Exercise 1 – True or False
Name: ___________________________________________
Score: ________
Section: ________________________________
Instruction: Write T if the answer is True and F if the answer is False on the space provided for each
number.
_________ 1. The default risk premium, as a component of interest rate, is additional compensation for
the risk that the issuer will not be able to pay on scheduled interest payments.
Answer: True
_________ 2. The market risk premium is a component of interest rate which is present in a long-term
corporate issued debt security but not on a long-term government-issued debt security. Answer: False
_________ 3. The default risk premium is present in treasury securities than incorporate-issued debt
securities because multinational companies can meet their short-term as well as long-term obligations.
Answer: False
_________ 4. The real risk-free rate as a component of interest rate is present in all kinds of debt security
whether corporate-issued or government-issued, while inflation premium is only present in
government-issued security such as the Treasury bill yield.
Answer: False
_________ 5. The Treasury bill (T-bill) yield or rate is the nominal risk-free rate which is composed of
real risk-free rate plus expected inflation rate for the year.
Answer: True
_________ 6. The interest rate components of an 8-year corporate issued bond are nominal risk-free rate,
plus average inflation for 8 years, plus maturity risk premium, plus default risk premium plus liquidity
premium.
Answer: False
_________ 7. Everything held constant, a 10-year treasury bond has a higher nominal interest rate than a
10-year corporate bond due to the effect of default and liquidity.
Answer: False
_________ 8. If the inflation rate is highly significant, the nominal risk-free rate computation uses the
cross- term format of [(1 + r*) x (1 + IP)] – 1].
Answer: True
_________ 9. The four most fundamental factors that affect the cost of money are (1) production
opportunities, (2) economic and political conditions, (3) risk, and (4) inflation.
Answer: False
_________10. Inflation premium is present in all types of debt securities, short-term or long-term,
treasury or corporate.
Answer: True
_________11. The difference between long-term government issued debt security and long-term
corporate issued security is the corporate bond yield spread.
Answer: True
_________12. The real risk-free rate is the increment of purchasing power that the lender earns to induce
him or her to forego current consumption.
Answer: True
_________13. If you earn 0.6 percent a month in your bank account, this would be the same as earning a
7.2 percent annual interest rate with annual compounding.
Answer: False
_________14. An investor earned a 5 percent nominal risk-free rate over the year. However, over the
year, prices increased by 2 percent. The investor's real risk-free rate was greater than his nominal rate of
return.
Answer: False
_________15. Households generally supply less funds to the markets as their income and wealth
increase, other things being equal.
Answer: False
_________16 An increase in the perceived riskiness of investments would cause a movement down along
the supply curve.
Answer: True
_________17. When the economic conditions of one country improve, the demand for funds will increase
causing the equilibrium on the interest rate to increase.
Answer: True
_________18. When the near-term spending needs decreases, the supply of funds increases causing the
equilibrium of interest rate to decrease.
Answer: True
_________19. The lack of restrictiveness of non-price conditions (fees, collateral, etc.) on borrowed funds
will cause the demand of funds to decrease causing the equilibrium of interest rate to increase.
Answer: False
_________20. When the flow of foreign funds improves, the supply of funds will increase causing the
equilibrium of interest rate to increase.
Answer: False
Exercise 2– Multiple Choice Concepts
Name: ___________________________________________
Score: ________
Section: ________________________________
Instruction: Encircle the letter that corresponds to your answer.
1. Which of the following statements would likely affect an increase in income tax rates?
Statement I
Statement II
Statement III
a.
b.
c.
d.
Decrease the savings rate.
Decrease the supply of loanable funds.
Increase interest rates.
Statements I and II are true.
Statements II and III are true.
Statements I and III are true.
All statements are true.
2. According to the liquidity premium theory of interest rates,
a. the term structure must always be downward sloping.
b. long-term security will always have a higher interest rate than short-term security
c. investors prefer certain maturities and will not normally switch out of those maturities.
d. investors are indifferent between different maturities if the long-term spot rates are equal to the
average of current and expected future short-term rates.
