The Missing Billionaires

1. Maximize Expected Utility, not just wealth

You can't do much better than using Expected Utility as your summary statistic for comparing spending policies.

Utility over wealth. Expected Utility is a powerful framework for making financial decisions that considers both the potential monetary outcomes and an individual's risk preferences. Unlike simply maximizing expected wealth, which can lead to dangerous and nonsensical policy recommendations, Expected Utility helps balance the desire for higher returns with the need to manage risk.

Practical application. To use Expected Utility:

• Define your personal utility function, typically using Constant Relative Risk Aversion (CRRA)
• Estimate the probability distribution of potential outcomes for each decision
• Calculate the Expected Utility by weighing each outcome's utility by its probability
• Choose the option with the highest Expected Utility

This approach allows for more nuanced decision-making, accounting for factors such as decreasing marginal utility of wealth and individual risk tolerance. It provides a consistent framework for evaluating various financial choices, from asset allocation to spending policies.

2. Sizing investments is more critical than selection

In investing, the natural tendency is to focus on the question of what to buy or sell. Nearly 100% of the financial press is dedicated to this question, so it's reasonable to suppose that the "what" decision is the most important thing we should be thinking about. It isn't.

Position sizing matters. The size of an investment position often has a more significant impact on overall portfolio performance and risk than the selection of individual investments. This concept is frequently overlooked, with most investors and financial media focusing primarily on which assets to buy or sell.

Key principles:

• Optimal bet size increases with expected return and decreases with variance
• The Merton share formula provides a useful rule of thumb for position sizing
• Diversification is crucial for managing risk
• Avoid over-concentration, even in seemingly attractive investments

Proper sizing helps manage risk while capitalizing on opportunities. It allows investors to participate in potentially profitable investments without exposing themselves to undue risk. Even great investments can lead to poor outcomes if sized inappropriately, while well-sized positions in moderately attractive investments can contribute positively to overall portfolio performance.

3. Dynamic asset allocation outperforms static strategies

Believing that the expected return of the stock market changes over time is not at odds with a belief in market efficiency.

Adapt to market conditions. Dynamic asset allocation, which adjusts portfolio composition based on changing market conditions, can significantly outperform static strategies over the long term. This approach recognizes that the attractiveness of different asset classes varies over time due to changes in valuations, economic conditions, and other factors.

Key components of dynamic allocation:

• Use metrics like cyclically adjusted earnings yield to estimate expected returns
• Consider the relative attractiveness of stocks versus bonds
• Incorporate momentum signals for additional insight
• Regularly rebalance to maintain target allocations

By adjusting allocations based on expected returns and risks, investors can potentially achieve higher risk-adjusted returns compared to static strategies. However, it's important to implement dynamic allocation systematically and avoid the pitfalls of short-term market timing or overreacting to temporary market movements.

4. Optimal spending considers longevity and market conditions

The essence of financial planning is deciding, in advance, a desired spending and investment policy conditional on relevant aspects of our life, varying investment opportunities, and our personal preferences.

Balancing act. Determining an optimal spending policy requires balancing current consumption with the need to preserve wealth for future years. This decision becomes more complex when considering uncertain lifespans and variable investment returns.

Factors to consider:

• Personal time preference
• Risk tolerance
• Expected investment returns
• Longevity risk
• Desired bequests or charitable giving

The Merton-Samuelson framework provides a valuable approach to this problem, suggesting that spending should be a proportion of current wealth, adjusted for factors like age and market conditions. This allows for flexibility in spending as wealth fluctuates, while still providing a structured approach to ensure long-term financial security.

5. Human capital is a crucial part of your financial portfolio

For young people, it is typical that their human capital far outweighs their financial capital.

Beyond financial assets. Human capital, representing an individual's future earning potential, is often the largest asset for young professionals. Recognizing and managing this asset is crucial for optimal financial decision-making.

Implications of human capital:

• Influences optimal asset allocation (e.g., stock-like vs. bond-like careers)
• Affects risk tolerance and capacity
• Guides decisions on education and career development
• Impacts insurance needs (e.g., life and disability insurance)

Young investors with high human capital might justifiably take more financial risk, potentially even using leverage to invest in equities. As one ages and human capital decreases, financial asset allocation typically becomes more conservative. Understanding the nature of your human capital (e.g., stability, correlation with market) can help inform better investment and career decisions.

6. Tax considerations significantly impact investment decisions

It is only your after‐tax wealth that you are able to spend or give away, so it's proper to be focused on after‐tax outcomes.

Tax-aware investing. Taxes can significantly impact investment returns and should be a key consideration in financial decision-making. However, tax decisions often involve trade-offs between current tax liability and future investment potential, requiring careful analysis.

