RSK4805 Assignment 3
(COMPLETE ANSWERS)
2024 - DUE 15 August 2024
100% GUARANTEED
,RSK4805 Assignment 3 (COMPLETE ANSWERS) 2024 -
DUE 15 August 2024
Question 1 (25 marks) 1.1 A bank estimates that its profit next
year is normally distributed with a mean of 0.8% of assets and a
standard deviation of 2% of assets. How much equity (as a
percentage of assets) does the company need to be 99% sure
that it will have positive equity at the end of the year? (Use z-
values rounded to two decimal places) (2)
To determine how much equity (as a percentage of assets) the company needs to ensure a 99%
probability of having positive equity at the end of the year, we can use the concept of Value at
Risk (VaR) based on the normal distribution.
Step 1: Understand the problem
Mean profit (μ\muμ) = 0.8% of assets
Standard deviation of profit (σ\sigmaσ) = 2% of assets
We need to find the equity percentage that ensures a 99% probability that the profit will
be positive.
Step 2: Find the z-value for a 99% confidence level
For a 99% confidence level, we look at the z-table for the z-value corresponding to the 1% tail
(because 1% is the remaining area in the left tail of the distribution).
z-value=−2.33\text{z-value} = -2.33z-value=−2.33
Step 3: Calculate the required equity
The equity needed corresponds to the Value at Risk (VaR) formula:
Required Equity=μ+z×σ\text{Required Equity} = \mu + z \times \sigmaRequired Equity=μ+z×σ
Substituting the values:
Required Equity=0.8%+(−2.33)×2%\text{Required Equity} = 0.8\% + (-2.33) \times
2\%Required Equity=0.8%+(−2.33)×2% Required Equity=0.8%−4.66%\text{Required Equity}
= 0.8\% - 4.66\%Required Equity=0.8%−4.66% Required Equity=−3.86%\text{Required
Equity} = -3.86\%Required Equity=−3.86%
Since the company needs positive equity to ensure solvency:
, Equity Required=3.86%\text{Equity Required} = 3.86\%Equity Required=3.86%
Conclusion
The company needs to hold 3.86% of assets as equity to be 99% sure that it will have positive
equity at the end of the year.
1.2 Given the following information for a listed company, the
expected return if invested in the shares of this company is
7.80%. Calculate the variance and the standard deviation of this
expected return. (3) State of Economy Probability Percentage
Return State 1 0.30 13% State 2 0.35 8% State 3 0.15 2% State 4
0.20 4%
To calculate the variance and standard deviation of the expected return, we can follow these
steps:
Step 1: Calculate the Expected Return
The expected return (E(R)E(R)E(R)) is given as 7.80%.
Step 2: Calculate the Variance
Variance is calculated using the formula:
Variance=∑[Probability of State×(Return in State−E(R))2]\text{Variance} = \sum \left[\
text{Probability of State} \times (\text{Return in State} - E(R))^2\
right]Variance=∑[Probability of State×(Return in State−E(R))2]
Given the data:
State 1: Probability = 0.30, Return = 13%
State 2: Probability = 0.35, Return = 8%
State 3: Probability = 0.15, Return = 2%
State 4: Probability = 0.20, Return = 4%
Variance=0.30×(13%−7.80%)2+0.35×(8%−7.80%)2+0.15×(2%−7.80%)2+0.20×(4%−7.80%)2\
text{Variance} = 0.30 \times (13\% - 7.80\%)^2 + 0.35 \times (8\% - 7.80\%)^2 + 0.15 \times
(2\% - 7.80\%)^2 + 0.20 \times (4\% - 7.80\%)^2Variance=0.30×(13%−7.80%)2+0.35×(8%
−7.80%)2+0.15×(2%−7.80%)2+0.20×(4%−7.80%)2
(COMPLETE ANSWERS)
2024 - DUE 15 August 2024
100% GUARANTEED
,RSK4805 Assignment 3 (COMPLETE ANSWERS) 2024 -
DUE 15 August 2024
Question 1 (25 marks) 1.1 A bank estimates that its profit next
year is normally distributed with a mean of 0.8% of assets and a
standard deviation of 2% of assets. How much equity (as a
percentage of assets) does the company need to be 99% sure
that it will have positive equity at the end of the year? (Use z-
values rounded to two decimal places) (2)
To determine how much equity (as a percentage of assets) the company needs to ensure a 99%
probability of having positive equity at the end of the year, we can use the concept of Value at
Risk (VaR) based on the normal distribution.
Step 1: Understand the problem
Mean profit (μ\muμ) = 0.8% of assets
Standard deviation of profit (σ\sigmaσ) = 2% of assets
We need to find the equity percentage that ensures a 99% probability that the profit will
be positive.
Step 2: Find the z-value for a 99% confidence level
For a 99% confidence level, we look at the z-table for the z-value corresponding to the 1% tail
(because 1% is the remaining area in the left tail of the distribution).
z-value=−2.33\text{z-value} = -2.33z-value=−2.33
Step 3: Calculate the required equity
The equity needed corresponds to the Value at Risk (VaR) formula:
Required Equity=μ+z×σ\text{Required Equity} = \mu + z \times \sigmaRequired Equity=μ+z×σ
Substituting the values:
Required Equity=0.8%+(−2.33)×2%\text{Required Equity} = 0.8\% + (-2.33) \times
2\%Required Equity=0.8%+(−2.33)×2% Required Equity=0.8%−4.66%\text{Required Equity}
= 0.8\% - 4.66\%Required Equity=0.8%−4.66% Required Equity=−3.86%\text{Required
Equity} = -3.86\%Required Equity=−3.86%
Since the company needs positive equity to ensure solvency:
, Equity Required=3.86%\text{Equity Required} = 3.86\%Equity Required=3.86%
Conclusion
The company needs to hold 3.86% of assets as equity to be 99% sure that it will have positive
equity at the end of the year.
1.2 Given the following information for a listed company, the
expected return if invested in the shares of this company is
7.80%. Calculate the variance and the standard deviation of this
expected return. (3) State of Economy Probability Percentage
Return State 1 0.30 13% State 2 0.35 8% State 3 0.15 2% State 4
0.20 4%
To calculate the variance and standard deviation of the expected return, we can follow these
steps:
Step 1: Calculate the Expected Return
The expected return (E(R)E(R)E(R)) is given as 7.80%.
Step 2: Calculate the Variance
Variance is calculated using the formula:
Variance=∑[Probability of State×(Return in State−E(R))2]\text{Variance} = \sum \left[\
text{Probability of State} \times (\text{Return in State} - E(R))^2\
right]Variance=∑[Probability of State×(Return in State−E(R))2]
Given the data:
State 1: Probability = 0.30, Return = 13%
State 2: Probability = 0.35, Return = 8%
State 3: Probability = 0.15, Return = 2%
State 4: Probability = 0.20, Return = 4%
Variance=0.30×(13%−7.80%)2+0.35×(8%−7.80%)2+0.15×(2%−7.80%)2+0.20×(4%−7.80%)2\
text{Variance} = 0.30 \times (13\% - 7.80\%)^2 + 0.35 \times (8\% - 7.80\%)^2 + 0.15 \times
(2\% - 7.80\%)^2 + 0.20 \times (4\% - 7.80\%)^2Variance=0.30×(13%−7.80%)2+0.35×(8%
−7.80%)2+0.15×(2%−7.80%)2+0.20×(4%−7.80%)2
