FINA 351 – Managerial Finance, Ch. 10 (Ref 10b)
1.
Investors face a number of risks, including inflation, interest-rate, liquidity, default (or credit), and
taxability risk. The table below helps show why certain investments offer returns as rewards for risks.
A. What investment is considered to be the most “risk-free”? Which three specific types of risks for this
investment are very low and why are these risks so low?
B. What type(s) of risk do T-bonds have that T-bills do not?
C. What type(s) of risks would a 30-year T-bond have that a 30-year municipal bond would not have?
D. What type(s) of risks would a municipal bond have that a T-bond would not?
E. What type(s) of risk do corporate bonds have that T-bonds do not?
F. Do you think that junk bonds would usually have a return greater or smaller than investment-grade
corporate bonds? Why?
G. Why do large and small stocks usually have more default risk than corporate bonds?
H. Why do stocks not have maturity (or interest-rate) risk?
I.
What type(s) of risk would real estate investments have that large stocks would not have?
J. What type(s) of risk would penny stocks have that large stocks would not have?
K. Would you agree with an investment advisor who gave the following advice to an elderly retiree?
“At this point in your life, it would be best to allocate more of your investment portfolio to stocks
than to bonds” Why or why not?
L. Would you agree with an investment advisor who gave the following advice to a young, college
graduate? “At this point in your life, it would be best to allocate more of your investment portfolio to
bonds than to stocks.” Why or why not?
The information in this table is based on the data in Chapter 10, specifically the average data in each
investment category from 1926-2011. It is only a rough estimate of the various risk factors inherent in
investments.
A
B
Real
RiskFree
Rate
Inflation
Risk
Premium
D
Interestrate or
Maturity
Risk
Prem.
E
Liquidity
Risk
Premium
F
Default or
Credit Risk
Premium
G
Total Risk
Premiums
(Sum Col.
B thru F)
H
Total
Return
(Sum
Col. B
thru F)
T-Bills
0.5%
3.1%
0.0%
0.0%
0.0%
3.1%
3.6%
L/T T-Bonds
0.5%
3.1%
2.5%
0.0%
0.0%
5.6%
6.1%
L/T Corp.
Bonds
0.5%
3.1%
2.5%
0.0%
0.3%
5.9%
6.4%
Large Stocks
0.5%
3.1%
N/A
0.0%
8.2%
11.3%
11.8%
Small Stocks
0.5%
3.1%
N/A
0.3%
12.6%
16.0%
16.5%
Investment
Type
C
2. Refer to Figure 10.13 in your text.
A. What is the average risk premium for stocks in 17 countries from 1900-2010?
B. What is the average risk premium for stocks in the U.S.? In Denmark? In Italy?
C. Why do you think risk premiums differ from country to country?
3. Explain the rule of thumb and the graph below to someone who is saving for retirement. Why should a
retirement portfolio be “rebalanced” every few years as one ages (e.g. gradually switching from equity to
fixed income)?
Rule of Thumb:
Subtract your age from 110:
the result is the maximum
percentage of your portfolio
that should be in equities
(stocks). As you age, your
allocation will need to change
(or be rebalanced).
4. The following information is available:
o Total return on XYZ, 30-year, corporate bond is 8%
o Return on U.S. Treasury Bill is 3%
o Current inflation rate, 2%
o Return on 30-year U.S. Treasury Bond is 5%
o The XYZ corporate bond is regularly traded and is very marketable, as are Treasury securities.
The table below shows the different risk premiums that make up the total 8% return on the
corporate bond. Based on this information, answer the questions below:
Component
Rate
Real risk-free rate
1%
Current inflation risk premium
2%
Interest-rate risk premium
2%
Default risk premium
3%
Liquidity risk premium
0%
TOTAL return on XYZ, 30-year, corp. bond
8%
(A) How was the real risk-free rate of 1% calculated?
(B) How was the interest-rate risk premium of 2% calculated?
(C) How was the default risk premium of 3% calculated?|
(D) Why is the liquidity risk premium zero?
5.
Answer the following questions about normally distributed investment returns (use Figure 10.10 in your
text, reproduced below, which includes 1926-2011 data):
A. What percent chance is there that you will get a return on an investment in T-Bills that is higher
than 6.7%? [Hint: notice that a T-bill has an average return of 3.6% and a standard deviation of 3.1%. Moving
one standard deviation to the right of the average (3.6% + 3.1%) gives us 6.7%. The question is asking, what is the
area under the curve that is greater than (or to the right of) one standard deviation? The answer is approx. 16% or
about 1/6 of the area under the curve.]
B.
What is the probability that your return will be less than -3.7% on long-term government bonds?
C.
What range of returns on long-term government bonds would you expect to see 95% of the time?
D.
What percent chance is there that long-term corporate bonds will return more than 31.6%?
E.
About how often would you expect to see a return on large stocks less than -28.8%?
F.
What chance is there that returns on large stocks will fall between –49.1% and 72.7%?
G.
What is the approximate probability (give a range) that your portfolio of small stocks will double
in value in one year? (Hint: doubling in value in one year means 100% return).
1926-2011
Type of Security
T-Bills
Interm. T-Bonds
L/T Gov't. Bonds
L/T Corp. Bonds
Large Co. Stocks
Small Co. Stocks
SD
3.1
5.7
9.8
8.4
20.3
32.5
99%
-3 SD
-5.7
-11.6
-23.3
-18.8
-49.1
-81
95%
-2 SD
-2.6
-5.9
-13.5
-10.4
-28.8
-48.5
68%
-1 SD
0.5
-0.2
-3.7
-2
-8.5
-16
AVG
3.6
5.5
6.1
6.4
11.8
16.5
68%
+1 SD
6.7
11.2
15.9
14.8
32.1
49
95%
+2 SD
9.8
16.9
25.7
23.2
52.4
81.5
99%
+3 SD
12.9
22.6
35.5
31.6
72.7
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