MATH260: Consultio International - University of Liverpool Project
Dear Team,
Background
As an internationally estimated financial institution Consultio International are responsible for total client assets of £508 billion from over two-million clients across Asia Pacific, Europe, the Middle East, South America and Canada. Consultio International (CI) provides world class investment solutions and retirement expertises to institutions, individuals and their advisers to help their clients build better futures for themselves and generation to come. The financial services provided a wide range of clients include: wealthy management, pensions and retirement, share dealing, investment trusts, corporate bonds and gilts, regular investing, spread betting & CFDs and risk management services.
Risk management
Risk management is at the heart CI’s strategy, as well as many of their clients, in order to protect respective shareholders and other stakeholders’ financial interests. This is achieved through informed risk decisions and robust risk management support by a consistent risk-focused culture. The team of Risk Investment Analysts at CI has a wealth of risk management experience and intrigate knowledge of the financial services sector. Many of the mathematical models used to price financial products are developed in-house and well supported by empirical evidence, however, a degree of uncertainty cannot be avoided. For example, a put option is a contract giving the owner the right, but not the obligation, to sell a specified asset at a specified price called the strike price at a specified time in the future. It can be used to limit the risk for an investor: if a particular asset for which we have the put option, falls below the agreed threshold, i.e., the strike price K, the put option guarantee the threshold value. The client investors of CI who hold stakes in Lloyds Banking Group PLC (Lloy.L) may wish to manage the risk of their portfolio by purchasing a financial put product. Theses are trading in high volumes. Following consultation with the Global Markets Risk Director the mis-pricing of a financial put option could lead to a significant lose to Consultio International. You will investigate this in detail, as well as other related issues, using our model which is based on the a statistical model widely used in the sector; further details are included in Task 1.
Portfolio management
Portfolio management involves the selection, prioritisation and oversight of asset investment in line with the strategic objectives to the organisation. Our investment managers are decision-makers who devise and implement investment strategies and processes to meet a host of institional goals and con- straints. They construct and manage portfolios, make decisions on what and when to buy and sell investments. As part of Task 2 you will study and evaluate a portfolio held by a client who shall be referred to as Investor A. As part of this task you will provide analyses and advice on a range of risk and reward matters associated with investment assets held in the portfolio.
Requirement
As a group, prepare a written report suitable for the management of Consultio which could be pre- sented to the client at our next meeting scheduled for 9 am on Monday 13th May. Ensure the report addresses the specific tasks set out of the following pages. The report should be thorough, but not long-winded, including detailed calculations, justified assumptions, appropriate finanical models, use of summaries, images, table or other graphics to support calculations, and clearly presented conclu- sions. Any computer code used to arrive at valuations presented in the report must be included in an appendix to the report. The final report must be ready for internal review by Friday 10th May.
Kind regards,
Consultio International - Director of Risk Management
Task 1:
As part of this task you will report on the price P(0) of a European put option, which expires in T = 1 years, to sell one share of Lloyds Banking Group with strike price K = 55 pence. You should assume the share price of Lloy.L changes day-by-day by a factor of p and the opening price is S(0) = 48 pence. There are 252 trading days in the one year. If p > 1, then the share price rises in value. You will view p as a random variable, the average value p is bigger than one reflects the average trend of the stock market to have rising stock values. The value of p will change day-by-day in a certain interval around p reflecting stock market volatility. You may assume the model to predict the daily movements in the share price S(t) given by,
where r follows a normal distribution N(µ,σ2 ) with average daily return µ and standard deviation σ . In-house analyst predict the expect return associated to the share is 17 .64% over the one-year period with standard deviation 31.75%.
(a) Using MATLAB, or similar software, run a simulation of the stock market in order to estimate the cost associated to the financial contract to CI. The payoff formula for L payable by Consultio International is given by
where v = S(252) is the simulated share price after 252 days of trading in one year. Estimate the
average loss〈L）by
where N is the number of simulations and Li is the loss to CI on the ith-simulation. [25 marks]
(b) Use the confidence interval with error bar ϵL given by,
to indicate how close your estimation is to the true value L of the average loss for CI. Given CI will sell the put option for the fair price, which is equal to the average loss, explain the estimated value of P(0) based on your analysis. [5 marks]
(c) Suppose European call options C with expiry T = 1 years giving the owner the right to buy one share of Lloyds Banking Group with strike price K = 55 pence are available to purchase in the market. Estimate the fair value of a call option stating clearly, with justification, any assumptions that you make. Briefly desribe the circumstances for which arbitrage opportunities exist and summarise the trading strategies to realise the gains. [10 marks]
Task 2: The client, Investor A, currently has a portfolio of assets totalling £200, 000 as listed in the table below. The annual expected portfolio return is estimated each year based on the official bank rate of interest, r%, set by the Bank of England.
(a) Calculate the current expected percentage return on the portfolio of assets per annum based on the current basic rate of interest and summarise the advantages and disadvantages of increasing the proportion of equities held in the portfolio. [10 marks]
(b) Within the corporate bonds asset class, there is a bond with face value £10, 000 and a coupon rate of 4% paid annually, due to expire in one year’s time. The investor is considering selling this bond today and re-investing the funds into other asset classes. What is the market value of the bond today? [10 marks]
(c) Investor A owns share in Lloyds Banking Group in the equities asset class. The investor wishes to hedge against the falling price of the stock in one time’s year, so would like to explore potential financial products to manage their fiancial risk. Prepare an analysis of the benefits and drawbacks in one year’s time, for a portfolio with a share in Lloyds Banking Group and a short position for a European call option with strike price 55 pence, associated with this stock. [10 marks]
(d) In order to diverisfy the portfolio, the investor will be advised to incoporate stocks from inter- national markets. Identify two non-UK companies operating overseas and open their latest finan- cial statements. By reviewing the statements from the CEO, Finance Director, Chairman, or other members of the Board of Directors, identify, compare, and briefly summarise key systematic and non- systematic risks affecting future profitability suitable for presentation to the client. [10 marks]