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ACF310

Financial Modelling

2018/19

Question 1

Information on two funds is collected as follows:

• Fund has an expected annual return of 12.18% and the standard deviation of its annual return is 10.83%

• Fund x has an expected annual return of 9.15% and the standard deviation of its annual return is 6.93%

• The correlation between the returns on the two funds is 0.67

• The risk-free interest rate is 3.50% per annum

Required:

(a) Construct an optimal portfolio with these two funds and solve for the weights of the two funds in the portfolio. 8 marks

(b) What are the expected return, and the risk measured by the standard deviation of return, of the portfolio you have made in (a)? 5 marks

(c) Construct a portfolio comprising the optimal portfolio and the risk-free asset, with a required expected return of 12.18% per annum. What is the weight of the risk-free asset in this new portfolio? What is the risk of the new portfolio? 4 marks

(d) Construct a portfolio comprising the optimal portfolio and the risk-free asset, with a required expected return of 9.25% per annum. What is the weight of the risk-free asset in this new portfolio? What is the risk of the new portfolio? 4 marks

(e) Discuss briefly the implications of diversification with your results in (c) and (d). 4 marks

(Total: 25 marks)

Question 2

The spot exchange rate and the three-month forward exchange rate of sterling vis- à-vis the US dollar are quoted in New York as follows:

S0 = $1.3129/£ with a spread 127 - 131

F0,90 = $1.3396/£ with a spread 394 - 399

The interest rate at which the trader can borrow or lend in the US is 3.45% per annum and that in the UK is 1.75% per annum now, and they are expected to

remain unchanged in the next three months.

Required:

(a) Calculate and compare the forward premium and interest rate differential to verify that arbitrage opportunities may or may not exist in this case. 5 marks

(b) Set up procedures to exploit the arbitrage opportunities. Work out how big the arbitrage profit is, taking into account the transaction costs in the foreign exchange market as indicated by the bid-ask spread in the quotations. 20 marks (Total: 25 marks)

Question 3

A simplified constant payment mortgage (CPM) loan of £500,000 is negotiated between a bank and a borrower. The loan is to be repaid in 25 years, its APR is

5.5% and payments are made annually.

Required:

(a) What is the annual payment for the loan? 5 marks

(b) What is the loan balance at the beginning of year 5 and year 18 respectively? 7 marks

(d) Discuss briefly why annual amortisation is so much greater in year 18 than that in year 5 for CPM loans. 5 marks

(Total: 25 marks)

Question 4

‘Fidelity Large Value’ is a well - established American mutual fund . You obtained data for the last sixty months and ran the following regression to assess the performance of this fund:

(FUND − RF)t = a + F * (RM − RF)t + s * SMBt + h * HMLt + et

FUND – RF is the return of the fund minus the risk free return

RM – RF is the return of the market minus the risk free return

SMB is the return of the small minus big factor

HML is the return of the high minus low factor

The tables in Appendix give the regression output.

Use the regression output to answer the following:

(a) How successful is the model in explaining the stock returns of this fund? 4 marks

(b) Which variables are significant at the 10%, 5% and 1% level? 4 marks

(d) Why is the 99% confidence interval larger than the 95% interval? 4 marks

(e) If the RM - RF, SMB and HML variables are 1%, 0.3% and 0.5%, what is the

expected monthly return for the Fidelity Large Value fund? 4 marks