Instructions to candidates:

  1. You are required to attempt ALL questions in section A (total 40 marks) each question is worth 10 marks.

Answer TWO questions in section B (total 60 marks) each question is worth 30 marks.
Additional Material: A formula sheet will be provided.

  1. It is expected that this paper will take you 3 hours to complete.


  1. The maximum word count permitted is 4000. Where appropriate the bibliography is not included in the word count. You should write the total number of words at the top of your submission, if you are scanning in handwritten notes you should count the average number of words per line and multiply by the average number of lines per page to give a rough approximation.


  1. Submissions must be in the form of a Microsoft Word file. Do NOT submit in .pages formats from Apple products. Any handwritten answers/diagrams/graphs etc should be scanned into the document using Microsoft Lens. Please note – Turnitin can only accept one document for upload. If you are scanning anything in, you must combine them into one file prior to upload.

If you are scanning in any documents you must ensure that you have at least 20 typed words (for example, just type the word ‘exam’ 20 times) within the document you submit This is to ensure Turnitin/Canvas will allow you to upload the document. You must ensure you check your file before submitting. Only ONE submission will be allowed.

  1. A submission point has been created and should appear under the Assignments section located on the left side of the menu within your Canvas course home page. Your uploaded submission should be a single file, so please combine any separate files into one. To avoid system overload please ensure you submit in good time within the 24-hour period. You must ensure you check your file before submitting it via Canvas.


  1. Please note the software only allows uploads of up to 100mb

*Remember, if you encounter IT difficulties that significantly affects your ability to complete this exam or when uploading your answer(s) you may submit a PEC detailing these.  
Please note that if you are ill or unable to complete the exam for any reason your only option is to request a deferral (usually until August) of the exam. If you request a deferral and it is accepted, your progress on the programme may be delayed. We cannot allow requests for extensions for take home exams.


Answer all questions in this section
Section Total: 40 marks

  1. Consider the following two projects:

Year                  Y 0 Y 1 Y 2 Y 3 Y 4 Y 5 Y 6 Y 7 Discount

Project C/F C/F C/F C/F
Alpha -79 20       25      30

C/F C/F C/F C/F       Rate
35      40 N/A N/A       15%
 25     25      16%
C/F: Cash Flow
Suppose the two projects are mutually exclusive.

  1. Calculate the payback periods for Alpha and Beta. Which project is better according to the payback rule?

(2 marks)

  1. Calculate the NPVs for Alpha and Beta. Which project is better according to the NPV rule?
    • marks)
  1. c) What is your investment decision based on your results in a) and b)? Explain.
  • marks)


  1. d) Critically evaluate the investment appraisal rules including NPV, IRR and Payback periods?

(3 marks)

[QUESTION 1 Total Marks: 10 marks]


  1. Consider the following expected returns, volatilities, and correlations:


Stock Expected Return Standard Deviation
Duke Energy 14% 6%
Microsoft 44% 24%

Duke Energy and Microsoft is perfectly negatively correlated (the correlation is -1).

  1. a) Calculate the expected return and volatility of a portfolio that is equally invested in Duke Energy and Microsoft.
  • marks)
  1. b) Consider a portfolio consisting of only Duke Energy and Microsoft. What percentage of your investment (portfolio weight) that you would place in Duke Energy stock to achieve a risk-free investment?
  • marks)
  1. c) ‘When we combine many stocks in a large portfolio, the risks of each sock will average out and be diversified.’ Critically evaluate the above statement.

(5 marks)

[QUESTION 2 Total Marks: 10 marks]


  1. You are trying to plan for retirement in 10 years, and currently you have £150,000 in a savings account and £252,000 in stocks. In addition, you plan to deposit £8,000 per year into your savings account at the end of each of the next 5 years, and then £10,000per year at the end of each year for the final 5 years until you retire.
  2. Assuming your savings account returns 8% compounded annually, and your investment in stocks will return 12% compounded annually, how much will you have at the end of 10 years? (Ignore taxes)


  • marks)


  1. If you expect to live for 20 years after you retire, and at retirement you deposit all of your funds (including savings and stock investments) into a bank account paying 11%, how much can you withdraw each year after you retire (marking 20 equal withdrawals beginning one year after you retire) so that you end up with a zero-balance at death?


  • marks)


[QUESTION 3 Total Marks: 10 marks]


  1. The Capital Market Line (CML) is a straight line that passes through the risk-free interest rate and the Tangent Efficient Portfolio.


  1. Explain the meaning of the Tangent Efficient Portfolio.


  • marks)


  1. What are the implications of the Capital Market Line to an investor?


  • marks)


  1. ‘The Capital Market Line was constructed under the assumption that borrowing rates are the same as lending rates. However, since borrowing rates are usually higher than lending rates, the Capital Market Line becomes invalid in reality.’ Critically evaluate the above statement.

(4 marks)
[QUESTION 4 Total Marks: 10 marks]


Answer two questions in this section
You can answer Question 5A or 5B but not both

Question 5A (30 marks)

You are considering whether to invest in a newly formed investment fund. The fund’s investment objective is to acquire home mortgage securities at what you hope will be bargain prices. The fund sponsor suggested to you that the fund’s performance will hinge on how the national economy performs in the coming year. Specially, he suggested the following possible outcomes are possible:

State of Economy Probability Fund Returns
Rapid    Expansion     of
0.05 100%
Modest Growth 0.45 35%
Continued Recession 0.45 5%
Falls into Depression 0.05 -100%


  • What is your estimate of the expected rate of return from this investment?

