Class Introduction and A Brief History of Risk and Return

1. 1 Class Introduction and A Brief History of Risk and Return

2. Class Introduction • Class Expectations • Review of Syllabus • Text • Calculator • Grading • Assignments • Form Groups

3. Returns: Dollar and Percentage • Quick Review: • What is a return? • Dollar terms • Selling Price + Distributions – Buying Price = Dollar Returns • Percentage terms • Dollar Returns / Original Investment • Why do we like percentage returns? • Comparable across different investments

4. Dollar Returns • Total dollar returnis the return on an investment measured in dollars, accounting for all interim cash flows and capital gains or losses. • Problem 1 – 100 Shares of Stock • Buying Price $89 • Dividend Received during year $1.20 • Selling Price $97 Dollar Return Per Share $97.00 + $9.20 -$89.00 = $9.20

5. Percent Returns • Total percent returnis the return on an investment measured as a percentage of the original investment. • Problem 1 – 100 Shares of Stock • Buying Price $89 • Dividend Received during year $1.20 • Selling Price $97 Dollar Return = ($97 + $1.20) - $89 = $9.20 Percentage Return = $9.20 / $89 = 0.10337 or 10.34%

6. Historical Average Returns • A useful number to help us summarize historical financial data is the average. • Using the data in Table 1.1, if you add up the returns for large-company stocks from 1926 through 2005, you get about 984 percent. • Because there are 80 returns, the average return is about 12.3%. How do you use this number? • If you are making a guess about the size of the return for a year selected at random, your best guess is 12.3%. • The formula for the historical average return is:

7. Arithmetic Averages versusGeometric 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?” • How to calculate a geometric average. Geo Average = (Ending Value/Beg. Value)(1/n-1) – 1 where n is the number of years and n -1 is the number of returns • If you are working with returns you take the cumulative return Geo Average = (1+ Cumulative Return)(1/n) – 1

8. Example: Calculating a Geometric Average Return • Problem 5 Jurassic Jalopies and Stonehenge Construction • The spreadsheet below shows us the geometric average return.

9. Arithmetic Averages versusGeometric 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. • When we talk about average returns, we generally are talking about arithmetic average returns. • For the purpose of forecasting future returns of more than one year: • The arithmetic average is probably "too high" for long forecasts. • The geometric average is probably "too low" for short forecasts. • Unless we match the investing horizon with the horizon we used for calculating the return. For example, if you take a ten-year history, calculate a ten-year geometric average then this is the right rate for predicting a ten-year return.

10. Geometric versus Arithmetic Averages

11. A $1 Investment in Different Typesof Portfolios, 1926—2005.

12. Financial Market History

13. The Historical Record:Total Returns on Large-Company Stocks.

14. The Historical Record: Total Returns on Small-Company Stocks.

15. The Historical Record: Total Returns on U.S. Bonds.

16. The Historical Record: Total Returns on T-bills.

17. The Historical Record: Inflation.

18. Return Variability: The Statistical Tools • The formula for return variance is ("n" is the number of returns): • Sometimes, it is useful to use the standard deviation, which is related to variance like this:

19. Return Variability Review and Concepts • Varianceis a common measure of return dispersion. Sometimes, return dispersion is also call variability. • Standard deviationis the square root of the variance. • Sometimes the square root is called volatility. • Standard Deviation is handy because it is in the same "units" as the average. • Normal distribution:A symmetric, bell-shaped frequency distribution that can be described with only an average and a standard deviation. • Does a normal distribution describe asset returns?

20. Historical Returns, Standard Deviations, and Frequency Distributions: 1926—2005

21. The Normal Distribution and Large Company Stock Returns

22. Frequency Distribution of Returns on Common Stocks, 1926—2005

23. Risk and Return • Risk-free rate:The rate of return on a riskless, i.e., certain investment. • Risk premium:The extra return on a risky asset over the risk-free rate; i.e., the reward for bearing risk. • By looking at Table 1.3, we can see the risk premium earned by large-company stocks was 8.5%. The T-Bill average return was 3.8% and the large company stocks average return was 12.3%.

24. Risk and Return • The risk-free rate represents compensation for just waiting. • Therefore, this is often called the time value of money. In your previous class (BA 340 or BA 360) this was the real rate of return and inflation. • First Lesson: If we are willing to bear risk, then we can expect to earn a risk premium, at least on average. • Second Lesson: Further, the more risk we are willing to bear, the greater the expected risk premium.

25. Useful Internet Sites • cgi.money.cnn.com/tools/millionaire/millionaire.html(millionaire link) • finance.yahoo.com(reference for a terrific financial web site) • www.globalfindata.com(reference for historical financial market data—not free) • www.robertniles.com/stats(reference for easy to read statistics review)