Some Lessons from Capital Market History
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Transcript of Some Lessons from Capital Market History
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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
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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
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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?
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3: Dividend yield
%11.4
0411.$38.90
$1.60
P
D yield Dividend
t
1t
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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?
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5: Capital gains yield
%71.9
0971.$28.42
$28.42 - $31.18
P
PP yield gains Capital
t
t1t
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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 $31.64 a share.
What is the total return on this stock in dollars?
What is the percentage total return?
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7: Total return
72.2$
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
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History of securities (p.367)
• Large company• Small company• Long-term Government bond• Treasury bill• inflation
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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 $18.20 a share. The inflation rate for the period is 3.5%.
What is your nominal rate of return?
What is your real rate of return?
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9: Nominal vs. real returns
%52.38
)rounded( 3852.50.13$
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(
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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?
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11: Risk premium
7.1%
.071
.025-.096 stockscompany -largeon premium Risk
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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?
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13: Average return
%58.4
0458.5
229.5
.004.132-.216.093.048 return Average
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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?
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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
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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?
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17: Standard deviation
The variance, 2, as computed previously, is .016125.
%70.12
1270.
016125.
2
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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?
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19: Probability distributions
17.28% to8.12%-
.1728 to0812.-range %68
1270.0458.
1x rangey probabilit %68
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20: Probability distributions
29.98% to-20.82%
.2998 to2082.-range %95
254.0458.
)1270.2(0458.
2x rangey probabilit %95
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21: Probability distributions
42.68% to-33.52%
.4268 to3352.-range %99
381.0458.
)1270.3(0458.
3x rangey probabilit %99
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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?
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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%
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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?
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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%
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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
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• Arithmetic average: good for guess the return of one period: optimistic
• Geometric average: good for guess the return of long term: pessimistic
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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
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Chapter
McGraw-Hill/Irwin Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.
12
•End of Chapter 12•End of Chapter 12