Risk averse

What Is Risk Averse?

Being risk averse describes an individual's preference for a certain, lower return over a potentially higher, but uncertain, return, even if the uncertain option has a higher expected monetary value. This concept is fundamental to behavioral finance and investment theory, influencing how individuals and institutions make investment decisions. A risk averse individual prioritizes the avoidance of potential losses over the pursuit of potential gains. This preference stems from the diminishing marginal utility of wealth, meaning that each additional unit of wealth provides less satisfaction than the previous one. Consequently, the disutility of losing a certain amount of wealth is greater than the utility of gaining the same amount.

History and Origin

The foundational understanding of risk aversion is deeply rooted in utility theory, particularly the work of Daniel Bernoulli in the 18th century. In 1738, Bernoulli proposed a new theory on the measurement of risk, suggesting that individuals do not evaluate outcomes in terms of their monetary values but rather in terms of the subjective utility derived from those outcomes. His theory explained the St. Petersburg Paradox by positing that the marginal utility of money decreases as wealth increases, leading individuals to make decisions that maximize expected utility rather than expected monetary value.⁴ Further development in expected utility theory occurred in the mid-20th century with the work of John von Neumann and Oskar Morgenstern, who provided an axiomatic framework for rational decision-making under uncertainty, formalizing the concept of a concave utility function for risk-averse individuals.

Key Takeaways

• Risk aversion describes a preference for a sure outcome over a gamble with an equal or even higher expected value.
• It is a core concept in behavioral finance, explaining why individuals avoid uncertainty.
• Risk aversion implies a concave utility function, where the pleasure from a gain is less than the pain from an equivalent loss.
• Financial professionals assess an individual's level of risk aversion to tailor suitable investment strategies.
• Factors like age, financial situation, and investment goals often correlate with an individual's degree of risk aversion.

Formula and Calculation

In the context of expected utility theory, risk aversion is represented by the concavity of a utility function, (U(W)), where (W) is wealth. A risk-averse individual's utility function exhibits diminishing marginal utility of wealth, meaning that for an increase in wealth (\Delta W), (U(W + \Delta W) - U(W)) is smaller for larger (W).

A common way to quantify the degree of risk aversion, particularly in academic settings, is through the Arrow-Pratt measures of risk aversion:

1. Absolute Risk Aversion (ARA):

   $$ARA(W) = -\frac{U''(W)}{U'(W)}$$

   This measures how an individual's willingness to take on risk changes with their level of wealth.

2. Relative Risk Aversion (RRA):

   $$RRA(W) = -W \frac{U''(W)}{U'(W)} = W \times ARA(W)$$

   This measures how an individual's willingness to take on risk changes with their wealth proportionally.

In these formulas:

• (U'(W)) is the first derivative of the utility function with respect to wealth, representing marginal utility.
• (U''(W)) is the second derivative of the utility function, representing the rate of change of marginal utility. For a risk-averse individual, (U''(W) < 0), implying a concave utility function.

A higher positive value for ARA or RRA indicates a greater degree of risk aversion. These measures are central to discussions in Modern Portfolio Theory and the Capital Asset Pricing Model.

Interpreting the Risk Averse Investor

An individual characterized as risk averse will generally prefer investments with lower volatility and more predictable outcomes, even if these investments offer lower expected return. This investor will often require a risk premium to accept any degree of uncertainty. Their investment strategy will typically lean towards conservative options such as bonds, certificates of deposit, or highly diversified, low-volatility portfolios. The interpretation of a risk-averse stance is critical for financial advisors, as it directly informs the appropriate asset allocation and product selection for clients.

Hypothetical Example

Consider Sarah, a 45-year-old professional who recently received a bonus of $10,000. She has two options:

• Option A: Deposit the $10,000 into a high-yield savings account guaranteed to return 2% ($200) annually.
• Option B: Invest the $10,000 in a new tech startup. There's a 50% chance it returns 20% ($2,000) and a 50% chance it loses 10% ($1,000).

Analysis for Option B:

• Expected monetary value = ((0.50 \times $2,000) + (0.50 \times -$1,000) = $1,000 - $500 = $500)
• Expected return = ((0.50 \times 20%) + (0.50 \times -10%) = 10% - 5% = 5%)

Despite Option B having a higher expected return (5% vs. 2%) and expected monetary value ($500 vs. $200), a risk averse Sarah would likely choose Option A. The certainty of gaining $200 outweighs the possibility of a larger gain (or a significant loss) associated with the startup. Her decision highlights a preference for minimizing potential downside, aligning with her overall financial planning goals of capital preservation.

