.  No doubt Einstein heard, “isn’t that just like Newtonian physics”? when he presented e = mc2 .  After all, physics is physics.   At a much lower level of complexity, we have heard some comparisons that need clarification.  The video explains how Portfolio Navigation is different from rebalancing and LDI but it does not address two other faulty comparisons.

  1. Isn’t this just another form of momentum investing?  Perhaps the most notorious form of momentum investing was called Portfolio Insurance, developed by two professors at U.C. Berkeley.  It involved a mathematical formula for increasing equity exposure as the market went up and decreasing exposure as the market went down.  Yes, Portfolio Navigation does involve mathematics but the underlying methodology seeks to do quite the opposite, i.e., a large rise in the market will cause the DTR to decrease, thus decreasing equity, because you will then need a lower rate of return to achieve your desired pay out.  Whereas Portfolio Insurance failed in 1987 because they were trying to unload positions as the market crashed, Portfolio Navigation would be increasing equity exposure after a decline sufficient to increase the DTR.  The market place could not accommodate all sellers and no buyers but it would have welcomed our buy orders.

 In the study performed ex ante at P&I magazine in 2000 the high tech mutual funds of 1998 were replaced by  large cap value and Income and growth funds.  With the CIFs managed at Fiserv , the change in the UP ratio and DTR alpha resulted in a decrease in equity in mid 2007.

  1. Isn’t this just doubling down?  A strategy in the Black Jack card game calls for doubling your bet when you lose as a way to recoup losses.  Yes, Portfolio Navigation increases equity exposure as the portfolio value declines,  but only enough to get back on course to obtain a DTR  needed to achieve your desired payout.  Doubling the equity exposure would be a crude and foolish strategy.
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PMPT Interviews with Clare Murphy and Dr. Sam Savage

This video is another clip from a half hour program produced at KMVT in Silicon Valley. The clip is an interview with the former Executive Director of the City and County of San Francisco Retirement System, Clare Murphy; and Dr. Sam Savage from Stanford University.
The important thing to take away from my interview with Clare is the changes she introduced during her 25 year tenure as CEO. As the assets under management grew from $600 million to $16 billion the use of outside active managers grew from approximately 10 to 40 managers. This constituted about 80% of the AUM. This is contrary to the view that the more money one has the more you rely on passive indexes. Clare was on the cover of Institutional Investor Magazine in 2005 and was semi finalist for public fund of the year award.
Sam has written an excellent book titled, The Flaw of Averages. It is the best book on interpreting statistics I have read, and it is written for practitioners, not statisticians. Sam mentions the work of Bradley Efron who received the National Medal of Science award in 2007 for his bootstrap methodology. The National Medal of Science is an honor bestowed by the President of The United States on those who have made important contributions to the advancement of knowledge in the sciences.
Sam says, Efron is one of those rare individuals who straddle a technological divide. Schooled in classical statistics, he inspired a revolution that supplanted it. Efron’s work has been critical to my own. I believe it is a quantum leap forward from what currently passes for estimating “the shape of the future “ Sam describes and what I call the shape of uncertainty.
If you would like to see the complete video go to the KMVT Channel.

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Portfolio Navigation History

A new approach to guiding portfolios through storms in financial markets.

A brief history of navigation:
The magnetic compass was first invented by the Chinese in AD1080 but it was not used for navigation until AD 1111. Knowledge of the direction pointing North made it possible to estimate the direction one was heading. That was useful when a ship was leaving the harbor, but useless when one was out of sight of land. Until the 17th century sea captains relied on guesses about the currents, winds and speed to estimate their location. This was called, “dead reckoning”, probably because it often marked the crew for dead if the estimates proved wrong.
Due to coastal fog, many ships missed the harbor entrance to London and ended up on the rocks. This caused the King of England to offer the equivalent of a million dollars to the man who could solve the longitude problem. Everyone knew how to obtain their latitude, so knowing the longitude would fix their location where the two lines crossed. In 1736 an unknown amateur watch maker created a watch that solved the problem. Unfortunately, he lacked any formal training in watch making as well as any academic credentials, so his solution to the problem was blocked by the learned establishment for the rest of his life. The result was, John Harrison died a pauper and many lives were lost unnecessarily.
When I was in the U.S. Air Force, navigation training still began with dead reckoning and every flight plan began with estimates of the winds aloft, the lines of magnetic variation we would cross and our planned airspeed, all of which never proved correct. So the essence of navigation remained the same: determine your current location periodically and plot a new heading to your destination. It would have been unthinkable to “stay the course” in hopes that friendly winds would blow you back on course.
Portfolio navigation:
I believe the basics of navigation apply to portfolio management. If we view the client’s portfolio as a vehicle that needs to be navigated through financial markets, wouldn’t the return needed on the portfolio be akin to the heading the portfolio manager needs to steer in order to reach the planned destination? We call that heading the Desired Target Return® or DTR®. And if financial storms blew the portfolio off course, wouldn’t the ability to plot a new DTR to the desired destination be preferred to “staying the course?