Key tax considerations:

• Capital gains realization timing
• Asset location (taxable vs. tax-advantaged accounts)
• Tax-loss harvesting opportunities
• Impact of taxes on optimal asset allocation
• Estate planning and gifting strategies

While minimizing taxes is important, it shouldn't be the sole driver of investment decisions. The Expected Utility framework can help balance tax considerations with other factors like risk and return potential. In some cases, paying taxes sooner to achieve a more optimal portfolio allocation may lead to better long-term outcomes.

7. Understand and account for risk versus uncertainty

In general, the kind of parameter uncertainty we are likely to encounter results in the Expected Utility framework suggesting a reduction in the optimal allocation to risky assets.

Beyond known probabilities. While risk refers to known probabilities of potential outcomes, uncertainty deals with situations where probabilities are unknown or unknowable. Both affect financial decision-making, but uncertainty requires additional consideration.

Dealing with uncertainty:

• Use Bayesian approaches to update beliefs as new information arrives
• Consider a range of possible scenarios rather than point estimates
• Be cautious of overfitting models to limited historical data
• Recognize that uncertainty often increases with time horizon

Accounting for uncertainty typically leads to more conservative allocations to risky assets, especially over longer time horizons. However, it's important to balance this caution with the need to take appropriate risks to meet long-term financial goals. Regularly updating beliefs and adjusting strategies as new information becomes available can help navigate uncertain environments.

8. Options and alternative investments require careful evaluation

Expected Utility is a particularly useful paradigm to apply to assessing options, as their inherently nonlinear payoffs make the use of simpler metrics like the Sharpe ratio misleading.

Beyond traditional assets. Options and alternative investments can offer unique payoff structures and diversification benefits, but they also come with complexities and risks that require careful analysis. The Expected Utility framework is particularly well-suited for evaluating these investments.

Considerations for options and alternatives:

• Nonlinear payoff structures
• Liquidity constraints
• Higher fees and transaction costs
• Potential for tail risks
• Tax implications

While these investments can potentially improve portfolio performance, they often don't add as much value as their proponents claim. For most individual investors, a well-diversified portfolio of traditional assets may provide similar benefits with less complexity and lower costs. If considering options or alternatives, it's crucial to thoroughly understand their characteristics and how they fit into your overall financial plan.

9. Behavioral biases can lead to suboptimal financial decisions

We suspect most endowments, or individuals, would find this profile unattractive. The cause of the problem is often referred to as "volatility drag," a phenomenon we met in Chapter 3.

Mind over matter. Cognitive biases and emotional reactions can lead investors to make decisions that deviate from what would be optimal based on Expected Utility. Recognizing and mitigating these biases is crucial for successful long-term investing.

Common behavioral biases:

• Loss aversion
• Recency bias
• Overconfidence
• Anchoring
• Herd mentality

To combat these biases:

• Develop a systematic investment process
• Use quantitative models to inform decisions
• Regularly review and rebalance portfolios
• Seek outside perspectives to challenge your assumptions
• Focus on long-term goals rather than short-term market movements

By understanding and accounting for behavioral biases, investors can make more rational decisions and avoid common pitfalls that erode long-term performance.

10. Endowments and foundations face unique challenges

There is much to learn from exploring how endowments and foundations should and actually do determine how to spend their resources over time, and it gives us a setting in which to get more familiar with the concepts introduced in the previous chapter.

Perpetual portfolios. Endowments and foundations face unique challenges in balancing current spending needs with the desire to preserve capital for future generations. Their investment and spending policies must consider factors beyond those relevant to individual investors.

Key considerations for endowments:

• Infinite time horizon
• Spending rate sustainability
• Intergenerational equity
• Donor restrictions and mission alignment
• Liquidity needs and portfolio illiquidity

The Expected Utility framework can help endowments make more informed decisions about spending rates and asset allocation. However, additional factors like organizational mission and stakeholder expectations must also be considered. The goal is to find a balance that allows for meaningful current impact while preserving the endowment's ability to support its mission in perpetuity.

11. The equity risk premium puzzle challenges economic models

The heart of the "puzzle" is that the long‐term realized returns of stocks and bonds simply don't agree very well with the equilibrium predictions from the most commonly used economic models.

Theory meets reality. The equity risk premium puzzle highlights the discrepancy between theoretical models of asset pricing and observed market returns. This puzzle has important implications for how we think about risk, return, and economic equilibrium.

Key aspects of the puzzle:

• Historical equity returns have been higher than standard models predict
• Risk-free rates have been lower than models suggest
• Resolving the puzzle requires unrealistically high levels of risk aversion

Possible explanations include:

• Behavioral factors not captured by traditional models
• Rare disaster risk not reflected in historical data
• Incomplete markets and borrowing constraints

Understanding this puzzle is important for setting realistic return expectations and developing more accurate economic models. While the debate continues, investors should be cautious about relying too heavily on historical returns or simplistic models when making long-term financial decisions.

Last updated: February 10, 2025