Practical Applications

Risk aversion is a pervasive concept across various facets of finance:

• Portfolio Management: Understanding an investor's risk aversion is paramount for constructing suitable portfolios. Financial advisors use risk assessment questionnaires to gauge a client's comfort with risk, which then informs portfolio diversification strategies.
• Regulatory Compliance: Regulators, such as the Financial Industry Regulatory Authority (FINRA) in the United States, mandate that financial professionals make suitable recommendations based on a client's investment profile, which explicitly includes their risk tolerance. FINRA Rule 2111, known as the "Suitability Rule," requires broker-dealers to have a reasonable basis to believe that a recommended transaction or investment strategy is suitable for the customer. This assessment considers the customer's age, financial situation, needs, and risk tolerance.³
• Insurance Markets: The existence of insurance is a direct consequence of widespread risk aversion. Individuals and businesses pay premiums (a certain loss) to avoid larger, uncertain losses.
• Market Behavior: Aggregate levels of risk aversion can influence broader market trends. During periods of heightened uncertainty, a collective increase in risk aversion can lead to a "flight to quality," where investors sell off riskier assets and move into safer havens like government bonds, impacting asset prices and market liquidity.²

Limitations and Criticisms

While risk aversion, particularly as modeled by expected utility theory, provides a powerful framework for understanding economic behavior, it faces several limitations and criticisms, primarily from the field of behavioral economics:

• Allais Paradox: This classic thought experiment demonstrates that individuals often make choices inconsistent with expected utility theory's predictions. People may exhibit risk-averse behavior in one scenario and risk-seeking behavior in another, even if the underlying probabilities and outcomes are mathematically equivalent.¹ This highlights that human decision-making under uncertainty is not always perfectly rational or consistent.
• Framing Effects and Loss Aversion: Prospect theory, developed by Daniel Kahneman and Amos Tversky, suggests that individuals evaluate potential outcomes relative to a reference point (e.g., their current wealth) rather than in absolute terms. They also exhibit "loss aversion," where the psychological impact of a loss is roughly twice as strong as the pleasure from an equivalent gain. This implies that risk aversion is not simply a function of diminishing marginal utility but also of how choices are presented and perceived.
• Context Dependency: An individual's risk aversion can vary depending on the context of the decision, their emotional state, or even the size of the stakes involved. This context dependency challenges models that assume a constant or stable degree of risk aversion.
• Measurement Challenges: Accurately measuring an individual's true risk aversion is complex. Self-reported questionnaires can be imprecise, and observed behaviors in experimental settings may not perfectly translate to real-world investment decisions.

These criticisms do not invalidate the concept of risk aversion but rather suggest that more nuanced models, incorporating psychological factors, are needed for a comprehensive understanding of human choice under uncertainty.

Risk Averse vs. Risk Tolerance

Risk averse and risk tolerance are two sides of the same coin, describing an individual's attitude towards financial risk.

While a risk-averse person seeks to minimize potential losses, a person with high risk tolerance is willing to endure greater potential losses for the chance of higher gains. Financial professionals assess both to create an appropriate risk-return tradeoff for a client's portfolio.

FAQs

What does it mean to be "risk averse"?

To be risk averse means you prefer a definite outcome with a lower potential payoff over an uncertain outcome with a potentially higher payoff, even if the uncertain option has a statistically higher average return. It's about valuing certainty and minimizing the chance of loss.

How is risk aversion measured in finance?

In finance, risk aversion is typically assessed through questionnaires that probe an individual's comfort level with potential investment losses. It can also be conceptually measured through the curvature of a utility function, which mathematically represents an individual's satisfaction derived from wealth.

Does being risk averse mean you should never invest in stocks?

Not necessarily. While highly risk averse individuals might favor lower-risk assets like bonds or cash, a balanced approach often involves some exposure to growth assets like stocks. The key is to engage in diversification and choose an asset allocation that aligns with your specific risk comfort level and financial goals, ensuring that any stock investments are within your personal risk tolerance.

Can risk aversion change over time?

Yes, an individual's level of risk aversion can change due to life events, changes in financial circumstances, or evolving investment experience. For example, a person approaching retirement might become more risk averse as their time horizon shortens, while a younger investor with stable income might become less risk averse over time.

Is risk aversion always a bad thing?

No, risk aversion is not inherently bad. It is a natural human trait that helps protect against undue financial exposure. For some, being risk averse ensures stability and security, which are valid financial objectives. The crucial aspect is to understand one's own risk profile and ensure that investment decisions align with it.