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lena liecken is a senior bond analyst at taurus investment Management. Kristel Kreming,
a junior analyst, works for liecken in helping conduct fixed-income 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 mar-
ket price equal to par value. The risk-free 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 III
Bond III is a zero-coupon bond with three years to maturity. Liecken evaluates similar bonds and estimates a recovery rate of and a risk-neutral default probability of , assuming conditional probabilities of default. Kreming creates Exhibit 2 to compute Bond III's credit valuation adjustment. She assumes a flat yield curve at , with exposure, recovery, and loss given default values expressed per 100 of par value.
Bond IV
Bond IV is an AA rated bond that matures in five years, has a coupon rate of , 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.
Default Probabilities
Kreming calculates the risk-neutral probabilities, compares them with the actual default probabilities of bonds evaluated over the past 10 years, and observes that the actual and risk-neutral 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 risk-free bond in practice includes liquidity and tax considerations, in addition to credit risk.
-based on exhibit 1, the expected future value of bond i at maturity is closest to:
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