# Problem solving finance and financial market

**Paper, Order, or Assignment Requirements**

**Answer all 11 questions:**

**Question 1**

Assume that the following data represent **all **risky securities in the economy.

- What is the market portfolio
*i.e.*what percentage of each security must be invested to

achieve the market portfolio? What is the standard deviation of the market portfolio? (4

marks)

- If the risk free rate of return is 5% and the expected return on the market portfolio is 13%,

what are the Capital Market Line and Security Market Line equations? (4 marks)

iii. A pension fund that you are advising wishes to have an expected rate of return of 17%.

How should the fund invest to obtain this? What would be the standard deviation and the beta

of the pension fund’s portfolio? (4 marks)

[Total 12 marks]

**Question 2**

The policy-making committee of Bank ABC recently used reports from its securities analysts

to develop the following efficient equity only portfolios.

- If the risk free rate of interest is 5% which portfolio is best? (2 marks)
- Assume that the policy-making committee would like to earn an expected rate of return of

20% with a standard deviation of 10%, is this possible? (2 marks)

iii. 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? (2 marks)

- 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? (2 marks)

[Total 8 marks]

**Question 3**

You have the following 7 years of data covering shares A and the Market Portfolio

**Year Share A Market Portfolio**

2009 5% 14%

2010 7% 9%

2011 4% 2%

2012 6% 15%

2013 1% 5%

2014 -3% -6%

2015 4% 7%

The standard deviation of share A is 3.41

The standard deviation of the market portfolio is 7.23

The covariance of A with the market is 20.71

(i) Calculate for each of the above years, the yearly returns of a portfolio created by

allocating your money 30% between share A and 70% the market portfolio. (2 marks)

(ii) Calculate the average expected rate of return and standard deviation of a portfolio made

up 30% share A and 70% in the market portfolio (4 marks)

(iii) Calculate the beta of stock A, what does the beta reveal about the defensive or aggressive

qualities of stock A? (4 marks)

[Total 10 marks]

**Question 4**

A bond fund manager is evaluating the fund’s holding of various categories of bonds:

**Bond Total market Macaulay yields to maturity**

**Category value Duration Current Expected**

A $50 million 1 year 10% 9%

B $100 million 3 years 10% 9%

C $50 million 5 years 10% 9%

D $100 million 7 years 10% 9%

E $200 million 12 years 10% 9%

(i) Calculate the bond portfolio’s current Macaulay duration and modified duration.

(4 marks).

(ii) What is the approximate value of the portfolio if indeed the interest rate suddenly falls to

9% as expected? (2 mark)

(iii) Suggest a strategy that the bond manager might adopt if he expects interest rates to fall

even further to 9% across all maturities. (2 mark)

[Total 8 marks]

**Question 5**

Consider the following bond data:

**Credit Years to Annual Macaulay Yield to**

**Bond rating maturity coupon duration maturity**

1 AAA 8 £9 ? 10.0

2 A 10 £11 5.98 13.5

3 BBB 7 £10 4.86 14.5

(i) Calculate the Macaulay duration of bond 1 (2 marks)

(ii) You expect bond yields to rise across all maturities by 1%. What strategy will you

employ in respect of bonds 2 and 3. (2 marks)

(iii) If you expect a boom and rise in yields generally combined with a reduction of the

corporate bond spreads which of bonds 1 and 2 bonds would you choose to buy. Explain your

reasoning. (4 marks)

(iv) Consider Bond 3, if the yield to maturity on this bond were to move downward to 13%

because of a credit rating upgrade, what would be the expected percentage price change in

this bond? (2 marks)

[10 marks]

**Question 6**

Company A has introduced a new product. As a result, you expect earnings and dividends to

grow at 12% for the next 3 years. After which the growth rate will fall to 5% indefinitely. The

beta on Company A’s stock is 2, the risk free rate of interest is 6% and the market risk

premium is 6%.

(i) Calculate the fair value of the stock if the last dividend (Do) was 60 pence. (4 marks)

(ii) Calculate the fair value for the stock at the end of year 3 and at the end of year 4.

(4 marks)

(iii) If your projections prove wrong and the stock grows only at 10% per year but for 5 years

and then falls to 4% indefinitely will you have overpaid or underpaid for the stock, if you pay

the fair value calculated from part (i)? (2 marks)

[Total 10 marks]

**Question 7**

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

June 2016 94

(i) Explain what the purchase of such a contract implies (2 marks).

(ii) If you think 3 month interest rates in June 2016 will be 4% would you buy or sell the

contract. Explain your reasoning and the profits you can expect if you are correct.

(4 marks).

(iii) Briefly explain how a corporate Treasurer who is looking to borrow £1 million of funds

for 3 months from June 2016 might use the above contract to hedge interest rate risk.

(4 marks).

[Total 10 marks]

**Question 8**

The dollar/pound ($/£) exchange rate is currently $1.67/£1 and the following options and

futures prices exist for June 2016

**June 2016 Futures (contract size £50,000)**

$1.65/£1

**June 2016 Options**

**The underlying contract is right to buy £100,000 **at $1.65/£1

**Strike price call option premium put option premium**

$1.65/£1 $0.05 $0.03

You work for an American travel company and are due to pay in June 2016, £200,000 for

hotel bookings to the UK Hotel chain. Discuss the relative merits of using the futures or

options contracts to hedge the exchange rate risk, in your answer consider a range of possible

future spot rates for sterling.

[Total 8 marks]

**Question 9**

You are given the following information about the stock of Company A.

Share price $75, risk free rate of interest 10%, time to expiration 6 months, volatility as

measured by the **variance **is 40% (0.4) and exercise price is $70.

(i) Calculate the appropriate call value of the stock according to the Black-Scholes option

pricing formula. **Show your workings in full. **(6 marks).

(ii) Calculate an appropriate put premium. **Show your workings in full. **(4 marks)

[Total 10 marks]

**Question 10**

State which of the following statements are true and which are false:

**(You obtain 1 mark for a correct response and lose 1 mark for an incorrect response to**

**each part of this question. If you do not attempt a part you neither gain or lose ****–**

**negative marks to this question will form part of your total mark !).**

(i) A put premium for a strike price of 200 pence is 15 pence while and the share is currently

priced at 195 pence. The time value for the put premium is greater than the intrinsic value.

(ii) The Black-Scholes model cannot provide a reasonable estimate of the price of an

American option on a dividend paying stock.

(iii) The owner of a call option breaks even as soon as the price of a stock equals the exercise

price.

(iv) For an option writer the risk of writing a put option is reduced if the writer has a short

position in the underlying stock.

(v) The holder of a put option will make a profit once the share price falls below the strike

price.

(vi) Both parties to a put option contract will have to make margin payments.

(vii) If implied volatility rises, then other things being equal put premiums will have fallen.

(viii) The maximum gain from writing a put option is limited but the maximum loss is not.

[Total 8 marks]

**Question 11**

Complete the following table for the expected rate of return on equity for different rates of

profit (p) on combined debt and equity and levels of primary gearing assuming that the rate of

interest on debt is 6.5%

D**ebt/Equity Ratio Expected Rate of Return on Equity**

**(Gearing) p=10% p=20% p=30%**

**0.5 ? ? ?**

**1.5 ? ? ?**

**2.0 ? ? ?**

(4marks)

What can you conclude about the impact of primary gearing on the variability of the return on

equity? (2 marks)

[Total 6 marks

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