Notes on Chapter 11: Risk and Return in Capital Markets

Chapter 11: Risk and Return in Capital Markets

11.1 A First Look at Risk and Return

Understanding investment growth over time is crucial. By analyzing various investment types from 1925 to 2018, such as the Standard & Poor’s 500 (S&P 500), small stocks, world portfolios, corporate bonds, and treasury bills, we can observe differing growth trajectories.

11.2 Historical Risks and Returns of Stocks
Computing Historical Returns

Realized returns reflect the actual profit or loss generated from an investment. For example, the realized return can be calculated with the formula:

R=(P<em>f−P</em>i)+DPiR = \frac{(P<em>f - P</em>i) + D}{P_i}

where:

  • $R$ is the realized return,
  • $P_f$ is the final price,
  • $P_i$ is the initial price, and
  • $D$ is any dividends received.
Average Annual Returns

The average annual return can be found using:

R<em>avg=1n∑</em>i=1nRiR<em>{avg} = \frac{1}{n} \sum</em>{i=1}^{n} R_i

where $R_i$ are individual annual returns over the period of $n$ years.

Variance and Volatility of Returns

Variability in returns is quantified using variance and standard deviation.

  • Variance:

σ2=1n−1∑<em>i=1n(R</em>i−Ravg)2\sigma^2 = \frac{1}{n-1} \sum<em>{i=1}^{n} (R</em>i - R_{avg})^2

  • Standard Deviation:

σ=variance\sigma = \sqrt{variance}

These measures provide insights into investment risk. For instance, if the standard deviation of S&P 500 returns is calculated as 24.1%, this indicates a degree of risk associated with investing in large corporations.

Historical Tradeoff Between Risk and Return

The historical data suggests a direct relationship between risk and return: higher volatility is generally associated with higher average returns. Analysis of large portfolios exhibits this trend distinctly.

Common Versus Independent Risk
  • Common Risk: This type of risk affects all securities in the market equally (e.g., economic downturns). It does not get reduced through diversification.
  • Independent Risk: Risks that are uncorrelated and specific to individual securities. When diversified, these risks become negligible since their impact diminishes.
Diversification in Stock Portfolios

Investors can mitigate independent risks through diversification, which spreads exposure across numerous assets. This prevents any single lost investment from severely impacting the total portfolio performance. For example, betting on multiple independent events like coin flips diminishes total risk compared to a single bet.

Key Insights
  • High average returns often accompany higher volatility.
  • Diversifiable risks do not command a premium since they can be eliminated through portfolio diversification.
  • The only risk that requires a premium is systematic risk due to its pervasive nature across all investments.
Conclusion

In summary, when investing, it is crucial to consider the balance between risk and return. Understanding the dynamics of realized returns, volatility, and the principles of diversification will guide investors in making informed decisions.

Investors must remain cognizant of the type of risk they are exposed to and aim to structure their portfolios to optimize returns while minimizing unnecessary risk exposure. The presented formulas for calculating returns and risk metrics serve as essential tools in this analysis.