[Company name]
RSK4805
Assignment 3
2024 - DUE 15
August 2024
QUESTIONS WITH DETAILED ANSWERS
,RSK4805 Assignment 3 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)
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%
1.3 Describe an exchange-traded fund (ETF) and identify an advantage of an ETF
compared to a closed-end fund (CEF). (2)
1.4 Suppose you currently hold a security valued at R750, and the prevailing risk-free
rate is 5.5%. You plan to sell this security in three months. The theoretical forward
contract price is calculated at R760.12 and will be used to hedge against potential price
declines. Now, if the dealer offers a tradable price to unlock the arbitrage profit of R745
on the forward contract, determine the arbitrage opportunity available to you, and
subsequently, provide a calculation for the potential arbitrage profit. (5)
1.5 You are a risk manager at a big corporation. How can you update the volatility
estimate for an asset when the closing price yesterday was R375, and the estimated
daily volatility was 1.2%? Today’s closing price is R371. You need to consider the
following two methods for updating the volatility estimate: a) EWMA model with λ = 0.95
b) GARCH (1,1) model with ω = 0.000003, α= 0.05, and β = 0.95 (Round all calculations
to eight decimal places) (5) Page 3
, 1.6 An analyst provided data for two assets, Asset A and Asset B, including their current
daily volatilities, prior and current daily closing prices, coefficient of correlation between
the returns of these two assets, the covariance, and the parameter λ used in the EWMA
model. With today's closing prices at R55 and R35 for Asset A and Asset B respectively,
the new covariance estimate between the two assets is 0.000120. Additionally, the new
variance estimates for Asset A and Asset B are 0.000392 and 0.000189, respectively.
The analyst now seeks an update on the correlation estimate between the two assets,
considering the current trading prices of these assets. Calculate the revised correlation
estimate between the assets. (3)
1.7 A binary option pays off R240 if a stock price is greater than R50 in six months. The
current stock price is R43, and its volatility is 35% per annum. The risk-free rate is 6%
(continuously compounded) and the expected return on the stock is 11.5%
(continuously compounded). Calculate the value of this option. (5) Total (Question 1):
25
1.1 Equity Requirement for Positive Equity at 99% Confidence Level
Given:
• Mean profit μ=0.8%\mu = 0.8\%μ=0.8% of assets
• Standard deviation σ=2%\sigma = 2\%σ=2% of assets
• Confidence level = 99%
We need to find the equity as a percentage of assets such that the bank is 99% sure it
will have positive equity at the end of the year.
Using the Z-score formula: Z=X−μσZ = \frac{X - \mu}{\sigma}Z=σX−μ
At 99% confidence, the Z-value is 2.33 (rounded to two decimal places).
We want the equity to be greater than 0, so: 0=0.8%+(2.33×2%)−Equity0 = 0.8\% +
(2.33 \times 2\%) - \text{Equity}0=0.8%+(2.33×2%)−Equity
RSK4805
Assignment 3
2024 - DUE 15
August 2024
QUESTIONS WITH DETAILED ANSWERS
,RSK4805 Assignment 3 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)
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%
1.3 Describe an exchange-traded fund (ETF) and identify an advantage of an ETF
compared to a closed-end fund (CEF). (2)
1.4 Suppose you currently hold a security valued at R750, and the prevailing risk-free
rate is 5.5%. You plan to sell this security in three months. The theoretical forward
contract price is calculated at R760.12 and will be used to hedge against potential price
declines. Now, if the dealer offers a tradable price to unlock the arbitrage profit of R745
on the forward contract, determine the arbitrage opportunity available to you, and
subsequently, provide a calculation for the potential arbitrage profit. (5)
1.5 You are a risk manager at a big corporation. How can you update the volatility
estimate for an asset when the closing price yesterday was R375, and the estimated
daily volatility was 1.2%? Today’s closing price is R371. You need to consider the
following two methods for updating the volatility estimate: a) EWMA model with λ = 0.95
b) GARCH (1,1) model with ω = 0.000003, α= 0.05, and β = 0.95 (Round all calculations
to eight decimal places) (5) Page 3
, 1.6 An analyst provided data for two assets, Asset A and Asset B, including their current
daily volatilities, prior and current daily closing prices, coefficient of correlation between
the returns of these two assets, the covariance, and the parameter λ used in the EWMA
model. With today's closing prices at R55 and R35 for Asset A and Asset B respectively,
the new covariance estimate between the two assets is 0.000120. Additionally, the new
variance estimates for Asset A and Asset B are 0.000392 and 0.000189, respectively.
The analyst now seeks an update on the correlation estimate between the two assets,
considering the current trading prices of these assets. Calculate the revised correlation
estimate between the assets. (3)
1.7 A binary option pays off R240 if a stock price is greater than R50 in six months. The
current stock price is R43, and its volatility is 35% per annum. The risk-free rate is 6%
(continuously compounded) and the expected return on the stock is 11.5%
(continuously compounded). Calculate the value of this option. (5) Total (Question 1):
25
1.1 Equity Requirement for Positive Equity at 99% Confidence Level
Given:
• Mean profit μ=0.8%\mu = 0.8\%μ=0.8% of assets
• Standard deviation σ=2%\sigma = 2\%σ=2% of assets
• Confidence level = 99%
We need to find the equity as a percentage of assets such that the bank is 99% sure it
will have positive equity at the end of the year.
Using the Z-score formula: Z=X−μσZ = \frac{X - \mu}{\sigma}Z=σX−μ
At 99% confidence, the Z-value is 2.33 (rounded to two decimal places).
We want the equity to be greater than 0, so: 0=0.8%+(2.33×2%)−Equity0 = 0.8\% +
(2.33 \times 2\%) - \text{Equity}0=0.8%+(2.33×2%)−Equity
