RSK4805 Assignment 3
2024 - DUE 15 August
2024
[Company address]
,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 (2 marks)
The profit next year is normally distributed with a mean (μ\muμ) of 0.8%
and a standard deviation (σ\sigmaσ) of 2%. We need to calculate the equity
required to ensure the company has positive equity 99% of the time.
2024 - DUE 15 August
2024
[Company address]
,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 (2 marks)
The profit next year is normally distributed with a mean (μ\muμ) of 0.8%
and a standard deviation (σ\sigmaσ) of 2%. We need to calculate the equity
required to ensure the company has positive equity 99% of the time.
