Learning Objectives: Define the hazard rate and use it to define probability functions for default time as well as to calculate conditional and unconditional default probabilities. Describe recovery rates and their dependencies on default rates. Define a credit default swap (CDS) and explain its mechanics including the obligations of both the default protection buyer and the default protection seller. Describe CDS spreads and explain how CDS spreads can be used to estimate hazard rates.
Questions:
24.14.1. GlobalTech Corp., a publicly traded technology firm, has various bonds in the market with different maturities. As part of a risk management exercise, financial analysts at GlobalTech are tasked with evaluating the firm's credit risk using its credit spreads and the Merton model.
Data provided:
a. 2.4%
b. 4.0%
c. 6.0%
d. 5.0%
24.14.2. Imagine you are part of the risk management department at Quantum Financial Solutions, a firm that specializes in credit risk assessment. With growing concern over economic volatility, Quantum Financial has decided to enhance its internal training modules to better equip analysts in understanding complex risk dynamics. Due to a recent uptick in corporate bond defaults triggered by an economic downturn, your team is examining the interplay between recovery rates and default rates to refine loss estimation models for the firm’s bond portfolio.
You are tasked with creating a training segment that explains how recovery rates are influenced by default rates, especially under varying economic conditions. Which of the following best describes how recovery rates are typically influenced by default rates during economic downturns?
a. Recovery rates increase as default rates increase because more defaults provide more data for improving recovery strategies.
b. Recovery rates decrease as default rates increase due to market saturation with defaulted securities and reduced asset valuations.
c. Recovery rates are independent of default rates, as they are solely determined by the original credit rating of the bond issue.
d. Recovery rates and default rates are inversely proportional due to the high liquidity of defaulting securities in economic downturns.
24.14.3. An investor is considering buying protection through a Credit Default Swap (CDS) on Company X's 5-year bond, which is currently trading at par. The bond pays a semi-annual coupon of 5% when the risk-free rate is 3%. The investor approaches a bank to buy CDS protection at a spread of 200 basis points (bps) per annum, payable semi-annually. The investor is also financing the position by borrowing funds at an all-in cost of 4% annually.
One year into the contract, the yield on Company X’s bond drops to 3.75%, enhancing the bond's value to 104.60% of par. However, the investor has made semi-annual CDS payments and needs to finance the position at the agreed rate. If Company X defaults after one year, the CDS contract stipulates a physical settlement, and the recovery rate on the bond is assumed to be 40%.
Which of the following statements regarding the Credit Default Swap (CDS) entered into by the investor is NOT correct?
a. The investor's net position improved because the drop in yield led to an increase in the bond's value, which is higher than the cost of CDS protection payments and financing.
b. If Company X defaults after one year and the bond's recovery rate is 40%, the investor would have to deliver the defaulted bond to the protection seller and would only incur a loss equivalent to 60% of the bond's par value.
c. The CDS spread paid by the investor can be used to estimate the hazard rate for Company X's bond by dividing the CDS spread by one minus the recovery rate, assuming a constant hazard rate for simplicity.
d. The annual cost of the CDS protection at 200 basis points, when financed at a 4% annual rate, implies the investor will have a net outflow of 50 basis points per period, as the financing cost exceeds the CDS spread.
Answers:
Questions:
24.14.1. GlobalTech Corp., a publicly traded technology firm, has various bonds in the market with different maturities. As part of a risk management exercise, financial analysts at GlobalTech are tasked with evaluating the firm's credit risk using its credit spreads and the Merton model.
Data provided:
- Five-year CDS spread for GlobalTech: 240 basis points.
- Expected recovery rate in the event of default: 40%.
- Credit spreads for 3-year, 5-year, and 10-year bonds are 50, 60, and 100 basis points, respectively.
- The firm’s bonds are trading close to their par value.
a. 2.4%
b. 4.0%
c. 6.0%
d. 5.0%
24.14.2. Imagine you are part of the risk management department at Quantum Financial Solutions, a firm that specializes in credit risk assessment. With growing concern over economic volatility, Quantum Financial has decided to enhance its internal training modules to better equip analysts in understanding complex risk dynamics. Due to a recent uptick in corporate bond defaults triggered by an economic downturn, your team is examining the interplay between recovery rates and default rates to refine loss estimation models for the firm’s bond portfolio.
You are tasked with creating a training segment that explains how recovery rates are influenced by default rates, especially under varying economic conditions. Which of the following best describes how recovery rates are typically influenced by default rates during economic downturns?
a. Recovery rates increase as default rates increase because more defaults provide more data for improving recovery strategies.
b. Recovery rates decrease as default rates increase due to market saturation with defaulted securities and reduced asset valuations.
c. Recovery rates are independent of default rates, as they are solely determined by the original credit rating of the bond issue.
d. Recovery rates and default rates are inversely proportional due to the high liquidity of defaulting securities in economic downturns.
24.14.3. An investor is considering buying protection through a Credit Default Swap (CDS) on Company X's 5-year bond, which is currently trading at par. The bond pays a semi-annual coupon of 5% when the risk-free rate is 3%. The investor approaches a bank to buy CDS protection at a spread of 200 basis points (bps) per annum, payable semi-annually. The investor is also financing the position by borrowing funds at an all-in cost of 4% annually.
One year into the contract, the yield on Company X’s bond drops to 3.75%, enhancing the bond's value to 104.60% of par. However, the investor has made semi-annual CDS payments and needs to finance the position at the agreed rate. If Company X defaults after one year, the CDS contract stipulates a physical settlement, and the recovery rate on the bond is assumed to be 40%.
Which of the following statements regarding the Credit Default Swap (CDS) entered into by the investor is NOT correct?
a. The investor's net position improved because the drop in yield led to an increase in the bond's value, which is higher than the cost of CDS protection payments and financing.
b. If Company X defaults after one year and the bond's recovery rate is 40%, the investor would have to deliver the defaulted bond to the protection seller and would only incur a loss equivalent to 60% of the bond's par value.
c. The CDS spread paid by the investor can be used to estimate the hazard rate for Company X's bond by dividing the CDS spread by one minus the recovery rate, assuming a constant hazard rate for simplicity.
d. The annual cost of the CDS protection at 200 basis points, when financed at a 4% annual rate, implies the investor will have a net outflow of 50 basis points per period, as the financing cost exceeds the CDS spread.
Answers:
