QUESTION 1
a) Give an analytical derivation of the Capital Asset Pricing Model (CAPM) and supplement your analysis with diagrammatic illustrations where appropriate
b) The shares of BFC Inc, a company in the hotel sector, have a beta (β) of 1.10. What does this imply for the variation in BFC Inc equity returns vis-àvis the returns on the market. If the expected return on the market portfolio is 15.5% and the risk-free rate is 6.5%, what is the expected return on BFC Inc equity?
c) Using the result from part (b), price BFC Inc stock that has just paid a dividend of $3 per share and has a dividend growth of 5% fore-ever
d) Assuming now that BFC Inc has just paid the same dividend as in (c) above, but dividend is projected to grow at a 10 percent rate for the next five years after which the growth rate will drop to 5% and stay at that rate forever. Using the same discount rate as calculated in (b), what is the intrinsic value of the stock today? What are the implications of such valuation for you as an investor?
QUESTION 2
i) Examine the nature of the efficient markets hypothesis (EMH) and explain how the different forms of efficiency can be tested.
ii) Discuss the implications of the EMH for users of the financial markets.
QUESTION 3
a) You have just been appointed a portfolio manager of Malou investment. An investor has two assets available from which to form his desired portfolio. Asset X has an expected return of 4% and standard deviation of 9%. Asset Y has an expected return of 8% and standard deviation of 12%.
i) Assume that the returns of the two assets are perfectly positively correlated. If the investor wishes to place portfolio weight 1/3 on asset X and weight 2/3 on asset Y compute the expected return and standard deviation of the portfolio.
ii) Assume now that the two asset returns are perfectly negatively correlated. If the investor places portfolio weight of α on asset X, write down an expression for the variance of the portfolio. Demonstrate that, in this scenario, the investor can form a portfolio with zero variance and find the appropriate weights associated with this portfolio
b) If correlation among security returns were perfect-if returns of all securities moved up and down together in perfect unison, diversification could do nothing to eliminate risk. The fact that security returns are highly correlated, but not perfectly correlated, implies that diversification can reduce risk but not eliminate it' Markovitz(1981). Comment on the above.
c) Discuss the assumptions underlying the diversification theory
QUESTION 4
i) Compare and contrast the various types of fixed income securities
ii) A new issue of callable bonds will generally carry a higher interest rate than a comparable issue of uncallable bonds. Discuss
iii) As any investment, the price of a bond is simply the present value of all its future cash flows Discuss using an illustrative example
iv) Assuming all maturities are exact. You observe that a Boops & Co, 7 1/8% 4 year, semi-annual coupon bond trading at 102.347 percent of par. The bond is callable at 101 in two years and is putable at 100 in two years
a) What the current yield?
b) What is the yield to maturity?
c) What is the yield to call?
Comment on all your answers
QUESTION 5
Write on any 3 of the following (equal marks)
(i) Bond Convexity
(ii) Bond Market Indices
(iii) Options and Futures Investments
(iv) Sharpe and Treynor indices
(v) Un-hedged position of bond and equity portfolios