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The following logit model has been produced to calculate the probability of default of corporate firms.
Model A:
Constant
WC/TA
RE/TA
EBIT/TA
ME/TL
S/TA
Coefficient
-5.14
1.41
-1.26
-9.46
-0.66
2.8
Standard error of the coefficient
0.32
1.42
0.38
3.68
0.34
0.72
p-value
0
0.01
0.05
Where: WC/TA is Working capital/Total assets
RE/TA is Retained earnings/Total assets
EBIT/TA is Earnings before interest and taxes/Total assets
ME/TL is market value of equity/Total liabilities
S/TA is Sales/Total assets
The Pseudo-R2 for this model is 33% and the Likelihood Ratio (LR) test is 122, which is significant at
the 1% level.
The insignificant factors RE/TA and ME/TL are removed from Model A and the following logit model
is produced.
Model B:
-4.69
-4.73
-0.32
0.26
0.36
4.93
0.25
0.2
The Pseudo-R2 for this model is 28% and the Likelihood Ratio (LR) test is 106, which is significant at
A Likelihood Ratio (LR) test is calculated to compare the log-likelihood of the two models. The LR
value is calculated as 15.5 with a p-value of 0.0%.
a. Explain the overall fit of the model and how well it predicts default. (30% question weight)
Answer (Purchase past paper to get the full solution)
The overall fit of the model is evaluated by looking at Pseudo-R2. Thus for the model A, it is 33% fit. Evaluation of the model fit with just one R2 measure is difficult. Rather, Pseudo-R2 measure helps to compare different models and choose the one with the highest fit.
b. Describe the impact of each factor of probability of default. (20% question weight)
The higher the absolute value (positive or negative) of the coefficient, the higher its impact on the probability of default in the given model. However, standard error of the coefficient should also be taken into consideration, since it shows close the prediction will be. For example, EBIT/TA is the largest coefficient in the absolute terms, but it also comes with the highest standard error. Calculating T ratios can provide answers on the “error weighted” impact of each factor
c. Calculate the t-ratio for each factor in Model A. (20% question weight)
T ratio
0.99
(3.32)
(2.57)
(1.94)
3.89
S/TA and RE/TA have the greatest impact on probability of default if assessed by T-ratios
d. Discuss which model you would choose to calculate the probability of default of corporate
firms and give a rationale for including OR excluding the RE/TA and ME/TL from the model.
(30% question weight)
Model A is a better fit to calculate probability of default as measured by higher Pseudo R2. Excluding RE/TA and ME/TL from the model not only decreased Pseudo R2 measure, but also has smaller Likelihood ratio, which shows the relative fit of Model A and Model B coefficient sets.
QUESTION 2 ANSWER ALL PARTS
a. Explain how default occurs for a limited liability company within a structural model. How
does the Merton model predict probability of default? (40% question weight)
b. Describe the payoff to equity and bond holders at maturity T within Merton’s Distance to
Default (DtD) model. Explain the relationship between DtD and probability of default. (20%
question weight)
c. The following information is given for three limited liability companies:
Company A
Company B
Company C
Asset value
70,362
71,832
76,103
Asset volatility
25.80%
28.50%
23.10%
Asset drift rate
4.50%
4.20%
4.60%
Short-term liabilities
16,358
17,106
17,250
Long-term liabilities
34,435
33,469
34,800
Calculate the Distance to Default (DtD) for each company and compare the results. Explain
the main drivers of DtD based on the information available in the above table. Which
company is the most risky? (40% question weight)
QUESTION 3
Explain the Cumulative Accuracy Profile (CAP) test for discrimination of a logit model used to
calculate the probability of default. Your answer should include a description of how it is calculated,
interpretation, results for a perfect discriminating model, and the advantages and disadvantages of
this test compared to other discrimination tests. (70% question weight)
The following information is given:
Observation
Rating (A is the best)
Default (Yes=1,No=0)
1
A
2
3
4
5
B
6
7
8
C
9
10
Based on the above information, plot the cumulative accuracy profile and comment on the
performance of the model used to calculate the Rating. (30% question weight)
QUESTION 4 ANSWER ALL PARTS
a. Describe how to set up an Excel spreadsheet that produces random walk simulations for a
stock price. The stock price can move up by £1 or down by £1 with equal probability. Explain
in detail how this simulation can be carried out in Excel over 25 days. Provide details of all
commands that you need to use.
b. Explain why the simulation in part a) is not ideal for simulating stock prices. Explain how
Geometric Brownian Motion is a preferred method, and how this can be implemented in
Excel. You should also identify and discuss any potential weaknesses of this model.
(70% question weight)
QUESTION 5
The financial crisis has put credit risk management into the regulatory spotlight and financial
institutions have had to adopt new processes and practices to understand their exposure and
likelihood of a financial loss.
Explain why and how banks have built credit risk models to measure the probability of a borrower
defaulting on their debt obligations and how these analytic techniques are used to manage a credit
portfolio.
In your answer please make reference to the different statistical techniques used to develop credit
risk models, how these are validated, and discuss the role of different stakeholders in the
development process.
NB: Purchase Credit Risk Analytics ASB 4416, 2018 past paper answer and solution by adding to cart
Last updated: Sep 29, 2019 02:59 PM
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