Ch.12

Learning Objectives

• Calculate the return on an investment.
• Discuss historical returns on various types of investments.
• Discuss historical risks associated with various investments.
• Explain implications of market efficiency.

Chapter Outline

• Understand returns from investments.
• Analyze the historical record of investment returns.
• Discuss average returns and variability.
• Explain concepts related to capital market efficiency.

Returns on Investment

• Definition of Return: Gain or loss from an investment, which consists of:
  • Income component: Direct cash received from the investment.
  • Capital gain/loss: Change in asset value.
• Dollar Returns Example:
  • Purchase of 100 shares of stock at $37 each:
    • Total outlay = 100 imes 37 = 3,700
    • Dividends = 1.85 imes 100 = 185
    • Stock value rises to $40.33:
      • New value = 100 imes 40.33 = 4033
      • Capital gain = (40.33 - 37) imes 100 = 333
      • Total return = 185 + 333 = 518

Percentage Returns

• Calculating Return Components:
  • Dividend yield: rac{D{t+1}}{Pt} = rac{1.85}{37} = 0.05 ext{ or } 5 ext{}
  • Capital gains yield: rac{P{t+1} - Pt}{P_t} = rac{40.33 - 37}{37} = 0.09 ext{ or } 9 ext{}
  • Total yield: 5 ext{} + 9 ext{} = 14 ext{}

The Historical Record

• Ibbotson and Sinquefield Studies: Analyzed historical rates of return on five investment categories:
  • Large-company stocks
  • Small-company stocks
  • Long-term corporate bonds
  • Long-term U.S. government bonds
  • U.S. Treasury bills

Average Returns: The First Lesson

• Average Return Calculation: Sum of returns over a period divided by the number of years.
• Risk-Free Return: T-bills are considered to be without default risk; serves as a benchmark.
• Risk Premium: Additional return required from a risky investment over risk-free investment.
  • Example: Risk premium for large-company stocks = 12.1 ext{} - 3.4 ext{} = 8.7 ext{}

The Variability of Returns: The Second Lesson

• Variance: Average squared difference between actual returns and average returns.
• Standard deviation: Positive square root of variance, indicating volatility.
  • Example of Returns: 10 ext{}, 12 ext{}, 3 ext{}, -9 ext{}
  • Average return = rac{10 + 12 + 3 - 9}{4} = 4 ext{}
  • Variance Calculation: Divide sum of squared deviations from average by total returns - 1.

Normal Distribution

• A bell-shaped curve that shows probability with respect to mean and standard deviation.
• Represent the range of expected returns based on standard deviation:
  • 68% within one standard deviation
  • 95% within two standard deviations

Implications of Investment Risk

• Market Volatility: Higher potential rewards come with increased risks. Historical case of 2008 showed drastic declines in the S&P 500.
  • Indicator of the market's response to risk, especially through unprecedented downturns.

The Efficient Markets Hypothesis

• Definition: Security prices in an efficient market reflect all available information.
• Market Forms:
  • Weak Form: No insider information; historical prices reflect all info.
  • Semi-Strong Form: All public information is reflected in prices.
  • Strong Form: Includes private information as well.
• Market Behavior: Prices adjust rapidly to new information, making predicting future prices challenging.

Average Return Types

• Geometric Average Return: Compounded return over multiple years.
• Arithmetic Average Return: Simple average computed yearly.
  • Example of Calculating Geometric Average: ext{Geometric average} = (1.10 imes 1.12 imes 1.03 imes 0.91)^{1/4} - 1

Questions for Consideration

• Understanding total return and distinguishing between arithmetic and geometric averages is crucial for investment strategy.
• Efficient markets imply a complex environment for investment choices, mandating thorough data analysis for informed decisions.