Learning Module 4: Credit Analysis Models

Learning Module 4 Credit Analysis Models EXAMPLE 1 Analysis of Credit Risk (1) 1. A fixed income analyst is considering the credit risk over the next year for three corporate bonds currently held in her bond portfolio. Her assessment for the exposure, probability of default, and recovery is summarized in this table Corporate Bond Exposure (per 100 of par value) A 104 B 98 C 92 Probability of Default Recovery (per 100 of par value) 0.75% 40 0.90% 35 0.80% 30 Although all three bonds have very similar yields to maturity, the differences in the exposures arise because of differences in their coupon rates. Based on these assumptions, how would she rank the three bonds, from highest to lowest, in terms of credit risk over the next year? Solution: She needs to get the loss given default for each bond and multiply that by the probability of default to get the expected loss. The LGD is the exposure minus the assumed recovery. Corporate Band LGD (per 100 of par value) POD Expected Loss A 64 0.75% 0.180 Corporate Bond LGD (per 100 of par value) B E9 POD Expected Loss 0.90% 0.567. C 62 0.80% 0.496 Based on the expected losses, Bond B has the highest credit risk and Bond A, the lowest. The ranking is B, C, and A. Note that there is not enough information to recommend a trading strategy because the current prices of the bonds are not given. EXAMPLE 2 Analysis of Credit Risk (2) 1. A fixed-income trader at a hedge fund observes a three year, 5% annual payment corporate bond trading at 104 per 100 of par value. The research team at the hedge fund determines that the risk-neutral annual probability of default used to calculate the conditional POD for each date for the bond, given a recovery rate of 40%, is 1.50%. The government bond yield curve is flat at 2.50%. Based on these assumptions, does the trader deem the corporate bond to be overvalued or undervalued? By how much? If the trader buys the bond at 104, what are the projected annual rates of return! Solution: The trader needs to build a table similar to that shown in Exhibit 2; this table is presented in Exhibit 4. Exhibit 4: CVA Calculation for Example 2 Date Recovery LGD POD POS Expected Loss PV of Expected Loss Exposure 109.8196 43.9274 65.8911 107.4390 42.9756 105.0000 3 64/4634 42.0000 1 1.50000% 1.4775% 94.5000% 0.9884 970225% 0.9524 63.0000 1.4553% 95.5672% 0.975610 0.9643 0.951814 0.928599 0.9066 0.9169 DF 0.8514 4.4328% CVA- 27222 The exposures are the values for the bond plus the coupon payment for each date assuming a yield to maturity of 2.50%. The exposure is 109.8186 for Date I when two years to maturity remain The assumed recovery for Date 1 is 43.9274 (= 109.8186 x 0.40) for a loss given default of 65.8911 (= 109.8186-43.9274). (Note that all calculations are carried out on spreadsheets to preserve precision. The rounded results are reported in the text.) The expected loss is 0.9884 (65.8911 x 0.0150), The discount factor for Date 1 is 0.975610= 1/(1.0250)¹. The present value of the expected loss is 0.9643 (= 0.9884 x 0.975610). The credit valuation adjustment for the bond is 2.7222, the sum of the pres- ent values of expected loss. If this five-year, 5% bond were default free, its price would be 107.1401. 5 (1.0250) 105 (1.0250)2 (1.0250) 107.1401. Therefore, the fair value of the bond given the assumed credit risk param- eters is 104.4178 (107.14012.7222). If this three-year, 5% bond were default free, its price would be 107.1401. The projected annual rates of return for default on Dates 1, 2, and 3 are -57.76%, -33.27%, and -22.23%, respectively. If there is no default, the rate of return is 3.57%, which is the yield to maturity. Note that these rates of return neglect coupon reinvestment risk because internal rate of return cal- culations implicitly assume reinvestment at the same rate. The calculations are as follows: 104 43.9274 (1+IRR) IRR-0.5776. 104= 5 42.9756 (1+IRR) (1+IRR) IRR - 0.3327. 104 5 (1+IRR) (1+IRR) 42.0000 (1+IRR) IRR-0.2223. 