This view challenges the basic assumptions about why people invest and how best to manage those investments. Portfolio Navigation assumes people are trying to get from where they are financially to where they need to be at some specified time in the future. More specifically, they want to reach a financial goal that provides a certain payoff that will achieve the goal. If a 401(k) investor wants to replace 70% of salary at retirement, doesn’t that define the goal and allow a reasonable estimate of where the portfolio needs to be in order to make that payout at retirement? Viewed as a navigation problem, would it make sense to put an investor in one portfolio until retirement and say, “just stay the course and maybe you’ll get there”? Only if one has no knowledge of portfolio navigation.

Just as the compass was the beginning of the science of navigation, Modern Portfolio Theory was the beginning of a new science of portfolio management. Portfolio Navigation provides a way to use the compass, along with the equivalence of longitude and innovations in equipment, to navigate the financial markets of the world and bring the portfolio safely to its desired destination. We hope this will prevent many portfolios from ending up on the rocks.

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Real Engineering versus Financial Engineering

Here are two clips from e-mails I have received. The first is from a leading European University that teaches financial engineering. The second is from the prospectus of a fixed income mutual fund company. The first is a theoretical argument. The second is a CYA disclaimer statement.



Ever since the CAPM claimed that it was less risky to borrow money and invest it in the market portfolio than invest in a portfolio on the efficient frontier that lies below the security market line, both academics and practitioners have argued that leverage and going short are beneficial strategies for investors. Of course, the CAPM assumes there is such a thing as a risk-free rate and investors can lend and borrow at that rate, plus a few chapters of additional assumptions. Financial engineering is the latest development in this theoretically correct but practically wrong ruse. I am not opposed to the use of derivatives to alter the risk-return characteristics of portfolios but we need to keep in mind that engineers build real things and we build paper things that do not hold up unless a lot of assumptions prove to be correct. The misuse of financial instruments is not solely responsible for the financial collapse of 2008 but is certainly not blameless and does need to be regulated, not eliminated, to prevent future avoidable calamities.

I agree with professor Ducoulombier-investors should be fully informed of the risk-return characteristics of esoteric strategies. The investor should be entitled to the same disclosure protections by the SEC as the FDA provides to consumers of medications. For example:

  1. The investor should be told the percentage of the portfolio in derivatives, the resulting leverage and the effect that could have on losses, fees and expenses.
  2. An explanation of the assumptions being made should include examples of the consequences if those assumptions do not hold and a record of past occurrences.

“Order is indeed the dream of man, but chaos, which is only another word for dumb, blind, witless chance, is still the law of nature. You can plan all you want to but… “ Wallace Stegner

We are told that there is nothing to fear now. The fiscal cliff….a thing of the past. The sequester disaster….came and went. To paraphrase Stegner, never underestimate Govertment’s ability to make dumb, blind witless decisions that will upset the plans of learned men and women.

The flaws in our global financial system have not been corrected. That’s a shark that is still swimming out there in our sea of contentment. The promises of Governments, businesses and theories to transform our world of uncertainty into something we can count on have been proven unreliable. That pension benefit you were promised….here’s your 401(k), lots a luck. Remember this: we live in a world of uncertainty. There isn’t any knowing what is going to happen. But, there is a professional way to manage that uncertainty that might tilt the odds in your favor. That’s as good as it gets.

So, what are we professionals to do for those who put their trust in us? DON’T LET THEM SWIM WITH SHARKS! Make them stay in unleveraged shallow water. Don’t let them go beyond the diversified reef that provides some modicum of protection. Chasing the next Google will attract sharks.

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The Glidepath Obfuscation

Much attention has been given to the matter of the proper glidepath for 401(k) participants.  Most recently Rob Arnott, founder of Research Affiliates, has weighed in on this subject.  Arnott’s criticism of any mechanistic glidepath,[1] was in turn criticized by Steven Wallman[2] for missing the point that a glidepath reduces risk.   Arnott then accused Wallman of missing the point because “the numbers are what they are” and the numbers show a reduction in return that offsets the reduction in risk.  Well, Arnotts contrived numbers may show that but in my opinion, they are both missing the point.  To paraphrase Einstein, they are trying to solve today’s problems with outmoded methodologies of the past.

The main flaw in their logic is that both of them choose to ignore the return that each 401(k) participant needs to earn on their assets in order to meet a future payout, namely, retirement income. Both gentlemen choose not to estimate this return that we call the Desired Target Return® or DTR®.  Ipso facto, ignoring the DTR makes it impossible to calculate the risk of falling below the DTR or the potential to exceed that return.  In other words, they have identified the wrong problem which leads to the wrong solution to the real problem.

