FIN 406 – Security Analysis and Portfolio Management Practice Midterm II Solutions
Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit
FIN 406 – Security Analysis and Portfolio Management
Practice Midterm II Solutions
It’s your first day working as a fixed income trader at Goodman Socks. Time to earn your salary. You notice the following two U.S. Treasury bonds trading in the market. These bonds pay annual coupons and have a face value of $1,000.
|
Bond |
Maturity |
Coupon Price |
|
A B |
1 year 2 years |
|
a. List the cash flows for the bonds (from the coupons and principal) in the following table. (2 points)
|
Bond |
1 year |
2 years |
|
A |
1050 |
|
|
B |
70 |
1070 |
b. Using the principle of “no arbitrage,” calculate the prices of one-dollar zero-coupon bonds that mature in 1 and 2 years. That is, fill in the missing prices in the following table. [Hint: these prices are the same as the 1- and 2-year discount factors] (5 Points)
|
Bond |
Price |
1 year |
2 years |
|
Z1 |
0.95 |
1 |
0 |
|
Z2 |
0.91 |
0 |
1 |
= 
Bond Z1: 997.50 = 
1 × 1050 ⇒ 
1 = 0.95
Bond Z2: 1040.20 = 0.95 × 70 + 
2 × 1070 ⇒ 
2 = 0.91
c. Now it’s time to really make some money. You notice another U.S. Treasury bond with the following cash flows. Show that there is an arbitrage opportunity. Should you buy or sell Bond C to take advantage of the arbitrage? (3 points)
|
Bond |
Price |
1 year |
2 years |
|
C |
$1,136.00 |
$273.00 |
$963.00 |
= 
= 0.95 × 273 + 0.91 × 963 = 1135.68 < 1136.00 ⇒ sell Bond C
d. How would you trade to take advantage of the arbitrage opportunity? That is, describe the
portfolio of bonds A and B that can be used to offset the future cash flows generated by trading 1 unit of bond C. How much would you earn from trading 1 unit of bond C? (8 points)
|
Bond |
Units |
Today |
1 year |
2 years |
|
A |
0.2 |
-199.50 |
210 |
|
|
B |
0.9 |
-936.18 |
63 |
963 |
|
C |
-1 |
1136.00 |
-273 |
-963 |
|
Net |
|
0.32 |
0 |
0 |
× 1070 = 963 ⇒ 
= 0.9
× 
ℎ 
= 0.9 × 1070 = 963
× 
ℎ 
= 0.9 × 70 = 63
× 
ℎ 
= 0.9 × (−1040.20) = −936. 18
× 1050 = −(63 − 273) ⇒ 
= 0.2 
× 
ℎ 
= 0.2 × 1050 = 210
× 
ℎ 
= 0.2 × (−997.50) = −199.50
Question 2 – 20 points
You made so much money trading fixed income securities at Goodman Socks that you’ve decided to take a break from all the hustle and bustle on Wall Street. You’ve landed a new job at the corporate headquarters of a prestigious firm called PJ Cleaning. PJ’s finances much its operations by issuing 2 year fixed-rate risk-free debt. Currently, PJ’s has $100 million of risk-free debt outstanding. This debt has an annual coupon rate of 5% and matures in 2 years. Coupons are paid once per year. The current term structure is flat at 2% per year, compounded annually. Accordingly, the current market value of PJ’s debt is $105.82 million.
a. What is the duration of PJ’s debt? (4 points)
= 
= 
= 
1 × + 2 × 
= 1.954
=1 
=1
b. Suppose yields rise by 200 basis points (from 2% to 4%). Calculate the modified duration and use it to approximate the new market value of PJ’s debt. (4 points)
1.954
∗ = = = 1.915
1 + 
1.02
|
∆ |
|
|
= −
∗∆
= −1.915 × (0.04 − 0.02) = −0.0383
New 
= 
× 
1 +
= 105.82 × (1 − 0.0383) = 101.77
c. Using 1-year and 3-year zero-coupon Treasury bonds, construct a portfolio to immunize PJ’s debt. Specifically, state the amount to invest in each of the 1-year and 3-year bonds. (6 points)
× 1 + (1 − 
) × 3 = 1.954 ⇒ 
= 0.523
invest 
× 
= 0.523 × 105.82 = 55.36 in 1-year zero
invest (1 − 
) × 
= (1 − 0.523) × 105.82 = 50.46 in 3-year zero
d. Suppose that the 1-year spot interest rate is 4% and that the 2-year spot interest rate is 10%. Both rates are per year and compounded annually. What is the forward rate between years 1 and 2? (6 points)
2 = − 1 = − 1 = 0. 163
Question 3 – 12 points
Expectations or liquidity? That is the question …
a. The following plot depicts risk-free bond yields over time for different maturities. Is the plot suggestive of the expectations hypothesis or the liquidity preference hypothesis? BRIEFLY explain why. (6 points)
This plot supports the expectations hypothesis because long-maturity yields foreshadow future short- maturity yields.
b. The following plot depicts risk-free bond yields over time for different maturities. Is the plot suggestive of the expectations hypothesis or the liquidity preference hypothesis? BRIEFLY explain why. (6 points)
This plot supports the liquidity preference hypothesis because long-maturity yields are higher than short- maturity yields, reflecting a liquidity premium.
2022-03-05