MPT and the Fiduciary Wars–Part 2

There have been a number of legal interpretations of fiduciary responsibility in terms of asset allocation and management for trustees, and much of this earlier interpretation focussed on MPT as a fiduciary’s obligation.   

The following are excerpts from documents written in 2004/2005 by a US firm Tulman Investment Advisory, now Trade Investment Analysis Group, who focus on expert witness services in securities litigation.   My comments are noted in between.

“The Prudent Investor Rule (Rule) gives personal representatives and fiduciaries both the authority and the requirement to consult the well-established principles, strategies, and tools of Modern Portfolio Theory (MPT). The Rule requires the test of fiduciary conduct be undertaken from a portfolio formulation perspective without considering the subsequent performance of the portfolio. “

MPT ignores valuation risks arising from significant cyclical and structural risks, that we have seen over the last 15 years, that are not properly valued.  These types of “out of equilibrium risks” cannot happen in a general equilibrium. 

It is inconceivable that fiduciaries are able to ignore these significant risks in portfolio construction planning and management. The only way that subsequent performance can be ignored is if expectations regarding return, standard deviation and correlation are either a) correct and this is an extremely tall order or b) sufficiently conservative as to have effectively discounted the risk that is being ignored.

In fact, you could say that the modern portfolio assumption that markets are efficient is as bad, if not worse, than the implied belief that high cost active fund management can en masse beat the market.  Each is the consequence of the other’s agenda.

“Formulation means assembling and maintaining a portfolio of assets with a risk tolerance suitable for the purposes, term, distribution requirements, and other conditions of the trust. MPT guides the fiduciary in constructing and managing a portfolio that provides the highest expected return for that risk tolerance. The responsible fiduciary must do no less. “

A couple of issues here:

Number 1, the only way to test if the MVO portfolio is suitable for distribution requirements and term, under MPT, is to run a Monte Carlo simulation, but the Monte Carlo suffers from the similar weaknesses – it assumes you start from an equilibrium point (even if you do fatten the tails), that returns are random and independent and ignores the potential return distribution from out of equilibrium conditions. Quite often in highly valued markets, with significant structural and economic risks, the Monte Carlo analysis will fail to capture risks to the ability of assets to meet liabilities given unpriced risks in the market place.

Number 2: even under MPT there can be no real fixed expected return.  This can only happen if the dynamics of the universe are constant – when the world is deleveraging, or leveraging up the dynamics are changing all the time.  MPT takes expected to mean the average expected return of a probability distribution of standard deviations in a general equilibrium – this means that there are thousands of potential outcomes, even in a perfect MPT scenario.  The expected return under general equilibrium is the average of thousands of reruns of which the current path is only one.  There is no certainty in a random path independent equilibrium.

Asset prices, whether in equilibrium or not, have to price for uncertainty when in fact there are clearly times when asset pricing depends quite heavily on unduly optimistic or pessimistic expectations that conform to neither reality.

Number 3: return expectations taken from an historical data set are biased by the single thread of that time series. Reliance on historical data, without adjustment for outsized out of equilibrium risks should, one would assume, be tantamount to negligence.  Even those return assumptions taken from the Black Litterman model require an estimate of the risk premium an input for the equilibrium risk free rate (amongst other assumptions), and assumptions regarding the users views of returns and confidence in those returns.  If risk premiums are drawn from historical averages there is a feed back loop from historical data into the model that may be at odds with the current covariance structure.

“…Finally, MPT requires that the fiduciary develop defensible expectations of return and risk for all potential assets. …Further, we allude to the potential damages or surcharges associated with the inefficient allocation of assets and/or mistaken determination of an appropriate portfolio risk level…”

Again, there is no guarantee that MPT will provide an efficient portfolio or that expectations of return and risk will be correct.  In a sense, in as much as they ignore out of equilibrium risks, they are indeed indefensible.

“The relationship between the Act and MPT implies that fiduciaries ignoring the tenets of MPT are potentially inconsistent with the Act and the Rule and may put themselves at risk.”

“The primary rule of MPT is the following dictum: For every level of expected risk, a portfolio can be constructed to achieve the highest expected return or, alternatively, for any given level of expected return, a portfolio can be constructed to have the lowest expected risk. “

Again, this assumes a linearity that simply does not exist in reality: in anything other than a stable general equilibrium, with a normal probability distribution of random independent price movements, the stated stability of risk and return expectations under uncertainty simply does not exist.

“The expected return of any portfolio can be forecast in a relatively straightforward manner: it is the weighted average of the expected returns of the assets in the portfolio…..”

“The risk (standard deviation) of a portfolio, ….encompass the inter-asset correlations or how each asset moves with every other asset in the portfolio. Because the portfolio is the appropriate level of analysis under the Rule, estimating the expected returns, standard deviations, and correlations for every asset in the portfolio are all reasonable duties of the fiduciary….”

Estimating the inputs of a mean variance optimiser are far from easy or reliable and problems associated with input estimation are well known. In an out of equilibrium world, point in time price volatility and factors affecting demand and supply that drive correlations are more important than the longer term equilibrium parameters used. What is more, standard deviation does not provide much information regarding absolute or relative valuation risks (i.e significant market pricing errors) and as such correlation is under used as an efficient allocation method.   

“The importance of asset return correlations is probably the most practical contribution of MPT and constitutes the portfolio effect. This effect means that the fiduciary cannot make portfolio decisions by viewing the risk and return characteristics of one asset or asset class in isolation but must take into account how this asset’s return correlates with all the other assets in the portfolio. “

“It follows from the Rule and MPT that a fiduciary should adopt the portfolio that provides the appropriate level of risk and lies on the Efficient Frontier (providing the highest expected return for that level of risk).”

“That is, how the portfolio actually performs (realized returns) is not the standard of judgment —rather it is the fiduciary’s formulation of the portfolio that should be evaluated.”

It is naïve to believe that it is possible to know whether a portfolio actually lies on an efficient frontier, especially when we are ignoring out of equilibrium risks within a linear general equilibrium model used to construct a portfolio.

“In the absence of compelling evidence that the future will be materially different than the past (at least over the life of the trust), the fiduciary determines to extrapolate the historical record to develop expected returns, standard deviations, and correlations.”

Again even within MPT circles, there is much agreement over the problems that these linear models are exposed to when using historical data.  Extrapolating the historical record is a risky proposition, but it has not stopped people from using historical data.

“A fiduciary who rejects risky assets without considering their possible role in enhancing portfolio return is inconsistent with the Rule and MPT.”

Only if a risky asset is properly priced could you afford to take this position. Blindly adding assets because their co-variances allow you to smooth portfolio standard deviation is risky and again ignores risks that the MVO and MPT models do not evaluate. 

“Fiduciaries are thus bound to consider MPT in constructing the portfolio under their control. To do otherwise exposes the fiduciary to claims of misconduct and the resulting potential assessment of damages and surcharges more defensible practice would be for the fiduciary to begin with the portfolio recommended by MPT. The tools to develop these portfolios are readily available to investment practitioners and should pose no barrier to the conscientious fiduciary. To ignore these tools places the fiduciary in a precarious position.”

“For the IPS to be considered appropriately constructed, its contents must be consistent with tenets of the Prudent Investor Rule (Rule) and Modern Portfolio Theory (MPT).”

There is far too much blind faith in the ability of academic models to deal with the reality of markets and human behaviour.  While portfolio structure needs to allocate according to risk, relative price movements and hence return, it also needs to be structured with respect to the impact of out of equilibrium risks on the ability of assets to meet financial needs over time.   

That MPT ignores absolute and hence relative valuation risks, is indefensible.

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