“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