3. Miss Malto wants to be able to buy 6 percent more goods and services in the future to induce her to
invest today. During the investment period prices are expected to rise by 2 percent. Which
statement(s) below is/are true?
I.
II.
III.
a.
b.
c.
d.
6 percent is the desired real risk-free interest rate.
8 percent is the approximate nominal rate of interest required.
2 percent is the expected inflation rate over the period.
I and II are true
II and III are true
I and III are true
All are true
4. Inflation causes the supply curve to shift to the ________ and causes the demand curve for loanable
funds to shift to the ________.
a. right; right
b. right; left
c. left; left
d. left; right
5. Which of the following statements would increase the supply of funds, all else being equal?
Statement I
Statement II
a.
b.
c.
d.
The perceived riskiness of all investments decreases.
Current income and wealth levels increase.
Statement I only
Statement II only
Statements I and II
None of the above
6. It refers to the relationship between maturity and yield to maturity.
a. term structure
b. correlational structure
c. bond indenture
d. Fisher effect
7. Which of the following pertains to the unbiased expectations theory?
a. liquidity premiums are negative and time-varying.
b. markets are segmented and buyers stay in their segment.
c. the long-term spot rate is an average of the current and expected future short-term interest
rates.
d. the term structure will most often be upward sloping.
8. According to the ____________________ theory, interest rates are determined by the interaction
between the aggregate demand and supply of loanable funds for each segment.
a. Liquidity premium
b. Market segmentation
c. Unbiased expectations
d. Fischer effect
9. You go to the Bangko Sentral ng Pilipinas and notice that yields on almost all corporate and Treasury
bonds have decreased. The yield decreases may be explained by which one of the following?
a. Increases in the Philippine government budget deficit
b. Newly expected decline in the value of the peso
c. A decrease in Philippine inflationary expectations
d. An increase in current and expected future returns of real corporate investments
10. The difference between long-term corporate bonds and long-term government banks is
a. inflation premium and default risk premium.
b. special provision and maturity risk premium.
c. default risk premium and liquidity premium.
d. default risk premium and maturity risk premium.
Exercise 3 – Multiple Choice Concepts
Name: ___________________________________________
Score: ________
Section: ________________________________
Instruction: Encircle the letter that corresponds to your answer.
1. In general, financial security with good credit standing will offer ____.
a. higher yield
b. lower yield
a. the same yield
b. yields depending on the move of the lender.
2. Credit (default) risk is likely to be lowest for:
a. AAA corporate securities
b. Treasury bonds
c. BBB corporate securities
d. AA corporate securities
3. According to the market segmentation theory, if most investors suddenly preferred to invest in
long-term securities and most borrowers suddenly preferred to issue short-term securities, there would
be
a. Upward pressure on the price of long-term securities and upward pressure on the yield of
long-term securities.
b. downward pressure on the price of long-term securities.
c. downward pressure on the short-term yields.
d. downward pressure on the yield of long-term securities.
4. Holding other factors such as risk constant, the relationship between the maturity and the yield of debt
securities is called the:
a. default structure of interest rates
b. market segmentation theory
c. liquidity structure of interest rates
d. answer not given
5. If shorter-term securities have lower annualized yields than longer-term securities, the yield curve
a. is horizontal.
b. is upward sloping.
c. is downward sloping.
d. Answer not given
6. Assume that annualized yields of treasury bills and treasury bonds are equal. If investors suddenly
believe interest rates will increase, their actions may cause the yield curve to
a. become inverted.
b. become flat.
c. become upward sloping.
d. be unaffected.
