Credit Risk


Kevin Crotty
BUSI 448: Investments

Where are we?

Last time:

  • More interest rate risk
  • Convexity
  • Callable bonds

Today:

  • Credit risk
  • Credit ratings

Credit risk

Credit risk: the risk that the issuer of a bond (borrower) will not pay back all or part of the promised cash flows.

Issuers with credit risk:

  • Corporations
  • Households
  • Governments

Credit ratings

Investment-grade versus high-yield

Moody’s S&P + Fitch
Investment Grade
  • Aaa
  • Aa
  • A
  • Baa
  • AAA
  • AA
  • A
  • BBB
High-Yield (Junk)
  • Ba
  • B
  • \(\leq\) Caa
  • BB
  • B
  • \(\leq\) CCC
  • Higher ratings generally mean less default risk.
  • There are + and - notches for the ratings above.

Purposes of ratings



  • Proxy for credit risk
  • Regulation
    • Ex: Capital req’s are often tied to ratings
  • Contracting
    • Downgrades may trigger contract clauses

Modeling corporate credit

Modeling corporate credit

  • Why would a 5-year IBM bond have a different yield from a 5-year AAPL bond?
    • industry differences
    • firm-specific information
    • capital structure

Let’s take a look at some data.

Regression analysis #1

\[ y_{it} = \beta_0 + \beta_1 \cdot \text{ttm}_{it} + \beta_2 \cdot \text{rating}_{it} + \varepsilon_{it} \]

  • rating is numeric 1, 2, 3, …
    • we might want to do this differently

Average yield by ratings class

  • Let’s calculate the average yield within each ratings class.
  • What should we expect to see as credit ratings decline?

Code to average by ratings class:

df.groupby('RATING_CAT')['ytm'].aggregate(['mean','count'])

Regression analysis #2

  • It’s possible that yield-ratings relation will be non-linear.
  • One way to capture this is to add dummy variables for each ratings bin:

\[ y_{it} = \beta_0 + \beta_1 \cdot \text{ttm}_{it} + \sum_{k=AA,A,...} \beta_k \cdot 1[\text{rating}_{it}=k] + \varepsilon_{it} \]

Code to generate dummy variables:

rating_dummies = pd.get_dummies(df.RATING_CAT)
df = df.merge(rating_dummies,left_index=True,right_index=True)

Regression versus within-class averages


  • How do the within-class averages compare to the dummy-variable regressions?
  • NOTE: this would be exact if we hadn’t controlled for time-to-maturity.

For a risky bond, YTM \(\neq\) expected return!

  • YTM: IRR of a bond based on promised cash flows.

\[ \begin{align*} E[r] =& (1-p_{\text{default}})\cdot YTM \\ &+ p_{\text{default}}\cdot r_{\text{default}} \end{align*} \]

YTM overestimates expected returns for risky bonds.

Credit Spreads

Yield Spreads

  • Bonds with credit risk are often quoted as an interest rate spread relative to some benchmark rate
    • Treasury of same maturity or a interest rate swap

\[ \text{Spread} = YTM_{\text{risky}} - YTM_{\text{maturity-matched risk-free}} \]

  • Spread is related to the default probability times the expected loss given default (in risk-neutral terms).
    • \(\uparrow\) in probability of default increases spread
    • \(\uparrow\) in expected loss given default increases spread

CDS

Credit default swaps

Credit default swaps: an insurance contract against default by a risky borrower

Two cash flow streams:

  1. CDS buyer pays CDS seller a period payment (premium)

  2. If firm defaults, the CDS seller pays the buyer the bond’s par value less the bond’s market value.

  • CDS contracts are intended to make an investor in an issuer’s debt whole in the case of default.

CDS cash flows

No-arbitrage relation

  • There is a no-arbitrage relation between a corporate bond, risk-free debt, and a CDS.
  • The cash flows from owning a risky bond + CDS should be the same as owning a risk-free bond.
  • The Law of One Price says that two portfolios that generate the same cash flows in the future should have the same price today!
    • This implies that:

\[ \text{Bond Yield Spread} = \text{CDS spread} \]

Cash flows with and without default

Let \(R<100\) denote the recovery for a defaulted bond.

With default, the payoffs are:

Risky Bond Risk-free Bond CDS
R 100 100-R

With no default, the payoffs are:

Risky Bond Risk-free Bond CDS
100 100 0
  • Risky Bond + CDS provides $100 either way!

Uses of CDS

  • Hedging of credit risk by long bond investors
  • Speculation
    • buy CDS if you think an issuer will default
    • sell CDS to collect premiums

Economic debates

  • Empty creditor problem:
    • is it good for bondholders to not have exposure to firm’s credit risk?
    • will these investors monitor effectively?
  • Counterparty risk:
    • CDS writers could be on the hook for a large amount in the event an issuer defaults. Will they be good for it?
  • Legal questions:
    • What constitutes a default?

For next time: Asset Management





BUSI 448