BBA FN415 (18) Lect 12 ActuarialDefaultRisk(b).pptx

FN415.13 1

Measuring Actuarial Default Risk (b)

Measuring Actuarial Default Risk (b)

Cumulative Default Rate

 _{This is the proportion of issuers rated R that}

FN415.13 5 Average Default Rate

 _{We can express the total cumulative default rate as an}

average) per period default rate d, by setting

 _{As we move from annual to semiannual and}

ultimately continuous compounding, the average default rate becomes

 _{Where d}a_{, d}s _{, d}c _{are default rates using annual,}

Example: Computing Cumulative default probability

 _{Consider a B-rated firm that has default rates of}

d₁ = 5%, d₂ = 7%. Compute the cumulative default probabilities.

 In the first year, k₁ = d₁ = 5%. After one year, the survival rate is S₁ = 0.95. The probability of

defaulting in year 2 is then

k₂ = S₁ x d₂ = 0.95 x 0.07 = 6.65%.

 _{After two years, the survival rate is}

(1 – d₁) (1 – d₂) = 0.95 x 0.93 = 0.8835.

 _{Thus, the cumulative probability of defaulting in}

years 1 and 2 is

FN415.13 7 Transition Probabilities

 _{The transition matrix gives the probability of}

moving to one rating conditional on the rating at the beginning of the period.

 _{The usual assumption is that these moves follow a}

Transition Matrix

 _{In year 1, with probability}

D[t₁ | B(t₀)] = P(D₁ | B₀) = 3%

 _{In year 2, after going from B to A in the first year,}

then A to D in the second; or from B to B, then to; or from B to C, then to D.

 _{The default probability is}

P(D₂| A₁).P(A₁) + P(D₂| B₁).P(B₁) + P(D₂| C₁).P(C₁) = (0.00 x 0.02) + (0.03 x 0.93) + (0.23 x 0.02) = 3.25%.

 _{The cumulative probability of default over the two}

years is then

Time Variation in Default Probabilities

 _{Defaults are also correlated with economic}

activity. Moody's, for example, has compared the annual default rate to the level of industrial

production since 1920.

 _{Moody's reports a marked increase in the default}

rate in the 1930s at the time of the Great Depression and during the recent recessions.

 _{These default rates, however, do not control for}

structural shifts in the credit quality.

 _{Recent years, many issuers came to the market}

Recovery Rates

Credit risk also depends

on the loss given default

(LGD). This can be

measured as 1 minus the

recovery rate

or fraction

FN415.13 15 The Bankruptcy Process

 _{Normally default is a state that affects all}

obligations of an issuer equally especially

 _{when accompanied by a bankruptcy filing. In most}

countries, formal bankruptcy process provides a centralized forum for resolving all the claims

against the corporation.

 _{The bankruptcy process creates a pecking order}

for a company's creditors.

 _{This spells out the order in which creditors are}

FN415.13 17 Estimates of Recovery Rate



_{Recovery rates are commonly estimated}

from the market prices of defaulted debt

shortly after default.



_{This is the best estimate of the future}

recovery



_{It takes into account the value of the}

firm's assets, the estimated cost of the

bankruptcy process, and various means

of payment (e.g., using equity to pay

Factors affecting Recovery Rate



_{The status or seniority of the}

debtor.



_{The state of the economy}



_{The obligor’s characteristics}

FN415.13 21 Trading Prices vs Discounted recovery rate

 _{The evidence, however, is that trading prices are, on}

average lower than the discounted recovery rate.

 _{The averaged is counted recovery rate is systematically}

higher than the indication given by trading prices.

 _{This creates an interesting trading opportunity. Buying}

the defaulted debt and working through the recovery process should create value.

 _{Indeed, this largely explains the existence of the}

hedge fund category called distressed securities funds.

 _{Such funds invest in selected distressed securities and}

Assessing Corporate Rating



_{The primary inputs for the credit rating}

process are accounting variables such as

balance sheet leverage and debt coverage



_{The weight assigned to these variables may}

change if their informativeness changes over

time



_{Accounting information is backward looking}



_{Economic prospects are crucial}