Construction of the Market Data Thresholds Reviewed in this Essay
The market data thresholds reviewed in this essay are constructed as follows:
We use five sources for market signals:
- Credit default swaps (CDS): A credit default swap is a financial contract offering protection against default on an obligation—such as a bond or loan.
- Moody’s expected default frequencies (EDF): An EDF measures the expected probability of default of an entity in the next 365 days.
- Option implied equity volatilities: The option implied volatility of a firm’s stock price is calculated from out-of-the-money option prices using a standard option pricing model.
- Market leverage ratios: The market leverage ratio is the ratio of market value of equity to market value of equity plus book value of debt.
- Marginal expected shortfalls (MES): An MES is the expected loss on equity when the overall market declines by more than a certain amount.
We examine six specific measures for each of the five signals:
- The absolute level of the signal observed at month-end relative to the historical range of that signal for each firm.
- The difference between the level of the signal and the median level of the signal for a group of low-risk financial peers (defined as financial firms whose average issuer debt rating is A as calculated by Markit) relative to the historical range of the difference.
- The one-month and three-month changes in the signal for a firm relative to its historical range of one-month and three-month changes.
- The one-month and three-month changes in the differences between the signal and the median level of the low-risk peer group, relative to the historical range of the changes in differences.
We review these signals for 33 firms (listed in Box 3 in the essay):
- 10 financial organizations that required private or public resolution in the face of failure during the financial crisis (“resolved financial organizations”).31
- 23 large banks that were above $50 billion as of December 2004 or December 2011, were not controlled by a foreign banking organization and were not resolved privately or publicly (“nonresolved large banks”).
We construct the thresholds as follows:
- Each market indicator is measured as of month-end along with the median value of the indicator for a group of A-rated financial firms (as defined by Markit).
- The resulting time series of monthly observations are then used to calculate (a) the value of the indicator for each firm relative to the A-rated firm median, (b) the one-month and three-month changes in the market indicator and (c) the one-month and three-month changes in the indicators relative to the A-rated firm. This gives us a total of 30 different signals (five absolute levels for each indicator listed above, five relative levels, 10 one-month change measures and 10 three-month change measures).
- We create these monthly time series starting in 2001. The accompanying table lists the number of months for which we have signals for each market data type for each firm. For each level measurement beginning in 2006, we calculate the 95th percentile observation corresponding to each firm’s unique time series over a rolling five-year window. We then compare the value of the firm’s current data point to the 95th percentile.
- The one-month and three-month change measurements are treated slightly differently than the thresholds based on levels. For those signals, we measure the average and standard deviation (of nonoverlapping changes) within each firm’s unique time series over a rolling five-year window and then use those data points to calculate a statistical z-score for each measure (defined as the current observation minus the average value and divided by the standard deviation). Z-scores that are 1.65 or greater (which are equivalent to the observations being above the 95th percentile, assuming the changes are normally distributed) are then identified. Firms with two consecutive such scores breach their thresholds.
- Firms that had two consecutive months in which the same signal was above its rolling 95th percentile breach their threshold. We consider a firm in breach of the threshold until it has two months in a row where the signal is no longer above the 95th percentile. The market leverage ratio, in which lower values signal greater distress, is measured at the fifth percentile.
- We do not allow for a breach of a given signal unless we have at least 20 monthly observations over the rolling two-year period leading up to each measurement.