Jacoby, Stangeland and Wajeeh, 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

Jacoby, Stangeland and Wajeeh, 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

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

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

Jacoby, Stangeland and Wajeeh, 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 Q. The following are TSE 300 returns for the period: Year (t)Return (R t ) % Calculate: a. holding period return (HPR) b. geometric average return (GAR) c. arithmetic average return (R) Historic Returns - Example 2

7 A. a. holding period return HPR = (1 + R 1994 )(1 + R 1995 )(1 + R 1996 )(1+ R 1997 ) -1 = ( )( )( )( ) -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 While return measures reward, we need some measure of uncertainty (variability) associated with that return Other Return Statistics Source: William M. Mercer Ltd.

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

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

Jacoby, Stangeland and Wajeeh, Calculating Variance with a Table

Jacoby, Stangeland and Wajeeh, Using Return Statistics The Normal Distribution (based on TSE return data) Probability Return on TSE300 stocks 68% 95% > 99%  – 3  %  – 2  %  –  %  %  +  %  + 2  %  + 3  %

13 U.S. Common stocks 13.0% 9.2% 20.3% Long-term U.S. corporate bonds Long-term U.S. government bonds U.S. Treasury bills 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