Dan is a fixed income portfolio manager and his current portfolio comprises: Dan is concerned how interest rate changes will affect the value of his portfolio, especially in the event of the tapering on quantitative easing policy. He has compiled the following information about the term structure of interest rates using government bonds. All government bonds have face value of $1,000 and pay coupons on a semi-annual basis, and assume likewise for the bonds in Dan's portfolio.

(a) Calculate all the implied 6-month forward rates beginning after 6 months up until 24 months. (10 marks) (b) Calculate the value of Dan's corporate bond portfolio.

(10 marks) (c) Calculate the duration for each of the bonds in Dan's portfolio.

(10 marks) FIN201 Assignment 2

SIM UNIVERSITY Assignment 2 – Page 3 of 4 (d) Apply convexity of the bond price to compute the change of Dan's portfolio value using both duration and convexity if interest rates rise by 2%. (10 marks)

Question 2 Given that the expected annual inflation rates for Singapore and the United States are 2.2% and 1.4% respectively, as a junior economist in a hedge fund, you decide to calculate some estimates for foreign exchange rates in the future. The current spot USDSGD rate is 1.3000 ($1.3000 Singapore Dollar buys $1 US Dollar). Assume 30 days per month and 360 days per year.

(a) Using the assumptions of purchasing power parity, what is the expected spot rate for USDSGD 6 months from now? (7 marks)

(b) Subsequently, you are told that the annual interest rates for Singapore and the US are correspondingly 1.63% and 0.65%. You recall learning about arbitraging the market and decide to approach the Jim, the FX strategist to investigate if an arbitrage opportunity exists between these two currencies. Jim says that with the 3-month USDSGD forward rate trading at 1.2950, there is money to be made. Calculate and explain the arbitrage profit by illustrating the transactions to be made on a USD 1 million notional.

(18 marks) Question 3

Sally is considering a proposal to build a new factory in the deepest part of western China. If the new factory is successful, Sally estimates that the company could realise a profit of $10 million. If it fails, the company could make a loss of $8 million. Running through the various scenarios, Sally thinks that there is a 70% chance that the new factory will fail.

One of Sally's managers has suggested to Sally that the company build a small pilot factory in the nearest current urban setting. If the pilot factory works, then Sally can consider building the full factory. The pilot factory would cost $1 million to build. Sally thinks that there is a 50-50 chance that the pilot will succeed. If the pilot works, there is a 75% chance that the full factory (if constructed) will also succeed. If the pilot fails, there is only a 35% probability that the full factory will succeed (if constructed).

(a) Illustrate the decision-making process using decision trees, and calculate the expected monetary value of building the pilot factory and not building the pilot factory.

(10 marks) (b) Analyse whether Sally should build the pilot factory if the cost of the pilot factory is increased to $1.5 million (5 marks)

FIN201 Assignment 2 SIM UNIVERSITY Assignment 2 – Page 4 of 4 Question 4

MegaCo's stock price is currently trading at $25. The stock price is expected to either increase by 5% or decrease by 3.5% every quarter. Risk-free rate is 4% per annum. Assume 360 days per year and 90 days per quarter.

(a) Calculate the probabilities of the up and down moves for a binomial tree.

(5 marks)

(b) Apply the binomial option pricing model to calculate the value of a 3-month call option with a strike price of $26 per share of MegaCo's stock. (6 marks)

(c) Apply the binomial option pricing model to calculate the value of a 6-month put option with a strike price of $24.50 per share of MegaCo's stock