Discuss some of the empirical literature which identifies the determinants of spot and forward exchange parity.
Candidates should attempt ALL questions in Section A and Section B
This is individual work, carried out upholding the values of academic integrity.
Students are expected to spend 8hrs on this paper.
You should rely on your own knowledge when answering the questions. All assumptions and information needed for the questions are provided in this paper, DO NOT access the internet for help with your answer or to get additional information.
The answers should be typed in Microsoft Word, clearly stating which questions you are attempting.
Referencing is required.
The word limit is 2,000 words; this limit does not include equations and graphs.
Equations should be typed using Microsoft Word Equation Function.
Information on graphs: Graphs should be typed; however, clear pictures of hand drawn and pasted graphs will also be accepted.
SECTION A
There are 4 questions in this section. Attempt ALL questions. This section is worth 40 marks. Each question has 10 marks.
Question 1:
The five-factor asset pricing model of Fama and French (2015) is shown below:
R_it-R_Ft=a_i+b_i (R_Mt-R_Ft )+s_i SMB_t+h_i HML_t+〖r_i RMW_t+c〗_i CMA_t+e_it,
where R_it is the ordinary stock return of firm i at day t, R_Ft is the risk-free rate at day t and R_Mt-R_Ft is the market premium. The rest of the notation is defined in the original paper, which is available on Canvas (Topic 2) and online (https://doi.org/10.1016/j.jfineco.2014.10.010). Explain in detail how each of the four factors (SMB, HML, RMW and CMA) is constructed. What is the rationale for including these four new factors in the traditional capital asset pricing model when estimation is on time series data?
[10 marks]
Question 2:
Explain two different parity conditions for spot and forward exchange rates and illustrate your answer with diagrams (and) or equations and using properly-defined mathematical notation. Discuss some of the empirical literature which identifies the determinants of spot and forward exchange parity.
[10 marks]
Question 3:
When pricing a financial instrument — for example, when pricing a bond — analysts usually make use of a yield curve. Define the term “yield curve” using properly-defined mathematical notation. How is an appropriate yield curve for bond pricing constructed, and how exactly is it used to price a bond?
What common shapes of yield curves have been observed historically and under what market conditions do we observe them? Compare and contrast these shapes with those observed in commodity forward curves.
Given the bonds listed below, identify the ones with the longest and shortest duration, assuming all other bond features are the same.
• 8-year maturity, 6% coupon
• 8-year maturity, 11% coupon
• 15-year maturity, 6% coupon
• 15-year maturity, 11% coupon
Justify your answers.
[10 marks]
Question 4:
Briefly explain what an interest rate swap is. Give at least two applications of interest rate swaps. Describe how an interest rate swap can be replicated using forward rate agreements. Is the fixed-rate payer in an interest rate swap ‘short the bond market’ or ‘long the bond market’? Please, explain your reasoning.
[10 marks]
SECTION B
There are 2 questions in this section. Attempt ALL questions. This section is worth 60 marks.
Question 5:
Alpha and Gamma are two Oil & Gas companies. Tables 1 and 2 display the income statements (and balance sheets) of Gamma and Delta, respectively. Also, Table 3 displays the current evaluation of these two firms.
