Hw2 2020

Group Homework #2
FINA 4120 - Spring 2018
The assignment can be done in a group of no more than THREE students. Write ALL the group members’
names on the cover sheet.
Please hand in along with your answers any supporting calculations and graphs (if necessary). Your work
should be neat and well organized so that I can easily find your solutions to each of the questions.
1. This question is based on materials from Lecture notes – topic 4.
Suppose that you invest in a 10-year 8% Treasury Note sold at par and the interest rate drops to 6% after
your purchase. What will be the Total Dollar Return and the Realized Yield if you hold the bond (a) for 3
years; (b) for 7 years; (c) to maturity. In each case, decompose the Total Dollar Return into (1) Total Coupon
Interest; (2) Interest on Interest; (3) Capital Gain / Loss.
2. Imagine that currently in the market the following bonds are available:
Maturity Coupon Rate Price
0.5 0% $ 97.087
1.5 8% $101.120
1.5 0% $ 89.900
2.0 0% $ 84.663
Maturity is in years, coupons are paid semiannually but quoted annually on a bond equivalent basis, and
prices are quoted per $100 face value.
(a) Construct a 2-year spot yield curve from this information. More precisely, calculate a spot rate for each
six-month period. Report the rate on a bond equivalent basis.
(b) In six months, your company plans to issue a 1.5 year zero coupon bond with a face value of $500,000 to
finance a small acquisition. If the traditional expectations theory of the term structure is correct, and if the
risk of your company's bonds is similar to that of the above bonds, what is the expected price of your
company's bond at issue (i.e., in six months hence)?
(c) Having heard reports that interest rates could rise sharply in the next six months, you suggest to the CFO
that the company issue the bond immediately, locking in current rates, and invest the proceeds in a six month
bond. In other words, today you would issue a bond maturing in two years with a face value of $500,000
("Bond X"). If you follow this strategy, how much money does the firm initially borrow? How much will be
available to finance the acquisition in six months?
3. Imagine that the yield curve is currently flat. The Treasury announces that they will no longer issue
securities with maturities longer than two years. As a result, long-term government bonds will be refinanced
using only relatively short-term debt. If the "market segmentation theory" of the yield curve is correct, what
will happen to the slope of the yield curve as a result of this policy change? Explain briefly.
4. True, False, or Uncertain and Explain. According to the “liquidity preference theory” of the yield curve, if
the yield curve is flat, rates investors expect to be available in the future are the same as current rates.
5. Imagine that the following Treasury bonds are available:
Maturity Coupon Rate Price

1 0% $ 94.340
3 9.5% $105.403
3 0% $ 80.496
Maturity is in years, coupons are paid annually, and prices are quoted per $100 face value.
(a) Construct the three-year spot yield curve. State the results as effective annual rates.
(b) Use the curve in part (a) to compute the implied one-year forward rates in the yield curve, 1f1 and 2f1.
(c) You plan to invest $1 million in a 3 year 7% coupon bond (annual coupon payments), and plan to sell it at
the end of two years. At the time that you sell it, it will only have one coupon payment left. Using your
calculations in parts (a) and (b), calculate the arbitrage-free holding period return (i.e., the total dollar return
you will earn if future market rates equal the implied forward rates in the yield curve).
6. Calculate the requested measures for bonds A and B (assume each bond pays interest semiannually):
A B
Coupon 8% 9%
Yield-to-Maturity 8% 8%
Maturity (in 2 5
years)
Par 100 100
Price 100.000 104.055
(a) Price value of a basis point.

(b) Macaulay duration.
(c) Modified duration.
(d) Calculate the actual price of the two bonds for a 100 basis point increase in interest rates.
(e) Using duration, estimate the price of the bonds for a 100 basis point increase in interest rates.
7. A newly issued bond has a maturity of 10 years and pays a 7% coupon rate (with coupon payments
coming once annually). The bond sells at par value of $100.
(a) What are the duration, modified duration and dollar duration of the bond? What is its convexity?
(b) Find the actual price of the bond assuming that its yield to maturity immediately increases from 7%
to 8%?
(c) What price would be predicted by using duration? What is the prediction error?
(d) What price would be predicted by using duration-with-convexity? What is the prediction error?
8. You are managing a portfolio of $1 million. Your target duration is 10 years, and you can choose from
two bonds: a zero-coupon bond with maturity of 5 years, and a perpetuity, each currently yielding 5%.
(a) How much of each bond will you hold in your portfolio?
(b) How will these fractions change next year if your target duration is now 9 years?
9. Pension funds pay lifetime annuities to recipients. If a firm will remain in business indefinitely, the
pension obligation will resemble perpetuity. Suppose, therefore, that you are managing a pension fund
with obligations to make perpetual payments of $2 million per year to beneficiaries. The yield to maturity
on all bonds is 16%.
(a) If the duration of 5-year maturity bonds with coupon rates of 12% (paid annually) is 4 years and the
duration of 20-year maturity bonds with coupon rates of 6% (paid annually) is 11 years, how much of
each of these coupon bonds (in market value) will you want to hold to both fully fund and immunize your
obligation?
(b) What will be the par value of your holdings in the 20-year coupon bond?
10. Consider the following yield curve:

Assume that the yields are Effective Annual Yields.
Zero coupon bond yields

Maturity 3 Month 6 Month 2 Year 3 Year 5 Year 10 Year 30 Year
Yield (%) 1.79 2.07 2.58 2.79 3.32 4.07 4.83
(a) Calculate the 2f1 -- one year forward rate from year 2 to year 3.
(b) Implement a “rolling down the yield curve” strategy by purchasing a 2 year zero coupon bond, and
selling it 6 months prior to expiration. Assuming that the yield curve remains the same for the next
1.5 years, what is the return using this strategy?
11. True, False, or Uncertain and Explain.

(a) Suppose that you want to invest $1,000 in a Treasury bond with 10 years to maturity. Two are
available, one with a coupon rate of 6%, and the other with a coupon rate of 11%. If you expect to hold
the bond until maturity, buying the 6% bond reduces the riskiness of your total return (relative to buying
the 11% bond).
(b) In a volatile interest rate environment, a barbell strategy can usually be expected to outperform a
bullet strategy.

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Group Homework #2

FINA 4120 - Spring 2018

1. This question is based on materials from Lecture notes – topic 4.

Interest; (2) Interest on Interest; (3) Capital Gain / Loss.

Maturity Coupon Rate Price

prices are quoted per $100 face value.

six-month period. Report the rate on a bond equivalent basis.

company's bond at issue (i.e., in six months hence)?

available to finance the acquisition in six months?

5. Imagine that the following Treasury bonds are available:

Maturity Coupon Rate Price

(a) Price value of a basis point.

10. Consider the following yield curve:

Zero coupon bond yields

11. True, False, or Uncertain and Explain.

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