Question 1.1 (10 marks)
1.1.1 An equity investor contacts you to explain to him the difference between systematic and non-
systematic risk. He also wants to know which of the two he should focus on more and whether
systematic or non-systematic risk can lead to bankruptcy of a financial institution. Provide a
suitable response to the equity investor to answer his questions. (4)
1.1.2 The expected return on the market portfolio is 15% and the risk-free rate is 6.5%. Calculate
the expected return on an investment with a beta of 1.5 and indicate whether this investment
has more, less or equal systematic risk. (3)
1.1.3 The return of the market last year was 11.5% and the risk-free rate was 6%. The hedge fund
manager has a beta of 0 and an alpha of 2.1%. Given the performance of the market last
year, what return did the hedge fund manager earn? (1)
1.1.4 What is the difference between the assumptions driving returns of the capital asset pricing
model and the arbitrage pricing theory? (2)
Question 1.2 (10 marks)
1.2.1 ABC Bank is considering funding its long-term loans with short-term deposits. They contact
you to explain to them what the risks will be if they opted for this strategy. (4)
1.2.2 List one of the scandals involving mutual funds despite regulation being implemented. (1)
1.2.3 Use table 1 to calculate the minimum premium an insurance company should charge for a
R2.5 million five-year term life insurance policy issued to a man age 42. Assume that the
premium is paid at the beginning of each year and that the interest rate is zero. (Round
calculations to 6 decimal places.) (5)
Male Female
Probability Probability
Age of death Survival Life of death Survival Life
(Years) within 1 year probability expectancy within 1 year probability expectancy
Source: U.S. Department of Social Security, www.ssa.gov/OACT/STATS/table4c6.html.
Question 1.3 (10 marks)
1.3.1 Assets within ABC Bank consist of $300 million in corporate loans, $50 million of residential
mortgages and $45 million in OECD government bonds. Calculate the total risk-weighted
assets of ABC Bank. (2)
1.3.2 Explain the term “systemic risk” relating to banking. (2)
1.3.3 The Basel Committee introduced incremental risk charge because the instruments in the
trading book often attracted less capital than the instruments in the banking book. Explain
how the incremental risk charge is calculated. (3)
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1.3.4 Indicate whether the following statement is true or false and give a reason for your answer.
“Instruments are assigned to the banking book and the trading book at initiation and they can
be freely moved between the two books.” (3)
Question 2 [30 marks]
Question 2.1 (4 marks)
“Market makers earn a profit in both exchange and over-the-counter derivatives markets by charging
a commission on each trade.” Indicate whether this statement is true or false and give a detailed
justification for your answer. (4)
Question 2.2 (6 marks)
You enter into a futures contract to sell maize for R1 800 per tonne. The contract is for delivery of
1 000 tonnes. The initial margin is R160 000 and the maintenance margin is R70 000.
2.2.1 What change in the futures price will lead to a margin call? (Indicate the amount gained/lost
as well as the new price per tonne.) (3)
2.2.2 What will happen if you do not meet the margin call? (1)
2.2.3 In what circumstances can you withdraw R60 000 from the margin account? (Indicate the
amount gained/lost as well as the new price per tonne.) (2)
Question 2.3 (10 marks)
2.3.1 Can the vega of a derivative portfolio be changed by taking a position in the underlying asset?
Explain your answer. (3)
2.3.2 The vega of a derivative portfolio dependent on the dollar–sterling exchange rate is 250 ($
per %). Estimate the effect on the portfolio of an increase in the volatility of the exchange rate
from 12% to 14%. (2)
2.3.3 Portfolio A consists of a one-year zero-coupon bond with a face value of $2,000 and a 10-
year zero-coupon bond with a face value of $6,000. Portfolio B consists of a 5.95-year zero-
coupon bond with a face value of $5,000. The current yield on all bonds is 10% per annum
(continuously compounded). The value of Portfolio A is $4,016.95 and Portfolio B is
$2,757.81.
a) Show that both portfolios have the same duration. (1)
b) What are the percentage changes in the values of the two portfolios for a 6% per annum increase
in yields? (4)
Question 2.4 (10 marks)
2.4.1 What is the difference between the exponentially weighted moving average model and the
GARCH(1,1) model for updating volatilities? (2)
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