PMPT Marries Prospect Theory

Introduction:

 Believing in a theory as evidence mounts disproving its merits will lead at first to disappointment and then to a better theory.  Concocting a strategy that solved the previous market fiasco without any theoretical foundation will lead nowhere.  All will soon discover you never believed in anything except making money…for yourself.

After 12 years of chasing various strategies to dead ends, I returned to academia for nine years to learn what there was to know about managing uncertainty in financial markets.  I believe theories provide a belief system that serves as an aid for getting the job done and the job is to help investors accomplish their financial goals.  We must remember that theories are beliefs based on assumptions, not facts and when you start treating assumptions as facts you are in big trouble.  Still, a theoretical foundation is better than a “get a hunch bet a bunch strategy.”

The key, I believe, is to maintain a questioning mind.  The idea that we should not act in the best interests of investors because it calls into question some theory we believed, or that it contradicts something we said in the past, is egocentric nonsense.  There was a time that I believed the Sortino Ratio was the best way to measure performance.  When the evidence began to accumulate in the 1990’s that I was wrong, I wrote a paper pointing out the flaw and posted it on my website.  Then I began work on a better measure.  I didn’t wait for the new “upside potential ratio” to be developed and tested before discarding a flawed statistic.  Those who continue to use it do so because it makes their performance look better than they are.[1]

In chapter 26 of “Thinking Fast and Slow” Daniel Kahneman points out some of the flaws in Prospect Theory, starting with when the reference point is assumed to be zero   He goes on to say,  “Prospect theory has flaws of its own, and theory induced blindness to these flaws has contributed to its acceptance.”  That led him to posit a two system approach to understanding the decision making process of human beings.  System 1 deals with intuitive responses that are automatically and effortlessly arrived at.  System 2 is concerned with the deliberate and effortful mental activities associated with quantitative reasoning.  I like to think of our approach to investing as being associated with System 2.

Kahneman worked closely with Amos Tversky to develop  a body of work that came to be known as behavioral economics.  Dr. Hal Forsey and I have worked closely for many years to develop a body of knowledge that has come to be called post modern portfolio theory or PMPT.  I was a professor of finance while Dr. Forsey was a math professor.  We tried to find solutions to the biases identified by researchers like Kahneman and Taversky (K&T).  We drew on the research of a number of theoreticians that we examined in order to develop a theoretically based strategy for managing portfolios.  The strategy is called Portfolio Navigation.

The purpose here is to point out how we attempt to incorporate some of the findings of K&T in our strategy.  K&T pointed out that classical utility theory lacks a reference point from which to evaluate gains and losses.  They said the reference point may be an outcome to which one feels entitled (e.g., retirement income).  We call this reference point the Desired Target Return® or DTR®. Returns below the DTR incur risk of not accomplishing the goal.  Returns above the DTR are the gains in excess of what is needed.  Prospect Theory implies losses loom larger than gains.  We agree (see Figure 2).

The S shaped utility function of prospect theory in Figure 1 indicates investors are risk averse to returns above the DTR and become risk takers for returns far below the DTR.

Figure 1

This may well be the way people behave but it is contrary to one of the oldest strategies on Wall Street, “Ride your gains and cut short your losses.”  People like Bernard Baruch used this simple rule of thumb to overcome some of the System 1 responses that Khaneman uncovered.   The foolishness of ignoring a small probability of a disastrous outcome can be illustrated by considering the small probability of a parachute not opening.  Something akin to considering only the probability of a mechanical failure while ignoring the magnitude factor of breaking every bone in your body after plummeting to earth is foolhardy at best and should never be offered to clients as a low risk strategy.

Peter Fishburn proposed the utility function in Figure 2 .  We view it as a System 2 type theory of choice.

Figure 2

 Figure 2 indicates people should figure out what return they need to achieve in order to accomplish some financial goal.  Fishburn called that the target rate of return.  We call it the DTR®.  This seems a more sensible way to behave.  Investors are viewed as risk neutral for achieving returns above the DTR.   They like the notion of acquiring greater wealth than they need; yet they are risk averse to losses that result in failure to achieve their goal.   When Hal Forsey and I built our first optimizer we set the investment objective as, maximize the expected return for a given level of downside risk.

Then I became aware of the behavioral research of Shefrin and Statman at Santa Clara University.  They cited studies that showed what investor’s really want is a portfolio that gives them “upside potential” but protects them against “downside risk.”  However, the studies used only probabilities to measure these concepts subjecting investors to the “faulty parachute” type of reasoning.  Hal and I corrected this error with the following mathematical changes that penalize losses by squaring the differences of returns below the DTR while only taking simple differences for returns above the DTR.

Figure 3

Recent findings in neuroscience provide evidence that a System 2 approach that captures what investors intuitively want but don’t know how to quantify should be superior to asking them to fill out a risk tolerance questionnaire they don’t understand.  It seems that the part of the brain just inside our temples, called the dorsolateral prefrontal cortex is involved with events in the outside world that require explicit, analytic and rule based reasoning.  The part of the brain behind our forehead deals with emotions, whether something is good or bad, and is called the medial prefrontal cortex.  Preference questionnaires require the wrong part of the brain, the emotional part, to deal with events in the outside world (like portfolio management) instead of the rational part of the brain. This led us to develop a new optimizer.

Theory or  Strategy?

 Interestingly, the theoretical differences between Prospect Theory and our approach disappear in our portfolio navigation strategy.  For example, we calculate the DTR as a return that must be earned on the assets in order to meet some future payout or liability.  If market circumstances cause the DTR calculation to change, we change the asset mix of the portfolio.  The result is that after a series of gains that changes the DTR from say, 8% to 6% we reduce the equity exposure to one that is commensurate with a 6% return.  The result is, we are telling the investor to take less risk, which is consistent with prospect theory.  If a series of losses cause the DTR to change from 8% to 10% we increase equity to achieve the higher return.  In effect becoming risk takers after a substantial decline in the portfolio value.

In other words, by framing portfolio management as a navigation problem instead of a wealth maximization problem we systematically change the reference point in prospect theory to achieve a desired outcome.  The result might be said to rationalize what we said previously was an irrational theory.  So what?  So long as it benefits investors we will use it.

Is Portfolio Navigation a theory or a strategy or a theoretically based strategy?  We don’t care.  It is more than just a hunch and we plan to use it…but will keep an open mind for better navigational tools to get investors from where they are financially to where they need to be.


[1] See chapter 3 of “The Sortino Framework for Constructing Portfolios.

About Frank Sortino

Frank Sortino is finance professor emeritus from San Francisco State University and Director of the Pension Research Institute which he founded in 1981. For 10 years he wrote a quarterly analysis of mutual funds for Pensions and Investments Magazine and he has written two books on the subject of Post Modern Portfolio Theory. He has been a featured speaker at many conferences in the U.S., Europe, South Africa, and the Pacific Basin. Dr. Sortino received his Ph.D in Finance from the University of Oregon and has carried out research projects with many institutions like Shell Oil, Netherlands and The City and County of San Francisco Retirement System.
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