Chapter 2

1. Chapter 2 Rates of Return Chapter 2: Rates of Return

2. Background • Investors want to maximize their returns (or wealth) • Chapter discusses • The calculation of a return • Historical returns offered by different types of investments Chapter 2: Rates of Return

3. The Investor’s Goal • Goal is to maximize what is earned relative to the amount put into an investment • Maximize either the • Rate of return • Investment’s terminal value Equivalent Chapter 2: Rates of Return

4. The Investor’s Goal • Some claim wealth-maximizing investors are performing harmful greedy activities • Law abiding wealth maximization is beneficial to both investor and general population • Seek out securities issued by firms producing high quality goods and services • Capital is used to benefit general population • Investors can request management actions at stockholder meetings • Helps nation compete internationally • Creates new job opportunities Chapter 2: Rates of Return

5. Ethics Box: The Need for Ethics in Investment • Some level of ethics is necessary • Ethics concerned with standards of right and wrong • Concepts of trust and fairness are relevant to investments • Investors trust investment firms to act in their best interest and to safeguard their assets • Fairness means a ‘level playing field’ and the absence of fraud • Decreasing information asymmetry increases efficiency and fairness • An investment professional should • Be loyal • Act with due care • Keep information confidential • Avoid conflicts of interest Chapter 2: Rates of Return

6. The One-Period Rate of Return • Rate of return measures change in an investor’s wealth over time • Measures the success or failure of the investment • Measures holding period return • Defined as Chapter 2: Rates of Return

7. Examples: One Period Return • You purchased one share of Coca-Cola one year ago for $54. You sold it today for $64, and you received dividends of $0.80 during the year • Your income from dividends = 80¢ • Your capital gain is $10 ($64 - $54) • Your return is $10.80  $54 = 20% Chapter 2: Rates of Return

8. Examples: One Period Return • You purchased a U.S. T-bond for $900. One year later you sold the bond for $910. You received $35 in interest during the year. Your rate of return is • You bought a six-month T-bill for $9,800 with a maturity value of $10,000. After the bond matures your six-month return is • Since there are two six-month periods in one year, your annual return is • 1.02042 – 1 = 1.0412 – 1 = 4.12% Chapter 2: Rates of Return

9. Figure 2-1:Wealth Indices for Average U.S. Investments in Different Asset Classes Compared to Inflation, 1926-99 • If you had invested $1 on December 31, 1925 in each of the following, you would have Small company stocks are the most risky, but offer the highest return. In some years inflation exceeds T-bill returns—leading to a drop in purchasing power for T-bill investors. T-bills are the least risky—smoothest growth path, but lowest return. Chapter 2: Rates of Return

10. Noticeable tendency for higher risk assets to offer the higher return. Table 2-1:Average Annual Rate of Return and Risk Statistics for Asset Classes and Inflation in the U.S., 1926-99 Chapter 2: Rates of Return

11. Realized One-Period Rates of Return • We can calculate one period rates of change for the indexes Includes dividends, coupon interest on bonds Chapter 2: Rates of Return

12. Average Rates of Return • Arithmetic mean return (AMR) measures average historical one-period rates of return • Compound average rate of return, or geometric mean return (GMR) is AMR  GMR because compound interest grows more rapidly than simple interest Chapter 2: Rates of Return

13. Example: Average Rates of Return • A three-year investment earned the following annual returns: • If you placed $100 in this investment at the beginning of year 1, at the end of the third year it would be worth • $100 (1.0428)3 = $113.40 Chapter 2: Rates of Return

14. Assessing Risk • An asset is riskier if • Its one-period rates of return fluctuate over a wide range • Such as small company stocks • Measures of risk include • Variance—the average of squared deviations from AMR Both measure total risk • Standard deviation—square root of variance Chapter 2: Rates of Return

15. Example: Variance & SD • Calculate the variance and standard deviation of the previous example Chapter 2: Rates of Return

16. Risk Rankings • Both standard deviation and variance result in the same risk rankings • Advantages of standard deviation • Considers every outcome • Unlike range which only considers high and low values • Well known by statisticians • Programmed into calculators and software • Measures the wideness of probability distributions • Measure of dispersion around arithmetic mean • Also widely used in mathematics, econometrics, etc. Chapter 2: Rates of Return

17. Interpreting Historical Return and Risk • Examining the historical returns and risk leads to the following observations: • Large company common stocks • Earn higher returns than bonds • If a firm is declared bankrupt, all creditors are paid in full before common stockholders receive any proceeds • Common stockholders usually receive nothing which makes it more risky than debt • Stockholders demand a higher average rate of return Chapter 2: Rates of Return

18. Interpreting Historical Return and Risk • Small company stocks • Earned highest returns of all other investments • But, riskier than any of the other investments • The percentage of small firms declared bankrupt is greater than the percentage of large firms • Investors require a higher rate of return for investing in a small firm • Long-term corporate bonds • Bonds issued by the U.S. Treasury are unlikely to be defaulted • However, bonds issued by corporations are more likely to be defaulted Chapter 2: Rates of Return

19. Interpreting Historical Return and Risk • Long-term U.S. Treasury bonds • Mature about 20 years from initial offering date • Involve no default risk • Intermediate-term U.S. Treasury Bonds • Mature about 5 years after issue date • Experience smaller price fluctuations than long-term U.S. Treasury bonds • U.S. Treasury bills • Mature in less than one year • No horizon premium necessary • U.S. Treasury is unlikely to default • No default premium needed • AKA risk-free assets • Probably no other security in world with less risk Chapter 2: Rates of Return

20. Interpreting Historical Return and Risk • Opportunity cost • What it could earn in its highest paying alternative use • Example: The opportunity cost of attending college includes foregone wages • Less obvious expenses than out-of-pocket expenses • Example: The opportunity cost of holding cash rather than investing in large company stocks was 13.3% a year Chapter 2: Rates of Return

21. Required Rate of Return • Should only invest if you expect to earn a return greater than your cost of capital • Interest expense paid for borrowed funds • Cash dividend payment paid to stockholders • Opportunity costs • AKA required rate of return • Minimum rate of return an investment must earn to increase investor’s wealth • RRR < r leads to a wealth increase • RRR = r leads to no change in wealth • RRR > r leads to a wealth decrease Chapter 2: Rates of Return

22. Combining Risk Premiums To Compute Required Rate of Return Chapter 2: Rates of Return

23. Combining Risk Premiums To Compute Required Rate of Return Chapter 2: Rates of Return

24. The Largest Investors in the World • U.S. pension funds are the largest investors in the world • Hire professional money managers • Owners/sponsors of largest pensions Chapter 2: Rates of Return

25. The Largest Investors in the World • Firms hired to manage pension assets include Chapter 2: Rates of Return

26. Ethics and Pension Funds • Managers of defined benefit plans (guarantee fixed income in retirement) • Have duty to maintain sufficient funds for future obligations • Some funds become overfunded • Should these funds be allowed to divest excess funds? • Managers of defined contribution plans (employee and employer contributions accumulate in individual accounts) • Must offer at least three different funds • Must seek to maximize risk-adjusted return • Have a fiduciary duty to vote fund’s stock solely in beneficiaries’ interests Chapter 2: Rates of Return

27. The Bottom Line • Investors wish to maximize their wealth (return) over the long-run • Arithmetic mean is not a compounded return like the geometric mean • AMR  GMR • Realized returns represent historical data • Investors desire investments with an expected return greater than their required rate of return or hurdle rate Chapter 2: Rates of Return