Risk and return

What Is Risk and Return?

Risk and return are fundamental concepts in finance, representing the inseparable relationship between the potential for gain (return) and the possibility of loss (risk) in an investment. Within the broader field of portfolio theory, this pairing posits that higher potential returns typically come with higher levels of risk, and conversely, lower risk generally correlates with lower potential returns. Understanding risk and return is crucial for investors as they make decisions about asset allocation and construct a portfolio that aligns with their financial objectives and risk tolerance.

History and Origin

The systematic study of risk and return began to formalize in the mid-20th century, notably with the groundbreaking work of Harry Markowitz. In 1952, Markowitz published "Portfolio Selection" in The Journal of Finance, a paper that laid the foundation for Modern Portfolio Theory (MPT). Before MPT, investors often focused solely on maximizing returns from individual assets. Markowitz's innovation was to demonstrate that investors should consider the overall risk and return characteristics of an entire portfolio, emphasizing the benefits of diversification to reduce portfolio volatility. His work introduced the concept of the efficient frontier, illustrating how to achieve the maximum expected return for a given level of risk. This pioneering contribution to financial economics earned him a share of the Nobel Memorial Prize in Economic Sciences in 1990.²

Key Takeaways

Risk and return are intrinsically linked, meaning higher potential rewards typically accompany higher levels of risk.
Investors must balance their desire for returns with their capacity and willingness to undertake risk.
Understanding and quantifying risk is as important as forecasting returns for sound investment decisions.
Diversification is a primary strategy for managing portfolio risk without necessarily sacrificing expected return.
Various financial models and metrics exist to assess and manage the risk and return trade-off.

Formula and Calculation

The relationship between risk and return can be quantified using several financial metrics. Two foundational concepts are expected return and standard deviation (as a measure of risk or volatility).

Expected Return ((E(R))):
The expected return of an asset is the average return an investor anticipates receiving over a period, based on the probability of various outcomes. For a single asset:

E(R_i) = \sum_{j=1}^{n} (P_j \times R_j)

Where:

(E(R_i)) = Expected return of asset (i)
(P_j) = Probability of outcome (j)
(R_j) = Return of asset (i) in outcome (j)
(n) = Number of possible outcomes

For a portfolio:

E(R_p) = \sum_{i=1}^{n} (w_i \times E(R_i))

Where:

(E(R_p)) = Expected return of the portfolio
(w_i) = Weight (proportion) of asset (i) in the portfolio
(E(R_i)) = Expected return of asset (i)
(n) = Number of assets in the portfolio

Risk (Standard Deviation, (\sigma)):
Standard deviation is a widely used measure of an asset's or portfolio's total risk, quantifying the dispersion of returns around the expected return. A higher standard deviation indicates greater volatility and, thus, higher risk.

For a single asset:

\sigma_i = \sqrt{\sum_{j=1}^{n} (P_j \times (R_j - E(R_i))^2)}

Where:

(\sigma_i) = Standard deviation of asset (i)'s returns
(P_j) = Probability of outcome (j)
(R_j) = Return of asset (i) in outcome (j)
(E(R_i)) = Expected return of asset (i)
(n) = Number of possible outcomes

For a portfolio, the calculation involves the standard deviations of individual assets and the covariance between them, reflecting the benefits of diversification.

Interpreting the Risk and Return

Interpreting risk and return involves understanding that they are two sides of the same coin in financial markets. An investor's perception and management of this relationship directly influence their investment choices. For instance, a growth-oriented investor might interpret a high-risk security as an opportunity for substantial gains, aligning with their higher risk tolerance. Conversely, a conservative investor would interpret the same security as too volatile and potentially damaging to their capital, preferring lower-risk assets even if they offer more modest returns. The interpretation also extends to various financial models, such as the Capital Asset Pricing Model (CAPM), which uses beta to quantify systematic risk.

Hypothetical Example

Consider two hypothetical investment options: Fund A and Fund B.

Fund A: Invests primarily in established, large-cap companies.

Historical Average Annual Return: 7%
Historical Standard Deviation (Volatility): 10%

Fund B: Invests primarily in emerging market technology startups.

Historical Average Annual Return: 15%
Historical Standard Deviation (Volatility): 30%

An investor, Sarah, is evaluating these funds.

Step 1: Understand the Returns.
Fund B has a higher historical average annual return (15%) compared to Fund A (7%). This suggests a greater potential for capital appreciation.

Step 2: Understand the Risk.
Fund B also has a significantly higher historical standard deviation (30%) than Fund A (10%). This indicates that Fund B's returns have been much more volatile, meaning its actual returns in any given year could deviate significantly from its 15% average, potentially experiencing large losses. Fund A, while offering lower returns, has been considerably more stable.