Framing portfolio management as an asset management problem leads both men to focus on which assets to use to achieve the highest terminal wealth.  Wallman says young people should start out with stocks and end up in bonds to reduce the risk of a hit to terminal wealth.  Arnott says investors would more often have ended up with greater wealth if they started out with bonds and ended up in stocks.  We agree with Wallman that 401(k) participants who wanted to retire in 2008 should not have been heavily weighted in stocks in 2007.  We also agree with Arnott that age alone should not determine the asset allocation between stocks and bonds and starting to decrease equity 20 years before retirement is ridiculous.

But gentlemen, investing is an asset-liability management problem, not an asset management problem.  Stocks and bonds are only the vehicles we use to get investors from where they are financially to where they need to be at some point in the future.  Your argument is as foolish as debating whether or not people should begin every trip by air or by bus.  The proper combination and timing of vehicles depends on where they are going and where they are starting from, not on their age or their preferences.

Lest we be misunderstood, we have the greatest respect for Rob Arnott and his understanding of financial theory.  He was, after all, the editor of the Financial Analysts Journal.  But let’s see how his adherence to the MPT framework leads him astray as regards a much needed solution to managing 401(k) plans for participants.


  1. Arnott uses 141 years of stock and bond market returns to make the case that “Prudent Polly”, who begins at 22 years of age with an 80% equity position and at age 30 begins her descent in equity until age 63, at which time, she liquidates her portfolio and purchases an annuity with the funds she has accumulated.  With 20/20 hindsight he shows she could have done better by maintaining a 50/50 mix of stocks and bonds or steadily increasing equity exposure.  This implies history is going to repeat itself, an assumption he later decries.  We believe Bradley Efron’s “Bootstrap” procedure is a superior way to describe future return distributions and provide evidence in our paper titled, “Portfolio Navigation”  that a glidepath longer than five years is like starting your descent into Kennedy Airport when you are over Chicago.
  2.  Arnott uses three measures of risk to make his point: the standard deviation of returns for the past 141 years, the range of returns from the 10th percentile to the 90th percentile and the ratio between the 10th and the 90th percentiles.  However, none of these risk measures incorporate the return Polly needs to earn in order to replace a predetermined percentage of salary. Furthermore, we have shown that reliance on the probability of a low return for capturing the risk that Polly is facing is inadequate and misleading.[3]  The disastrous results of using Value at Risk (VAR) in 2008 testify to that.   We believe a relevant measure of risk should capture the risk of not achieving the retirement income she needs and propose deviations below her DTR as a more appropriate risk measure.
  3. Arnott then says it is much more important for Polly to know “how large a lifetime inflation-indexed annuity she can buy at retirement” because that is “an important measure of success.”  In other words, Polly is stuck with whatever amount of money she is lucky or unlucky enough to accumulate at retirement, because nobody bothered to estimate how much she would need to replace, say, 70% of her salary at retirement.  This implies the goal is to make as much money as she can.  We believe the goal is to replace 70% or more of her income and the way to measure that is to estimate the potential to exceed her DTR.
  4. Arnott then calls attention to his assumption that she was only saving $1000 per year and nothing can make up for investing too little too late.  We agree, but believe an appropriate methodology would notify her periodically how much more she needs to invest, as we do in our Mapvest® report.
  5. Arnott then attempts to correct for assuming the past is prologue by randomly drawing annual returns from the 141 years of annual returns to generate a better picture of uncertainty.  However, first he attempts to make the outcomes look more like today’s by assuming “ risk in the future resembles the past but returns in the future are lower.”  This ad hoc adjustment seems to imply his methodology is flawed. Furthermore, only selecting annual returns that did happen cannot account for what has never yet happened.  But the bootstrap procedure does address this without subjective adjustments.  We believe the methodology we used in our paper “Portfolio Navigation™” is a superior way to compare strategies and leads to a more reliable way to manage Polly’s portfolio over time.

Summary and conclusions:

Instead of framing portfolio management as an asset management problem where the solution is to maximize wealth and whoever makes the most money wins, we believe one should frame it as an asset-liability management problem.  From this perspective, the solution more closely resembles a navigation problem that will transport Polly’s portfolio from where it is to where it needs to be at some specified time in order to meet or exceed an estimated payout schedule.

Bickering over trivial matters like the glidepath only serves to obscure the real problem.  Target date funds are a dismal failure, yet the most popular choice for defined contribution plans.  Therefore, instead of trying to fix a seriously flawed methodology, we should all work to scrap it for a superior approach oriented toward accomplishing the investor’s real goal of replacing income at retirement.  Making money is not the goal in and of itself.  Making money is how one accomplishes the goal of meeting or exceeding some specified future payout. How much money is needed and how much risk is involved can only be determined if one bothers to estimate the DTR. This is a critical variable that should no longer be ignored.

[1] RA Fundamentals, September 2012

[2] www.fa-mag.com, November 19,2012

[3] The Sortino Framework for Constructing Portfolios, pg 27.

Download this post as a pdf:  The Glidepath Obfuscation

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