e

9.7 Term structure of credit spreads

The term structure of credit spreads corresponds to the spread between the yields on default-free and credit risky zero-coupon bonds.

Using either the structural or reduced form model, under the frictionless market assumption, the credit spread is entirely due to credit risk.

9.7.1 Determinants of the term structure of credit spreads

Credit spread is equal to the difference between the average yields on the risky zero-coupon bond and the riskless zero-coupon bond.

In practical applications, the "true" credit spread will consist of both:

  • Expected percentage loss (as in the structural and reduced form models); and
  • Liquidity risk premium The credit spread is equal to the expected percentage loss per year on the risky zero-coupon bond: (t T) (t T)

"True" credit spread: (t T) (t T) E(P r nt oss) qu t pr u

9.7.2 Present value of the expected loss on a bond over a given time horizon

The present value of expected loss, PV of E(loss),is calculated as follows:

( ) [ ( ) ( )]

  • This represents the present value of the cash flow, if riskless, minus the present value of the cash flow considering credit risk.

Example. Consider Powder Corporation, which has promised to pay investors 25 euros on 30 September 2014. Today is 11 August 2011. The risk-free zero-coupon yield is 0.3718%. Credit spread for payment due on 30 September 2014 is 0.2739%. Calculate the PV of the expected loss implied by the credit spread.

Solution:

  • PV of CF = D(t/T) x Xt
  • PV of CFrf= P(t/T) x Xt
  • Total yield = 0.3718% + 0.2739% = 0.6457%
  • Years to maturity = 3 years and 51 days = 3.1397 years V of V of V of E(loss)

Note: For a coupon bond, the sum of PV of the loss for each cash flow is calculated.

Lesson Wrap-Up

This lesson should leave you able to explain the term structure of credit spreads in a fixed-income context and connect it to the decisions made by issuers, investors, or analysts.

Review Prompts

  1. Explain determinants of the term structure of credit spreads in your own words.
  2. Explain present value of the expected loss on a bond over a given time horizon in your own words.
  3. State one exam-style risk, valuation, or market implication of the term structure of credit spreads.