(3 marks)

  • If the estimated beta of this investment is 2.0 and the riskfree rate of interest is currently 2.5%, what is the slope of the security market line for the real estate mortgage security investment? Interpret the meaning of the security market line based on your calculation.
    • marks)


  • You are also considering the investment of your money in a market index fund that has an expected rate of return of 10%. What is the slope of the security market line for this investment opportunity?


  • marks)


  • Based on your analysis of parts 2) and 3) above, which investment should you take? Why?

(5 marks)

  • Critically evaluate the advantages and disadvantages of the CAPM.

(10 marks)
[QUESTION 5A Total Marks: 30 marks]



Question 5B (30 marks)

Companies A and B have been offered the following rates per annum on a £20 million five-year loan:

Fixed rate Floating rate
5.0% LIBOR+0.1%
6.4% LIBOR+0.6%


  • Company A requires a floating-rate loan; company B requires a fixed-rate loan. Design a swap that will net a bank, acting as intermediary, 0.1% per annum and that will appear equally attractive to both companies.
    • marks)


  • Discuss the possible reasons that company A and B prefer to enter into the swap contract.
    • marks)


  • Identify and discuss the comparative advantage possessed by both companies.
    • marks)


  • Should the spreads between the rates offered to Company A and B be different in fixed and floating markets? Explain why the comparative advantage cannot be arbitraged away.
    • marks)


  • ‘Swap rates are not risk-free lending rates. However, they are close to risk-free.’ Using an example of a 5-year swap rate explain the meaning of the above statement.

(10 marks)

[QUESTION 5B Total Marks: 30 marks]

You can answer Question 6A or 6B but not both

Question 6A (30 marks)

A survey of over 200 European fund managers conducted in 2008 and published in the Hedge Fund Journal (May 2008) revealed that a wide range of portfolio performance measures were being employed, and often more than one at a time.

  • The single most popular β based performance measure was Jensen’s Alpha. Compare and contrast this metric with two other well-known β based measures, the T-squared and the Treynor measures.

(15 marks)

  • The single most popular measure was Sharpe’s ratio, used by around 80% of fund managers, but around 70% also used the Information ratio. Define these two measures and calculate their values for the funds below, together with the funds’ rankings. In all cases assume the market (MKT) is the benchmark, with a mean return of 3%, and that the risk free rate is a constant 1%.


Fund Fund returns [Fund return – MKT return]
SD: 4.8%
SD: 9.9%
SD: 10.0%

(5 marks)

  • Explain the concept of market timing with regard to fund management and how a regression involving the return on the fund (Ri) and the return on the market (Rm) has been used to test for the existence of timing ability among fund managers.

 (10 marks)
 [QUESTION 6A Total Marks: 30 marks]



Question 6B (30 marks)

A non-callable 4-year UK government bond pays semi-annual coupons.  The face value is £1000, the annual coupon rate is 6% and the yield to maturity is 4% per year.

  • Show clearly how the current market price and annual modified duration are calculated from the data above. Then discuss how the modified duration may be used to estimate the price change resulting from a 1% change in the annual yield.
    • marks)


  • Explain in detail what is meant by convexity with regard to the relationship between price and yield, and how this will impact on your price change estimate in part (a). Assume convexity is 15.18.

(10 marks)
 (c) In addition to convexity, are there any other limitations to using the modified duration to estimate bond price changes? Discuss.

  • marks)

(d) Some bonds are issued with embedded options, which impacts the relationship between price and yield. Explain this phenomenon with regard to ‘call’ and ‘put’ options.
 (10 marks)

[QUESTION 6B Total Marks: 30 marks]

You can answer Question 7A or 7B but not both

Question 7A (30 marks)

A company has a portfolio of stocks worth £10 million. The beta of the portfolio is 1.40. The company would like to use the FTSE 100 index futures contract to hedge the portfolio’s exposure to the market. The index future price is 3,500 and each contract is on £10 times the index.

  1. Explain the basic principle of hedging a risk and available hedging strategies using futures.
    • marks)


  1. What strategy should the company take if they wish to hedge the portfolio’s exposure to the stock market?


  • marks)


  1. Why should the company take the hedging strategy stated in your answer to Question b)?


  • marks)


  1. How many contracts should the company hold if they wish to completely eliminate the market risk?


  • marks)
  1. e) Suppose that the company has changed its mind and decides to increase the beta of the portfolio from 1.40 to 1.75. What position in the futures contracts should they take and how many contracts are needed?

(6 marks)
 [QUESTION 7A Total Marks: 30 marks]



Question 7B (30 marks)

A European call option and put option on a stock both have a strike price of £20 and an expiration date in three months. Both sell for £3. The risk-free interest rate is 10% per annum with continuous compounding and the current stock is £22.

  1. Devise two portfolios, one containing a European call option and cash and another consisting of a European put option and a share of stock, and assuming that the underlying stock does not pay dividends, derive the put-call parity.
    • marks)


  1. Does the put-call parity still hold when the underlying stock is expected to pay dividends? If yes, what adjustment should be made and explain why.
    • marks)


  1. Using the put-call parity examine the relationship between the prices of the European call option and European put option when £1 dividend on the stock is expected in one month.
    • marks)
  1. d) Identify the arbitrage opportunity open to a trader based on the above information and your answer to question c.

(8 marks)

  1. e) What is the profit one could realise by arbitraging?

(4 marks)

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