Chapter

McGraw-Hill/Irwin Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.

12•Some Lessons from Capital

Market History •Some Lessons from Capital

Market History

Chapter 12 – Index of Sample Problems

• Slide # 02 - 03 Dividend yield• Slide # 04 - 05 Capital gains yield• Slide # 06 - 07 Total return• Slide # 08 - 09 Nominal vs. real returns• Slide # 10 - 11 Risk premium• Slide # 12 - 13 Average return• Slide # 14 - 15 Variance• Slide # 16 - 17 Standard deviation• Slide # 18 - 23 Probability distributions• Slide # 24 - 26 Arithmetic vs. geometric averages

2: Dividend yield

The common stock of Abaco Co. is expected to pay $1.60 in dividends next year. Currently, the stock is selling for $38.90 a share.

What is the dividend yield?

3: Dividend yield

%11.4

0411.$38.90

$1.60

P

D yield Dividend

t

1t

4: Capital gains yield

Last year, you purchased shares of Baker and Sons, Inc. at a price of $28.42 a share. Since that time you have received $1.20 in dividends per share. Currently, the stock is selling for $31.18 per share.

What is the capital gains yield?

5: Capital gains yield

%71.9

0971.$28.42

$28.42 - $31.18

P

PP yield gains Capital

t

t1t

6: Total return

Zoma Enterprises pays $.80 a year as a dividend on their common stock. Currently, this stock sells for $28.12 a share. Last year at this time the stock was selling for $31.64 a share.

What is the total return on this stock in dollars?

What is the percentage total return?

7: Total return

72.2$

80$.64.31$12.28$

DPP return Dollar 1tt1t

%60.8

(rounded) 0860.64.31$

72.2$64.31$

80$.64.31$12.28$

P

DPP return Percentage

t

1tt1t

History of securities (p.367)

• Large company• Small company• Long-term Government bond• Treasury bill• inflation

8: Nominal vs. real returns

Last year, you purchased shares of Benson and Judges, Inc. stock for $13.50 a share. Since then you received $.50 per share in dividends. Today, you sold your shares for $18.20 a share. The inflation rate for the period is 3.5%.

What is your nominal rate of return?

What is your real rate of return?

9: Nominal vs. real returns

%52.38

)rounded( 3852.50.13$

50$.50.13$20.18$

P

DPP return of rate Nominal

t

1tt1t

33.84%r

(rounded) 3384.r

r035.13502.

r035.1035.13852.1

)035.1()r1(3852.1

)h1()r1()R1(

10: Risk premium

Assume that the following are the average annual returns for the past decade:

Large-company stocks 9.6%

Long-term corporate bonds 5.8%

U.S. Treasury bills 2.5%

Inflation 1.9%

What is the risk premium on large-company stocks for this time period?

11: Risk premium

7.1%

.071

.025-.096 stockscompany -largeon premium Risk

12: Average return

A stock returned 4.8%, 9.3%, 21.6%, -13.2% and 0.4% for the past five years, respectively.

What is the average rate of return for the past five years?

13: Average return

%58.4

0458.5

229.5

.004.132-.216.093.048 return Average

14: Variance

A stock returned 4.8%, 9.3%, 21.6%, -13.2% and 0.4% for the past five years, respectively.

What is the variance?

15: Variance

Actual

Return

Average Return

Deviation Squared

Deviation

.048 .0458 .0022 .0000

. 093 .0458 .0472 .0022

.216 .0458 .1702 .0290

-.132 .0458 -.1778 .0316

.004 .0458 -.0418 .0017

Totals .0000 .0645

%61.1

016125.15

0645.2

16: Standard deviation

A stock returned 4.8%, 9.3%, 21.6%, -13.2% and 0.4% for the past five years, respectively.

The variance is .016125.

What is the standard deviation?

17: Standard deviation

The variance, 2, as computed previously, is .016125.

%70.12

1270.

016125.

2

18: Probability distributions

A stock has an average rate of return of 4.58% and a standard deviation of 12.70%. Assume that the returns are normally distributed.

What range of returns would you expect to see 68% of the time?

95% of the time? 99% of the time?

19: Probability distributions

17.28% to8.12%-

.1728 to0812.-range %68

1270.0458.

1x rangey probabilit %68

20: Probability distributions

29.98% to-20.82%

.2998 to2082.-range %95

254.0458.

)1270.2(0458.

2x rangey probabilit %95

21: Probability distributions

42.68% to-33.52%

.4268 to3352.-range %99

381.0458.

)1270.3(0458.

3x rangey probabilit %99

22: Probability distributions

A stock has an average rate of return of 12.9% and a standard deviation of 15.3%. Assume the returns are normally distributed.

What is the probability that you will lose more than one-third of your investment in this stock in any one year?

23: Probability distributions

The probability of losing more than one-third (33%)of your investment in this stock in any one year is less than ½ of 1%.

68% .129 – (1 .153)

-2.4% .129 + (1 .153) 28.2%

95% .129 – (2 .153)

-17.7% .129 + (2 .153) 43.5%

99% .129 – (3 .153)

-33.0% .129 + (3 .153) 58.8%

24: Arithmetic vs. geometric averages

A stock has the following year-end prices and dividends.

Year Price Dividend

0 $38.16 ---

1 $39.43 $.60

2 $38.04 $.62

3 $45.09 $.65

4 $44.10 $.70

What are the arithmetic and geometric returns for this stock?

25: Arithmetic vs. geometric averages

Year Price Dividend Annual return

0 $38.16 --- ---

1 $39.43 $.60 ($39.43 - $38.16 + $.60) $38.16 = 4.90%

2 $38.04 $.62 ($38.04 - $39.43 + $.62) $39.43 = -1.95%

3 $45.09 $.65 ($45.09 - $38.04 + $.65) $38.04 = 20.24%

4 $44.10 $.70 ($44.10 - $45.09 + $.70) $45.09 = -0.64%

26: Arithmetic vs. geometric averages

%64.5

0564.4

.0064-.2024.0195-.049 average Arithmetic

Annual returns: 4.90%, -1.95%, 20.24% and -.64%

%29.5

05286.

105286.1

1]2288.1[

1]9936.2024.19805.049.1[

1)]0064.1()2024.1()0195.1()049.1[( average Geometric

4

1

4

1

4

1

• Arithmetic average: good for guess the return of one period: optimistic

• Geometric average: good for guess the return of long term: pessimistic

Capital market efficiency

• Degree of reflecting information• Efficiency Market Hypothesis (EMH)• Strong form: all available information• Semistrong form: all public information• Weak form: current price reflect all past

stock’s price

Chapter

McGraw-Hill/Irwin Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.

12

•End of Chapter 12•End of Chapter 12