7. The yield offered on a corporate bond is ____________ related to the prevailing risk-free rate and
____________ related to the security's risk premium.
a. negatively; negatively
b. negatively; positively
c. positively; negatively
d. positively; positively
8. According to the liquidity premium theory, an investor who earns a 6.0% yield on two-year security
will ____ the expected yield from consecutive investments in one-year securities.
a. equal
b. be less than
c. be greater than
d. cannot be determined
9. The theory of the term structure of interest rates, which states that investors and borrowers choose
securities with maturities that satisfy their forecasted cash needs, is the
a. Fischer effect theory.
b. pure expectations theory.
c. liquidity premium theory.
d. segmented markets theory.
10. Other things being equal, the yield required on AA-rated bonds should be ____ the yield required on
AAA-rated bonds whose other characteristics are the same.
a. greater than
b. equal to
c. less than
d. All of these are possible, depending on the size of the bond offering.
11. An upward-sloping yield curve indicates that Treasury securities with ____ maturities offer ____
annualized yields.
a. shorter; lowest
b. shorter; higher
c. longer; lower
d. longer; higher
12. The yield curve for corporate bonds
a. is irrelevant to the investors
b. would typically lie below the Treasury yield curve.
c. identical to the Treasury yield curve.
d. typically has the same slope as the Treasury yield curve.
Exercise 4 – Multiple Choice - Problems
Name: ___________________________________________
Score: ________
Section: ________________________________
Instruction: Encircle the letter that corresponds to your answer.
1. Ms. Alto invested in the current one-year Treasury bill with a rate of 3.15 percent. The expected
one-year rate 12 months from now is 5.15 percent. According to the unbiased expectations theory,
what should be the current rate for a two-year Treasury security?
a. 3.70 percent
b. 4.15 percent
c. 2.36 percent
d. 4.74 percent
0.5
Answer: 1R2 = [(1 + .0315)(1 + .0515)] − 1 = 0.04145 or 4.15%
2. What is the real risk-free rate of return (r*) if a 1-year T-bills currently yield 7.00% and the future
inflation rate is expected to be constant at 2.60% per year?
a. 3.80%
b. 3.99%
c. 4.19%
d. 4.40%
Answer:
r = r* + IP
0.07 = r* + 0.026
r* = 0.07 – 0.026
= 0.044 or 4.40%
3. Currently, 10-year T-bonds have a yield of 5.00% and 10-year corporate bonds yield 6.75%. Also,
corporate bonds and T-bonds have a liquidity premium of 0.30% and zero, consecutively. The
maturity risk premium on both Treasury and corporate 10-year bonds is 1.15%. What is the default
risk premium on corporate bonds?
a. 1.08%
b. 1.20%
c. 1.32%
d. 1.45%
Answer
DRP + LP = Corporate bond – T-bonds
DRP + 0.30% = 6.75% - 5.00%
DRP = 6.75% - 5.00% - 0.30%
DRP = 1.45%
4. ABC Corporation's 5-year bonds yield 6.50% and 5-year T-bonds yield 4.70%. The real risk-free rate
is r* = 2.5%, the inflation premium for 5-year bonds is IP = 1.50%, the default risk premium for
ABC’s bonds is DRP = 1.35% versus zero for T-bonds, and the maturity risk premium for all bonds is
found with the formula MRP = (t – 1) × 0.1%, where t = number of years to maturity. What is the
liquidity premium (LP) on ABC's bonds?
a. 0.36%
b. 0.41%
c. 0.45%
d. 0.50%
Answer:
DRP + LP = Corporate bond – T-bonds
1.35% + LP = 6.50% - 4.70%
LP = 6.50% - 4.70% - 1.35%
= 0.45%
5. Currently, the interest rate on a 1-year T-bond is 5.0% and that on a 2-year T-bond is 6.37%.
Assuming the pure expectations theory is correct, what is the market's forecast for 1-year rates 1 year
from now?
a. 7.36%
b. 7.76%
c. 8.16%
d. 9.04%
Answer
R2 = [(1 +1R1) (1 + E(2r1))]1/2
(1.0637)2 = (1.05) (1 + E(2r1))
1.1315 = 1 + E(2r1)
1.05
E(2r1) = 1.0776 – 1
= 0.0776 or 7.76%
1
6. Utangan Corporation requires a 4 percent increase in purchasing power to induce to lend. Urangan
expects inflation to be 3 percent next year. The nominal rate the firm must charge is about
a. 4 percent.
b. 3 percent.
c. 1 percent.
d. 7 percent.
