Advanced Investments and Portfolio Management
Instructions
Show all workings in assignment calculations. In questions involving the use of a
financial calculator, you are required to show all financial calculator steps in your
answer. If you answer a question using a financial calculator, you do not need to detail
the equivalent mathematical formula.
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. (2
marks)
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