SMM148 Theory of Finance

Answer any THREE questions out of FIVE

Question 1

(a.) Suppose you have 600 monthly observations of stock market returns. The mean value is 0.55% and the standard deviation is 6.25. What would be the lower boundary under normality so that only 5% of your observations are less than this calculated value? What conclusion would you draw if 30 of those 600 observations fall below that lower boundary? [30 marks]

(b.) To simplify the equation of the dividend discount model we make some assumptions about future dividends. Outline two different assumptions which are often used about future cash flows and show that qualitatively the model suggests the same relationship. [40 marks]

(c.) Carefully explain how you would calculate the weights in a market cap weighted stock market index, the weights in a price weighted index and the weights in an equally weighted index. Why is the market cap weighted index widely used when providing investable products following a stock market index? [30 marks]

Question 2

(a.) Your friend is risk averse, likes high return but dislikes risk. Explain to your friend how you should allocate your wealth, based on the theory developed by H. Markowitz, if you have TWO risky assets and ONE risk free rate to invest in. You might want to assume that he/she has £1,000 to invest. Use diagrams and state the key equations. It is important that your explanations are structured and can be followed by someone who is not an expert in finance. [65 marks]

(b.) Carefully explain whether a UK investor should diversify internationally. Would you recommend to invest in the optimum weights based on the approach suggested by H. Markowitz which you calculated based on historic data? [35 marks]

Question 3

(a.) Carefully show how you would derive the Security Market Line from portfolio theory. [30 marks]

(b.) Suppose mutual fund 1 has a beta of 0.8 and is half as risky as mutual fund 2 when measured by the common factor (e.g. the stock market). The two assets have an expected return of 9% (mutual fund 1) and 12% (mutual fund 2) respectively.

(i.) For the two mutual funds to be correctly priced state the equation of the Security Market Line. What is the risk free rate and what is the market return?

(ii.) Suppose the risk free rate is 4% and the expected market return is 10%. Based on the CAPM, how would you assess the attractiveness of those two mutual funds ? [40 marks]

(c.) Explain what we understand by firm specific risk and how you could measure firm specific risk of a company, based on the CAPM. [30 marks]

Question 4

(a.) Calculate duration of a 3 year 1.5% coupon paying bond with a face value of $1,000. The yield to maturity for the 3 year bond is 1.75% and the coupon payments are made semi-annually. Calculate the approximate price change (based on duration) and the full price change if yield to maturity falls by 0.25%. [35 marks]

(b.) 50 days ago, a 270 day Certificate of Deposit (CD) with a principal investment of £ 1m has been issued at a yield of 5%. Calculate the current price of this CD if the current yield is 4.5%. Explain how you would price a US Treasury Bill. [35 marks]

(c.) Explain what we understand by a callable and convertible bond, why they are issued and why it is more challenging to calculate the fair value of those corporate bonds. [30 marks]

Question 5

(a.) Carefully explain why speculators prefer buying derivatives rather than the (underlying) financial assets in the spot market. [30 marks]

(b.) Carefully explain how an arbitrageur would use options markets to make a riskless profit. [30 marks]

(c.) You have imported goods from the UK and on the 15th of February you have to settle the bill of £ 5,000,000. You are considering hedging your currency risk using a Pound Sterling futures contract. Today is the 18th of December and the spot exchange rate is 2.0215 ($/£). You can buy/sell the following futures contracts :

January expiry (25th of January) 2.0275

February expiry (24th of February) 2.0335

March expiry (22nd of March) 2.0450

On the 15th of February when you have to make the payment the spot rate is 2.0095 ($/£) and the prices of the futures contracts are :

February expiry (24th of February) 2.0118

March expiry (22nd of March) 2.0207

(Note one Pound Sterling Futures contract is worth £ 62,500.)

Carefully explain how you would hedge your currency risk and what your hedges and unhedged outcome would be. What is the link between the hedged error and the basis? Explain. [40 marks]