Show ALL of your work. Each problem is equally weighted. Do any 12 out of 14 questions.
1. From the following data create a discount curve (i.e. find discount factors):
a. A zero coupon bond Pz(0, 0.5) = 99.20.
b. A coupon bond paying 3% quarterly P(0, 0.25) = 100.5485.
c. A coupon bond paying 6% quarterly P(0, 0.75) = 103.1655.
d. A coupon bond paying 5% semiannually P(0, 1) = 103.0425.
Use the following discount factors (discount curve) problems 2, 3 and 4:
t Z(0, t)
2. Using the previous discount curve price the following: A zero coupon bond expiring at t = 0.75.
3. Using the previous discount curve price the following: A 1-year 6% coupon bond paying quarterly.
4. Using the previous discount curve price the following: A 6-month coupon bond paying 7% semiannually.
5. For the following scenario, check if there is a mispriced security:
a. A coupon bond paying 1% quarterly P(0, 0.25) = 100.6498.
b. A coupon bond paying 4% semiannually P(0, 0.25) = 101.8980.
c. A coupon bond paying 3% quarterly P(0, 0.50) = 101.2978.
d. A coupon bond paying 5% quarterly P(0, 0.75) = 103.4425.
e. A coupon bond paying 4% semiannually P(0, 1.00) = 103.5880.
6. What is the price of a 0.75-year floating rate bond that pays a semiannual coupon equal to floating rate plus 2% spread? We know the following:
a. There is a zero coupon bond Pz(0, 0.25) = 99.70.
b. There is a zero coupon bond Pz(0, 0.50) = 99.20.
c. There is a coupon bond paying 3% quarterly P(0, 0.75) = 101.7380.
7. A Treasury dealer quotes the following 182-day bill at a 3.569% discount.
What is the price of the security?
Use the following discount factors when needed in problems 8,9, 10,11, and 12
t Z(0, t)
8. Calculate the duration of the following security: 5-year zero coupon bond.
9. Calculate the duration of the following security: 2-year fixed coupon paying 5% quarterly ($5/4 =$1.25 every 3 months).
10. What is the dollar duration of the following portfolio?
i. Long a 1.5-year zero coupon bond.
ii. Short a 2-year fixed coupon bond paying 1% quarterly ($1/4 =$0.25 paid every 3 months).
11. Compute the 95% VaR for the following portfolio:
i. A 1.5-year fixed rate bond paying 2% quarterly.
ii. A 0.75-year floating rate bond paying float plus 80 basis points semiannually.
You know that the reference rate was set to 6% six months ago.
iii. A 0.25 zero coupon bond.
Additionally you know that μdr = 0 and σdr = 0.4233.
12. Ms. White wants to invest $100,000 for the next five years. She purchases an annuity from a financial institution. Currently the term structure is flat at 10% (yearly compounded).
i. If the payments are made yearly, what is the amount that the financial institution will agree to pay Ms White?
ii. Assume that there is a 5-year fixed coupon bond that pays 12% coupon every year. What is the price and duration of the bond?
iii. How much must the financial institution invest in the long-term bond in order to hedge the position? What should it do with the remainder of the money?
Use the following discount factors when needed in problem 13 and 14.
t Z(0, T)
13. Calculate the convexity of the following security: a 5-year zero coupon bond.
14. Calculate the convexity of the following security: a 3-year fixed rate bond paying 4% coupon on a semiannual basis.
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