“Realativity”
in Finance: How a Simple Assumption Led to Many  

Investment
theory has implications for asset allocation, asset pricing and risk-adjusted
performance. The statement in finance that “investors maximize the utility of
wealth, is largely incorrect” assumes that investors are principals with a
deterministic goal. Recommendations from theory are often (blindly) adopted
resulting in meaningful systemic risks. Instead, investors delegate to maximize
(multiple) goal(s) relative risk-adjusted returns. Investors care about whether
their managers are lucky/skilled and their IPSs tell their exact risk
specification. This Op-Ed examines the implications for asset allocation,
rebalancing, factor investing, fees and regulations, highlights attempts to
resolve challenges, suggests innovations, and argues for a  relative investment theory paradigm to
capture the realities of investing.

Part I – The Problem

Finance theory hangs on the critical
assumption/statement that “investors maximize the utility of wealth”.[1] This
seemingly innocuous representation of investor behavior masks critical
assumptions and ignores investment realities. This anchoring assumption has
resulted in prescriptions for the three key facets of investing: asset pricing,
asset allocation and risk-adjusted performance, and impacted how portfolios
globally are managed.  I examine the
implications for asset allocation, rebalancing, factor investing, fees and
regulations.

The two hidden assumptions are:
first, that investors act as principals, and second, that individuals seek
wealth for wealth’s sake, as opposed to require wealth to satisfy a stochastic
goal. This introduces relativity at two levels of investment decision-making.
The second is not new as even Socrates said, “If a man is proud of his wealth, he should not
be praised until it is known how he employs it.”[2]
Investors should not be ranked based on wealth or absolute returns, but rather on
wealth relative to some goal (i.e., funded status) or goal-relative returns. Examples of (stochastic) goals include saving for
retirement, a child’s education, health etc.[2]
 Implicit in the assumption of wealth
maximization in Modern Portfolio Theory is that the safe asset is the wealth-preserving
Treasury Bill (or a principal-protected asset).

The
1960’s Capital Asset Pricing Model (CAPM), used to forecast expected returns
makes no mention of goals. Goals-based investing (GBI) is the new investing
craze for asset allocation, but still only marginally reflected in asset
pricing literature,[3]
and often incorrectly represented in investment products as the wrong safe
asset is used.

The
Investment Policy Statements (IPS) of the New Mexico Employees’ Retirement
Association (NMPERA) and the Los Angeles County Employees’ Retirement
Association (LACERA) reveal the academic naivete. The LACERA IPS states: “The
Fund’s long-term performance objective is to generate risk-adjusted returns
that meet or exceed its defined actuarial target as well as its policy
benchmark, net of fees, over the Fund’s designated investment time horizon.”[4]
The actuarial target proxies the pension benefit payments (goal). Further, LACERA
articulates an explicit relative risk budget. NMPERA’s IPS explicitly states
that the Board established a 10.5% annualized target volatility for the
strategic asset allocation (SAA) and a 1.5% annualized tracking error for all
delegated decisions.[5]

Evidence of Implications of the Questionable
Assumption

Practitioners
should probably not be seriously concerned about theory until it begins to
affect investment practice and what is taught to the next generation of
practitioners. We examine the
challenges faced globally with specific focus on retirement security, asset
allocation and rebalancing, compensation of asset managers, and regulation.

Retirement Security – DB Plans. Social security (SS) and employer-provided
defined benefit (DB) systems are in trouble. Prof. Franco Modigliani and I
demonstrated 25 years ago that SS trust funds should earn a rate of return
commensurate with the pension obligation (GBI) and not an arbitrary Treasury
return. SS Administration ignored this recommendation and the SS Trust Fund
will run out in 2033, leading to lower benefits, higher taxes or both a decade
earlier than planned.

In the employer DB segment, many sponsors
managed, and still manage, assets independent of their liabilities, typically
using a Markowitz mean-variance optimization technique that depends on
error-prone inputs on expected returns and covariances. The decline in funded
status in DB plans with asset-focused investment strategies was global and
expensive. Employers have walked away from DB pensions, in turn increasing
retirement insecurity. One can point a finger to poor regulation and the
Silicon Valley Bank (SVB) debacle, while not directly retirement related, is a
classic example of poorly regulated investments.

Every fund and consultant around the world
has their own assumptions, reflecting the lack of scientific basis that theory provides,
and the likelihood of future problems, given that each fund and vendor makes
their best guess at what the future looks like based on their biases.

Retirement Security – DC Plans: Asking individuals to make the multiple,
complex decisions of saving, investing, and decumulation is a prescription for
disaster globally. Individuals in DC plans do not care about a “wealth number”
at retirement, but rather aim to maintain the pre-retirement standard-of-living
to death (i.e., guaranteed real retirement income). T-Bills/Bonds, considered
safe, provide highly volatile retirement income as economic parameters like
interest rates and inflation change. Target Date Funds (TDFs) rotate from
“risky” stocks to “risky” bonds (relative to the retirement income goal), based
purely on one’s age. In short, the legacy of the primary assumption in finance
threatens retirement security globally in all pillars.

