Learning Objectives: Define and explain CDS-bond basis. Compare default probabilities calculated from historical data with those calculated from credit yield spreads. Describe the difference between real-world and risk-neutral default probabilities and determine which one to use in the analysis of credit risk. Using the Merton model, calculate the value of a firm’s debt and equity, the volatility of firm value, and the volatility of firm equity.
Questions:
24.15.1. Analysts are assessing credit risk in a portfolio of corporate bonds from various sectors, utilizing the CDS-bond basis concept along with analyses of default probabilities from historical data and credit yield spreads.
The CDS-bond basis for Tech Innovations deviates from zero due to factors that include bond price discrepancies from par and contractual clauses in CDS agreements that affect payoffs. Tech Innovations' spread is currently 300 basis points, and its bond yield spread is 270 basis points, resulting in a CDS-bond basis of 30 points.
Additionally, are also comparing default probabilities. Historical data shows that the average seven-year cumulative default probability for a company like Tech Innovations is 2.3%. The credit spread for a five-year bond issued by Tech Innovations is 320 basis points and reflects a recovery rate of 45%. Using the formula λ=s(T)/(1−R), analysts calculate the implied default probability.
Which option accurately describes the analysis conducted by the investment bank's financial analysts and provides the best assessment of Tech Innovations' credit risk?
a. Tech Innovations' CDS-bond basis is positive, indicating lower default risk than bond yield spreads alone suggest. However, the calculated default probability from credit spreads is higher than historical averages, implying overvaluation of risk.
b. Positive CDS-bond basis suggests that the market perceives a higher risk of default than indicated by bond yield spreads alone, and the default probability calculated from credit spreads is lower than historical data, indicating undervaluation of risk.
c. Positive CDS-bond basis may indicate inefficiencies or specific risks not captured by the bond market, and the default probability calculated from credit spreads is higher than historical data, suggesting that market participants expect worsening conditions.
d. Analysts incorrectly calculated the CDS-bond basis as positive when it should be negative due to the high CDS spread over the bond yield spread. The default probability calculated from credit spreads aligns perfectly with historical data, indicating a stable risk assessment.
24.15.2. ACME Financial employs two probability measures for credit risk modeling―real-world and risk-neutral probabilities. Real-world probability gauges the borrower's likelihood of default, drawing from historical default rates and economic analysis. Risk-neutral probability measures prices of financial derivatives under the assumption that investors are risk-neutral, adjusting real-world probabilities using the market price of risk to discount future payoffs at the risk-free rate.
An analyst is assessing a corporate bond from Zigzag Corp with a historical default rate of 2% per year. In the derivatives market, the risk-neutral probability derived from the pricing of credit default swaps (CDS) suggests a 3% annual probability of default. This difference reflects the market's risk premium expectations and variations in valuing future uncertainties in pricing models.
Which probability measure should the analyst use to assess the credit risk of Zigzag Corp's bond for ACME Financial’s portfolio, and why?
a. Real-world probability, because it provides an actual historical perspective on the default rates, which is essential for long-term investment analysis in bonds.
b. Risk-neutral probability is crucial for determining the fair value of derivatives and aligns with the market's view on Zigzag Corp's default risk.
c. Real-world probability, as it reflects the optimistic perspective and underestimates the risk compared to risk-neutral probabilities, thus providing a safety margin.
d. Risk-neutral probability, to ensure that the pricing of risk in the credit derivatives market is consistent with the market expectations and financial models used by ACME Financial.
24.15.3. RegalTech has estimated its total assets V_0 to be $240 million, and its current equity E_0 is valued at $150 million with an equity volatility s_E of 30%. Using Ito's Lemma, calculate the volatility of RegalTech's assets s_V. Assume N(d_1 ) and N(d_2 )calculated from the Black-Scholes model as part of the Merton model are 0.95 and 0.9968. The firm asset volatility is nearest to:
a. Sv≈20
b. Sv≈30
c. Sv≈19
d. Sv≈51
Answers here:
Questions:
24.15.1. Analysts are assessing credit risk in a portfolio of corporate bonds from various sectors, utilizing the CDS-bond basis concept along with analyses of default probabilities from historical data and credit yield spreads.
The CDS-bond basis for Tech Innovations deviates from zero due to factors that include bond price discrepancies from par and contractual clauses in CDS agreements that affect payoffs. Tech Innovations' spread is currently 300 basis points, and its bond yield spread is 270 basis points, resulting in a CDS-bond basis of 30 points.
Additionally, are also comparing default probabilities. Historical data shows that the average seven-year cumulative default probability for a company like Tech Innovations is 2.3%. The credit spread for a five-year bond issued by Tech Innovations is 320 basis points and reflects a recovery rate of 45%. Using the formula λ=s(T)/(1−R), analysts calculate the implied default probability.
Which option accurately describes the analysis conducted by the investment bank's financial analysts and provides the best assessment of Tech Innovations' credit risk?
a. Tech Innovations' CDS-bond basis is positive, indicating lower default risk than bond yield spreads alone suggest. However, the calculated default probability from credit spreads is higher than historical averages, implying overvaluation of risk.
b. Positive CDS-bond basis suggests that the market perceives a higher risk of default than indicated by bond yield spreads alone, and the default probability calculated from credit spreads is lower than historical data, indicating undervaluation of risk.
c. Positive CDS-bond basis may indicate inefficiencies or specific risks not captured by the bond market, and the default probability calculated from credit spreads is higher than historical data, suggesting that market participants expect worsening conditions.
d. Analysts incorrectly calculated the CDS-bond basis as positive when it should be negative due to the high CDS spread over the bond yield spread. The default probability calculated from credit spreads aligns perfectly with historical data, indicating a stable risk assessment.
24.15.2. ACME Financial employs two probability measures for credit risk modeling―real-world and risk-neutral probabilities. Real-world probability gauges the borrower's likelihood of default, drawing from historical default rates and economic analysis. Risk-neutral probability measures prices of financial derivatives under the assumption that investors are risk-neutral, adjusting real-world probabilities using the market price of risk to discount future payoffs at the risk-free rate.
An analyst is assessing a corporate bond from Zigzag Corp with a historical default rate of 2% per year. In the derivatives market, the risk-neutral probability derived from the pricing of credit default swaps (CDS) suggests a 3% annual probability of default. This difference reflects the market's risk premium expectations and variations in valuing future uncertainties in pricing models.
Which probability measure should the analyst use to assess the credit risk of Zigzag Corp's bond for ACME Financial’s portfolio, and why?
a. Real-world probability, because it provides an actual historical perspective on the default rates, which is essential for long-term investment analysis in bonds.
b. Risk-neutral probability is crucial for determining the fair value of derivatives and aligns with the market's view on Zigzag Corp's default risk.
c. Real-world probability, as it reflects the optimistic perspective and underestimates the risk compared to risk-neutral probabilities, thus providing a safety margin.
d. Risk-neutral probability, to ensure that the pricing of risk in the credit derivatives market is consistent with the market expectations and financial models used by ACME Financial.
24.15.3. RegalTech has estimated its total assets V_0 to be $240 million, and its current equity E_0 is valued at $150 million with an equity volatility s_E of 30%. Using Ito's Lemma, calculate the volatility of RegalTech's assets s_V. Assume N(d_1 ) and N(d_2 )calculated from the Black-Scholes model as part of the Merton model are 0.95 and 0.9968. The firm asset volatility is nearest to:
a. Sv≈20
b. Sv≈30
c. Sv≈19
d. Sv≈51
Answers here:
