1-1 1 A Brief History of Risk and Return

1-2 A Brief History of Risk and Return Two key observations: 1. There is a substantial reward, on average, for bearing risk. 2. Greater risks accompany greater returns.

1-3 Dollar & Percent Returns Total dollar return = the return on an investment measured in dollars $ return = dividends + capital gains Total percent return is the return on an investment measured as a percentage of the original investment. % Return = $ return/$ invested The total percent return is the return for each dollar invested.

1-4 Percent Return Dividend Yield Capital Gains Yield

1-5 Example: Calculating Total Dollar and Total Percent Returns You invest in a stock with a share price of $25. After one year, the stock price per share is $35. Each share paid a $2 dividend. What was your total return? DollarsPercent Dividend$2.00$2/25 = 8% Capital Gain$35 - $25 = $10$10/25= 40 % Total Return$2 + $10 = $12$12/$25 = 48%

1-6 Annualized Returns Effective Annual Rate (EAR) Where: HPR = Holding Period Return M = Number of Holding Periods per year

1-7 Annualized Returns – Example 1 P 0 = $20P.33 = $22 t = “.33” since 4 months is 1/3 of a year 4-month HPR = 3 periods per year Holding Period Return (HPR) Annualized Return (EAR) You buy a stock for $20 per share on January 1. Four months later you sell for $22 per share. No dividend has been paid yet this year.

1-8 Annualized Returns – Example 2 P 0 = $20P 2 = $28 HPR = 2 years (t = 2) HPR per year = ½ (0.50) Holding Period Return (HPR) Annualized Return (EAR) Suppose the $20 stock you bought on January 1 is selling for $28 two years later No dividends were paid in either year.

1-9 A $1 Investment in Different Types of Portfolios, 1926—2006

1-10 Financial Market History

1-11 The Historical Record: Total Returns on Large-Company Stocks

1-12 The Historical Record: Total Returns on Small-Company Stocks

1-13 The Historical Record: Total Returns on U.S. Bonds.

1-14 The Historical Record: Total Returns on T-bills.

1-15 The Historical Record: Inflation

1-16 Historical Average Returns Historical Average Return = simple, or arithmetic average. Using the data in Table 1.1: Sum the returns for large-company stocks from 1926 through 2006, you get about 984 percent. Divide by the number of years (80) = 12.3%. Your best guess about the size of the return for a year selected at random is 12.3%.

1-17 Average Annual Returns for Five Portfolios

1-18 Average Returns: The First Lesson Risk-free rate: Rate of return on a riskless investment Risk premium: Extra return on a risky asset over the risk-free rate Reward for bearing risk The First Lesson: There is a reward, on average, for bearing risk.

1-19 Average Annual Risk Premiums for Five Portfolios

1-20 Risk Premiums Risk is measured by the dispersion or spread of returns Risk metrics: Variance Standard deviation The Second Lesson: The greater the potential reward, the greater the risk.

1-21 Return Variability Review and Concepts Variance (σ 2 ) Common measure of return dispersion Also call variability Standard deviation (σ) Square root of the variance Sometimes called volatility Same "units" as the average

1-22 Return Variability: The Statistical Tools for Historical Returns Return variance: (“N" =number of returns): Standard Deviation

1-23 Example: Calculating Historical Variance and Standard Deviation Using data from Table 1.1 for large-company stocks:

1-24 Return Variability Review and Concepts Normal distribution: A symmetric, bell-shaped frequency distribution (the bell-shaped curve) Completely described with an average and a standard deviation (mean and variance) Does a normal distribution describe asset returns?

1-25 Frequency Distribution of Returns on Common Stocks, 1926—2006

1-26 Historical Returns, Standard Deviations, and Frequency Distributions: 1926—2006

1-27 The Normal Distribution and Large Company Stock Returns

1-28 Arithmetic Averages versus Geometric Averages The arithmetic average return answers the question: “What was your return in an average year over a particular period?” The geometric average return answers the question: “What was your average compound return per year over a particular period?”

1-29 Geometric Average Return: Formula Where: R i = return in each period N = number of periods Equation 1.5

1-30 Geometric Average Return Where: Π = Product (like Σ for sum) N = Number of periods in sample R i = Actual return in each period

1-31 Example: Calculating a Geometric Average Return Using the large-company stock data from Table 1.1:

1-32 Geometric Average Return

1-33 Arithmetic Averages versus Geometric Averages The arithmetic average tells you what you earned in a typical year. The geometric average tells you what you actually earned per year on average, compounded annually. “Average returns” generally means arithmetic average returns.

1-34 Geometric versus Arithmetic Averages For forecasting future returns: Arithmetic average "too high" for long forecasts Geometric average "too low" for short forecasts

1-35 Blume’s Formula Form a “T” year average return forecast from arithmetic and geometric averages covering “N” years, N>T.

1-36 Check This 1.5a Compute the Average Returns Arithmetic Average Geometric Average

1-37 Check This 1.5b

1-38 Check This 1.5b

1-39 Risk and Return The risk-free rate represents compensation for the time value of money. First Lesson: If we are willing to bear risk, then we can expect to earn a risk premium, at least on average. Second Lesson: The more risk we are willing to bear, the greater the expected risk premium.

1-40 Historical Risk and Return Trade-Off

41 Chapter 1 End A Brief History of Risk and Return