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# 金融代写|金融风险管理代写Financial Risk Management代考|CHEE6420 Credit risk

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## 金融代写|金融风险管理代写Financial Risk Management代考|Credit risk

Rating agencies

Probabilities of default are the basis for all the credit ratings by S\&P, Moody’s, Fitch

Tables with historical default rates for the rating are available

As these tables are long-term, they need to be adjusted for the business cycle and other factors

Ratings give no indication of the credit risk for non-rated companies
\begin{tabular}{|rrrr}
\hline Financial Risk Management (Lecture 5) & Credit risk & Andreas Krause \
\hline \multicolumn{2}{|c|}{ Default probabilities }
\end{tabular}
Altman’s Z score

Using accounting figures the following model has been developed

$z=1.2 \frac{\text { Working capital }}{\text { Assets }}+1.4 \frac{\text { Retained earnings }}{\text { Assets }}$
$-\quad+3.3 \frac{E B I T}{A s s e t s}+0.6 \frac{M V \text { equity }}{\text { Book liabilities }}$
$-\quad+0.999 \frac{\text { Sales }}{\text { Assets }}$

Interpretation

The interpretation of default from this score is more qualitative

$z>3$ : Default probability negligible

$2.7<z \leq 3$ : Default unlikely

$1.8<z \leq 2.7$ : Default reasonable

$z \leq 1.8$ : Default likely

More formally we can define the probability that a company defaults in specific time period as

Prob(default in $[t, t+\Delta t] \mid$ no default before $t)=$ Prob(default before $t+\Delta t)-\operatorname{Prob}($ default before $t)$

$\quad=\frac{1-D(t+\Delta t)-(1-D(t))}{D(t)}=\frac{D(t)-D(t+\Delta t)}{D(t)}$

$D(t)$ is the probability of the company surviving until $t$

## 金融代写|金融风险管理代写Financial Risk Management代考|Using corporate bonds

Using corporate bonds

Corporate bonds have yields above that of government bonds

This difference in yields is called the spread

The spread incorporates the default and potential losses in case of a default
\begin{tabular}{rrrr}
\hline Financial Risk Management (Lecture 5) & Credit risk & Andreas Krause & $14 / 27$ \
\hline Estimating default probabilities & Estimation based on bond prices
\end{tabular}
Default probability

$\lambda$ : default rate, $R$ : recovery rate, $s$ : spread

$\lambda(1-R)=s$

$\lambda=\frac{s}{1-R} \approx s$

Empirical performance

Default rates estimated from bonds are much higher than historical default rates

Reasons for this include

Distribution for credit risk is skewed, which reduces diversification (no upside “risk”), hence unsystematic risk needs to be compensated

High correlation of defaults in times of market stress make a higher premium necessary

## 金融代写|金融风险管理代写FINANCIAL RISK MANAGEMENT 代考|CREDIT RISK

\begin } { \text { tabular} } | \text { rrrr } } \backslash \text { hline 金蟚风风险管理（第 } 5 \text { 讲) \& 信用风风险 \& Andreas Krause } \backslash \backslash \text { hline } \backslash \text { multicolumn } { 2 } | c | } \text { 违约概率 } } \backslash \text { end } { \text { tabular } }

$z=1.2 \frac{\text { Working capital }}{\text { Assets }}+1.4 \frac{\text { Retained earnings }}{\text { Assets }}$
$-\quad+3.3 \frac{E B I T}{\text { Assets }}+0.6 \frac{M V \text { equity }}{\text { Book liabilities }}$
$-\quad+0.999 \frac{\text { Sales }}{\text { Assets }}$

$z>3$ : 违约概率可忽略不计
$2.7<z \leq 3:$ : 默认不太可能
$1.8<z \leq 2.7$ : 默认合理
$z \leq 1.8$ : 默认可能

$$=\frac{1-D(t+\Delta t)-(1-D(t))}{D(t)}=\frac{D(t)-D(t+\Delta t)}{D(t)}$$
$D(t)$ 是公司存活到 $t$

## 金融代写|金融风险管理代写FINANCIAL RISK MANAGEMENT 代考|USING CORPORATE BONDS

$\lambda$ : 违约率， $R$ : 恢复率， $s:$ 传播
\begin{aligned} & \lambda(1-R)=s \ & \lambda=\frac{s}{1-R} \approx s \end{aligned}

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