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Homework answers / question archive / Case 1: Daniela Ibarra is a senior analyst in the fixedincome department of a large wealth management firm
Case 1:
Daniela Ibarra is a senior analyst in the fixedincome department of a large wealth management firm. Marten Koning is a junior analyst in the same department. The firm invests in a variety of bonds. Ibarra is presently analyzing a set of bonds with some similar characteristics, such as four years until maturity and a par value of €1,000.
Exhibit 1 includes details of these bonds.
EXHIBIT 1 A Brief Description of the Bonds Being Analyzed
Bond Description
B1 A zerocoupon, fouryear corporate bond with a par value of €1,000. The wealth
management firm's research team has estimated that the riskneutral probability of
default (the hazard rate) for each date for the bond is 1.50%, and the recovery rate is
30%.
B2 A bond similar to B1, except that it has a fixed annual coupon rate of 6% paid annually.
B3 A bond similar to B2 but rated AA.
B4 A bond similar to B2 but the coupon rate is the oneyear benchmark rate plus 4%.
Ibarra asks Koning to assist her with analyzing the bonds. She wants him to perform the analysis with the assumptions that there is no interest rate volatility and that the government bond yield curve is flat at 3%. Answer the questions (1–4) based on the assumptions made by Marten Koning, the junior analyst.
1. The market price of bond B1 is €875. The bond is:
A. fairly valued.
B. overvalued.
C. undervalued.
2. Koning realizes that an increase in the recovery rate would lead to an increase in the bond’s fair value, whereas an increase in the probability of default would lead to a decrease in the bond’s fair value. He is not sure which effect would be greater, however. So, he increases both the recovery rate and the probability of default by 25% of their existing estimates and recomputes the bond’s fair value. The recomputed fair value is closest to:
A. €843.14.
B. €848.00.
C. €855.91.
3. The fair value of bond B2 is closest to:
A. €1,069.34.
B. €1,111.51.
C. €1,153.68.
4. The market price of bond B2 is €1,090. If the bond is purchased at this price and there is a default on Date 3, the rate of return to the bond buyer would be closest to:
A. −28.38%.
B. −41.72%.
C. −69.49%.
Case 2:
Anna Lebedeva is a fixedincome portfolio manager. Paulina Kowalski, a junior analyst, and Lebedeva meet to review several positions in Lebedeva’s portfolio. Lebedeva begins the meeting by discussing credit rating migration. Kowalski asks Lebedeva about the typical impact of credit rating migration on the expected return on a bond.
Lebedeva asks Kowalski to estimate the expected return over the next year on a bond issued by Entre Corp. The BBB rated bond has a yield to maturity of 5.50% and a modified duration of 7.54. Kowalski calculates the expected return on the bond over the next year given the partial credit transition and credit spread data in Exhibit 1. She assumes that market spreads and yields will remain stable over the year.
EXHIBIT 1 OneYear Transition Matrix for BBB Rated Bonds and Credit Spreads
AAA AA A BBB BB B CCC, CC, C
Probability (%) 0.02 0.30 4.80 85.73 6.95 1.75 0.45
Credit spread 0.60% 0.90% 1.10% 1.50% 3.40% 6.50% 9.50%
1. The most appropriate response to Kowalski’s question regarding credit rating migration is that it has:
A. a negative impact.
B. no impact.
C. a positive impact.
2. Based on Exhibit 1, the oneyear expected return on the Entre Corp. bond is closest to:
A. 3.73%.
B. 5.50%.
C. 7.27%.
Case 3:
Lena Liecken is a senior bond analyst at Taurus Investment Management. Kristel Kreming, a junior analyst, works for Liecken in helping conduct fixedincome research for the firm’s portfolio managers. Liecken and Kreming meet to discuss several bond positions held in the firm’s portfolios.
Bonds I and II both have a maturity of one year, an annual coupon rate of 5%, and a market price equal to par value. The riskfree rate is 3%. Historical default experiences of bonds comparable to Bonds I and II are presented in Exhibit 1.
EXHIBIT 1 Credit Risk Information for Comparable Bonds
Bond Recovery Rate Percentage of Bonds ‘That
Survive and Make Full
Payment
I 40% 98%
II 35% 99%
Bond III
Bond III is a zerocoupon bond with three years to maturity. Liecken evaluates similar bonds and estimates a recovery rate of 38% and a riskneutral default probability of 2%, assuming conditional probabilities of default. Kreming creates Exhibit 2 to compute Bond III’s credit valuation adjustment. She assumes a flat yield curve at 3%, with exposure, recovery, and loss given default values expressed per 100 of par value.
EXHIBIT 2 — Analysis of Bond II
Date 
Exposure 
Recovery 
Loss Given Default 
Probability of Default 
Probability of Survival 
Expected Loss 
Present Value of Expected Loss 
0 







1 
94.2596 
35.8186 
58.4410 
2.0000% 
98.0000% 
1.1688 
1.1348 
2 
97.0874 
36.8932 
60.1942 
1.9600% 
96.0400% 
1.1798 
1.1121 
3 
100.0000 
38.0000 
62.0000 
1.9208% 
94.1192% 
1.1909 
1.0898 
Sum 



5.8808% 
3.5395 

3.3367 
Bond IV
Bond IV is an AA rated bond that matures in five years, has a coupon rate of 6%, and a modified duration of 4.2. Liecken is concerned about whether this bond will be downgraded to an A rating, but she does not expect the bond to default during the next year. Kreming constructs a partial transition matrix, which is presented in Exhibit 3, and suggests using a model to predict the rating change of Bond IV using leverage ratios, return on assets, and macroeconomic variables.
EXHIBIT 3 Partial OneYear Corporate Transition Matrix (entries in %)
From/To AAA AA A
AAA 92.00 6.00 1.00
AA 2.00 89.00 8.00
A 0.05 1.00 85.00
Credit Spread (%) 0.50 1.00 1.75
Default Probabilities
Kreming calculates the riskneutral probabilities, compares them with the actual default probabilities of bonds evaluated over the past 10 years, and observes that the actual and riskneutral probabilities differ. She makes two observations regarding the comparison of these probabilities:
Observation 1: Actual default probabilities include the default risk premium associated with the uncertainty in the timing of the possible default loss.
Observation 2: The observed spread over the yield on a riskfree bond in practice includes liquidity and tax considerations, in addition to credit risk.
1. The expected exposure to default loss for Bond I is:
A. less than the expected exposure for Bond II.
B. the same as the expected exposure for Bond II.
C. greater than the expected exposure for Bond II.
2. Based on Exhibit 1, the loss given default for Bond II is:
A. less than that for Bond I.
B. the same as that for Bond I.
C. greater than that for Bond I.
3. Based on Exhibit 1, the expected future value of Bond I at maturity is closest to:
A. 98.80.
B. 103.74.
C. 105.00.
4. Based on Exhibit 1, the riskneutral default probability for Bond I is closest to:
A. 2.000%.
B. 3.175%.
C. 4.762%.
5. Based on Exhibit 2, the credit valuation adjustment (CVA) for Bond III is closest to:
A. 3.3367.
B. 3.5395.
C. 5.8808.
6. Based on Exhibit 3, if Bond IV’s credit rating changes during the next year to an A rating, its expected price change would be closest to:
A. −8.00%.
B. −7.35%.
C. −3.15%
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