Chapter

12

•

Some Lessons from Capital Market History

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

Chapter 12 – Index of Sample Problems • • • • • • • • • •

Slide # 02 - 03 Slide # 04 - 05 Slide # 06 - 07 Slide # 08 - 09 Slide # 10 - 11 Slide # 12 - 13 Slide # 14 - 15 Slide # 16 - 17 Slide # 18 - 23 Slide # 24 - 26 Dividend yield Capital gains yield Total return Nominal vs. real returns Risk premium Average return Variance Standard deviation Probability distributions 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 Dividend yield  D t  1 P t  $1.60

$38.90

 .

0411  4 .

11 %

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 Capital gains yield  P t  1 P t  P t  $31.18

$28.42

$28.42

 .

0971  9 .

71 %

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 Dollar return  P t  1  $ 28  P .

12 t  D t  1  $ 31 .

64  $.

80   $ 2 .

72 Percentage return  P t  1   P t $ 28 .

12 P t   D t  1 $ 31 .

64 $ 31 .

64   $ 2 .

72  $ 31 .

64  .

0860 (rounded)  $.

80   8 .

60 %

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 Nominal rate of return  P t  1   P t $ 18 .

20 P t   D t  1 $ 13 .

50 $ 13 .

50  .

3852 ( rounded )  $.

50  38 .

52 % ( 1  R )  ( 1  r )  ( 1  h ) 1  .

3852  ( 1  r )  ( 1  .

035 ) 1 .

3852  1 .

035  1 .

035 r .

3502  1 .

035 r r  .

3384 (rounded) r  33.84%

10: Risk premium

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

Large-company stocks Long-term corporate bonds 9.6% 5.8% U.S. Treasury bills Inflation 2.5% 1.9%

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

11: Risk premium Risk premium on large company stocks  .096

.025

 .071

 7.1%

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 Average return  .048

 .093

 .216

.132

 .004

5  .

229 5  .

0458  4 .

58 %

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 .048

. 093 .216

-.132

.004

.0458

.0458

.0458

.0458

.0458

Totals .0022

.0472

.1702

-.1778

-.0418

.0000

Squared Deviation .0000

.0022

.0290

.0316

.0017

.0645

 2  .

0645 5  1  .

016125  1 .

61 %

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.

   2  .

016125  .

1270  12 .

70 %

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 68 % probabilit y range 68 % range  x  1   .

0458  .

1270  .

0812 to .1728

 8.12% to 17.28%

20: Probability distributions 95 % probabilit y range  x  2   .

0458  ( 2  .

1270 ) 95 % range  .

0458  .

254  .

2082 to .2998

 -20.82% to 29.98%

21: Probability distributions 99 % probabilit y range  x  3   .

0458  ( 3  .

1270 ) 99 % range  .

0458  .

381  .

3352 to .4268

 -33.52% to 42.68%

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 68%

.129 – (1



.153)

-2.4%

.129 + (1



.153)

95% 99%

.129 – (2



.153)

-17.7%

.129 + (2



.153) .129 – (3



.153)

-33.0%

.129 + (3



.153)

28.2% 43.5% 58.8% 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%.

24: Arithmetic vs. geometric averages

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

0 1 2 3 4

Price

$38.16

$39.43

$38.04

$45.09

$44.10

Dividend

-- $.60

$.62

$.65

$.70

What are the arithmetic and geometric returns for this stock?

25: Arithmetic vs. geometric averages Year Price Dividend Annual return 0 1 2 3 4 $38.16

-- $39.43

$.60

$38.04

$.62

$45.09

$.65

$44.10

$.70

-- ($39.43 - $38.16 + $.60)  $38.16 = 4.90% ($38.04 - $39.43 + $.62)  $39.43 = -1.95% ($45.09 - $38.04 + $.65)  $38.04 = 20.24% ($44.10 - $45.09 + $.70)  $45.09 = -0.64%

26: Arithmetic vs. geometric averages Annual returns: 4.90%, -1.95%, 20.24% and -.64% Arithmetic average  .049

.0195

 .2024

.0064

4  .

0564  5 .

64 % Geometric average  [( 1  .

049 )  ( 1  .

0195 )  ( 1  .

2024 )  1 ( 1  .

0064 )] 4  1  [ 1 .

049  .

9805  1 .

2024  .

9936 ] 4 1  1  [ 1 .

2288 ] 4 1  1  1 .

05286  1  .

05286  5 .

29 %

• •

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

12

•

End of Chapter 12

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