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PPT Structural Models of Credit Risk are Useful: Evidence from Hedge Ratios on Corporate Bonds PowerPoint presentation | free to download

Structural Models of Credit Risk are Useful: Evidence from Hedge Ratios on Corporate Bonds

underestimating hedge ratio (beta) of debt to equity (or equity risk premium) or. Explaining Structural Model Spreads with Empirical Betas. PowerPoint PPT presentation

Title: Structural Models of Credit Risk are Useful: Evidence from Hedge Ratios on Corporate Bonds

Structural Models

• Structural models of credit risk represent

default in terms of the value of the firms

assets (that collateralise the debt)

• So possible reasons for underestimating spreads
• underestimating default probability (or LGD)
• underestimating hedge ratio (beta) of debt to

  Source Huang Huang

  Structural Models and Default Probabilities

• Actually structural models appear to provide

reasonably good (or at least not bad) estimates

of default probabilities

Lelands Estimates of Default Probabilities

• Leland uses default boundary model with realistic

input parameters to calculate default

probabilities

• B-rated bonds asset volatility is 32

• A-rated bonds asset volatility is 23 (Base

  Dotted line is actual.

Dotted line is actual.

Default Frequencies in Structural Models of

Debt, Working Paper, Univ. of California,

Berkeley, September 2002.

Short-Term vs. Long-Term Default Probabilities

• Long-term (7-8 years and longer) default

frequencies fit quite well

• Short-term (1-6 years and below) default

  frequencies are too low

What do we do in this paper?

• Existing research
• default probabilities (partial) success
• spreads failure (i.e. so far no success for

variable that depends on prices)

Why are hedge ratios important — I?

• Determine risk premia
• In all structural models the bond value is

determined as the price of the replicating

portfolio

Why are hedge ratios important — II?

• Hedge ratio
• measures exposure of debt value to value of

collateralising assets

Focus of Paper

• Estimate hedge ratio regressions

• In a world governed by structural models, hedge

  ratio regressions would produce

• coefficients bj,E close to one
• high explanatory power (R2 close to 1)
• . but not exactly as a result of (a)

  non-linearity (b) discreteness

• We show that (a) and (b) are not important and

  test hypothesis that bj,E 1

• Consider other systematic factors (a la

  Collin-Dufresne) and examine their relation to

  underlying credit risk

Main Findings — 1

• Simple structural model (Merton, 1974) provides

reasonably good estimates of hedge ratios of

corporate debt to equity

Entire Sample Final Sample

Bonds 10,370 1360

Issuers 2,114 396

Descriptive Statistics Final Dataset

A Simple Time-Series Hedging Regression

• We run the following regression

• Results
• estimated hedge ratios small (0.006 0.04 for

  IG) but highly (statistically) significant

• R2 much less than 100
• sensitivity to Treasury returns (duration) low

Hedge Ratios

• Are these hedge ratios reasonable?
• compare with hedge ratios implied by Merton model
• In one-factor structural models the hedge ratio,

bE, is

where DE is the delta of equity to the firms

asset value and L is the debt-to-asset value ratio

Hedge Ratios from the Merton Model

Asset Volatility Asset Volatility Asset Volatility Asset Volatility Asset Volatility Asset Volatility Asset Volatility

Leverage 10 15 20 25 30 40 50

10 0.00 0.00 0.04 0.58 2.53 9.25 17.19

20 0.00 0.03 0.70 2.63 4.80 13.52 21.39

40 0.10 1.42 6.88 10.41 16.44 23.73 31.58

50 0.49 53.19 8.05 11.88 17.50 24.17 29.68

60 2.06 4.47 13.255 16.60 19.53 24.79 34.08

70 3.20 7.98 15.25 14.73 21.79 27.83 29.87

Source Schaefer / Strebulaev

Explaining Structural Model Spreads with

Empirical Betas

• Implies default-boundary structural models

produce very similar hedge ratios to Merton

The story so far

• Merton model produces hedge ratios in line with

empirical estimates

Stochastic Interest Rates

• In Merton model ( effectively, Black-Scholes)

riskless interest rates are fixed

corporate debt

Low Duration Puzzle Regressions on riskless

bonds only

Including Stochastic Interest Rates

• Merton (1974) with affine interest rates (Shimko

et. al. (1993), Lando (2004))

Other Factors Running a kitchen sink regression

• Hedge ratios for equity and riskless debt are not

much changed

Sensitivity to SMB

• Sensitivity to corporate debt returns to SMB
• not result of sensitivity of underlying assets to

SMB

Conclusion 1

• Hedge ratios provide a good measure of credit

exposure and, in this sense, structural models

seem to capture credit exposure better than

commonly supposed

risk related factors still incomplete