FNCE 4302 Midterm
Fixed Income Analytics Midterm Exam
FNCE 4302 – Fixed Income Securities
Instructions:
Please have this exam to me by 6:00pm, Monday October 31st (6 days from now). If you have
extenuating circumstances that will keep you from getting this to me by then, please let me
know as soon as you know and I may grant extensions on a case-by-case basis. You may email
your exam to me at XXXXXXXXXX.
Please attach two (and only two) documents to the email you send me. The first should be a
Word of PDF file with all of your answers on it. The second should be one file (if Excel, with
multiple worksheets in it) with your work in it, which should fully support the final answer that
is on the Word or PDF file and it should be abundantly clear to me how you a
ived at your final
answer. Please title each file “Last name, First name—Midterm” with your first and last name
eplacing. If you have any questions, please contact me immediately and I will do my best to
espond at that time.
You may refer to anything that I shared on the course site, any notes that you took in class, any
notes or books from other finance classes taken at UConn. You may not discuss the midterm
with your classmates or anyone else.
All coupon-paying bonds have semiannual coupon payments unless the problem states
otherwise.
Mortgages make monthly payments on the first of each month
Good luck!
Student’s Signature: ____________________
1) An 11% coupon bond and 10 years to maturity is callable in three years at $1,100. If the
ond is selling today at $975 (face value is $1,000), what is the yield to call?
2) A 2-year option-free bond (par value is $1,000) has an annual coupon of 6%. An investor
determines that the spot rate for 1-year is 5% and the year 2 spot rate is 8%. What is the
ond price?
3) A bond has a yield to maturity of 7% with quarterly interest payments. The bond has a face
value of $100,000 and matures in 13 years. Each coupon payment will be $1,800. What is
the cu
ent bond price?
4) Given the following spot and forward rates:
• Cu
ent 1-year spot rate is 5.5%
• One-year forward rate one year from today is 7.63%
• One-year forward rate two years from today is 12.18%
• One-year forward rate three years from today is 15.5%
a) What is the value of a 4-year, 10% annual pay, $1,000 face value corporate bond?
) If you purchased this bond on September 23, 2022 and it pays its coupon annually on
December 15, what is the clean (flat) purchase price?
5) We have the following option-free bonds which we assume are accurately priced:
Maturity Yield (bond equiv. yield) Market Value
6 months 3.60% $100
1 year 4.00% $100
18 months 4.40% $100
2 years 4.80% $100
a) Use the boostrapping technique to find the four zero-coupon spot rates (Z1 – Z4)
ZERO-COUPON SPOT RATE
Z1
Z2
Z3
Z4
) Find the three implied forward 6-month interest rates (1f1 – 1f3)
IMPLIED FORWARD RATE
1F1
1F2
1F3
c) Using 6-month spot rate and the rates you calculated in (b) above, what should be the
co
ect price for a similar option-free bond which matures in 2 years and has a 5.2%
coupon rate?
d) What is the yield to maturity for the bond in (d)?
6) Calculate the effective duration of an option-free 20-year 7% annual-pay par bond based on
a 25-basis point (bps) change in yield.
a) What would be the approximate change in price and the actual change in price if the
yield was to go up by 200bps?
) Explain the difference between the approximate and actual change in price.
7) A bank loan department is trying to determine the co
ect rate for a 2-year loan to be made
two years from now. If cu
ent implied Treasury effective annual spot rates are 1-year:
2.0%, 2-year: 3.0%, 3-year: 3.5%, and 4-year: 4.5%, what is the base (risk-free) forward rate
for the loan before adding a risk premium?
8) A bond investor has gathered the following information on a 10-year, semi-annual pay US
corporate bond:
Cu
ently trading at par value
Annual coupon of 10%
Estimated price if rates increases by 50bps is 96.99%
Estimated price if rates decreases by 50bps is 103.14%
a) What is the effective duration?
9) Will the estimate of the increase in an option-free bond’s price, based only on its duration
e too small, too large, or not enough information to determine and why?
10) You manage a portfolio consisting of the following bonds:
Bond Face Value Price Coupon Rate Time until Maturity
A $10 million XXXXXXXXXX% 10 years
B $20 million XXXXXXXXXX% 7 years
C $25 million XXXXXXXXXX% 3 years
D $30 million XXXXXXXXXX% 8 years
E $15 million XXXXXXXXXX% 15 years
a. Calculate the market value of your portfolio.
. Calculate the duration of the portfolio.
c. If interest rates go up by 2 basis points (for all maturities), what effect do you expect
it to have on the value of your portfolio based on your previous answers? Give me a
percentage change based on your answer to (b).
d. Calculate the convexity measure for Bond A.
11) All else being equal, which of the following bond characteristics most likely result in less
einvestment risk and why?
a) Shorter maturity
) Higher coupon
c) lower duration
12) If an investor owns longer-term coupon bonds, but has a short-term investment horizon, is
the investor more concerned in interest rate risk or reinvestment risk and why?
13) As compared to an equivalent noncallable bond, should a callable bond’s yield be higher,
lower or the same and why?
14) Given the following bonds:
a) 5-year, 8% coupon bond
) 15-year, 8% coupon bond
c) 15-year, 12% coupon bond
Which of the following bond’s would have the longest duration and why (you do not need
calculate to answer)?
15) An investor paid a full (dirty) price of $1,059.04 each for 100 bonds. The purchase was
etween coupon dates and accrued interest was $23.54 per bond. What is the bond’s flat
(clean) price?
16) The 4-year spot rate is 9.45%, and the 3-year spot rate is 9.85%. What is the 1-year spot
ate three years from today?