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SEMESTER 1 EXAMINATIONS 2021-22

INTRODUCTION TO FINANCE

SECTION A

You must answer ONE question from this section.

QUESTION 1

a) Show and explain the mathematical valuation of a common share in detail. (15 marks)

b) Compare and contrast in detail the characteristics of a common share and a bond regarding risk in investment. (20 marks)

c) Discuss in detail the factors that affect the market value of a bond. (40 marks)

d) Suppose you bought a thirty-year long-term bond five years ago.  The bond pays £10,000 at the end of the year for thirty years and then returns the face value at the end of the thirtieth year.  When you bought the bond the market interest rate (yield to maturity) was 10% per year and the face value of the bond is £100,000.  You have received the first five-coupon payment, but the market interest has also increased to 13% per year, and you are thinking of selling the bond.

(i) What price do you expect to receive? (15 marks)

(ii) What price would you have received if the market interest rate had fallen to 7% per year? (10 marks)   

QUESTION 2

a) Discuss in detail the relationship between the interest rate and the time value of money, annuity and perpetuity. (20 marks)

b) “The Net Present Value (NPV) is not any better than Internal Rate of Return (IRR) due to the incremental cash flow problems.”  Do you agree with this statement?  Defend your answer in detail.  (50 marks)

c) Consider three investments options A, B and C.  All cash flows are in nominal terms.

All payments are made at the end of the year.  If the market interest rate is 10% per year,

Calculate the Payback Period, Discounted Payback Period, Modified Internal Rate of Return (MIRR) and the Net Present Value (NPV) of the three options.  Please show all calculations. (20 marks)

d) Consider two investment options: X and Y.  End of the year cash flows are in nominal terms for X and in real terms for Y are as follows:

All payments are made at the end of the year.  If the nominal interest rate 10% per year and the real interest rate is 7% per year,

Calculate the REAL net present value options of X and Y and explain which option you would pick.  Please show all calculations including the annual real cash flows for option X.  (10 marks)

SECTION B

You must answer ONE question from this section.

QUESTION 3

The following table summarises information (expected return and standard deviation, in annual percentage) about two assets, a risky asset A, and a risk-free asset F. The correlation between returns on the two assets is 0.

Suppose there are two investors in the financial market. The first investor’s risk appetite (the maximum amount of risk he or she is willing to take) is defined by the portfolio standard deviation , whereas the second investor’s risk appetite is . Each investor maximises the expected portfolio return given his or her risk appetite. There is no difference between bid and ask rates on trading in Assets A and F. Please answer the following questions. Justify your answers and show all workings.

a) What is the optimal portfolio solution for the first and the second investors? (20 marks)

b) Is there an opportunity for trading in Assets A and F between the two investors? Why? (10 marks)

c) If the answer to part b) is “YES”, design the optimal trading strategy between the first and the second investor. Explain in detail the strategy. (10 marks) 

d) What is the expected portfolio return (in annual percentage) derived from the trading strategy designed in c) for each investor?  (10 marks)

e) Assuming that each investor is endowed with GBP 1,000,000, what is the expected portfolio return in GBP on the trading strategy designed in part c) for each investor? (5 marks)

In the following figure (Figure 1), the mean variance efficient frontier and the capital market line are visualised.

Figure 1 

f) In Figure 1, discuss the properties of investment portfolios A, B, M, and C. Which of the four portfolios has the highest Sharpe ratio? Why? Note: part f) is independent of parts a)-e). (15 marks)

g) In Figure 1, suppose an investor can borrow and lend at a risk-free rate. What determines the location of optimal portfolio solutions (i.e., whether an optimal portfolio is located on the left or on the right of point M)? Discuss. (Assume that all portfolios include Asset F.) Note: part g) is independent of parts a)-e). (15 marks)

h) Now suppose that an investor can borrow and lend at a risk-free rate. However, the borrowing rate is higher than the lending rate. How will Figure 1 change? Draw a new figure and discuss. Note: part h) is independent of parts a)-e). (15 marks)

QUESTION 4

Suppose an investor considers investing in oil futures market. The monthly return on the crude oil futures contract (West Texas Intermediate) is calculated as the percentage monthly rate of change in the price of the crude oil futures contract. The sample period runs from February 1986 to February 2021. It comprises a total of 419 monthly observations. The return is displayed in the following time series chart (Figure 2): 

Figure 2

The autocorrelation function of returns is estimated. The coefficient of autocorrelation of order 1 is 0.25 (, whereas the coefficient of autocorrelation of order 2 is -0.10 (. Autocorrelations of higher order are assumed to take on values 0. There are two investors in the oil futures market. The first investor designs a trading strategy for April 2021, whereas the second investor designs a trading strategy for May 2021. They receive advice from a financial analyst. Please answer the following questions. Justify your answers and show all workings.

a) Suppose the financial analyst wishes to test if the null hypothesis  (i.e., returns on the oil futures contract are not autocorrelated) is supported by the data. What is the value of the Ljung-Box Q test statistic? What is the outcome of the test?  (Assume the test statistic is distributed with a Chi-Square distribution with  degrees of freedom, .) From the statistical tables of the Chi-Square distribution, the critical value at 5% level of significance is 5.9915.) (25 marks)

b) In relation to part a), does the weak-form efficient market hypothesis (EMH) hold? Does the semi-strong-form EMH hold? Does the strong-form EMH hold? Why? (20 marks)

c) Explain how you would test for the weak-form EMH in the oil futures market by means of the runs test. (Note: you don’t need to perform the test. However, you need to outline and explain the step-by-step procedure for this test.)  (10 marks)

d) Suppose the price of the crude oil futures contract in March 2021 decreases by 1 percent relative to February 2021. Should the investors buy or sell the oil futures contract in April 2021 and May 2021? Why? (Note: If the price is expected to increase, this is a signal to buy. If the price is expected to decrease, this is a signal to sell.) (25 marks)

e) Now suppose the price follows a martingale. The price in February 2021 is 59.06 USD per barrel of oil. What is the expected price in March 2021? (10 marks)

f) Now suppose the price follows a sub-martingale. The price in February 2021 is 59.06 USD per barrel of oil. The expected return on the oil futures contract in March 2021 is 12.5%. What is the expected price in March 2021? (10 marks)