Asset Pricing Exam Assignment -

Question 1: (a) Suppose your initial investment of £1,000 has increased to £1,250 one year later. Calculate the annual compounded, semi-annual, quarterly compounded, monthly compounded and continuously compounded returns.

(b) Suppose you have the following two projects. They both require an initial investment of £5,000. The expected future cash flows are given in the table below. 

Cash flows from investment

(i) Suppose the internal rate of return (IRR) for project-1 is 4.68% and project-2 is 6.41%.  Explain how you would use the IRR rule to choose between the two projects.   

(ii) Suppose the two projects have a positive NPV.  If they are mutually exclusive, explain why you should not use the IRR rule (as outlined in (i.)) to choose between those two projects.   

(iii) Calculate the net present value (NPV) if the discount rate for both projects is 4%. Intuitively what does a positive NPV imply?

(c) Carefully explain how you would calculate one-period and n-period geometric and arithmetic returns.  Explain, by using an example, how the geometric return measures the change in prices.  How would you use the geometric n-period return to calculate the correct terminal wealth?

Question 2: (a) Suppose a company has just announced that they will not pay a dividend for the next two years. In years 3 and 4 it is expected that dividends will be 50 pence each year after which they grow at a constant rate of 1% (forever).  What is the fair value of this stock, if the risk free rate is 2% and the required return for this company is 8%?  How would your valuation change if dividends remain constant at 50 pence rather than increasing at a constant rate?  

(b) Use the dividend discount model to explain how you could allow for the existence of a rational bubble.  Show that the bubble would grow by the expected rate of return and your valuation of the bubble today would be zero, if you believe the bubble will burst during your investment period.

(c) Briefly explain how well you would expect the Gordon growth model to comply with data on the aggregate stock market over time.  How might the model be improved?

Question 3: (a) A US Treasury Bill with 100 days to maturity and a face value of $ 1m is currently priced at $ 993722.20 and $993750.00.  Calculate the bid and ask discount rates for this US Treasury Bill. What would be the return (yield) an investor receives if she buys the bill today and holds it until maturity?

(b) A UK Certificate of Deposit (CD) has a current price of £ 10,036,895 and 30 days left until maturity.  The CD was issued 60 days ago at a rate of 2.5% with an initial investment of £10m. What is the current yield of this CD?

(c) Carefully explain using an example if you wish, how a 5 year coupon paying bond should be priced, if you do not know the yield to maturity.  What does the yield to maturity measure?  Is it a return the investor will receive?

(d) Explain the difference between a convertible and callable bond. Compared to a fixed coupon paying corporate bond from the same issuer and with the same maturity, what could you say about the yield to maturities of those two bonds?

Question 4 (a) Suppose you have the following information on two risky assets.

(i) Calculate the expected portfolio return and the portfolio standard deviation for the following two portfolios.   

(ii) Calculate the weights in the minimum variance portfolio as well as the portfolio expected return and the portfolio standard deviation.

(iii) Draw the efficient frontier of the two individual assets, the two portfolios calculated in (i) and the minimum variance portfolio, calculated in (ii).   

(b) Explain why a UK investor should diversify internationally. What do we mean by home country bias and do you think that it is a problem considering empirical results in this area?  What would be your recommendation on how a UK investor should diversify?

Question 5: (a) Various newspapers and financial advisors provide rankings of mutual funds' performance. Carefully explain any weaknesses in these rankings. What would your advice to your client be concerning the choice of her mutual fund investments? Use academic evidence on the performance of mutual funds in your answer.

(b) Carefully outline the bootstrapping methodology used by Cuthbertson, Nitzsche and O'Sullivan (2008) to analyse the performance of UK mutual funds.