Answer
r = r* + IP
= 4% + 3%
= 7%
7. This year, 2021, the real risk-free rate of interest is 7 percent. Inflation is expected to be 4 percent this
coming 2022, will increase to 5 percent in 2023 and increase to 6 percent in 2024. According to the
expectations theory, what should be the interest rate on 3-year, risk-free securities today?
a.
b.
c.
d.
6%
8%
12%
18%
Answer
4%+5%+6%
= 5%
𝐼𝑃 =
3
r = r* + IP
= 7% + 5%
= 12%
8. The following information was provided by APM.
r* = real risk-free rate
The maturity risk premium on 10-year T-bonds
The maturity risk premium on an on 1-year bonds
Default risk premium on 10-year, A-rated bonds
Liquidity premium
Going interest rate on 1-year T-bonds
3%
2%.
0%
1.5%.
0%.
9.5%.
What is the expected rate of inflation during the next year?
a. 3.5%
b. 4.5%
c. 5.5%
d. 6.5%
Answer
r = r* + IP + DRP + LP + MRP
9.5% = 3% + IP + 0 + 0 + 0
IP = 6.5%
9. The following information were provided to you for analysis.
Real risk-free rate is r*
Inflation premium for 5-year bonds is IP
Liquidity premium for Huang’s bonds
Liquidity premium from for T-bonds
3.0%
1.75%
0.09%
0.00%
The maturity risk premium for all bonds is found with the formula MRP = (t – 1) × 0.1%, where t =
number of years to maturity.
If Huang Corporation's 5-year bonds yield is 12.50%, and the 5-year T-bonds yield 5.15%, what is the
default risk premium (DRP) on Huang's bonds?
a. 5.94%
b. 6.60%
c. 7.26%
d. 7.99%
Answer
DRP + LP = Corporate bond – T-bond
DRP + 0.75% = 12.50% - 5.15%
DRP = 12.50% - 5.15% - 0.09%
= 7.26%
10. Currently, the real risk-free rate is r* = 2.75%, the inflation premium for 5-year bonds is IP = 1.65%,
liquidity premium is 2%, the default risk premium for Sarah bonds is DRP = 1.20% versus zero for
T-bonds, and the maturity risk premium for all bonds is found with the formula MRP = (t – 1) × 0.1%,
where t = number of years to maturity. If the 5-year T-bonds yield 4.80%, what is the yield of the
corporate bond?
a. 4.8%
b. 6.0%
c. 6.8%%
d. 8.0%
Answer
DRP + LP = Corporate bond – T-Bond
1.20% + 2.0% = Corporate bond – 4.80%
Corporate bond = 4.80% + 1.20% + 2.0%
= 8.0%
Exercise 5 – Multiple Choice - Problems
Name: ___________________________________________
Score: ________
Section: ________________________________
Instruction: Encircle the letter that corresponds to your answer.
1. Kimi is wanting to invest in government security. In this regard she conducted research and found out
that the real risk-free rate is 3.00%, the average expected future inflation rate is 2.25%, and a maturity
risk premium of 0.10% per year to maturity applies, i.e., MRP = 0.10%(t), where t is the years to
maturity. What rate of return would Kimi expect on a 2-year Treasury security, assuming the pure
expectations theory is NOT valid?
a. 5.25%
b. 5.45%
c. 6.75%
d. 6.95%
Answer
r = r* + IP + MRP
= 3.0% + 2.25% + 0.10(2)
= 5.45%
2.
