# Show all of your work. each problem is equally weighted. do any 12

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)
0.25 0.9980
0.50 0.9920
0.75 0.9870
1.00 0.9810

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)
0.25 0.9840
0.50 0.9680
0.75 0.9520
1.00 0.9360
1.25 0.9190
1.50 0.9040
1.75 0.8880
2.00 0.8730
2.25 0.8587
2.50 0.8445
2.75 0.8308
3.00 0.8175
3.25 0.8047
3.50 0.7924
3.75 0.7806
4.00 0.7691

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)
0.25 0.9840
0.50 0.9680
0.75 0.9520
1.00 0.9360
1.25 0.9190
1.50 0.9040
1.75 0.8880
2.00 0.8730
2.25 0.8587
2.50 0.8445
2.75 0.8308
3.00 0.8175
3.25 0.8047
3.50 0.7924
3.75 0.7806
4.00 0.7691

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.

The End

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