104 5 (1IRR) 5 (1+IRR) 105 (1+IRR IRR 0.0357. EXAMPLE 3 Credit Scoring 1. Tess Waresmith is a young finance professional who plans to eventually buy a two-family house, live in one unit, and rent the other to help cover the mortgage payments. She is a careful money manager and every year checks her FICO credit score. She is pleased to see that it has improved from 760 last year to 775 this year. Which of these factors can explain the improvement? A. She is now one year older and has not had any late payments on credit cards during the year. B. Her bank on its own raised her limit on a credit card from $1,000 to $2,500, but she has maintained the same average monthly balance. C. She applied for and received a new car loan from her credit union. D. She refrained from checking her FICO score monthly, which some of her friends do. Solution: Factors A, B, and C help explain the improvement. Going down the list: A. Age itself is not a factor used by Fair Isaac to determine the credit score. However, the average age of the accounts is a factor, as is the age of the oldest account. Therefore, other things being equal, the passage of time tends to improve the score. In general, age and credit score are highly correlated. B. The credit card debt-to-limit ratio is a component of the debt burden. Having a higher limit for the same average balance reduces the ratio and improves the credit score. C. Because the car loan is a new type of credit usage and thus does not have any late payments, it has a positive impact on the score. D. Refraining from self-checking one's credit score has no impact. Self-checking is deemed to be a "soft inquiry" and does not factor into the calibration of the FICO score. EXAMPLE 4 The Impact of Credit Migration on Expected Return 1. Manuel Perello is a wealth manager for several Latin American families who seek to keep a portion of their assets in very high-quality corporate bonds. Mr. Perello explains that the yields to maturity on the bonds should be adjusted for possible credit spread widening to measure the expected rate of return over a given time horizon. In his presentation to one of the families, he uses a 10-year. AAA rated corporate bond that would have a modified duration of 7.3 at the end of the year. Using the corporate transition matrix in Exhibit 7, Mr. Perello concludes that the expected return on the bond over the next year can be approximated by the yield to maturity less 32.5 bps to account for a possible credit downgrade even if there is no default. Demonstrate how he arrives at that conclusion. Solution: First, calculate the expected percentage price change using the modified duration for the bond and the change in the credit spread: From AAA to AA: -7.3 (0.90%-0.60%)-2.19%. From AAA to A: -7.3 × (1.10%-0.60%)-3.65%. From AAA to BBB: -7.3x (1.50%-0.60%)-6.57%. From AAA to BB: -7.3 × (3.40%-0.60%)-20.44%. From AAA to B: -7.3 x (6.50%-0.60%)-43.07%. From AAA to CCC, CC, or C: -7.3x (9.50%-0.60%)-64.97%. Second, calculate the expected percentage change in bond value over the year using the probabilities associated with the AAA rating row in the cor- porate transition matrix: (0.90000%) (0.0900-2.19%)+(0.0060×3.65%)+(0.0015×6.57%) + (0.0010-20.44%)+(0.0010-43.07%)+(0.0005 × 64.97%) =-0.3249%. EXAMPLE 5 An Equivalent Option Interpretation of Debt and Equity 1. Carol Feely is a junior credit analyst at one of the major international credit rating agencies. She understands that in the standard structural models, eq- uity is interpreted as a call option on the asset value of the company. Howev- er, she is not comfortable with the assumption that it is the debtholders who implicitly own the assets and write a call option on them. She claims that the model should start with the understanding that the shareholders own the net value of the company, which is A(7) - K, and that their limited liability is essentially the value of a long position in a put option at a strike price of K. Furthermore, the debtholders own a "risk-free" bond having a value of K at time 7 and a short position in the put that is held by the shareholders. Demonstrate that Ms. Feely's "embedded put option" interpretation provides the same values for debt and equity at time Tas does the more customary call option structural model. Solution: A long position in a put option on the asset value at a strike price of K takes the form max[K-A(T), 0). This put option has intrinsic value to its holder when K> A(T) and is worthless when K≤A(T). The values for E(T) and D(T) according to Ms. Feely at time Tare as follows: E(T)A(T)-K+ max[K-4(7), 0]. D(T)K-max[K-4(7), 0]. If A(T) > K at time T, the put option is out of the money, E(T) = A(T)-K+0 A(T)-K, and D(T) K-0 K. If A(T) < K. the put is in the money, E(T) =A(T)-K+K-A(T)] = 0, and D(T)=K-[K-A(T)] = A(T). This inter- pretation indicates that the value of limited liability to shareholders is the value of the put option that they purchase from the debtholders. Ms. Feely is correct in that the same payoffs as the embedded call option interpretation are obtained.