1. Jacoby, Stangeland and Wajeeh, 20001 uDollar Return = Dollar Dividend + Change in Market Value uPercentage Return = Dollar Return / Beginning Market Value = Dividend Yield% + Capital Gain Yield% uNotating Percentage Returns Historic (Ex Post) Returns c.g. yield dividend yield Chapter 9

2. Jacoby, Stangeland and Wajeeh, 20002 Q.Suppose a stock had an initial price of $42 per share, paid a dividend of $0.84 per share during the year, and had an ending price of $46.2. Calculate: a. Percentage total return b. Dividend yield c. Capital gains yield Historic Returns - Example 1

3. Jacoby, Stangeland and Wajeeh, 20003 Returns - Example 1 Outflows Total inflows = $47.04 Dividends = $0.84 Ending Market Value = $46.20 t – $42.00 Time: t - 1

4. 4 A. a. percentage total return b. dividend yield c. capital gains yield Historic Returns - Example 1

5. Jacoby, Stangeland and Wajeeh, 20005 uHolding Period Return HPR = (1 + R 1 )(1 + R 2 )... (1+ R T ) -1 u(Geometric) Average Return GAR = [(1 + R 1 )(1 + R 2 )... (1+ R T )] 1/T -1 = [1 + HPR] 1/T -1 u(Arithmetic) Average Return Returns

6. 6 Q. The following are TSE 300 returns for the 1994-1997 period: Year (t)Return (R t ) 1994-0.18% 199514.53 199628.35 199714.98 Calculate: a. holding period return (HPR) b. geometric average return (GAR) c. arithmetic average return (R) Historic Returns - Example 2

7. 7 A. a. holding period return HPR = (1 + R 1994 )(1 + R 1995 )(1 + R 1996 )(1+ R 1997 ) -1 = (1 - 0.0018)(1 + 0.1453)(1 + 0.2835)(1+ 0.1498) -1 = 68.72% b. geometric average return GAR = [(1 + R 1994 )(1 + R 1995 )(1 + R 1996 )(1+ R 1997 )] 1/4 -1 = [1 + HPR] 1/4 -1 = [1.6872] 1/4 -1 = 13.97% c. arithmetic average return Historic Returns - Example 2

8. 8 While return measures reward, we need some measure of uncertainty (variability) associated with that return Other Return Statistics Source: William M. Mercer Ltd.

9. Jacoby, Stangeland and Wajeeh, 20009 uHistoric Return Variance: Average value of squared deviations from the mean. A measure of volatility. uHistoric Standard Deviation: Also measures volatility. Other Return Statistics

10. Jacoby, Stangeland and Wajeeh, 200010 uHistoric Return Variance: uHistoric Standard Deviation: Other Return Statistics - An Example

11. Jacoby, Stangeland and Wajeeh, 200011 Calculating Variance with a Table

12. Jacoby, Stangeland and Wajeeh, 200012 Using Return Statistics The Normal Distribution (based on TSE 300 1994-1997 return data) Probability Return on TSE300 stocks 68% 95% > 99%  – 3  - 20.56%  – 2  - 8.90%  –  + 2.76%  + 14.42%  +  + 26.08%  + 2  + 37.74%  + 3  + 49.4%

13. 13 U.S. Common stocks 13.0% 9.2% 20.3% Long-term U.S. corporate bonds 6.1 2.3 8.7 Long-term U.S. government bonds 5.4 1.6 5.7 U.S. Treasury bills 3.8 3.2 Risk premium Arithmetic (relative to U.S. Standard Series mean Treasury bills) deviation -90%90%0% Modified from Stocks, Bonds, Bills and Inflation: 1998 Yearbook, TM annual updates work by Roger C. Ibbotson and Rex A. Sinquefield (Chicago: Ibbotson Associates). All rights reserved. -90%90%0% -90%90%0% -90%90%0% U.S. Historical Return Statistics