Finance I - Lesson 9: Risk and Return - Principles of Diversification

Risk and return lie at the core of modern investment decisions. Investors face uncertainty about future outcomes (risk) and require compensation (return) for bearing that uncertainty. This lesson explores fundamental risk metrics, illustrates how investors demand higher returns for riskier assets, and demonstrates why portfolio diversification is critical in mitigating certain types of risk. By understanding which risks are avoidable and which are inherent, learners grasp how to build more efficient portfolios while maintaining desired return objectives.

Types of Risk

Investment risk can be viewed from multiple angles: the volatility of returns, the probability of financial loss, or the uncertainty in outcomes. Two broad categories shape most portfolio analysis:

Measuring Risk

Investors often quantify risk via the variance or standard deviation of returns, representing how widely individual outcomes deviate from the mean (expected) return. A high standard deviation indicates that returns may fluctuate greatly from their average, signaling higher uncertainty—and thus higher risk. Correlation among assets is also vital; if two stocks move in tandem, combining them may not reduce overall volatility.

Diversification Flowchart

The flowchart below illustrates how combining multiple assets into a portfolio helps reduce total risk, up to the point where only systematic risk remains.

flowchart LR A((Many Single Stocks)) --> B{Correlation < 1} B --> C((Blended Portfolio)) C --> D[Reduced Unsystematic Risk] D --> E[Systematic Risk Remains]

Risk-Return Visualization

Investors expect higher returns for taking on greater risk. The chart below plots hypothetical risk (standard deviation) against expected returns for different assets. Note that the slope reflects how the market compensates risk with return.

Numerical Example: Two-Stock Portfolio

Assume two stocks (Stock A and Stock B) have individual volatilities of 20% and 25%, respectively. If they are perfectly correlated (correlation = 1.0), a combined portfolio’s risk is simply a weighted sum. However, if correlation is less than 1.0, total volatility can be reduced, demonstrating how diversification benefits rise when assets do not move in lockstep.

• Stock A: Expected Return = 10%, Std Dev = 20%
• Stock B: Expected Return = 14%, Std Dev = 25%
• Correlation: 0.30

If you invest 50% in Stock A and 50% in Stock B, the portfolio’s expected return would be (0.5 × 10%) + (0.5 × 14%) = 12%. The overall risk is computed using the formula:

σ_p = √[ (w_Aσ_A)² + (w_Bσ_B)² + 2w_Aw_Bσ_Aσ_Bρ_A,B ]

Inserting w_A = 0.5, w_B = 0.5, σ_A = 0.20, σ_B = 0.25, and ρ_A,B = 0.30 yields a portfolio volatility lower than either stock alone, emphasizing the risk-reducing impact of diversification.

Summary

By recognizing that risk includes both market-wide forces (systematic) and asset-specific elements (unsystematic), investors can construct well-diversified portfolios to eliminate much of the unsystematic risk. Measuring returns in relation to risk helps guide expectations of how the market rewards investors for bearing uncertainty. Diversification thus emerges as a fundamental principle, making it possible to lower overall volatility without significantly sacrificing expected returns. This sets the stage for deeper discussions on modern portfolio theory and the efficient frontier.

Suggested Reading:
Investments by Bodie, Kane, and Marcus (sections on risk, return, and diversification).