Finance Questions and Solutions

Question 1

A market portfolio is made up entirely of the following 4 securities:

Â	Total Value in Millions	Standard	Â	Â	Correlation with
Â	In millions	deviation	Â	A	B	C	D
Security A	$60	20%	A	1.0	0	0	0
Security B	$40	35%	B	0	1.0	0	0
Security C	$50	45%	C	0	0	1.0	0
Security D	$50	50%	D	0	0	0	1.0

 

• Calculate the standard deviation of the market portfolio. (2 marks)

• If the risk-free rate of interest is 4% and the expected rate of return on the market portfolio is 12%. Draw a diagram to depict the relevant capital market line. (3 marks)
• You have to advise someone seeking to obtain an expected rate of return of 15%. What investment strategy do you advise them to achieve this and what standard deviation can they expect? (3 marks)

You are given the following data about the returns on security A, RA and security B, RB. Along with the standard deviations of returns on asset A, ?A and the standard deviations of returns on asset B, ?B. Complete the following table for standard deviations of the portfolio for the two values of the correlation coefficient of returns on securities A and B (?_AB) and the differing weights attached to the two securities wA and wB.

RA = 10%, ?A = 30%

RB = 5%, ?B = 15%

wA	wB	?AB=0.5	?AB=0	Return
0.7	0.3	?	?	?
0.3	0.7	?	?	?

1. Calculate the Macaulay Duration for an £8 annual coupon bond with a face value of £100 and 4 years left to maturity if the bond’s yield to maturity is 6%. (Show your calculations) (4 marks)
   
   
2. What is the modified duration of the bond? (2 marks)
   
   
3. If 4 year yields to maturity were to suddenly to increase from 6% to 7% and the bond in problem (i) was selling for £106.93 at 6% yield, what would you expect the bond price to be after the yield increases to 7% ?(3 marks)

You have following investments in securities A, B and C.

Security return	Amount Invested	Beta	Expected
Â	Â	Â	1 Year Return
A	£20,000	1.3	12%
B	£30,000	1.8	22%
C	£50,000	2.0	27%

The current risk-free rate of interest is 5% and you have heard that analysts are expecting a 15% return on the market portfolio over the next year. Based on your expectations for the 1-year returns of each of the securities is your portfolio underpriced, overpriced or correctly priced? (show your workings and explain your reasoning) [7 marks]

You have the following 7 years of data covering returns on Share A and the Market Portfolio

Year	Share A	Market Portfolio
2015	6%	8%
2016	-5%	3%
2017	7%	14%
2018	2%	5%
2019	-1%	7%
2020	6%	-5%
2021	4%	13%

The standard deviation of Share A is 4.39

The standard deviation of the market portfolio is 6.42

The covariance of Share A with the market is 5.64

• Calculate for each of the above years, the yearly returns of a portfolio created by allocating your money 40% between Share A and 60% the market portfolio.(2 marks)

• Calculate the average expected rate of return and standard deviation of a portfolio made up of 40% share A and 60% in the market portfolio(3 marks)
• Calculate the beta of stock A. What does the beta reveal about the defensive or aggressive qualities of Share A?(3 marks)

You are an equity analyst working for an investment bank. You are analysing Company ABC shares. The last year’s dividend (Do) was 50 pence. You are predicting a 6% dividend growth for next 3 years and 9% for the following 2 years, and thereafter dividend growth is assumed to slow for the foreseeable future to 5%. The required rate of return on equity is deemed to be 13%.

1. Calculate the fair value price of the share.(Show your workings) (4 marks)

1. What is the fair value of the share at the end of year 5? (Show your workings) (4 marks)

The policy-making committee of Bank ABC recently used reports from its securities analysts to develop the following efficient equity only portfolios.

