Fixed Income-Credit Risk

Credit spread

Credit spread

• Profit made on a loan or bond portfolio,

Profit = Portfolio Value x (1 – Default probability) x Spread

• To break even, profit made should be equal to expected loss

• Therefore, spread is obtained by clearing the equation,

Spread = Default Probability x (1 – Recovery) / (1 – Default probability)

• As normally Default probability is very small, ( 1 – Default probability) is

almost 1, so credit spread is frequently expressed as

Spread = Default probability x (1 – Recovery)

• If recovery is assumed to be 0, Credit Spread = Default Probability

Average Default Probability

• It is the average default frequency measured over a long time of a given kind of

counterparties and products.

• A Rating Agency works with default probabilities measured over a long term so

theoretically valid over a long term

Implied Default Probability

• It is the default probability that will be obtained using the following formula, with

current credit spread of a given issuer,

Spread = Default probability x (1 – Recovery)

• Ratings estimated from default probabilities derived from the former formula using

Bond Credit Spreads can be considered market assumptions of issuer ratings

• Ratings estimated from default probabilities derived from the former formula using

Credit Default Swaps can also be considered market assumptions of issuer ratings

although with a more instantaneous nature than when bond spreads are used.

Long Term Default Probability

• If everything is rightly measured, in the long term the average of implied default

probabilities