QUESTION ONE

This question concerns efficient portfolios and Markowitz Diversification.

a. Discuss how a given investor chooses an optimal portfolio. Is this choice of portfolio always a diversified portfolio, or could it be a single asset? Explain your answer.

b. Compared with an investor who can only invest in risky assets, (i) describe and (ii) graph how the return-to-variability ratio can be improved for this investor, assume that the Investors can invest in a portfolio of risky stocks and can lend or borrow at the risk-free rate.

c. When a risk-free rate is available (i) explain and (ii) graph how two investors with different risk aversion levels will choose the same portfolio of risky assets but will invest in different proportions of their entire wealth in this portfolio.

d. Suppose M is the tangent portfolio of risky assets (tangent to the line that intercepts the risk-free rate, Rf) with an expected return of 12% and a standard deviation of 20%. Assume the risk-free rate is 4%. Suppose investor A invests 30% of the wealth in the M and 70% in the risk-free asset and suppose investor B invests 110% of the wealth in the M and borrows 10% at the risk-free rate. Calculate the expected returns and standard deviations for these two investors.

QUESTION TWO

This question concerns understanding the concept of market efficiency.

a. Discuss the three forms of the efficient market hypothesis (EMH). Provide examples to illustrate your understanding and include a diagram for these three forms of efficiency.

b. Discuss the role performed by a portfolio manager in a perfectly efficient market condition. In your discussion, include the FOUR (4) necessary steps in the portfolio management process and the limitations of the Efficient Market Hypothesis.

QUESTION THREE

This question concerns evaluating competing measures of bond risk with Macaulay Duration.

Consider a 5-year 9% bond with a maturity value of $1000. It has a yield-to-maturity (YTM) of 8% and the coupon is payable annually.

a. Calculate the bond price

b. Calculate the Macaulay Duration of this bond.

c. Calculate the actual price change for a 10bp increase in yield

d. Calculate the duration-model estimated % price change for a 10bp increase in yield
and the implied new price.

e. Comment on the discrepancy between actual and estimated price changes.