Purpose: Explain a spreadsheet related to operational risk and Enterprise Risk Management (ERM), specifically from the readings by Brian Noco and Renee Stos under bionic turtle.com.
Focus: Using a credit transition (migration) matrix to determine the amount of equity capital required.
Credit Transition (Migration) Matrix
Adapted from Standard & Poor’s credit migration matrix.
Definition: A single period matrix showing probabilities of credit rating changes.
Example: Firm starting at Single A:
2% chance of upgrading to AAA
3% chance of upgrading to AA
88% chance of remaining at Single A
Using the Matrix
Diagonal elements have the highest probabilities (stability).
Input Needed: Attitude towards risk and target probability of default.
Attitude Towards Risk
Firm’s risk orientation implies a target probability of default.
Higher risk appetite → Higher probability of default
Example: Targeting only a 6% probability of downgrading to speculative (junk) status.
Example Calculation
Assume firm wants a 6% chance to be downgraded to Double B or less.
Initially rated as Single A:
2% to Double B
1% to B
0.8% to CCC
2% chance to default
Total: ~5.8% (almost 6%) aligns with risk attitude.
Corresponds to a 2% probability of default for Single A rating.
Meron (Merton) Model
Purpose: Reverse engineer to find firm value and required equity capital.
Inputs:
Firm's debt: $10
Expected return on assets: 9%
Time period: 1 year
Volatility of assets: 20%
Result: Firm needs asset value of $14 to meet 2% default probability.
Detailed Calculation
Default Threshold: $10
Growth and Volatility model:
$14 grows at 9% to an expected value of $15.70.
20% volatility → Result is two standard deviations above default threshold.
41% mean above default threshold aligns with ~2% default probability.
Equity Cushion: $4 of equity required to meet the 2% probability of default.
Conclusion
Starting Point: Attitude towards risk and target probability of default.
Calculation Result: Firm value of $14 required for two standard deviations above the default threshold, giving a 2% default probability.
Implication: Need to start with an initial credit rating of Single A to meet the desired probability of downgrading to speculative status.
Notes
Crucial role of credit transition matrices in understanding operational risk and ERM.
Reinforces topics in readings by Renee Stos and Brian Noco.