SECTION ONE: Calculations and Analysis
Question 1 [10 marks]
a) For the bond with a coupon of 5.5% paid annually, with 10 years to maturity and a YTM of 6.10%, calculate the duration and modified duration. (3 marks)
b) For the bond described in a) above, calculate the convexity. (3 marks)
c) Calculate the price change for a 50 basis point drop in yield using duration plus convexity. (2marks)
d) Samantha and Roberta are discussing the riskiness of two treasury bonds A& B with the following features:
Bond Price Modified Duration
A 90 4
B 50 6
Samantha claims that Bond B has more price volatility because of its higher modified duration.
Roberta disagrees and claims that Bond A has more price volatility despite its lower modified duration. Who is right? (2 marks)
Question 2 [10 Marks]
A share now sells for $40.00. This price will either increase by 10% (by a factor of u = 1.10) or decrease by 20% (by a factor of d = 0.80) over a six–month period. A European call option on this share has an exercise price of $42 and a time to expiry of six months. The risk–free rate is 6% per year.
Use the one–period binomial option pricing model to find the price of the call option. You should present your calculations and explanations as follows:
a. Draw tree–diagrams to show the possible paths of the share price and call price over one six–month period. [2 Marks]
Note: Show the numbers that are known and use letter(s) for what is unknown in your diagrams.
b. Compute the hedge ratio and show clearly how to form a perfect hedge. [1 Marks]
c. Find the call option price. Explain your calculations clearly. [2 Marks]
An analyst disagrees with the current share price movement predictions and believes that the share price will either increase by 20% or decrease by 30% over a six–month period. Assume that the European call option has the same exercise price and the same time to expiry.
d. Would the analyst price the European call option at, above, or below the original price calculated in Part c? Why? [Maximum: 200 words] [5 Marks]
Question 3 [20 Marks]
You are given the following distributions of returns for two assets, X and Y:
Probability Returns
X
%
Y
%
0.2 11 –3
0.2 9 15
0.2 25 2
0.2 7 20
0.2 –2 6
A . Calculate the expected return and standard deviation for the returns of each asset.
(2 marks)
B . Calculate the covariance between the returns of asset X and asset Y.
(2 marks)
C . Complete the table below for the mean and standard deviation of the given portfolios.
(3 marks)
Hint: Use the weights in decimals in the calculations and then covert your answers into percentages. A few results are calculated for you in the table.
Percentage in X Percentage in Y E(rP)
(%)
σP
(%)
125 –25
100 0
75 25 9.50 6.18
50 50
25 75 8.50 5.96
0 100
–25 125 7.50 11.42
D . Discuss your results.
(2 marks)
E . Next, sketch the following relationships:
a. Between the expected return on the portfolios and the weight, w, invested in asset X.
b. Between the standard deviation of the portfolios and the weight in X.
c. Between the mean and standard deviation of the portfolios in a single graph (the mean–standard deviation plane).(3 marks)
F . Discuss your plots.
(2 marks)
4
G . Which portfolios are efficient?
(2 marks)
H . The minimum–variance portfolio weight in X, w*, is given by: YXXY22
YXXY2
2
−+
=
YX
Y
The minimum–variance portfolio is also called the global minimum–variance portfolio.
Find w* using this formula.
(2 marks)
I . Calculate the expected return and the standard deviation of the minimum–variance
portfolio, G. (2 marks)
Question 4 [10 Marks]
You are the manager for the bond portfolio of a superannuation fund. The policies of the fund allow for the use of active strategies in managing the bond portfolio. It appears that due to the weak economic prospects brought about by COVID–19 among other factors, growth is expected to below par and the Reserve Bank of Australia, in an effort to spur economic expansion, is moving towards a looser monetary policy.
For each of the situations below, state which bond you would prefer and briefly justify your answer in each case. (2 marks for each situation)
a) A 3% coupon Commonwealth of Australia non–callable bond due in 20 years.
Or
A 6% coupon Commonwealth of Australia non–callable bond due in 20 years.
b) Origin Energy Company 4.50% coupon, rated AAA due in 2040 and priced at 93.53 to yield5.02% to maturity.
Or
AGL Limited 5.50% coupon, rated Baa due in 2040 and priced at 95.94 to yield 5.85% to
maturity.
c) Vale Company 3.75% coupon, rated Baa due in 2040 and callable at 105.
Or
Vale Company 7.75% coupon, rated Baa due in 2040 and callable at 105.
d) Origin Energy Company 3.50% coupon, non–callable bond rated AAA due in 2026 and priced at 97.28 to yield 4.02% to maturity.
Or
5
AGL Limited 4.05% coupon, callable bond, rated AAA due in 2026 and priced at 97.43 to yield
4.55% to maturity.
e) Santos Limited Company 3.50% coupon bond rated A due in 2026 and priced at 97.28 to
yield 4.02% to maturity.
Or
Woodside Petroleum 4.05% coupon bond, rated A due in 2046 and priced at 92.47 to yield
4.55% to maturity.
Question 5 [10 Marks]
The following information pertains to three portfolios over a 6–year period. Market returns (%) and
the risk–free returns (%) are also provided.
Period Market Return Risk–free Return Portfolio 1 Portfolio 2 Portfolio 3
1 0.10 0.05 0.15 0.16 0.17
2 0.02 0.06 0.09 0.11 0.13
3 0.20 0.08 0.26 0.28 0.18
4 0.30 0.09 0.34 0.36 0.42
5 –0.04 0.08 –0.02 –0.03 –0.16
6 0.16 0.07 0.16 0.17 0.17
Without doing any calculations, answer the following:
a) Which portfolio would you expect to have the highest beta? (1 mark)
b) Which portfolio would you expect to have the highest standard deviation of returns?
(1 mark)
c) Which portfolio would you expect to have the highest Sharpe ratio? (1 mark)
Answer the following questions based on your calculations and knowledge of the topic:
d) Rank the three portfolios based on commonly used performance measures. (2 marks)
e) Overall, which portfolio exhibited the best performance based on a composite set of
performance measures? Comment on your findings. (2 marks)
f) If you wanted to find more details of the relative performance of the three portfolios what further analysis would you do? What additional details would you seek?
(3 marks)
SECTION TWO: Discussion Questions (Total 40 Marks)
You are an active fund manager. For each of the recent events given below discuss,
whether the event is exploitable by you to create a positive alpha for your portfolio. If
the event is exploitable, outline a strategy that you will use to create the positive alpha. For events that are not exploitable, explain why you are unable to create a positive alpha strategy. (5 marks per question) (suggested word limit 2000)
1. Retail traders aggressively buy ‘meme’ stocks targeting stocks short–sold by hedge funds.
2. Major governments in the world provide incentives for the use of hydrogen as a fuel.
3. Major fund management companies increase their allocations to Chinese equities.
4. Trading platforms such as Robinhood impose bans on individual traders trading meme
stocks.
5. The regulator decides to ban ALL analysts’ reports due to potential conflicts of interest.
6. Cybersecurity breaches become very common.
7. Major central banks permit investors to hold cryptocurrencies.
8. Major central banks of the world exit quantitative easing.