Let us assume that the real risk-free rate is r* = 3.5%, the default risk premium for ADT's bonds is
DRP = 1.90% versus zero for T-bonds, the liquidity premium on ADT's bonds is LP = 1.3%, and the
maturity risk premium for all bonds is found with the formula MRP = (t – 1) × 0.1%, where t = number
of years to maturity. If ADT Corporation's 5-year bonds yield 8.5% and 5-year T-bonds yield 5.3%,
what is the inflation premium (IP) on all 5-year bonds?
a. 1.02%
b. 1.20%
c. 1.32%
d. 1.40%
Answer
r = r* + IP + MRP + DRP + LP
8.5% = 3.5% + IP + (5 – 1)0.1% + 1.9% + 1.3%
IP = 8.0% - 3.5% - 0.4% - 1.9% - 1.3%
= 1.40%
3. Let us assume that the real risk-free rate is r* = 2.5%, the default risk premium for SGC's bonds is DRP
= 0.50%, the liquidity premium on SGC's bonds is LP = 2.0% versus zero on T-bonds, and the inflation
premium (IP) is 1.5%. If SGC Inc's 5-year bonds yield 7.5% and 5-year T-bonds yield 4.80%, what is
the maturity risk premium (MRP) on all 5-year bonds?
a. 0.70%
b. 0.80%
c. 0.90%
d. 1.00%
Answer
r = r* + IP + MRP + DRP + LP
7.5% = 2.5% + 1.5% + MRP + 0.50% + 2.0%
MRP = 7.5% - 2.5% - 1.5% - 0.50% -2.2%
= 0.8%
4. ABC Corporation invested in a 1-year T-bills that currently yield 7.00%. It is expected that the future
inflation rate to be constant at 2.60% per year. What is the real risk-free rate of return, r*? The
cross-product term should be considered, i.e., if averaging is required, use the geometric average.
a. 3.68%
b. 4.06%
c. 4.29%
d. 4.48%
Answer
r* = 1.070 - 1
1.026
= 0.0429 or 4.29%
5. ABC Corporation is planning to invest in a 1-year T-bond that yields 5.0% or in a 2-year T-bond that
yields 7.0%. Assuming that the pure expectations theory is correct, what is the market's forecast for
1-year rates 1 year from now to make an investment indifferent for both options?
a. 7.75%
b. 8.16%
c. 8.59%
d. 9.04%
Answer
R2 =
1.07 =
(1.07)2 =
1.1449 =
1.05
1.09039 – 1 =
E(2r1)
1
[(1 + 1R1) (1 + E(2r1)]1/2 - 1
[(1.05) (1 + E(2r1)]1/2 - 1
(1.05) (1 + E(2r1)]
1 + E(2r1)
E(2r1)
0.09039 or 9.04%
6. Assume MNO Corporations are indifferent among security maturities. Today, the annualized 2-year
interest rate is 12 percent, and the 1-year interest rate is 8 percent. What is the forward rate according
to the pure expectations theory?
a. 3.70%
b. 4.14%
c. 16.15%
d. 25.44%
Answer
R2 =
0.12 =
(1.12)2 =
1.2544 =
1.08
1.1615 – 1 =
E(2r1)
1
[(1 + 1R1) (1 + E(2r1)]1/2 - 1
[(1.09) (1 + E(2r1)]1/2 - 1
(1.09) (1 + E(2r1)]
1 + E(2r1)
E(2r1)
0.1615 or 16.15%
7. ABC Corporation is planning to invest in the 2nd period with a one-year maturity. Assume that the
current yield on one-year securities is 6 percent and that the yield on two-year security is 7 percent. If
the liquidity premium on two-year security is 0.4 percent, what is the expected one-year forward rate?
a. 6.42 percent.
b. 7.58 percent.
c. 8.07 percent
d. 14.49 percent.