Asset Management –Factor Investing: Papers elaborate extensively on not only
which factors make sense, but also which firm has the best factors. From a GBI
perspective, factor investing is a trivial topic as it accounts for probably
less than 2% of a fund’s risk; the SAA decision accounts for 90% of the risk
relative to the goal! One should hope 90% of the time and effort is spent on
the SAA decision.  Also, 90% of the fees
are paid for 10% of the risk (i.e., fees to active managers). This is why
changing the paradigm to goal-relative theory is critical.

Asset Management – Rebalancing: Another area that affects 100% of the return
is rebalancing. Many institutional (and
retail) investors compound their problems by using asset-focused rebalancing
processes on the assumption that the SAA is correct. These simplistic
goal-agnostic policies, designed more for expediency than true risk management,
rebalance portfolios to the SAA on a particular date (end of month or quarter)
or if a range limit is hit. While the portfolio drifts in the interim, the
portfolio is taking active bets, which is poor governance, and secondly, that
it is pure chance that these policies will add value. Worst of all, these
rebalancing policies experience the most serious drawdowns when the SAA (Tech
Bubble, GFC, 2018 etc.) is struggling, and hence poor risk management.

Compensation of Agents: Luck versus Skill: The LACERA IPS is very clear the objective
is generating appropriate net of fee returns. It is important to note that
any reduction in such fees leads to higher net returns and higher pensions, making
it vital to get this aspect of fund management correct. Were investors paying
for luck or skill?. Investors know that returns are noisy; the time taken to
discern luck from skill is not only a function of the excess return, but also
the volatility of the portfolio as also of the benchmark, the correlation of
the manager’s portfolio to the benchmark and the degree of confidence required.[6] What
is even more egregious is that managers in illiquid assets and investments
lacking in transparency get paid performance fees in either quarterly or annual
time frames. It is apparent that for such investments, especially with higher
volatility and leverage (and low correlation to any reasonable benchmark),
investors are paying for noise or for naïve, costless leverage, with little
recourse. Again, this is a wealth transfer from individuals in their retirement
plans to the richer asset management community.

 The
analysis thus far establishes that finance theory, through a single and its
most primary assumption, and insufficient care by practitioners, has led to the
finance industry adopting goal-independent asset allocation and rebalancing,
GBI-independent asset pricing and risk-adjusted performance measures that
ignore the skill of agents. The three incorrect facets of investing have
threatened, and continue to threaten, retirement security. Can anything be done
about it?

Part II – The Solutions

Reality is that investors have multiple stochastic goals,
maximize relative risk-adjusted returns, delegate assets to agents (investment
staff and external managers), express their risk tolerance in a specific
manner, and worry about the skill of their delegated agents.

Implications for Policy, Practice and Theory

The answer is yes, but it will take a
village to make this change. The practitioner community has to demand better
outcomes, require better products and regulation and change their compensation
mechanisms, and this is where better theory can turn the tide.

Regulation/Policy: First and foremost, regulation has to be
improved globally. Any investment product, instrument or asset allocation that
is not goal-focused must be deemed risky and not given legal protection –
starting with TDFs. After all, in DC plans, if individuals get poor retirement
outcomes from having been defaulted into TDFs, they have no recourse to the
sponsor, asset manager or regulator, and will be have to be bailed out as with
multi-employer plans. The time for remedial action is now as bailouts are
financed by taxpayers.

Interestingly, arguing for the application
of GBI to public pension plans is a political hot potato and unlikely to be
addressed in the US. However, if mistakes are made in the management of assets
in a DB plan, the fund’s sponsor bears that risk (which in the case of a
government fund are the tax payers of that state and county), but at least the
retirees are hedged (with some credit risk) from the risk of retiring poor.
This principle was extended in the multi-employer plan bailout as the US
federal government provided a backstop (but without better regulation, this
will only be one of many more bailouts).

Asset Management – DB Plans: Strangely, the recent crisis in the gilt
market, caused by investors apparently trying to implement Liability Driven
Investing (LDI; a specialized term for GBI), has been used to decry LDI in
favor of more equity investments in UK DB pensions![7] This
is a move in the wrong direction. Instead, a closer look at what happened in
the UK will probably reveal that it was the poor margin management of
(leveraged) LDI programs, and not effective LDI, that caused the trouble. The
fact that many US corporate and Dutch pension plans that have adopted some
variation of LDI strategies are now fully funded (and, in some cases, immunized
post full funding), after having been underwater for 20 years, indicates hope
that GBI will become the norm for DB pensions. On rebalancing, the ABN AMRO
pension fund adopted funded status-based rebalancing in 2008 and was one of the
few pension funds globally that preserved full funding through the Great
Financial Crisis.[8]
Some academics have made the case for using specifically curated equities for
LDI strategies, which makes sense where liabilities have equity-like properties
(e.g., in retiree health benefit plans). More interestingly, innovation and well-designed,
LDI strategies, which are independent of return forecasts and based on funded
status and risk tolerance, can be developed (see below for additional
suggestions).