Step 3: Relate Risk to Return.
The example clearly illustrates the risk and return trade-off. Fund B offers a higher potential reward but at the cost of substantially higher risk. Sarah must consider her personal risk tolerance. If she is comfortable with significant market fluctuations and potential short-term losses in pursuit of higher long-term gains, Fund B might be suitable. If capital preservation and stability are more important, Fund A would be the preferred choice, accepting a lower expected return for reduced volatility.

Practical Applications

The principle of risk and return is pervasive across numerous aspects of finance and investment:

Portfolio Management: Professional portfolio managers utilize these concepts daily to construct and manage client portfolios. They aim to optimize the risk-adjusted returns by employing strategies like asset allocation and diversification, balancing different asset classes (e.g., stocks, bonds, real estate) based on market conditions and client objectives.
Investment Analysis: Analysts use risk and return metrics, including beta and standard deviation, to evaluate individual securities and compare them against benchmarks or peers. This helps in identifying whether an asset's expected return justifies its inherent risk.
Regulatory Compliance: Regulatory bodies, such as the U.S. Securities and Exchange Commission (SEC), emphasize transparent risk disclosure in investment products. Funds and companies must clearly outline the risks associated with an investment to enable investors to make informed decisions. This ensures that investors are aware of the potential for loss commensurate with the stated return objectives.
Personal Financial Planning: Individuals employ risk and return considerations when planning for retirement, education, or other financial goals. A financial planner assesses an individual's risk tolerance and time horizon to recommend an appropriate portfolio strategy that balances potential growth with capital preservation needs.

Limitations and Criticisms

While central to modern finance, the traditional understanding of risk and return has its limitations and faces critiques:

Assumption of Normality and Rationality: Many models, including Modern Portfolio Theory and the Capital Asset Pricing Model, assume that returns follow a normal distribution and that investors are rational actors who make decisions to maximize utility based on expected return and standard deviation. In reality, financial market returns often exhibit "fat tails" (more extreme events than a normal distribution predicts), and investor behavior is frequently influenced by emotions and cognitive biases, as explored by behavioral finance.
Risk Measurement Challenges: Using historical volatility (standard deviation) as the sole measure of future risk can be problematic. Past performance is not indicative of future results, and unforeseen events can introduce new, unquantified risks. Moreover, standard deviation treats upside and downside deviations equally, whereas investors are typically more concerned with downside risk.
Limitations of Specific Models: Models like CAPM, despite their widespread use, have been criticized for their restrictive assumptions, such as the existence of a true "market portfolio" and the stability of beta over time. Empirical studies have shown that CAPM may not fully explain the cross-section of stock returns.¹
Market Inefficiencies: The efficient market hypothesis, which underpins some risk-return frameworks, suggests that all available information is immediately reflected in asset prices, making it impossible to consistently achieve abnormal returns. However, critics argue that markets can be inefficient due to information asymmetry or behavioral biases, leading to mispricing that is not fully captured by traditional risk metrics.

Risk and Return vs. Diversification

While closely related, risk and return are distinct from diversification.

Risk and Return: This refers to the inherent trade-off in financial markets where greater potential gains are typically associated with greater potential losses. It defines the fundamental relationship an investor must navigate.
Diversification: This is a strategy employed within the framework of risk and return to manage risk. It involves spreading investments across various asset classes, industries, or geographies to reduce the impact of any single investment's poor performance on the overall portfolio. The goal of diversification is to reduce unsystematic (specific) risk, thereby allowing an investor to achieve a given expected return with lower overall portfolio volatility, or to potentially enhance return for a given level of risk.

Essentially, risk and return describe what investors face, while diversification describes how investors can strategically navigate that fundamental trade-off.

FAQs

Q: Does higher risk always guarantee higher returns?

No, higher risk does not guarantee higher returns. It merely implies a higher potential for returns. There is always the possibility that a high-risk investment could result in significant losses instead of gains. The relationship reflects a trade-off, not a certainty.

Q: How do I determine my personal risk tolerance?

Determining your risk tolerance involves assessing your financial goals, time horizon, capacity for loss, and emotional comfort with market fluctuations. Tools such as questionnaires from financial advisors can help, but it also requires self-reflection on how you would react to significant market downturns.

Q: Can diversification eliminate all investment risk?

Diversification can significantly reduce unsystematic risk (risk specific to an individual security or industry). However, it cannot eliminate systematic risk, also known as market risk. Systematic risk is the risk inherent to the entire market or market segment, affecting all asset classes, and is influenced by macroeconomic factors like interest rates, inflation, or geopolitical events.