Lessons from Capital Market History

Learning Objectives

  • Calculate stock returns

  • Compare historical returns across major investment classes

  • Analysis of average annual returns for major investment classes

  • Study of variability in annual returns

  • Differentiate between mean and geometric averages

  • Grasp the concept of efficient capital markets

Dollar Returns

  • Definition: Gain or loss on investment called the return on investment.

  • Two forms of returns:

    1. Dividend income: Cash received while owning the investment.

    2. Capital gain/loss: Change in asset value over time.

  • Example Calculation:

    • Bought 100 shares at $37 each.

    • Received a dividend of $1.85 per share:

    • Dividend = $1.85 × 100 = $185.

    • Stock value rose to $40.33:

    • Capital gain = ($40.33 - $37) × 100 = $333.

    • Total dollar return = $185 + $333 = $518.

Percentage Returns

  • Definitions:

    • Dividend yield: ( \text{Dividend yield} = \frac{D{t+1}}{Pt} )

    • Example: ( \frac{1.85}{37} = 5\% )

    • Capital gains yield: ( \text{Capital gains yield} = \frac{P{t+1} - Pt}{P_t} )

    • Example: ( \frac{40.33 - 37}{37} = 9\% )

    • Total % Return = Dividend Yield + Capital Gains Yield = 14%.

Historical Returns

  • Ibbotson and Sinquefield Studies: Present historical rates of return for:

    1. Large-company stocks (S&P 500)

    2. Small-company stocks

    3. Long-term corporate bonds

    4. Long-term government bonds

    5. U.S. Treasury bills

  • Time Frame: From December 31, 1925 to December 31, 2021.

  • Average Returns:

    • Large-company stocks: 12%

    • Small-company stocks: 16%

    • Long-term corporate bonds: 6.1%

    • Long-term government bonds: 5.6%

    • U.S. Treasury bills: 3.3%

Risk Premium

  • Definition: The excess return of a risky investment over a risk-free investment.

  • Example calculation for large-company stocks:

    • Average return (12.0%) - Risk-free rate (3.3%) = Risk Premium (8.7%).

Variability of Returns

  • Variance: Average squared difference between actual returns and the mean.

  • Standard deviation (SD): Positive square root of variance.

  • Example of variance calculation for returns over 4 years with an average of 4%.

Historical Variance and Standard Deviation Formulas

  • Variance ( \text{Var}(R) = \frac{\sum{i=1}^{T} (Ri - \bar{R})^2}{T-1} )

  • Standard Deviation ( SD(R) = \sqrt{Var(R)} )

Capital Market Efficiency

  • Definition: Security prices reflect all available information.

  • Efficient Market Hypothesis (EMH): In an efficient market, all investments have zero NPV.

  • Types of Market Efficiency:

    • Strong form: All information reflected in prices.

    • Semi-strong form: All public information reflected.

    • Weak form: Prices reflect past prices only.

Average Returns Discussion

  • Arithmetic average: Average annual return over a multi-year period.

  • Geometric average: Average compound return per year over a multi-year period.

  • Comparison: Geometric averages are usually smaller than arithmetic averages due to volatility effects.

Example Calculations

  1. Total Return: If purchased stock at $37.90, received $1.30 dividends, and sold at $30.60, Total % Return = [-5.5%].

  2. Variance: For returns 12%, -9.5%, 4% over three years, variance = 1.18%, SD = 10.87%.

  3. Geometric Average Calculation: For returns 6%, 12%, -13%, 9%, 4%, Geometric Average = 3.2%.

Final Notes

  • Investment Strategies: Importance of understanding both technical and fundamental analysis, especially in relation to market efficiency.

  1. Calculate Stock Returns

    • Understand the components of a stock’s return are dividend income and capital gain.

    • Distinguish between dollar returns and percent returns.

    • Calculate percent returns, distinguishing between dividend yield and capital gains yield.

  2. Compare Historical Returns

    • Compare the historical returns over long time periods for major investment classes.

  3. Recall Average Annual Returns

    • Define and calculate the mean average return.

    • Calculate and understand risk premiums (the excess return on a risky asset).

    • Calculate and compare risk premiums of major investment classes.

    • Understand that there is a reward for bearing risk.

  4. Recall Variability of Annual Returns

    • Define a frequency distribution.

    • Define and calculate variance and standard deviation of historical returns.

    • Compare the historical standard deviations over long time periods.

    • Understand that the greater the potential reward, the greater the risk.

    • Know the impact of the Great Recession on the performance of major investment classes.

  5. Differentiate Between Mean and Geometric Averages

    • Calculate the geometric average annual return.

    • Know when it is appropriate to use each type of average.

  6. Understand the Concept of Efficient Capital Markets

    • Define an efficient market as one in which prices fully reflect available information.

      • Describe price behavior in response to new information in both efficient and inefficient markets.

      • Define the Efficient Market Hypothesis (EMH).

      • Explain why investments in an efficient market have zero NPV.

      • Understand that efficiency implies that investors should expect to earn normal returns, and firms should expect to receive fair value for the securities they sell.

  7. Differentiate Among the Three Forms of Market Efficiency

    • Define and identify examples of weak form efficiency.

    • Define and identify examples of semi-strong form efficiency.

    • Define and identify examples of strong form efficiency.

  8. Dispel Common Misconceptions About Market Efficiency

    • Understand that market efficiency does not mean that dart throwing is an effective means of selecting stocks; risk exposure and diversification still matter.

    • Understand that daily fluctuations in stock prices arise due to responses to new information, and support, rather than contradict, the idea of market efficiency.