Risk Modelling Case Study 2022

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Risk Modelling
Student’s Name
Institution Affiliation

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Question1
a. Rate sensitive liabilities are money held by banks as deposits that earns interests, and the
amounts of interest payable by the banks depends on prevailing interest rates. In that case,
the banks have to revalues the liabilities when the interest rates changes. On the other hand,
rate sensitive assets are money owed to the bank in form of loans, bonds and leases whose
value depends on the prevailing interest rates. A change in the interest rates results to either
repricing or revaluation of these assets
b. For a 30-day repricing period, the assets and liabilities that can be expected to change in
value as a result of revaluation or repayments are mortgage and 1-month T-bills. The
difference between the values of these assets and liabilities is 190 (340-150). Therefore, a 30
days repricing gap is equivalent to $190.
c. Increasing the interest rates goes up by 0.5%, it is expected that the company will generate
more income as follows.
1-month T- bills = 7.5%*3/12*150 = 2.8125
3 Months T-bills = 7.75% *3/12*150= 2.8125
Overnight repos = 5.5%*340 * 90= (16.83)
Net income = -11.205
d) Increasing the interest rate of RSA by 0.5% and the RSL by 0.75 % for the next two years
will mean that the interest income = 7.5%*150*2 + 7.75%*150*2+8%*100*2 -
340*5.75%*2 = 22.65 net interest

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e)
Row No. NII
Row 1
Row 2
Row 3
Row 4
Row 5
Row 6
Row 7
Row 7
f) Repricing model shortcomings are that the cash flows received or paid-out in a given period,
up to the maturity is considered with any other cash flow being ignored. Assumptions made on
run-offs are that they are independent from interest rates. Further the model ignores incomes
generated from off balance sheet items though it intends to incorporate the effect market values
has on the model
Question 2
a) The significant of different variables in the model is evaluated by using the p-value. The p-
values are as shown in the tables below
Variable P-value
Intercept 1.51e-10
Amount 8.73e-05
Real-estate < 2e-16
Urban 8.51e-11
New 0.221
Phipson & Smyth, (2010) notes that the p-vales should be evaluates against a level of
significance of 0.05. For any variable whose p-values is less than 0.05, it means that the
variable is key in the model. Where p-value is greater than 0.05, those variables are deemed
to have less impact in determining the outcome of a modes.

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The amount, Real-estate and Urban variable have p-values that are less than 0.5. This
therefore, means that the three variables are key to the logit model. However, the p-value for
new is greater than 0.05, which means that the period a business has been in operation did
not affect the interpretation of the model and could be omits while analyzing the data and still
make correct predictions using the remaining variables.
b) The values of the coefficients are as shown below
Variable Coefficient
Intercept -0.9271
Amount -1.0649
Real-estate -2.4247
Urban 0.9656
New -0.1662
Negative coefficient shows that the probability of defaulting decreases as the coefficient of the
variables becomes negative. On the other hand, positive values show that the probability of
default increases with increase in the value of the input variable. In this case, the amount, rea
estate and New variables have negative coefficients. Therefore, it means that persons with higher
amounts of loans are likely to honor their obligation, where loans are secured by a real estate, the
probability of default is less and the age of the business determined the ability of the owner to
repay. Businesses located in urban areas are likely to default in repaying the loan. The value for
real estate is what I could expect. However, I did not expect the default level to decrease as loan
values increased, neither that new business would have a lower risk of repayment. I would also
have expected that business operating in the urban to repay their loans in time.
c) P= eB 0 + B 1 x + B 2 X+B 3 X
1+ eB 0 +B 1 x+ B 2 X +B 3 X = (e^-0.9271-1.064-2.4247+0.9656-0.1662/ 1+e^-0.9271-
1.064-2.4247+0.9656-0.1662) = 0.3678
d) Model 1 is better in making predictions in that it captures more variables affect the ability of a
borrower to repay the loan. The location of the business and the length of period that a

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business has been in operations are variables that a lender should understand before advancing
a loan to a borrower. These variables were omitted in the second model with the amounts
borrowed and the security being the only variables used in the model. Even if the coefficients
for both variables are negative showing that the rate of default is expected to be lower, the
bank should consider the assessing the prevailing economic conditions that prompted the
model to indicate that businesses operating in the urban areas are likely to default in making
loan payments.
e) Computing the probability of default for a company using the 2nd model, the results are
P ( default )= eB 0 +B 1 x + B2 X
1+eB 0+ B 1 x+B 2 X = e^ -0.14902-1.05808-2.37474/ 1+ e^ -0.14902-1.05808-
2.37474
P(default) =0.027.
Comparing the value with the results obtained in step c, it is apparent that leaving out location
of the business and the period it has been in operation returns a lower default rate which could
mislead the bank when making the decision on the amounts of interest to charge customers for
the loans borrowed.
Question 3
a) The assumptions made when using delta model approach are that the returns are normally
distributed, the method mainly consider using historical data to compute variances and
correlations that contributes to a risk associated with an asset and the change in value of
the risk factor to the change in price of a derivative has a linear relationship
Greggs (GRG) and J D Wetherspoon (JDW) stock returns
VAR= delta * value at risk
or an equally weighted portfolio of the GRG and JDW stocks, the delta vale is given by

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σˆGRG,JDW = 0.00002.
at 99% confidence interval, the valued of delta from the Z-table is 2.576
Therefore, VAR = 0.00002*2.576 =5.152*10^-5 =0.005152%
For a stock whose value is 1,000,000 the value at risk becomes
Value at risk = 1,000,000*0.005152% = 51.52
b) Using historical simulation approach
Step 1 will entail collecting data for a specific historical period.
Step 2 is to calculating covariances of value at risk
Step 3 is to calculate the volatility.
Using these approaches, then calculate the weighted average using the following fomulas
Calculate the value at risk using
Where λ should be between 0 and 1 and Rt is the average rate of return
c) Monte Carlo simulation can be used to determine the weight average value of stocks
using the following assumptions
Estimate the expected returns for say the last five days and compute the averages using
the formula below:

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E (R) =∑
n =1
5
Rt
After the values are obtained, conduct a 99% confidence interval using a z-score rate of
2.576
Generate values corresponding within the range provided by an expected return at 99%
confidence interval and then use them independently to come up with estimates of VAR.

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Bibliography
Phipson, B., & Smyth, G. (2010). Permutation P-values Should Never Be Zero: Calculating
Exact P-values When Permutations Are Randomly Drawn. Statistical Applications In
Genetics And Molecular Biology, 9(1). doi: 10.2202/1544-6115.1585