,RSK4805 Assignment 3 (COMPLETE ANSWERS) 2024 -
DUE 15 August 2024 ; 100% TRUSTED Complete, trusted
solutions and explanations.
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 marks Page 4
Question 1 Solutions
1.1 Equity Required to Ensure Positive Equity at 99%
Confidence
DUE 15 August 2024 ; 100% TRUSTED Complete, trusted
solutions and explanations.
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 marks Page 4
Question 1 Solutions
1.1 Equity Required to Ensure Positive Equity at 99%
Confidence