Compensation of Agents: Pay for
Risk-Adjusted Skill Alpha only:
Muralidhar (2000), leveraging the work of Prof. Franco Modigliani, showed how
investors should risk-adjust the performance of agents to remove the
contribution of leverage and beta to performance, with this M-cube measure going
beyond the Sharpe ratio in doing so. The recommended performance measure
provides rankings of managers consistent with the Ambarish and Seigel (1996)
measure of confidence in skill. However, how much should be paid to managers
should be a function of time and confidence in skill as well (with potentially claw
back clauses). In an ideal world, the “2 and 20” should be 2 basis points (to
keep the lights on) and 20% of true risk-adjusted skill-based alpha. 

Financial Innovation – New Instruments: Muralidhar (2016) [9] and Merton
and Muralidhar (2017)[10]
argued that if the risk-free asset for DC plans does not exist, then
governments could issue a Retirement Security Bond (RSB) that promises fixed
real cash flows from the date of retirement, for the average life expectancy of
an economy, and indexed ideally to a standard-of-living index. They demonstrate
that this bond will not only bolster retirement security by providing
guaranteed real retirement income, but also improve longevity risk hedging and
serve as a currency for retirement. Brazil has launched this exact bond (called
“RendA+” or “Retirement Extra”) in January 2023 with exciting results: in the
first two months, 36,000 investors purchased this simple, low-risk bond (for a
total of R$500 million), at low cost and high liquidity, after answering two
simple questions (one’s retirement date and their target retirement income),
and the bond can be bequeathed to heirs if one dies unexpectedly.
Interestingly, Brazil is using this bond infrastructure to launch a similar
bond for education – an idea highlighted in Muralidhar (2016), and called Bonds
for Education and School Tuition (BEST) – among other goal-related instruments.[11]

Implications for Theory: Briefly, it has been shown in a relatively
simple normative model that if it is assumed that investors exist in an economy
with multiple stochastic goals, with assets to replicate the cash flows of
these goals (i.e., RendA+ and BEST), investors delegate to agents and maximize
goal-adjusted M-cube risk-adjusted performance based on their explicit
statement of risk tolerance per LACERA and NMPERA, then an asset pricing model
can be derived with interesting asset allocation recommendations.[12]
Vis-à-vis asset allocation, the allocation to the goal-hedge (or the relative
safe asset), risky assets (and, in turn, the absolute risk-free asset) are
independent of expected return forecasts and depend on the target relative
risk, the correlation of risky assets to the goal and volatilities. This too is
prone to error, but is an improvement on current theory with meaningfully fewer
parameters, and that too for parameters more stable than expected returns. In
addition, the asset pricing model offers different asset pricing formulae for
the absolute risk-free asset, the goal-replicating assets and risky assets as
opposed to a single equation for all risky assets and no guidance on the
absolute risk-free asset. More importantly, the equilibrium enforces strict
values not only for the expected returns, but also for correlations and volatilities,
which, in turn, potentially erases the “free parameter” problem of CAPM
highlighted by Prof. John Cochrane. Further developments will need to be made
to refine these models, but this approach at least takes the positive
observations of markets and investor behavior and offers recommendations as
opposed to arbitrary assumptions widespread in current theory that are not
observed in practice.

In Essence

A closer examination of the recent multiple
financial crises has revealed that a fair proportion of the challenges of
investment practice, especially in the retirement industry (and SVB), can be traced
to a single assumption that embedded many hidden assumptions and ignored market
realities. The resulting academic work on wealth/asset-only asset pricing,
asset allocation and risk-adjusted performance has been adopted incorrectly by
investors with one or more stochastic goals, and in the case of retirement, led
to, or likely to lead to, crises. Therefore, financial practices and regulation
need to be changed, with investors focusing more on the 90% decision than the
10% decision in two areas – asset allocation and manager compensation. Such
progress will require that industry and academia work together on innovations
(as demonstrated by Brazil) to ensure that individuals with limited financial
literacy and means can still meet a diverse set of goals.  As noted by the wise sage, Confucius, “When it is obvious that the goals cannot
be reached, don’t adjust the goals, adjust the action steps.”[13]  Hence,
the case for a Realativity in Finance Theory.

Acknowledgements

The author would like to
thank the late Prof. Franco Modigliani, Prof. Robert C. Merton and Lester
Seigel for providing the inspiration for the three key pillars of this paper,
the M-square measure, the DC Retirement challenge and the luck versus skill
equation. Thanks also to Jeanette Fernandes for valuable input. These are
personal views and all errors are mine.

Endnotes