R2 =
0.07 =
(1.07)2 =
1.1449 =
1.1449 – 1 =
1.06424
2R1 =
1
[(1 + 1R1) ((1 + 2R1 ) + LP)]1/2 - 1
[(1.06) ((1 + 2R1) + 0.004)]1/2
(1.06)(1.0042R1) - 1
1.064242R1 - 1
2R1
0.07579 or 7.58%
8. The annualized interest rate on three-year security is 10 percent, while the annualized interest rate on
two-year security is 7 percent. Use this information to estimate the one-year forward rate two years
from now.
a. 2.80%
b. 3.00%
c. 16.25%
d. 18.61%
Answer:
R1 = (1 + 1R3)3 -1
(1 + 1R2 )2
1.103 – 1
1.072
0.1625 or 16.25%
2
9. Assume that interest rates for one-year securities are expected to be 2 percent today, 4 percent one
year from now, and 6 percent two years from now. Using only the pure expectations theory, what are
the three-year securities?
a.
3.98%
b.
4.50%
c.
6.00%
d.
8.28%
Answer:
R3 =
(1 + 1R3)3 =
1R3 =
1R3 =
1
[(1 + 1R1) (1 + 2R1) (1 + 3R1)]1/3 - 1
[(1.02)(1.04)(1.06)]
√1.124448 - 1
0.0398 or 3.98%
10. Bangko Sentral ng Pilipinas reported the following interest rates of 2.25 percent, 2.60 percent, 2.30
percent, and 3.20 percent for three-year, four-year, five-year, and six-year Treasury note yields,
respectively. According to the unbiased expectations theory of the term structure of interest rates,
what is the expected one-year rate for year 6?
a. 3.66%
b. 4.51%
c. 4.61%
d. 7.82%
Answer
6
5
6F1 = [(1.0320) / (1.0230) ] – 1 = 7.82%
Exercise 6 – Straight Problems
Name: ___________________________________________
Score: ________
Section: ________________________________
Instruction: Write the answer in the space provided for each number.
1. Bangko Sentral ng Pilipinas (BSP) issued T-bills which are currently yielding 5%. Paolo, a broker at
BPI-Security, estimated that the inflation premium (expected average inflation rate per year), liquidity
premium, default risk premium, and maturity risk premium amount to 3%, 1.5%, 4%, and 3.5%,
respectively.
Required:
a. What is the real risk-free rate of return if the inflation rate is assumed to be low or insignificant?
Answer:
r=
5% =
r* =
r* =
r* + IP
r* + 3%
5% - 3%
2%
b. What is the interest rate for a corporate bond if the inflation rate of 3% is assumed to be too high
or significant (since the inflation rates for the past years only average 0.5% per year), hence use
of cross-term or crossing approach is necessary? (Note: Use the real risk-free rate of return
computed in the preceding number)
Answer:
r = r* + IP + MRP + DRP + LP
= [(1.02)(1.03) – 1] + 0.035 + 0.04 + 0.015
= 0.1406 or 14.06%
2. The real risk-free rate, r*, is 4%. Inflation is expected to average 4% a year for the first three years,
after which time inflation is expected to average 3% a year. Assume that there is a 1.5% maturity risk
premium, which applies to 4-year security. Maturity risk premium increases by 0.5% per year.
Assume that the liquidity premium on the corporate bond is 1% and is constant for all securities of
different terms or lengths.
Required
a. What is the default risk premium for a 4-year corporate bond that has a yield of 12%?
Answer:
r=
12% =
DRP =
=
r* + IP + MRP + DRP + LP
4.0% + [((4% x 3) + 3%)/4] + 1.5% + DRP + 1.0%
12.0% - 4.0% - 3.75% - 1.5% - 1.0%
1.75%
b. Assume that the default risk premium is 3.7%, what is the interest rate for a 7-year treasury bond?
Answer:
r=
=
=
=
r* + IP + MRP
4.0% + [((4% x 3) + (3% x 4)/7] + [1.50% + (0.5% x 3)]
4.0% + 3.43% + 3.0%
10.43%
c. Assume that the default risk premium is 1.2%, what is the interest rate for short-term corporate
security or commercial paper?