Â	Expected rate of	Standard deviation
Equity Portfolio	return	Â
1	7%	4%
2	10%	6%
3	19%	13%
4	15%	8%
5	24%	18%
i.  If the risk-free rate of interest is 5% which portfolio is best?		(1 mark)

 

1. Assume that the policy-making committee would like to earn an expected rate of return of 22% with a standard deviation of 10%, is this possible?(2 marks)
   
   
2. If a standard deviation of 30% was acceptable to the investment committee, what would be the expected return and how could it best be achieved?(3 marks)
   
   
3. Assume that the correlation coefficient between all of the above portfolios is zero. What is the expected rate of return on a combined portfolio made up of all the above 5 portfolios with an equal weighting given to each portfolio? Would the standard deviation of this combined portfolio be higher or lower than that of portfolio 4 or is it not possible to say?(3 marks)[Total 9 marks]

Currently the yields to maturity on 10 year bonds are as follows:

Bond Type	Yield to Maturity
Treasury	6.00%
AAA Corporates	6.50%
BBB Corporates	7.50%

You are a bond manger and currently have 30% of you portfolio in Treasuries 40% in AAA Corporates and 30% in BBB Corporates.

Your analysis of “normal” yield spreads suggest that AAA bonds should offer about 25 basis points above Treasuries and BBB bonds should offer about 250 basis points over Treasuries

How will you adjust your portfolio and what does this involve you in doing? [5 marks]

Assume that the rate of profits (p) on combined debt and equity is fixed at 22%.

Debt/Equity Ratio	Proportion of Profits absorbed by Interest
(Gearing)	r=10%	r=15%	r=20%
0.5	?	?	?
1.5	?	?	?
2.5	?	?	?

 

• Complete the table above for the proportion of profits absorbed by interest.(3 marks)
• What can you conclude about the impact of primary gearing on the vulnerability of a company to rises in interest rates?(2 marks)

The US interest rate is 6% the UK interest rate is 2% and the spot exchange rate is $1.20/£1 the underlying currency is £100,000.

• Calculate the appropriate futures price if the currency futures contract has 270 days left to expiration (3/4 of a 360 day year). [2 marks]

• Explain the rationale for your result in part (i) assuming that you initially have $120,000 today. [2 marks]

• If you think the spot rate on expiration of the futures contract will be $1.40/£1

1. What will you do with the futures contract you have priced in part (i) buy it or sell it? [1 mark]
2. What will be your profit in dollars if you are correct and the spot exchange rate on expiration is $1.40/£1? [2 marks]
3. What will be your loss in dollars if you are wrong correct and the spot exchange rate on expiration is $1/£1? [2 marks][9 marks]

• It is January 1 2022, the 3-month (91 days) $LIBOR spot interest rate is 5% and the 6 month (182 days) $LIBOR spot interest is 4%. Calculate the appropriate price of the March 31, 2022 $LIBOR interest rate futures contract.(4 marks)

• Explain the rationale behind your result given that the contract size is for $1 million.4 marks) [Total 8 marks]

The December 2022 FTSE 100 stock index futures contract is reading 6450 while the cash index is reading 6400. The futures contract is worth £10 per point.

1. Is the dividend yield higher or lower than the risk-free rate of interest?(1 mark)
2. You have £30 million of funds invested in FTSE 100 stocks under management and are concerned about a fall in the market by December 2022 expiration to 5500. Describe the hedging strategy that you may adopt to protect your fund against such a fall.(4 marks)
3. You are optimistic about the market prospects and predict that the FTSE 100 index will be reading 7500 by expiration. Describe a speculative strategy using the futures contract that you would adopt and the risks that you run.(4 marks)

You are given the following data on the 3-month sterling interest rate futures contract. The contract has a notional size of £1 million.

Sterling futures contract

September 2022  94.5

1. Explain what the sale of such a contract implies.(2 marks)
   
   
2. If you think 3-month interest rates in September 2022 will be 6.5% would you buy or sell the contract? Explain your reasoning and the profits you can expect if you are correct. (4 marks)
   
   
3. Briefly explain how a Corporate Treasurer who is looking to borrow £1 million of funds for 3 months from September 2022 might use the above contract to hedge interest rate risk.(4 marks)