The ability to use financial models to be able observe through mathematics real-world observations to be able to anticipate outcomes.
a. What makes a good model and what should one avoid when building a financial model?
b. Using an example of your choice describe the key stages of building a financial model.
2. ANSWER ALL QUESTIONS:
(Please show all your workings in this question).
a. i) Your father has approached you to assist him evaluate 3 options he has to invest in term deposit accounts for the 5 years. Assuming there are no taxes to be paid which investment would you propose your father to take if he wants to achieve a return on investment of 9% after 5 years. His options are: (6 marks)
1. Invest €100,000 for the next 3 years at 1.70% compounded at 2 monthly intervals and then invest the proceeds for 2 years at 1.60% compounded at 2 monthly intervals.
2. Invest €100,000 for the next 2 years at an interest rate of 1.60% and then invest the proceeds for
3 years at an interest rate of 1.70%. Both deposits are compounded quarterly.
3. Invest €100,000 for the next 4 years at an interest of 1.90% and then use the proceeds to invest for 1 year at an interest of 0.80%. Both deposits are compounded monthly.
ii) Your father now tells you he has the option of investing for 5 years at an interest rate of 1.90% would he still select one of the 3 above options? (2 marks)
b. You are looking to start-up a company but you are looking for cash injection for the first few years in order to meet set-up costs and other initial expenses of €75,000. A distant relative has contacted you with a desire to help you get started with your company. She offers to invest €100,000 in your company and has given you a choice to receive the funds in one of the following four options:
(8 marks)
a. Five thousand euro at the end of each of the first four years, starting one year from now; €10,000 at the end of each of the next four years; and €20,000 at the end of each of the last two years.
b. Twelve thousand euro at the end of each of the first 5 years, starting from one year now; €8,000 at the end of each of the last 5 years.
c. Ten thousand euro at the end of each of the first two years, starting one year from now; €15,000 at the end of each of the next four years; and €5,000 at the end of each of the last four years.
d. Ten thousand euro at the end of each of the next ten years, starting one year from now. Your relative points out that this option offers you the advantage of a steady cash flow.
Your relative points out that any of the options will be of advantage to you depending on the situation that you are looking create for yourself. With a compounded interest of 6% per annum which option would you select?
c. You have just been notified that you have won €1,500,000 in the Super 5 jackpot. You can accept your winnings in one of the following cash flow streams. Assume that you are not liable for any income taxes on the winnings. What is your preferred option if the compounded interest rate is 8% per annum?
1. €300,000 per year with first payment received immediately.
2. €500,000 per year at the end of the next three years.
3. A lump sum of €750,000 is received immediately and €75,000 every 6 months for the next 5 years.
d. Carry out the following interest rate conversions:
i. A semi-annually compounded interest rate of 4.50% converted to monthly compounding.
ii. A quarterly compounded interest rate of 3.00% converted to continuous compounding.
iii. A continuous compounding interest rate of 2.50% into an annually compounded interest rate.
3. ANSWER ALL QUESTIONS: (Please show all your workings in this question).
a. Describe two simulation methods and the approaches used to run these simulations.
b. A Process {X(t), t ≥ 0} is an arithmetic Brownian Motion with drift term μ = 0.20 and variance σ2 = 0.10. Calculate the probability that X(7) is between 2.50 and 5.50 given X(3) = 1.50.
c. The price of 2 stock, Bank of Valletta plc (BOV) and International Hotel Investments plc (IHI), are modelled as a geometric Brownian Motion
( )
( ) (0)
t B t
S t S e
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?
where B(t) is a Standard Brownian Motion. (7 marks)
i. BOV has the following values μ = 0.075 and σ2 = 0.025 and IHI has the following values μ = 0.09 and σ = 0.12. The current prices of BOV and IHI have a price of €2.20 and €0.80 respectively. What is the probability that BOV and IHI will fall 10% in 3 years' time? Which stock is more risky?
ii. What is the expected return, α, of the 2 stocks?
d. The current price of a Malta International Airport plc is €3.45. The stock follows a geometric Brownian motion with an expected return of 9% per year and a variance of 5.4% per year. Calculate the probability that the stock price will be below €3.39 in 2 years from now. (4 marks)
4. ANSWER ALL QUESTIONS:
a. What is Value at Risk? Describe 3 variants of the VaR and their uses.
b. A hedge fund manager, Joe Black, using the historical daily log returns of 4 stocks, Barclays, HSBC, Tesco and Vodafone, and has estimated the following parameters:
i. What is the 5 day Value at Risk with a confidence of interval of 95% and 99%?
ii. What is the 10 day Value at Risk with a confidence of interval of 95% and 99%?
iii. Joe Black, is a risk lover when it comes to financial stocks and risk averse with retail and telecommunication stocks. Joe needs to decide whether he should increase or decrease his allocation in these stocks depending on the VaR measures. What is your recommendation?
5. a. An Event Study is a proven financial modelling technique when analyzing events in finance. The CEO of HSBC has resigned. Using the steps involved in an event study how would you analyse the impact the CEO's departure HSBC's stock price using the CAPM.
b. Discuss and illustrate how Event Studies look into the reaction of markets to determine whether the Efficient Market Hypothesis is violated?
6. a. What is the opportunity cost of surrounding the time value of money?
b. Describe using examples discuss the difference sensitivity analysis and scenario analysis.
c. Describe using example 3 types of Scenario Analyses?
d. What is Reverse Stress Testing?