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Chapter10: Some lessons from capital market history

Questions and problems

BASIC QUESTIONS (1–23)

1.  
  <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0071010319/student/pg112_1a.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a>

Selected problems are available in McGraw-Hill Connect Plus.

2.  
3.  
4.  
Calculating Returns. Suppose you bought an 8% coupon bond one year ago for $1090. The bond sells for $1063 today

a.  
Assuming a $1000 face value, what was your total dollar return on this investment over the past year?

b.  
What was your total nominal rate of return on this investment over the past year?

c.  
  
<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0071010319/student/pg46_1.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a>

p. 325

5.

  
Nominal versus Real Returns. What was the average annual return on company shares as measured by the All Ordinaries Index from 1985 to 2009:

a.  
In nominal terms?

b.  
6.  
7.  
<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0071010319/student/pg325_1.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a>

  
<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0071010319/student/pg46_1.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a>

8.  
Risk Premiums. Refer to Table 10.1 in the text and look at the period from March 2000 to December 2004.

a.  
Calculate the average returns for the All Ordinaries Index and cash over this period.

b.  
Calculate the standard deviation of the returns for the All Ordinaries Index and cash over this time period.

c.  
Calculate the observed risk premium in each year for the All Ordinaries Index and cash. What was the average risk premium over this period? What was the standard deviation of the risk premium over this period?

d.  
9.  
Calculating Returns and Variability. You have observed the following returns on White Sands Ltd shares over the past five years: −25%, 36%, 9%, 11% and 17%.

a.  
What was the average return on White Sands shares over this five-year period?

b.  
10.  
Calculating Real Returns and Risk Premiums. For Problem 9, suppose the average inflation rate over this period was 4.2% and the average government bond rate over the period was 5.1%.

a.  
What was the average real return on White Sands shares?

b.  
11.  
12.  
Effects of Inflation. Look at Table 10.1 and Figure 10.7 in the text. When were cash rates at their highest over the period from 1985 to 2009? Why do you think they were so high during this period? What relationship underlies your answer?<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0071010319/student/pg111_4.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a>&<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0071010319/student/pg112_1.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a>

13.  
Calculating Returns.You purchased a $1000 zero coupon bond one year ago for $162.87. The market interest rate isnow 9%. If the bond had twenty years to maturity when you originally purchased it, what was your total return for the past year?<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0071010319/student/pg111_4.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a>

14.  
15.  
Calculating Returns. You bought a $100 000 bond from Melba's Bread last year. When you bought the bond, it had fifteen years until maturity and a YTM of 6.5%. The coupon rate is 9% paid annually. The current market rate for bonds of this type is 8%. What was your rate of return for the year?<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0071010319/student/pg111_4.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a>

16.  
p. 326

17.

  
18.  
19.  
20.  
Calculating Returns. A share was priced at $21.18 at the beginning of the year and $26.72 at the end of the year. The company also paid a dividend of $0.38 per share. What was the total return for the year?<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0071010319/student/pg112_1.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a>

21.  
22.  
23.  

Intermediate Questions (24–31)

24.  
Calculating Returns and Variability. You find a certain share that had returns of 13%, −18%, 9%, and 36% for four of the last five years. If the average return of the share over this period was 11%, what was the share's return for the missing year? What is the standard deviation of the share's returns?<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0071010319/student/pg111_4.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a>

25.  
26.  
Arithmetic and Geometric Returns. A share has had the following year-end prices and dividends:

<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0071010319/student/pg326_1.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a>


  
<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0071010319/student/pg46_1.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a>

27.  
Calculating Returns. Refer to Table 10.1 in the text and look at the period from March 1988 to December 1989.

a.  
Calculate the average return for cash and the average annual inflation rate (consumer price index) for this period.

b.  
Calculate the standard deviation of cash returns and inflation over this time period.

c.  
Calculate the real return for each year. What is the average real return for cash?

d.  
28.  
Calculating Investment Returns. You bought one of Tappan Manufacturing Ltd's 8% $1000 coupon bonds one year ago for $1028.50. These bonds make annual payments and mature nine years from now. Suppose you decide to sell your bonds today, when the required return on the bonds is 7%. If the inflation rate was 4.8% over the past year, what would be your total real return on investment?<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0071010319/student/pg111_4.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a>

p. 327

29.

  
Using Return Distributions. Suppose the returns on government bonds are normally distributed. Based on the historical record, what is the approximate probability that your return on these bonds will be less than −3.4% in a given year? What range of returns would you expect to see 95% of the time? What range would you expect to see 99% of the time?<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0071010319/student/pg112_1.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a>

30.  
Using Return Distributions. Assuming that the returns from holding an investment in company shares are normally distributed, what is the approximate probability that your money will double in value in a single year? What about triple in value?<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0071010319/student/pg112_1.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a>

31.  

Challenge Questions (32–33)

32.  
Using Probability Distributions. Suppose the returns on company shares are normally distributed. Based on the historical record, use the NORMDIST function in Excel® to determine the probability that in any given year you will lose money by investing in shares.<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0071010319/student/pg112_1.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a>

33.  
Using Probability Distributions. Suppose the returns on long-term bonds and cash/bills are normally distributed. Based on the historical record, use the NORMDIST function in Excel® to answer the following questions:

a.  
What is the probability that in any given year, the return on long-term bonds will be greater than 10%? Less than 0%?

b.  
What is the probability that in any given year, the return on cash/bills will be greater than 10%? Less than 0%?

c.  
In the March quarter of 1994, the return on long-term bonds was − 3.02%. How likely is it that such a low return will recur at some point in the future? Cash/bills had a return of 1.18% in this same quarter. How likely is it that such a high return on cash/bills will recur at some point in the future?<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/premium/0071010319/student/pg112_1.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (K)</a>

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