Answer:
r = r* + IP + DRP + LP
= 4.0% + 4.0% + 1.20% + 1.0%
= 10.20%
3. Due to the expected changes in the global economy, the inflation rate from 2020 to 2022 is projected
to average 4.5% per year after which the inflation is expected to average 3% per year. The real
risk-free rate, r*, is 1.5%, the maturity risk premium is 2%, liquidity premium is 1.8% and the default
risk premium is 2.2%.
Required:
a. What is the expected yield on a 360-day T-bill in 2021 to be purchased at the beginning of 2021?
Answer:
r = r* + IP
= 1.5% + 4.5%
= 6.0%
b. What is the expected yield on a 360-day T-bill in 2023 to be purchased at the beginning of 2023?
Answer: 4.50%
r = r* + IP
= 1.5% + 3.0%
= 4.50%
4. A Treasury bond that matures in 12 years has a yield of 8%. A 12-year corporate bond has a yield of
12%. Assume that the liquidity premium on the corporate bond is 1.8% and the maturity risk
premium is estimated to be 0.1 x (t – 1)%. The expected average inflation per year is 3.2%.
Required:
a. What is the default risk premium on the corporate bond?
Answer:
Treasury bond = 12 years
r = r* + IP + MRP
8.0% = r* + 3.2% + 0.1%(12 – 1)
r* = 8.0% - 3.2% - 1.1%
= 3.7%
Corporate bond
DRP = r – r* – IP - MRP – LP
= 12.0% - 3.7% - 3.2% - 1.1% - 1.80%
= 2.2%
b. What is the real risk-free rate?
Answer: 3.70%
Treasury bond = 12 years
r = r* + IP + MRP
8.0% = r* + 3.2% + 0.1%(12 – 1)
r* = 8.0% - 3.2% - 1.1%
= 3.7%
c. What will be the difference in the maturity risk premiums of a 10-year corporate bond and a
6-year corporate bond?
Answer: 0.40%
MRP = (10 – 6)0.10%
0.40%
5. What will be the difference in the maturity risk premiums of a 10-year corporate bond and a 10-year
Treasury bond?
Answer: Zero
Exercise 7 – Straight Problems
Name: ___________________________________________
Score: ________
Section: ________________________________
Instruction: Write the answer in the space provided for each number.
1. The following are estimates of yields/returns and premiums:
Treasury bill rate = 3%
Inflation premium (average yearly inflation rate) =1.8%
4-year Treasury bond yield = 5.5%
Default risk premium (DRP) = 2.2%
Liquidity premium (LP) = 1.4%
Note: The DRP and LP are the same for all securities of different terms.
Compute for the following:
a. Real risk-free rate of return (r*)
Answer:
r = r* + IP
3.0% = r* - 1.8% = 1.20%
b. Nominal risk-free rate of return (or)
Answer:
r = r* + IP
= 1.2% - 1.8% = 3.0%
c. Maturity risk premium
Answer:
MRP = r - r* - IP
= 5.5% - 1.2% - 1.8%
= 2.5%
d. Yield on a short-term corporate security
Answer: 6.60%
r = r* + IP + DRP + LP
= 1.2% + 1.8% + 2.2% + 1.4%
= 6.6%
e. Yield on a 4-year corporate security
Answer: 9.10%
r = r* + IP + MRP +DRP + LP
= 1.2% + 1.8% + 2.5% + 2.2% + 1.4%
= 9.1%
f.
Corporate bond yield spread
Answer: 3.60%
DRP + LP = 2.2% + 1.4%
= 3.6%
2. An analyst is evaluating securities in a developing nation where inflation is very high. As a result, the
analyst has been warned not to ignore the cross-product between the real rate and inflation. The
analyst has determined that the real risk-free rate is at 3% and the treasury bill yields 7.5%. What is
the inflation rate (inflation premium)?
