Exam (elaborations)
RSK4805 Assignment 3 2024 - DUE 15 August 2024
- Course
- RSK4805 (RSK4805)
- Institution
- University Of South Africa
RSK4805 Assignment 3 2024 - DUE 15 August 2024 QUESTIONS WITH ANSWERS
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[Date]RSK4805 Assignment
3 2024 - DUE 15
August 2024
QUESTIONS WITH 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 Profit Distribution and Equity Requirement (2 marks)
Given:
• Mean profit = 0.8% of assets
• Standard deviation = 2% of assets
• Confidence level = 99%
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