Table 1. Alpha Company
2019 2020 2021
Income Statement
Sales £5,000.00 £6,000.00 £7,000.00
Income before interest and taxes £454.55 £545.45 £636.36
Interest expenses £(150.00) £(150.00) £(150.00)
Income before tax £304.55 £395.45 £486.36
Income tax £(60.91) £(79.09) £(97.27)
Tax rate 20% 20% 20%
Net income £243.64 £316.36 £389.09
Preferred Dividend £(90.00) £(101.00) £(130.00)
Balance Sheet
Total assets £3,200.00 £3,455.00 £4,060.00
Long term debt £1,200.00 £1,540.00 £1,650.00
Equity preferred £500.00 £460.00 £360.00
Equity common £1,500.00 £1,455.00 £2,050.00
Total liabilities & equity £3,200.00 £3,455.00 £4,060.00
Table 2. Gamma Company
2019 2020 2021
Income Statement
Sales £3,000.00 £3,100.00 £2,800.00
Income before interest and taxes £280.37 £289.72 £261.68
Interest expenses £(100.00) £(120.00) £(99.00)
Income before tax £180.37 £169.72 £162.68
Income tax £(36.07) £(33.94) £(32.54)
Tax rate 20% 20% 20%
Net income £144.30 £135.78 £130.15
Preferred Dividend £(90.00) £(90.00) £(90.00)
Balance Sheet
Total assets £1,900.00 £2,025.00 £1,910.00
Long term debt £911.00 £1,211.00 £1,001.00
Equity preferred £0.00 £0.00 £0.00
Equity common £989.00 £814.00 £909.00
Total liabilities & equity £1,900.00 £2,025.00 £1,910.00
Table 3. Valuation of Alpha and Gamma
Alpha
Earnings per share £0.39
Dividend per share £0.13
Share price £2.41
Number of shares 1,000,000
Gamma
Earnings per share £0.33
Dividend per share £0.18
Share price £2.27
Number of shares 400,000
Task I [15 marks in total]
State the definition of Return on Equity (ROE) as a ratio of income and equity components.
[3 marks]
Use the data in Table 1 to calculate each one of the five ROE components based on the Dupont formula, for the company Alpha in 2020 and 2021.
[3 marks]
Do the same for Gamma, using data from Table 2.
[3 marks]
In each case b) and c) above use these five components to calculate the ROE and then verify that the result you obtain is indeed equal to the result obtained using the basic definition stated in a).
For the year 2021 only, critically compare each of the five ROE components for Alpha compared with Gamma. Discuss what conclusions might be drawn about the profitability of each company.
[3 marks]
Now focus on the company Gamma alone. Which components change most between 2020 to 2021? How can you interpret these findings?
[3 marks]
Task II [15 marks in total]
Use the results from part A and additional data from Table 3 to calculate the sustainable growth rate for both Alpha and Gamma, for 2021 only.
[3 marks]
Discuss the appropriateness of using these growth rates as a basis for estimating the value of the firm.
[3 marks]
Define the constant-growth dividend model, using properly-defined mathematical notation.
[3 marks]
Apply the constant-growth dividend model to the 2021 data to estimate the share price, for both Alpha and Gamma, using the sustainable growth rates just calculated and assuming a market capitalisation rate of 13%.
[3 marks]
Compare the computed share price values for Alpha and Gamma to their actual 2021 share prices given in Table 3. Comment on your results.
Question 6:
Task I [15 marks in total]
Suppose that the price of a bond futures contract that settles in three months is £105 and the price of the underlying bond is £98. The underlying bond has a coupon rate of 8%, par value of £100, and the next coupon payment is to be made in six months. The borrowing rate is 7.4% per annum. If an investor implemented a cash and carry trade, what would the arbitrage profit be?
[7 marks]
Using information in part (a), what is the theoretical futures price?
[4 marks]
Suppose that the futures price is £97.5. Given your answer to (b), is there an arbitrage opportunity and, if so, what strategy will generate that arbitrage profit?
[4 marks]
Task II [5 marks in total]
An investor has purchased a floating-rate, non-callable security with a 5-year maturity. The coupon formula for the floater is 6-month LIBOR plus 200 basis points and the interest payments are made semi-annually. At the time of purchase, 6-month LIBOR is 7.5%. In order to purchase the floater, the investor borrowed funds by issuing a 5-year note at par value with fixed semi-annual coupons of 7.0%.
With respect to the above transaction, assuming that there is no credit or liquidity risk, under what interest rate scenario can the investor lose money?
Task III [10 marks in total]
Suppose that the spot price of a barrel of crude oil is £25. Its 3-month futures contact has a value of £27 and cost-of-carry of 8%. Describe, in detail, the arbitrage strategy used to exploit this situation and the realised gains from this strategy. Use properly-defined mathematical notation in your answer.
