Transcript Chapter 9 – Index of Sample Problems
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.