Answer:
rrf =
1.075 =
(1.075/1.03) -1=
IP =
[(1 + r*)(1 + IP)] – 1
(1.03) (1 + IP)
IP
0.04368 or 4.37%
3. The treasury bond has a real-risk-free rate is 2.7% and inflation is expected to be 2% for the first two
years, 3% for the next three years, and 4% thereafter. Maturity risk premium is estimated to be [0.08
x (t -1)] %.
Required:
a. What is the nominal risk-free rate for a treasury bill?
Answer: 4.70%
r = r* + IP
= 2.7% + 2.0%
= 4.7%
b. What is the yield on a 6-year Treasury security?
Answer: 5.93%
r = r* + IP + MRP
= 2.7% + [(2.0% x 2) + (3% x 3) + 4%]/6 + [0.08%(5)]
= 5.93%
c. If a 10-year corporate bond yields 9.5% and the related liquidity premium is 1.1%, what is the
bond’s default risk premium?
Answer:
DRP = r - r* - IP – MRP - LP
= 9.5% - 2.7% - [(2.0% x 2) + (3% x 3) + (4% x 5)]/10 - [0.08%(9)] – 1.1%
= 1.68%
4. Suppose that the real risk-free rate is 3.25%, and the inflation is expected to be 2.50% for the first
three years, 3% for the next three years, and 3.50% thereafter. Maturity risk premium is estimated to
be [0.5 x (t – 1)] %. Suppose also that liquidity premium of 0.50% and default risk premium of
1.35% applies to AAA-rated corporate bond regardless of the term. What is the difference in the
yields on a 7-year AAA-rated corporate bond and on a 12-year Treasury bond?
Answer: 0.92%
7 Year Corporate bond
r = r* + IP + MRP + DRP + LP
= 3.25% + [(2.5% x 3) + (3% x 3) + 3.5%]/7 + [0.5%(7 - 1)] + 1.35% + 0.50%
= 10.96%
12 Year Treasury bond
r = r* + IP + MRP +
= 3.25% + [(2.5% x 3) + (3% x 3) + (3.5% x 6) ]/12 + [0.5%(12 - 1)]
= 11.875%
Difference = 12 Year Treasury bond – 7 Year Corporate bond
= 11.875% - 10.96%
= 0.915% or 0.92%
5. Ferdinand and Fernando, brothers, inherited a large amount of money from their parents. They plan
to invest their money instead of spending them on various luxuries (e.g. purchasing high-tech gadgets,
buying new cars, going on trips abroad, etc.). They consider themselves as risk-averse individuals.
After making a research, they found out the expected returns of certain types of securities and
investments, as shown in the table below:
Type of Security
Treasury bill
5-year Treasury Bond
SM Prime Holdings, Inc. Bond
JG Summit Holdings, Inc. Stock
Benguet Corporation Stock
Expected Return
1.50%
4.63%
5.47%
12.34%
20.75%
Based on the data that they researched, Ferdinand and Fernando plan to invest in treasury bills.
a. Sarah, a childhood friend of Ferdinand and currently working in a government institution, after
knowing that Ferdinand plans to invest in T-bills, offered and suggested investing in a 5-year
Treasury bond instead. If Ferdinand proceeds in buying the 5-year Treasury bond instead of the
Treasury bill, what would be the risk premium of the transaction?
Answer:
Risk premium = 4.63% - 1.50%
= 3.13%
b. Bernard, a former teammate of Fernando in their high school volleyball team and currently a
stockbroker, after knowing that Fernando plans to invest in T-bills, offered and suggested
investing in JG Summit Holdings, Inc. stock instead. If Fernando proceeds in buying the JG
Summit Holdings, Inc. stock instead of the Treasury bill, what would be the risk premium of the
transaction?
Answer:
Risk premium = 12.34%
1.50%
= 10.34%
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